Photoelectron Spectroscopy of Solvated Electrons in Liquid Microjets

By

Alexander Truesdell Shreve

A dissertation submitted in partial satisfaction of the

Requirements for the degree of

Doctor of Philosophy

in

Chemistry

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Daniel M. Neumark, Chair Professor Evan R. Williams

Professor Robert Dibble

Fall 2012

Photoelectron Spectroscopy of Solvated Electrons in Liquid Microjets

Copyright © 2012

By

Alexander Truesdell Shreve

1

Abstract

Photoelectron Spectroscopy of Solvated Electrons in Liquid Microjets

By

Alexander Truesdell Shreve

Doctor of Philosophy in Chemistry

University of California, Berkeley

Professor Daniel M. Neumark, Chair

This dissertation presents studies of the binding energies of solvated electrons in a variety of solutions. Solvated electrons play an important role in radiation chemistry and biology, and have been the subject of many studies since their discovery over a century ago. Information on their binding energies, however, has been limited to the results of theoretical calculations or inference from work with small solvent clusters. To directly measure the solvated electron vertical binding energies (VBEs) in bulk solution, a new apparatus was constructed coupling a liquid microjet source to a photoelectron spectrometer. Using two photons from individual pulses of a nanosecond laser, solvated electrons were generated and detached to vacuum. Their kinetic energies were then measured with a field-free time-of-flight spectrometer.

Studies are presented here that utilize this apparatus to measure the VBEs of solvated electrons in water, methanol, ethanol, and acetonitrile. Preliminary efforts to study solvated electrons in tetrahydrofuran are also described. The findings of these studies are compared to past work on small solvent clusters, doped with either an excess electron or an alkali metal atom.

A second generation liquid microjet apparatus is also described. Using a magnetic bottle time-of-flight spectrometer, the collection efficiency of the next generation apparatus will be significantly higher than the original apparatus.

i

Table of Contents

Abstract ........................................................................................ 1

Table of Contents .......................................................................... i

List of Figures .............................................................................. iii

List of Tables ............................................................................... vii

Acknowledgements .................................................................... viii

Chapter 1 Introduction ............................................................ 1 1.1 Overview .................................................................... 1 1.2 Bulk Solvated electrons ................................................ 1 1.3 Microsolvation in solvent clusters ................................... 2 1.4 Photoelectron spectroscopy ........................................... 5

1.4.1 Gas phase anions ............................................... 5 1.4.2 Gas phase neutrals ............................................. 6 1.4.3 Solvated electrons .............................................. 7

1.5 References .................................................................. 9

Chapter 2 Experimental Setup ............................................... 11 2.1 Overview .................................................................. 11 2.2 Principles of liquid microjets ........................................ 11 2.3 Practical application of microjets .................................. 14 2.4 Solvated electrons – generation and detachment ........... 18 2.5 Jets in vacuum – the microjet trap region ..................... 21 2.6 Field-free spectrometer – the detector region ................ 23 2.7 Data collection and processing .................................... 24 2.8 Calibration with anions ............................................... 25 2.9 Calibration with neutrals ............................................. 27 2.10 Streaming potentials .................................................. 29 2.11 Field-free collection efficiency ...................................... 32 2.12 Magnetic bottle spectrometer ...................................... 33 2.13 References ................................................................ 38

Chapter 3 Photoelectron Spectroscopy of Hydrated Electrons................................................................ 39

3.1 Abstract ................................................................... 39

ii

3.2 Introduction .............................................................. 39 3.3 Experiment ............................................................... 41 3.4 Results ..................................................................... 42 3.5 Discussion ................................................................ 43 3.6 Conclusions ............................................................... 45 3.7 Acknowledgements .................................................... 45 3.8 Figures ..................................................................... 46 3.9 References ................................................................ 50

Chapter 4 Photoelectron Spectroscopy of Solvated Electrons in Alcohol and Acetonitrile Microjets ...... 53

4.1 Abstract ................................................................... 53 4.2 Introduction .............................................................. 53 4.3 Experimental ............................................................. 55 4.4 Results ..................................................................... 57 4.5 Discussion ................................................................ 58 4.6 Conclusions ............................................................... 61 4.7 Acknowledgements .................................................... 61 4.8 Figures and tables ..................................................... 62 4.9 References ................................................................ 66

Chapter 5 Photoelectron Spectroscopy of Solvated Electrons in Tetrahydrofuran ................................. 69

5.1 Abstract ................................................................... 69 5.2 Introduction .............................................................. 69 5.3 Experimental ............................................................. 70 5.4 Preliminary results and discussion ................................ 71 5.5 Conclusions ............................................................... 75 5.6 Acknowledgements .................................................... 75 5.7 References ................................................................ 76

Appendix A Field-Free Spectrometer Machine Drawings ........... 77

Appendix B Magnetic Bottle Spectrometer Machine Drawings ............................................................... 89

Appendix C Data Acquisition Software ................................... 131 C.1 From C++ to LabVIEW ............................................. 131 C.2 Non-time-resolved data collection program ................. 132 C.3 Time-resolved data collection program ....................... 134 C.4 References .............................................................. 137

Appendix D Data Processing Routines .................................... 139 D.1 Overview and purpose .............................................. 139 D.2 LabTalk script .......................................................... 139

iii

List of Figures

1.1 Anion cluster binding energy progressions .................................. 3

1.2 Comparison of anion and alkali doped cluster progressions ........... 4

2.1 Schematic overview of the apparatus ....................................... 12

2.2 Microjet nozzle ...................................................................... 15

2.3 Flowing microjet .................................................................... 16

2.4 Diffraction from a microjet ...................................................... 19

2.5 Detailed apparatus schematic ................................................. 20

2.6 Charge separation and velocity profile schematic ....................... 29

2.7 Streaming potential measurement scheme ............................... 30

2.8 Jet-walk energy shift ............................................................. 31

2.9 Calculation of the solid angle subtended by the detector ............ 32

2.10 Magnetic bottle photoelectron spectrometer .............................. 34

3.1 Schematic drawing of the spectrometer.................................... 46

3.2 Typical time-of-flight spectra of hydrated electrons .................... 47

3.3 Photoelectron spectra of hydrated electrons at 266 nm .............. 48

3.4 Photoelectron spectra of hydrated electrons at 213 nm .............. 49

4.1 Photoelectron spectra of solvated electrons in alcohol and acetonitrile .......................................................................... 62

4.2 Vertical binding energy progressions of water, methanol, and acetonitrile anion clusters ................................................ 63

5.1 Charging instability in tetrahydrofuran microjets ....................... 72

5.2 Streaming potential corrections in tetrahydrofuran microjets ............................................................................. 73

iv

5.3 Preliminary photoelectron spectra of solvated electrons in tetrahydrofuran .................................................................... 74

A.1 Jet trap region side view ........................................................ 78

A.2 Jet trap region top view ......................................................... 79

A.3 Mounting ring part 1 .............................................................. 80

A.4 Mounting ring part 2 .............................................................. 81

A.5 Differential pumping sheath .................................................... 82

A.6 Skimmer – 1 mm opening ...................................................... 83

A.7 Skimmer – 0.1 mm opening ................................................... 84

A.8 Jet trap top........................................................................... 85

A.9 Jet trap bottom ..................................................................... 86

A.10 Viewport entrance modification ............................................... 87

B.1 Full apparatus layout ............................................................. 90

B.2 Dewar cross detail ................................................................. 91

B.3 Jet cross detail 1 ................................................................... 92

B.4 Jet cross detail 2 ................................................................... 93

B.5 Detector cross detail .............................................................. 94

B.6 Liquid nitrogen dewar modification .......................................... 95

B.7 Detector support plate ........................................................... 96

B.8 Trap bottom ......................................................................... 97

B.9 Ice breaker ........................................................................... 98

B.10 Ice breaker feedthrough ......................................................... 99

B.11 Trap mount flange ............................................................... 100

B.12 Magnet platform post ........................................................... 101

B.13 Magnet support board .......................................................... 102

v

B.14 Magnet baseplate ................................................................ 103

B.15 Iron cone ........................................................................... 104

B.16 Chamber door ..................................................................... 105

B.17 Differential pumping sheath .................................................. 106

B.18 Flight tube flange – full assembly .......................................... 107

B.19 Flight tube flange – outer tube components ............................ 108

B.20 Flight tube flange – outer tube .............................................. 109

B.21 Flight tube flange – inner tube components ............................ 110

B.22 Flight tube flange – inner tube .............................................. 111

B.23 Flight tube flange – connecting plate ...................................... 112

B.24 Flight tube in vacuum support ring ........................................ 113

B.25 Grid support post ................................................................ 114

B.26 Grid assembly mount ........................................................... 115

B.27 Grid ring bottom ................................................................. 116

B.28 Grid ring top ....................................................................... 117

B.29 Detector support rod ............................................................ 118

B.30 Detector mounting flange ..................................................... 119

B.31 Bottle assembly – full assembly ............................................ 120

B.32 Bottle assembly – wire support tube ...................................... 121

B.33 Bottle assembly – outer plastic tube ...................................... 122

B.34 Bottle assembly – mu metal shield ........................................ 123

B.35 Bottle assembly – retaining ring ............................................ 124

B.36 Bottle table stand bottom ..................................................... 125

B.37 Bottle table stand top .......................................................... 126

vi

B.38 Flight tube table stand bottom .............................................. 127

B.39 Flight tube table stand top .................................................... 128

B.40 Dewar drying rest ................................................................ 129

B.41 Alternative grid mount ring ................................................... 130

C.1 GUI for the non-time-resolved data acquisition program .......... 132

C.2 GUI for the time-resolved data acquisition program ................. 135

vii

List of Tables

4.I Literature bulk excess electron binding energy values ................ 64

4.II Wavelength dependent signal levels in acetonitrile .................... 64

4.III Dielectric continuum calculation parameters ............................. 65

viii

Acknowledgements

There are many people whose advice and assistance has been invaluable over the years. Without their contributions, this tome would not exist. In particular, I wish to thank:

• Dan Neumark for his advice and guidance.

• Michelle Haskins, without whom the bureaucracy of this institution would have been completely unnavigable. I never cease to be amazed by how quickly she can make problems go away.

• Madeline Elkins for being an awesome labmate and friend. I’m quite fortunate to have ended up with a lackey who I get along with so well.

• Neil Cole-Filipiak for introducing me to The Trappist and making the last couple of years far more enjoyable.

• Brad Parsons for teaching me most of what I know about vacuum systems. Even though I only had a few months of overlap with Brad, I learned a lot from him.

• Terry Yen, for teaching me everything I didn’t pick up from Brad and for making my first couple of years here far more fun than they would otherwise have been.

• The residents of the group lounge in D4, who have provided an entertaining diversion from doing actual work.

• Everyone else in the Neumark Group, who have been an excellent source of amusement and advice.

• Eric Granlund and Phil Simon for their advice and assistance in designing and machining all of my apparatus. Without their input, the machine would doubtlessly have taken much longer to get working and ended up as an even more actively user hostile piece of equipment than it is.

1

Chapter 1

Introduction

1.1 Overview

The behavior of excess electrons in bulk solution is a topic of considerable interest. While they have long been studied through a variety of techniques, direct information on the binding energies of these electrons has historically been rather limited. Due to the experimental complexities of directly measuring solvated electron binding energies in bulk solution, early efforts instead focused on their gas phase analogs, anionic solvent clusters. Although bulk properties may e inferred from these studies, it is still desirable to perform these measurements directly in bulk solution. It is the aim of the Liquid Microjet Photoelectron Spectroscopy project to bridge the gap from gas to liquid phase. With our apparatus, it is now possibly to directly measure bulk solvated electron binding energies with photoelectron spectroscopy.

The following sections of this chapter more thoroughly discuss the motivations and principles behind our work. Chapter 2 details the construction and operation of our field-free photoelectron spectrometer. Also presented is a newly reengineered version of the apparatus which will make use of a magnetic bottle spectrometer to significantly improve our collection efficiency. Chapter 3 covers our findings for the hydrated electron, while Chapter 4 presents the results of our work with methanol, ethanol, and acetonitrile. Chapter 5 details our efforts to study electron solvation in tetrahydrofuran and the difficulties in working with that particular system. Machine drawings for the current and next generation apparatus are presented in Appendices A and B respectively, while code used for the collection and processing are covered in Appendices C and D.

1.2 Bulk solvated electrons

Solvated electrons, or bare electrons in solution, have long been a system of interest. Their effects were first observed in the brilliant colors of doped ammonia solutions prepared by Davy in 1808 and Weyl in 1864.[1,2]

2

However, it wasn’t until work by Kraus in 1908 and Gibson in 1918 that the solvated electron was identified and implicated in the conductance and optical spectra of these solutions.[3,4] Eventually, in 1962 Hart and Boag identified solvated electrons in water as well.[5,6] Their assignment was based on the broad, structureless absorption spectrum centered at about 720 nm that appeared following irradiation of a water sample with high energy electrons.

Since this time, considerable effort has gone into advancing our understanding of solvated electrons. This work has been motivated by the key role this species plays in a variety of areas of physical science, due, in part, to their unusually high rate of diffusion and reactivity.[7] They play an important role in radiation chemistry since they are readily formed following exposure to ionizing radiation.[8,9] They have also been identified as a species of interest in aerosol chemistry, where they are believed to participate in the nucleation process.[10] Furthermore, solvated electrons formed in the presence of DNA may lead to rapid single-strand breakage, making them a relevant species in biological chemistry.[11-13] Finally, they are a critically important species from the perspective of theoretical chemistry. The solvated electron is the simplest quantum mechanical solute, and, as such, it is the best system to gain insights into the interplay between quantum mechanics and the statistical mechanics and dynamics that describe the solvent system.[14,15]

Significant advances have been made by both theoretical and experimental work, considerably illuminating many aspects of the behavior of solvated electrons. For example, insights have been gained in the dynamics of solvation,[8,16,17] the structure of electron’s local solvation environment,[15,18-21] the reactivity of the solvated electron.[22-26] Direct information on electron binding energies in bulk solution, however, has historically been relatively limited. Owing to experimental difficulties, direct measurement of solvated electron binding energies were historically limited to work with small solvent clusters.

1.3 Microsolvation in solvent clusters

Small clusters of solvent serve as an excellent proxy system to test solvation effects in general.[27-31] From a theoretical perspective, calculations on these systems are relatively tractable because of their small size.[32-36] Experimentally, the measurement of solvated electron binding energies becomes a straightforward problem within the context of clusters doped with an excess electron. At the smallest cluster sizes, structural and quantum effects will clearly dominate. However, as the cluster size is increased, the system must eventually transition to a regime where bulk, thermodynamically averaged properties dominate. Therefore, in principle,

3

inferences can be made about bulk properties from size dependent cluster properties.

As shown in Fig. 1.1, the vertical binding energies (VBEs) of anionic clusters have been measured for a variety of solvents, with multiple isomers typically observed. For each isomer, a linear trend in binding energy is revealed when plotted versus the inverse cube root of the number of solvent molecules, n-1/3, which serves as a proxy for cluster radius. Care must be taken in interpreting results from these species, however. These clusters can stabilize excess electrons in a variety of geometries; the electron may be localized on the surface of the cluster, partially embedded within it, or fully internally solvated.[36] In the case of water, for example, isomers II and III are weakly bound and generally accepted as surface states. Isomer I, however, was initially assigned to an internally solvated state.[27,37,38] This seemed reasonable because of the relatively high binding energy of the

Figure 1.1: Anion cluster binding energy progressions. In water and methanol, isomer I is potentially an internally solvated species, while isomers II and III are generally accepted as surface-bound excess electrons.[6,38,39] Acetonitrile is a more complex solvent, where isomer I is believed to be an internal, cavity-solvated electron as is observed in the other solvents, while isomer II is a dimer bound-species.[40,41]

4

species and the observation that the infinite cluster size extrapolated binding energy is in reasonable agreement with the predicted bulk VBE.[42-44] However, it is unclear whether the vertical binding energy is a good measure of the position of the excess electron within the cluster. Some theoretical and experimental work indicates that isomer I is actually a surface bound state,[34,45,46] while other experimental work supports the internal solvation model.[47] To date, no experiments have been designed to conclusively prove where excess electrons localize within solvent clusters. One major goal of the Liquid Microjet Photoelectron Spectroscopy project is to finally resolve the question of where the electron localizes in the cluster. In the work presented here, we directly measure solvated electron VBEs in bulk conditions using liquid microjets. If the bulk VBE is accurately predicted

Figure 1.2: Comparison of anion and alkali doped cluster progressions. Water, methanol, and acetonitrile anion cluster data from Refs. [6], [39], and [40,41] respectively. Alkali doped water, methanol, and acetonitrile cluster data from Refs. [48], [49], and [50] respectively. See text for details.

5

by an extrapolation of the cluster binding energies, it lends strong support in favor of the view that the electron is localized on the interior of the clusters.

In a separate set of experiments, the ionization potentials (IPs) of neutral clusters doped with a single alkali atom were studied as a function of cluster size.[48-51] In solvents with a large dipole moment, the valence electron from the alkali atom can be donated to the solvent, resulting in a solvated electron at large cluster size. Questions remain, however, about how well separated the electron and cation are in these systems.[51] As illustrated in Fig. 1.2, the behavior of these clusters is quite different from that of anion doped clusters. Above a certain size, the IPs stabilize at a constant value out to the largest studied cluster sizes. These measurements are believed to indicate adiabatic IPs rather than vertical IPs, however they give us another set of experiments we can compare our bulk results to.[49,52] Sodium doped water cluster IPs extrapolate to values in reasonable agreement with their anion counterparts.[6,48] However, the extrapolated adiabatic IPs of alkali doped methanol[49] and acetonitrile[50] are at significantly higher binding energies than the extrapolated VBEs from their respective anion clusters.[39-41] By measuring the bulk VBEs directly, we can resolve the question of which extrapolations work and which do not.

1.4 Photoelectron spectroscopy

In the studies presented in this dissertation, we use photoelectron spectroscopy (PES) to measure binding energies of electrons in bulk solution, while calibrating our apparatus by PES of gas phase anions or neutrals. PES is a versatile technique, widely applied to a variety of systems, and is the subject of several reviews.[53-55] A detailed explanation of gas phase anion PES is included in the thesis of A. Weaver[56], however a brief summary is presented here. This is followed by a description of our application of PES to neutral gas phase systems and solvated electrons.

1.4.1 Gas phase anions

Photoelectron spectroscopy makes use of the photoelectric effect to remove electrons from a system of interest. With gas phase anions, this is schematically represented by

,A h A eν− −+ → + (1.1)

where Aˉ and A are the anion and resulting neutral species, and hν is the photon energy. The detached electron then carries with it any energy beyond that which is needed for the transition from the internal state of the anion and the internal state of the neutral. More precisely,

6

( ) ( ) ( ) ( )0 0 ,elec elec vib vibeKE h E E E Eν − −= − + − + + (1.2)

where eKE is the electron kinetic energy, hν is the photon energy, and the ( )iE − and (0)

iE terms are the internal energies of the anion and neutral respectively. The vibrational terms are included only for the situations where we use a molecular system for calibration (e.g. CNˉ), and higher order terms (e.g. rotational energy) are ignored since they cannot be resolved in our spectra. Assuming the anions are in their electronic and vibrational ground states, the spacing between the peaks in the eKE distribution is determined by the states of the corresponding neutral. The conversion to binding energy (eBE) is then given by

.eBE h eKEν= − (1.3)

Assuming randomly oriented anions, as in our gas phase calibration data, the angular distribution of photoelectrons emitted by a one photon process is given by[57]

( )21 3cos 1 ,4 2totald

dσσ β θπ

= + − Ω (1.4)

where θ is the angle between the photon’s electric field vector and the direction of electron ejection, σtotal is the total photodetachment cross section, and β is the anisotropy parameter which contains information on the symmetry of the electronic state and is constrained such that -1 ≤ β ≤ 2. The selection rules are such that Δℓ = ±1 for a one photon process. By taking data at θ = 0° and θ = 90° we can then recover the anisotropy parameter from the peak intensities at each polarization. This is given by[58]

0° 90°

0° 90°

,12

I I

I Iβ −=

+ (1.5)

where 0°I and 90°I are the normalized peak intensities at 0° and 90° respectively. However, for our calibration data, we are only concerned with arrival times of each peak rather than their angular distributions. As such, we only use the polarization that maximizes the signal for the calibration system in question (θ = 90° for Iˉ and Brˉ).

1.4.2 Gas phase neutrals

Our use of PES to calibrate using neutral gas phase systems differs from our work with gas phase anions in several important ways. Because of their

7

relatively high binding energies, these systems are ionized by multiphoton detachment. Schematically, this process is given by

,A n hv A e++ ⋅ → + (1.6)

where A and A+ are the neutral and resulting cation species, n is the number of photons required to detach the electron, and hν is the photon energy. Equation 1.2 is then modified to account for the total energy added to the system,

( ) ( ) ( ) ( )0 0 .elec elec vib vibeKE n h E E E Eν − −= ⋅ − + − + + (1.7)

The conversion to binding energy similarly differs from Eq. 1.3, and is given by

.eBE n h eKEν= ⋅ − (1.8)

The angular distributions are also more complicated than they were in our work with gas phase anions because we are now dealing with multiphoton processes. The review by Reid provides a detailed treatment of the angular distribution of photoelectrons from multiphoton detachment.[53] However, since we are simply using these systems for calibration, we make no attempt to measure their anisotropies.

1.4.3 Solvated electrons

In our work, we are interested in investigating solvated electrons. As solvated electron lifetimes are hundreds of microseconds at most,[7] we must first generate them. Our approach to this is in situ generation through charge-transfer-to-solvent (CTTS) processes. As discussed in the next chapter, this involves the photodetachment of electrons from anions in solution, leading to the formation of equilibrated, ground state solvated electrons after some time delay (see § 2.4 for more details). Schematically, our process is then

( ) ( ) ( ) ( )*

1 ( ) 2 ( ) ,solv

tsolv solvsolv solv gasA h A A e h A eν ν∆− − − −+ → → + + → + (1.9)

where A- and A are the precursor anion and resulting neutral in solution, and hν1 and hν2 are the photons. As with the gas phase systems, the outgoing electron carries with it excess energy beyond what is needed to detach to the vacuum level. However, we sample a very dense manifold of solvent states and as a result our photoelectron spectra quite structureless and broad, on the order of 1 eV full width at half maximum. As such, we are unable to obtain information on the internal states of the solvent molecules from these spectra. Our conversion to binding energy is given by

8

2 .eBE h eKEν= − (1.10)

The quantity we are primarily concerned with in these studies is the vertical binding energy (VBE), which is taken as the peak of the binding energy distribution by the Franck-Condon principle.

The angular distribution of our spectra should, in principle, be rather straightforward. Aside from surface effects, the solvent molecules and solvated electrons should be randomly oriented and Eq. 1.4 and 1.5 should, in principle, still apply.[59,60] Since the solvated electron ground state is generally regarded as an s-like cavity in many solvents, e.g. water and alcohols,[15,19,61-63] it would be expected that we would detect an anisotropic distribution. Experimentally, however, we find that 0° 90°I I= , indicating that we are sampling an isotropic distribution. The exact cause of this is unknown, but it may be that the electron distributions are randomized by elastic scattering from the solvent molecules. Work on anionic methanol clusters with eKEs comparable to ours found the electron distributions became increasingly isotropic as the cluster size was increased from 70 to 460 solvent molecules, consistent with an increasing scattering probability.[39] However, at high eKEs (70 to 900 eV), Ottosson found that the anisotropies of photoelectron spectra from iodide and sodium were unchanged by solvation in microjets.[60] As such, it seems more work is needed before strong conclusions can be made about solvated electron anisotropies.

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1.5 References

[1] S J M Thomas, et al, ChemPhysChem 9 (2008) 59. [2] W Weyl, Ann. Phys. (Berlin) 197 (1864) 601. [3] C A Kraus, J. Am. Chem. Soc. 30 (1908) 1323. [4] G E Gibson, W L Argo, J. Am. Chem. Soc. 40 (1918) 1327. [5] E J Hart, J W Boag, J. Am. Chem. Soc. 84 (1962) 4090. [6] A Kammrath, et al, J. Chem. Phys. 125 (2006) 076101. [7] E J Hart, M Anbar, The Hydrated Electron, Wiley-Interscience, New

York, NY, 1970. [8] B C Garrett, et al, Chem. Rev. 105 (2005) 355. [9] J Belloni, Nukleonika 56 (2011) 203. [10] F Arnold, Nature 294 (1981) 732. [11] J Simons, Accts. Chem. Res. 39 (2006) 772. [12] C R Wang, et al, J. Am. Chem. Soc. 131 (2009) 11320. [13] J Gu, et al, Chem. Rev. 112 (2012) 5603. [14] P J Rossky, J Schnitker, J. Phys. Chem. 92 (1988) 4277. [15] J M Herbert, L D Jacobson, Int. Rev. Phys. Chem. 30 (2011) 1. [16] X Y Chen, S E Bradforth, Annu. Rev. Phys. Chem. 59 (2008) 203. [17] M C Larsen, B J Schwartz, J. Chem. Phys. 131 (2009) 154506. [18] L Kevan, J. Phys. Chem. 82 (1978) 1144. [19] L Kevan, Chem. Phys. Lett. 66 (1979) 578. [20] L Turi, D Borgis, J. Chem. Phys. 117 (2002) 6186. [21] L Mones, L Turi, J. Chem. Phys. 132 (2010). [22] A Singh, et al, Chem. Phys. Lett. 2 (1968) 271. [23] C C Lai, G R Freeman, J. Phys. Chem. 94 (1990) 302. [24] J A Kloepfer, et al, J. Chem. Phys. 117 (2002) 766. [25] A E Bragg, B J Schwartz, J. Phys. Chem. B 112 (2007) 483. [26] Q B Lu, et al, PNAS 108 (2011) 11778. [27] J V Coe, et al, J. Chem. Phys. 92 (1990) 3980. [28] U Buck, et al, Chem. Phys. Lett. 174 (1990) 247. [29] P Ayotte, M A Johnson, J. Chem. Phys. 106 (1997) 811. [30] L Lehr, et al, Science 284 (1999) 635. [31] R M Young, D M Neumark, Chem. Rev. (2012) 5553. [32] I Bakó, et al, Z. Phys. Chem. 218 (2004) 643. [33] T Takayanagi, J. Chem. Phys. 122 (2005) 244307. [34] P Jungwirth, et al, J. Phys. Chem. A 112 (2008) 6125. [35] L Mones, et al, J. Chem. Phys. 133 (2010) 144510. [36] L D Jacobson, J M Herbert, J. Am. Chem. Soc. 133 (2011) 19889. [37] J Kim, et al, Chem. Phys. Lett. 297 (1998) 90. [38] J R R Verlet, et al, Science 307 (2005) 93. [39] A Kammrath, et al, J. Chem. Phys. 125 (2006) 171102. [40] M Mitsui, et al, Phys. Rev. Lett. 91 (2003) 153002. [41] A T Shreve, et al, Chemical Science (submitted).

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[42] L Kevan, et al, J. Phys. Chem. 75 (1971) 2297. [43] J Schnitker, P J Rossky, J. Chem. Phys. 86 (1987) 3471. [44] J Schnitker, et al, Phys. Rev. Lett. 60 (1988) 456. [45] L Turi, et al, Science 309 (2005) 914. [46] N I Hammer, et al, J. Phys. Chem. A 109 (2005) 7896. [47] S F Fischer, W Dietz, Z. Phys. Chem. 221 (2007) 585. [48] I V Hertel, et al, Phys. Rev. Lett. 67 (1991) 1767. [49] I Dauster, et al, Phys. Chem. Chem. Phys. 10 (2008) 83. [50] F Misaizu, et al, Chem. Phys. Lett. 188 (1992) 241. [51] R M Forck, et al, J. Phys. Chem. A 115 (2011) 6068. [52] H Liu, et al, J. Chem. Phys. 115 (2001) 4612. [53] K L Reid, Annu. Rev. Phys. Chem. 54 (2003) 397. [54] A Stolow, et al, Chem. Rev. 104 (2004) 1719. [55] T Suzuki, Int. Rev. Phys. Chem. 31 (2012) 265. [56] A Weaver, Ph.D. Thesis, University of California, Berkeley, Berkeley,

CA, 1991. [57] J Cooper, R N Zare, J. Chem. Phys. 48 (1968) 942. [58] K M Ervin, W C Lineberger, in: N.G. Adams, L. Babcock (Eds.),

Advances in Gas Phase Ion Chemistry, JAI Press Inc, 1992, p. 121. [59] B Winter, M Faubel, Chem. Rev. 106 (2006) 1176. [60] N Ottosson, et al, J. Electron Spectrosc. and Rel. Phenom. 177 (2010)

60. [61] M Ogasawara, L Kevan, J. Phys. Chem. 82 (1978) 378. [62] M J Tauber, R A Mathies, J. Am. Chem. Soc. 125 (2003) 1394. [63] C M Stuart, et al, J. Phys. Chem. A 111 (2007) 8390.

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Chapter 2

Experimental Setup

2.1 Overview

The use of photoelectron spectroscopy (PES) to study solvated electrons directly in high vapor pressure bulk liquids presents a significant engineering challenge. To overcome these hurdles, we use a liquid microjet source. First described by Faubel, microjet sources work by applying high backing pressures to solution behind a micron sized orifice, creating a laminar stream of solution.[1] Our particular implementation is based on that of Saykally, where glass capillaries are used in place of the platinum-iridium apertures in Faubel’s design.[2] A schematic diagram of our apparatus is presented in Figure 2.1. Briefly, the liquid is introduced to vacuum through a microjet source, and is crossed with a laser 1-2 mm downstream from the nozzle. Solvated electrons are then generated by charge-transfer-to-solvent (CTTS) from anions in solution, and subsequently detached to vacuum and collected. In the initial version of the apparatus the microjet was coupled to a field-free time-of-flight (ToF) spectrometer, calibrated by the photodetachment signal from gas-phase anions or neutral gasses. At the time of writing, the apparatus is being recomissioned to replace the field-free spectrometer with a magnetic bottle ToF spectrometer. In the following sections each part of the experiment is discussed in greater detail, while machine drawings for the field-free and magnetic bottle spectrometers are presented in Appendices A and B respectively.

2.2 Principles of liquid microjets

We wish to study the binding energies and excited state lifetimes of electrons solvated in bulk liquids. In principle, this information is directly accessible through the use of photoelectron spectroscopy. However, to make a meaningful measurement, the electrons must be able to travel from the source to the detector without undergoing significant inelastic scattering. More precisely, the inelastic mean free path must exceed the distance between the source and the detector. As such, it is a high vacuum technique

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Figure 2.1: Schematic overview of the apparatus. The jet is introduced to vacuum by a feedthrough mounted on a 3-axis stage. The jet is crossed by a laser ~1 mm downstream before being collected in a cryotrap. The laser generates solvated electrons are by charge-transfer-to-solvent from anions in solution, and detaches them to vacuum. After crossing a skimmer, electrons undergo field-free flight to our detector. See text for further details.

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that requires chamber pressures better than ~10-5 Torr in a typical experimental configuration. The application of PES to solvents with equilibrium vapor pressures in excess of 1 Torr therefore poses a challenge, which we overcome through the use of liquid microjets.

First described by Faubel, liquid microjets are broadly useful, enabling the application of high vacuum techniques to bulk liquid systems.[1] When liquid is forced through a small orifice, diameter d, a microjet is formed. An effusive flow of solvent molecules from the jet into vacuum is achieved when d is reduced to be comparable to or smaller than the molecular mean free path, λ, satisfying the Knudsen condition. The molecular mean free path in the vapor is then

0

,cP

λ = (2.1)

where P0 is the equilibrium vapor pressure and c is given by

.2

kTcσ

= (2.2)

Here k is Boltzmann’s constant, T is the temperature, and σ is the molecular collision cross-section.[1] The jet can be treated as a cylindrical line source, with the pressure decreasing as 1/r, the radial coordinate in the plane of the gas expansion. The flow of gas molecules can then be described in terms of two annular regions around the jet: the vapor-phase regime where λ ~ r, and the free molecular flow regime where λ ≫ r. Since most collisions occur in the vapor-phase regime, it is desirable to expedite the transition to the molecular flow regime. This can be accomplished by sampling the jet with a skimmer within the vapor-phase regime. The skimmer aperture acts as a point source of molecules in the detector chamber, changing the pressure scaling from 1/r to 1/r2, thereby minimizing collisions. To quantify the effects of collisions, we can estimate the effective path length through vapor as[1,3]

0

00 0 0

0

ln ,r

r

r rP dr P rr r

µ = =

∫ (2.3)

where 0r is the radius of the jet. Although this has the somewhat awkward units of pressure multiplied by distance, typically Torr·cm, it is a convenient parameter to use because the number of collisions experienced between the jet and the skimmer is then simply

.colNcµ

= (2.4)

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Since the jets evaporatively cool in vacuum, it is important to note the temperature dependence of Eq. 2.2 and 2.3 when estimating the number of collisions. As described by Faubel in detail, this process is well treated by numerical simulation.[1] Briefly, as solvent molecules evaporate, they cool the surface of the jet and heat is transferred from the jet core outward. This establishes a radial temperature gradient in the jet, given by

2 ,p

dTdr r c

Λ= − (2.5)

where Λ is the heat of vaporization and cp is the specific heat capacity of the liquid. Differentiating Eq. 2.5 with respect to time, and dividing by the jet velocity, ,jetv dz dt= leads to an expression for temperature as a function of position along the jet,

0

0

12 .p jet

rdTdz r c v

Λ= −

(2.6)

The rate of decrease in the jet radius is then

,vapor

liquid

r uρρ

= (2.7)

where u is the mean velocity of the evaporating molecules. The specific implementation of this model used in our group was developed by the Saykally Group, and was detailed by Smith.[4] In it, the jet is treated as thirty concentric annular columns of equal radial width, each with distinct temperatures and heat exchange between them. The temperature dependence of the vapor pressure is explicitly accounted for, while other physical properties are treated as constant at their room temperature values.

2.3 Practical application of microjets

The particular implementation of microjets used in our lab was heavily influenced by collaboration with the Saykally Group where glass capillaries are often used as nozzle apertures[2] in place of the platinum-iridium plates used by Faubel.[1] Our apertures are fabricated from 10-30 µm I.D., 363-375 µm O.D. fused-silica capillaries, cut to 0.34” lengths. These capillaries are readily available as a standard chromatography supply, and we cut them using an appropriate diamond blade capillary column cutter (SGT Middelburg B.V.).

15

Figure 2.2 shows a detailed view of our nozzle assembly. The aperture capillary, a, is inserted into a 0.29-0.30” length of 0.020” I.D., 1/16” O.D. length of polyether ether ketone (PEEK) plastic tubing, b, and secured in a 1/16” Swagelok union, c. Assembled, the capillary protrudes from the front of PEEK ~0.01” while the PEEK protrudes ~0.04” from the union. Swagelok union c connects to the front piece of the inline filter holder, d (Idex, A-314). To reduce incidents of the capillary clogging, a 2 µm inline solvent filter, e (Idex, A-100), is used, held by pieces d and f. The back piece of the filter holder then attaches to a bored through, 1/4” to 1/16” Swagelok reducing union, g. A length of PEEK tubing, h, is fed through the union to supply solution. The nozzle is then attached to a 1/4” fluid feedthrough (MDC Vacuum, 610022) which feeds the PEEK tubing from the nozzle out to the solution supply.

It should be noted that the connections c-d and f-g mate pieces of two different connection standards and extra care needs to be taken to avoid overtightening either one. The f-g connection is made with an appropriate ferrule for the Swagelok side. The PEEK tube is inserted from the 1/4” side, and the ferrule is attached using a 1/16” Swage nut ahead of nozzle

Figure 2.2: Microjet nozzle.

a) Fused-silica capillary b) PEEK tubing c) 1/16” Swagelok union d) Inline filter holder front e) Inline filter frit f) Inline filter holder back g) 1/4” to 1/16” Swagelok reducing union, bored through h) PEEK tubing i) Assembled microjet nozzle

See text for further details.

16

assembly. Overtightening this connection tends to asymmetrically deform the connector on the union, causing the assembly to point to the side undesirably, and eventually leak. On the other hand, c-d connection is made without an appropriate ferrule for either side. As the connection is made repeatedly, the union is gradually deformed symmetrically by the filter holder, rounding the back edge as is visible in Fig 2.2. While it would be possible to use appropriate ferrules if we added a 1/16” stainless steel tube between c and d, and used stainless steel instead of PEEK for h, the extra complexity and susceptibility to bending the assembly is not worth the trade-off since the connections are quite reliable as is. The microjet region of the apparatus (see Fig. 2.1) reaches the same ultimate pressures with the nozzle assembly in place and not flowing as it does when the feedthrough is replaced with a blank (~10-6 Torr). These connections do not require frequent replacement either, despite heavy use. Union g is typically good for 1-1.5 years, while union c tends to last ~3 months.

Once assembled, the nozzle is connected to a syringe pump to provide backing pressure (Teledyne-Isco, 500D). A syringe pump was chosen over a high-performance liquid chromatography (HPLC) pump to maximize jet stability. Our pump is a piston-driven design with a single speed gear train. Once filled, the piston compresses the fluid, monotonically decreasing the solution volume. In contrast, HPLC pumps typically have a reciprocating piston design, which results in unwanted cyclic variations in the backing pressure. We also considered and rejected the idea of using a homebuilt solution vessel connected to a gas cylinder instead of a pump. Although this would provide a stable, constant backing pressure, the syringe pump has the advantage of operating either in a constant pressure or constant flow rate mode. To maintain consistent conditions day-to-day, we typically operate in the constant flow rate mode. The backing pressure required varies with the set flow rate, solvent identity and purity, capillary size, and the amount of tubing between the nozzle and the pump. For example, a 20 µm methanol jets flowing at 0.250 mL/min typically results in stable pressures between 50 and 100 atm while comparable acetonitrile jet stabilizes between 150 and 200 atm.

To test a new jet, pure solvent is run through it for at least 15 minutes until the backing pressure stabilizes, and typically over an hour. A good jet will generally have several millimeters of laminar flow before entering the

Figure 2.3: Flowing microjet. The red spot is backscatter from a laser pointer, beginning at the transition to the turbulent region.

17

turbulent regime. The transition away from laminar flow is visible to the naked eye. Because there is minimal backscatter in the laminar region, it appears dark, while the turbulent region backscatters enough ambient light to appear grey-white. A laser pointer can be helpful in identifying the transition as well. As shown in Fig. 2.3, the laser is quite visible on turbulent parts of the jet, but not at all visible on the laminar portion. Once a jet has stabilized with a laminar regime longer than ~2 mm, we coat it with graphite aerosol (Acheson-Colloid, Aerodag G) to reduce charge buildup and improve the day-to-day reproducibility of our data. This runs the risk of clogging the nozzle, so the jets are allowed another 10 minutes of flow after coating to ensure stability. If the jet clogs or does not stabilize with a satisfactory laminar region, the pump is stopped, union c is disconnected, and capillary a is replaced.

After satisfactory stabilization, the jet is stopped, the pump is drained, and a salt solution is loaded into the syringe pump. The microjet assembly is positioned within the chamber while the jet is off to allow better measurement of the displacement from the laser-skimmer plane (typically set to 1 mm). Normally the jet is then started at atmosphere before evacuating the chamber. The jet must always be started at atmosphere with water solutions since any water in a non-flowing capillary under vacuum will quickly freeze and break the glass. Solvents with much lower freezing points such as methanol do not strictly need to be started at atmosphere, but the evaporating solvent does leave behind salt deposits in capillary. This means that a jet starting under vacuum is more prone to flowing at an unfortunate angle, rapidly clogging, or even failing to start. In general it is best to avoid starting microjets under vacuum.

At the completion of a data run, the syringe pump needs to be cleaned to remove the salt. This typically requires 4-8 rinses with pure solvent, depending on the concentration of salt used. If the jet performed well throughout the run it will normally be reusable, and the final rinse of pure solvent is typically left to flow through the nozzle overnight. Failure to adequately rinse the pump significantly increases the likelihood of jet failure. Contamination usually leads to new jets that flow briefly, but clog within two minutes. If replacing the inline filter, e, does not fix the problem, flushing the pump an additional ~4 times will usually rectify the situation. Occasionally, however, either the pump lines or a fitting will corrode. If nozzle clogging problems persist through repeated rinse cycles, the pump should be disassembled and any corroded parts replaced. New lines should be thoroughly cleaned before use, typically by flushing stainless lines with house distilled water for ~1 minute and flushing the reassembled system an additional 4 times before testing a new nozzle.

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2.4 Solvated electrons – generation and detachment

With the microjet flowing in vacuum, the next step is the generation of solvated electrons. This is most conveniently accomplished by ejecting electrons from solvated anions into the solvent network, a process called charge-transfer-to-solvent or CTTS. Well characterized for a wide range of solvent-anion systems, CTTS bands are smooth, structureless absorption bands at ultraviolet wavelengths.[5-9] Photons at these wavelengths are energetic enough to detach an electron from the anion, but are below the threshold to eject the electron to vacuum. As a result, the system is left in a highly excited state with the electron stabilized by the solvent. The electron then may separate from the parent atom or molecule through solvent fluctuations, leading to a solvated electron. The solvation timescale and probability are dependent upon the identity of the anion and solvent, as well as wavelength used for excitation, but are typically on the order of 10 ps or less, with a quantum efficiency greater than 0.3.[10,11] To generate solvated electrons in solution by CTTS, we can simply cross the jet with a laser in directly front of the skimmer. Since the jet is only flowing at ~20 m/s, it is stationary on the timescales relevant for solvated electron generation and we do not need to offset the laser.

Once solvated electrons are present and equilibrated with the solvent, they can be detached to vacuum and detected. Since we wish to sample bulk solvated electrons rather than surface states, it is desirable to know how deep in the jet we can probe. Unfortunately, the electron effective attenuation length (EAL), the distance over which electron signal falls by 1/e, has not been directly measured in liquid water in the electron energy range we are concerned with (below 6 eV). Based on recent theoretical and experimental work, we expect that our probe depth is at least 10 nm and therefore deep enough to be considered truly bulk.[12,13]

Scattering in the vapor phase is also a concern; we want to measure electrons that have not lost energy from inelastic scattering events. Both elastic and inelastic scattering cross-sections have been measured for most solvents of interest. In the electron kinetic energy ranges appropriate for our work, vibrationally elastic scattering events are far more common than inelastic collisions, with cross-sections typically an order of magnitude greater for elastic scattering.[14-16] Using Eq. 2.5 and these literature cross-sections, we can estimate the number of collisions experienced by our electrons. Depending on the solvent in question, the electrons are expected to experience 5-15 elastic collisions and 0-1 inelastic collisions in the vapor sheath. Consequently, we expect that our data are not skewed by inelastic scattering.

All of the work presented here was taken with a 30 Hz Nd:YAG (Spectra-Physics, Pro-290). The pulse duration is normally 10 ns, however if the output power is cut by decreasing the delay between the lamp trigger and

19

the Q-switch trigger, pulse duration can be extended, up to a maximum of ~50 ns. The second and fourth harmonics (532 and 266 nm) were generated using a vendor supplied crystal arrangement inside the laser head. The 266 nm light was either used directly, mixed with residual 1064 nm in a BBO on the table to generate 213 nm, or focused into a 60 cm Raman cell. The Raman cell was filled with either 250 psi of deuterium or 325 psi of hydrogen. While the third anti-Stokes through the fourth Stokes lines were typically observed with both gasses, we only made use of the first and second anti-Stokes lines at 247 (D2), 240 (H2), and 231 nm (D2).

Since our laser pulse duration (10 ns) is significantly longer than the solvated electron equilibration time (up to 10 ps), we are able to perform this pump-probe experiment with individual pulses from our Nd:YAG. While we do not have control over the precise delay between the photon that generates a solvated electron and the photon that detaches it to vacuum, on average it will be long enough that we will sample an equilibrated population. This can be confirmed by varying that anion identity, or increasing the pulse duration as described above, and looking for changes in the photoelectron spectra.

Alignment of the laser is relatively easy thanks to our bulk target. When the laser is overlapped with the jet, a strong diffraction pattern is observed on the exit of the chamber (see Fig. 2.4). When the laser is far enough downstream from the nozzle that it is incident upon the turbulent or droplet region of the jet, the intensity of the diffraction pattern is significantly reduced. This allows us to verify we are in the laminar region by scanning the laser up and down. Also, when the laser vertical is correctly positioned, enough light scatters into the flight tube and onto the detector itself to cause a significant signal spike. This gives us a useful tool to confirm that the laser is well aligned, and to verify our calibration (see § 2.10).

Figure 2.4: Diffraction from a microjet.

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Figure 2.5: Detailed apparatus schematic.

a) Syringe pump b) Three-axis translation stage c) Microjet assembly d) Cryotrap e) Liquid nitrogen dewar f) Skimmer g) Differential pumping sheath h) Butterfly valve i) Magnetic shielding j) Gate valve k) MCP detector l) Gate valve m) Ion deflectors n) Einzel lens

I) Trap region II) Detector region III) Gas-phase anion source

See § 2.5 for details on the purpose and use of each component.

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2.5 Jets in vacuum – the microjet trap region

The liquid microjet photoelectron spectrometer consists of three spherical six-way cross chambers on a 10” Conflat (CF) flange standard, coupled to the gas-phase source previously detailed[17,18] through a gate valve. The liquid jet components are divided into two regions, the microjet trap region and the detector region. As shown in Fig. 2.5, these are regions I and II respectively, and the gas-phase anion source is region III. An overview of the trap region is presented here, while detailed machine drawings are presented in Appendix A.

The trap region extends from gate valve l, which separates the microjet apparatus from the gas source region, to either the skimmer and sheath (f and g respectively) while running or to gate valve j while vented. Under operating conditions, the skimmer is needed to provide differential pumping and change the pressure scaling away from the jet from 1/r to 1/r2 (detailed in § 2.2). However, to ensure the longevity of our microchannel plates (MCPs), we would like the detector to remain under vacuum at all times. To isolate the detector from the daily vent and clean cycle necessitated by the microjet source, gate valve j is included in the flight tube. Butterfly valve h is thus open during pump-down to provide reasonable pumping speeds between the skimmer and gate valve, and is then closed to retain differential pump when valve j is opened. In this manner we are able to bring the entire trap region from atmosphere to approximately 10-4 Torr in 20-30 minutes. Pumping of the trap region is provided by a 150 L/s turbomolecular pump (Leybold, Turbovac 150), with additional capacity provided by a liquid nitrogen dewar in the chamber, e, and the cryotrap that catches the jet, d. An Edwards 8 rotary vane dual stage mechanical pump backs the turbomolecular pump. To extend the useful life of the pump oil and reduce backstreaming of oil, a cryotrap is used on the foreline. A cryotrap was chosen over a molecular sieve trap because of the large amounts of solvent the pump is exposed to.

The microjet nozzle is fed into vacuum on a 3-axis translation stage, b, with a range of ±0.5” in X and Y, and 4.0” in Z (MDC Vacuum, 678026). This allows us to position the jet in front of the skimmer, f, for optimal signal, and translate vertically to stay within the laminar region of the jet or sample a range of temperatures. The jet is collected in a liquid nitrogen cooled trap, d, to minimize vapor from a standing pool of solvent. Originally the bottom piece of the chamber was a 10” to 2.75” zero-length CF reducer modified to include a tube and small opening. This collected the jet ~5” downstream from the nozzle. While this worked well under the initial calibration scheme, it has since become problematic. Walking the jet away from the interaction point coated the top of this tube with salt, reducing the reproducibility of our streaming potential measurements (see § 2.10 for details). As such, the bottom chamber piece has since been replaced with an unmodified 10” to

22

2.75” CF reducer. The cryotrap also includes an optional 2.75” CF tee, with a feedthrough for a 1/4” O.D. rod with several washers attached to the end. This serves as a crude ice breaker, and allows us to break icicles that form while running water jets. While this is a very low tech solution to the problem, it is highly effective and extended our typical water jet runs from 20-30 minutes to 120-180 minutes.

As mentioned above, differential pumping between the trap and detector is provided by skimmer f. We have several skimmers available for use, with openings of 1 mm, 500 µm, and 279 µm. A 100 µm skimmer was also briefly used; however the signal loss outweighed the differential pumping gains. The machine shop’s attempt to enlarge it to 250 µm is what resulted in our 279 µm skimmer. These skimmers attach to a sheath, g, which in turn attaches to a ring that is welded into the chamber cross. Although the bolt circle on the sheath has 6-fold rotational symmetry, two differently sized pegs are included to ensure consistent positioning. In practice, the skimmer is removed daily for cleaning while the sheath is rarely removed. Typically it is only removed when we need to access the mu-metal magnetic shield that bolts in place between the sheath and gate valve (once per ~18 months).

Not pictured in the schematic are the laser entrance and exit flanges (into and out of the page respectively). Entrance and exit windows are attached to 4.5” CF half nipple flanges with vacuum compatible epoxy (Loctite, Hysol 1C). These are then attached to 10” to 4.5” CF reducing nipples, modified to include a 2” O.D., 2.5” long tube stub. These tube stubs are set off-center and are angled towards the jet. Additional windows epoxied to these stubs serve as viewports. On the exit side a desk lamp is used to illuminate the chamber, with a video camera setup at the entrance side. In this manner we can monitor the chamber for icicle buildup, jet pointing instability, salt buildup, or other potential problems. These flanges also include mounts for laser baffles. However, the apparatus was originally designed with the intention of running with the jet ~4 mm away from the skimmer. Once we discovered that it is of considerable benefit to run with the jet closer to the skimmer, the exit baffles were removed so the laser can exit the chamber.

Also included in the trap region are a collection of ion optics, two sets of deflectors, m, and an einzel lens, n. These are attached to and supported by a 9 mm aperture immediately past gate valve l. The first set of ion deflectors are directly attached to the aperture plate, and are 2” long. An adapter plate attaches to the deflector support, mounted to 8” posts. The einzel lens plates mount 0.5” downbeam from this adapter, with a 0.5” inter-plate spacing. A further 1.75” downbeam from the final einzel lens plate is the final set of 2” deflectors. Although no longer used, these were critical for steering and focusing the anion beam originally used for calibration (see § 2.8 for details). All electrical feedthroughs for these electronics were on a 10” CF flange located on the bottom of cross nearest gate valve l.

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2.6 Field-free spectrometer – the detector region

The detector region has undergone a series of modifications over the life of this apparatus. Although the portion of the flight tube between the differential pumping sheath and the gate valve (Figure 2.5, g and j) has not been modified, the detector cross piece has seen systematic improvements. While the detector region is significantly less complicated that the trap region, an overview of each stage of the detector region is provided here.

During operation, the detector region consists of two pieces of mu-metal, i, to shield the flight tube from external magnetic fields, the detector, k, and several turbomolecular pumps. The mu-metal on the trap side of the gate valve attaches to a support ring welded to the trap cross piece, and extends from 1/8” behind the sheath to 1/8” away from the gate valve. The mu-metal piece on the detector side is supported in a more complicated manner. The detector mu-metal shield was not actually designed for this apparatus; it is reused from the velocity-mapped imaging setup previously used in this laboratory. In that experiment, a double-shielded setup was used, with two pieces of mu-metal attached to an aluminum ring, which in turn attached to a modified 10” double-sided CF flange with four support rods. We presently make use of the 10” double-sided flange, aluminum ring, and inner mu-metal piece. This assembly attaches between the cross and detector flange, and extends towards the gate. The result is shielding that begins ~0.5” away from the gate and extends to well beyond the detector.

Initial plans for the detector called for 40 mm MCPs, and a total flight length of ~40 cm. The goal was to have the detector as close to the gate as possible, and with such a short flight length a larger detector was deemed unnecessary. We quickly discovered, however, that this produced excessive ringing caused by electrical pickup on the output line. The detector was modified to reposition it closer to the mounting flange using thicker, more stable supports, and change to 70 mm MCPs simply because they were available. The result was a 63 cm flight tube and a chevron-stacked, dual-MCP detector that served our purposes well. Eventually the gain on those MCPs dropped below the usable threshold and required replacement. The detector supports were further strengthened at that time, and the detector was upgraded to a Z-stacked, triple-MCP arrangement. The result was a 59 cm flight length for the final configuration used on the apparatus. It should be noted that this detector was chosen because they were the only set of good MCPs available in the group at the time. They are far higher gain than is needed for this experiment; a chevron-stack would be more appropriate to purchase for use on this project.

The pumping speed on the detector region has been systematically improved as well. The detector was initially limited to 300 L/s of pumping, provided by a pair of Leybold Turbovac 150 turbomolecular pumps. The resulting conditions in the detector region were best described as borderline,

24

usually at or slightly exceeding 10-5 Torr while running. This was high enough that electron scattering in the vapor phase may have been an issue, and energizing the MCPs is contraindicated by the manual. As soon as was possible, a Seiko Seiki STP-400 turbomolecular pump was added to the region, bringing the pumping speed to 750 L/s. This brought the detector pressures down to ~7×10-6 Torr under identical jet conditions. Eventually, we decided to significantly improve the pumping speed and purchased an 1100 L/s pump (Leybold, 1000C). Because all ports on the detector cross were already occupied, we removed a Turbovac 150 to install the new pump, so our total pumping speed is now 1650 L/s. Under the same jet conditions, this brings the chamber pressure down to ~3×10-6 Torr. However, we no longer run under the original jet conditions, having reduced our jet diameter from 30 µm to 20 µm or less, and changed from water to more volatile solvents. Typical detector pressures under our new operating conditions range from ~2×10-6 Torr (ethanol) to ~6×10-6 Torr (tetrahydrofuran). With each of these turbomolecular pump configurations, backing pumping has been provided by an Edwards 12 rotary vane dual stage mechanical pump.

2.7 Data collection and processing

Our data collection cycle is initiated when a digital delay/pulse generator (Stanford Research Systems, DG535) triggers the laser firing sequence. As the laser pulse leaves the laser, a back reflection is picked up on a photodiode (Thor Labs, Det 10A) that triggers a delay generator (Systron Donner, 101 Pulse Generator), which in turn triggers an oscilloscope (Tektronix, TDS 3034B or DPO 3034). The delay generator is set such that the laser interacts with the microjet approximately 50 ns ahead of the oscilloscope trigger. Typical observed kinetic energies are 0.75 to 3 eV, so data are normally collected out to 2000 ns after the trigger which corresponds to a kinetic energy cutoff of 0.23 eV.

The oscilloscope is capacitively coupled to the detector anode (detailed in the thesis of A. Weaver[17]) such that each electron incident upon the detector causes a negative voltage spike. Normally 512 laser pulses are averaged before transferring the spectrum to a computer. Spectra collected with the older TDS 3034B oscilloscope were acquired using a modified version of the PES program written by H. Gomez.[19] Later spectra taken with the DPO 3034 were collected using a new LabVIEW program that is described in Appendix C.

Conversion of our TOF spectra to electron kinetic energy (eKE) is slightly more straightforward than the process detailed by Weaver.[17] Because our jet velocity is ~10 m/s rather than the ~105 m/s ion velocities typical in the anion experiments, we do not need to correct for a non-zero center of mass velocity. As such, our conversion to eKE is simply

25

( )

2

20

1 1 ,2 2e e eE m v m

t t= =

−

(2.8)

where me is the electron mass, ℓ is the length of the flight tube, and t0 corrects for the time difference between the laser-jet interaction and the oscilloscope trigger. While the values of ℓ and t0 are in principle known from direct measurement of the flight tube length and observation of the laser spike arrival time on the oscilloscope, they are subject to slight variations day-to-day and should be obtained through proper calibration (see §2.8 and 2.9).

With these values in hand, the TOF spectra are converted to eKE using Eq. 2.8 and by scaling the intensities by E-3/2 to account for the Jacobian. This process amplifies small fluctuations at low kinetic energy, which are typically dealt with by smoothing the spectra by convolution with a 10-15 meV FWHM Gaussian peak. The PES program written by Gomez performed both of these transformations within the data collection program. This capability has not yet been implemented in the new data acquisition suite, and most data analysis now is performed using the Origin commercial software package (OriginLab Corporation). However, Origin has no built in capacity to transform TOF to eKE, and the built-in package for Gaussian convolutions requires evenly spaced data. Through LabTalk, Origin’s scripting language, both the ability to convert from ToF to eKE and the ability to smooth unevenly spaced data, such as our eKE spectra, have been added. These scripts are presented in Appendix D.

2.8 Calibration with anions

As detailed above, the liquid microjet apparatus is coupled to the gas-phase anion source described elsewhere.[17,18] The initial implementation of the field-free liquid microjet photoelectron spectrometer made use of the gas source for calibration purposes. This calibration procedure is thoroughly detailed by T. Yen,[20] but a brief overview is presented here to highlight and motivate our calibration with neutrals (see § 2.9). Briefly, to calibrate our apparatus, we need to determine the effective flight tube length, ℓ, and the timing offset between the laser interaction with the sample and the triggering of the oscilloscope, t0. To calculate these parameters, I‾ and Br‾ were detached to their respective neutral 2

3 2P and 21 2P states, giving four

peaks of known binding energies. These photoelectrons were then detected with lab frame velocities given by

0

.labvt t

=− (2.9)

26

However, the these electrons were collinearly detached from ions moving at considerable velocities, so a center of mass correction is required to use these peaks for calibration. Their lab frame velocity was given by the sum of the center-of-mass (ion) velocity and velocity due to photodetachment,

.lab COM PDv v v= + (2.10)

The velocity of the center-of-mass frame came from the ion extraction voltage experimental parameter, Vext, the charge of the ion, qion, and the mass of the ion, mion, such that

.ext ionion

ion

V qvm

= (2.11)

The velocity from photodetachment alone is given by

( )2 ,PDe

v h eBEm

υ= − (2.12)

where me is the electron mass, h𝜈 is the photon energy, eBE is the electron binding energy. Combining Eq. 2.9-12, we have

( )0

2 .ext ion

ion e

V q h eBEt t m m

υ= + −− (2.13)

Rearranging, we are left with

( )1

02 .ext ion

ion e

V qt h eBE tm m

υ−

= + − +

(2.14)

By plotting the arrival times of our calibration peaks versus

( )1

2 ,ext ion

ion e

V q h eBEm m

υ−

+ −

we can then obtain our calibration parameters, ℓ

and t0, from the slope and intercept of a linear fit to the data. In practice, we work exclusively with singly ionized anions, that is ,ion eq q= and electron volts are our preferred units of energy. As such, the practical implementation Eq. 2.14 is of the form

( )1

02 ,ext e e

ion e

V q qt h eBE tm m

υ−

= + − +

(2.15)

27

where the voltage is in V, masses are in kg, the electron charge is in C, and the energies are in eV. This results in units of nm and ns for length and time respectively.

The quality of the calibration parameters can then be assessed in several ways. The flight tube length is known to within 1 cm, and in principle the laser maximum is at roughly t0+2 ns. However, the laser spike is only observed in the presence of a jet, so the most recent jet timing served for a reference value. For a reasonable fit, the length would be within 1 cm of the measured value, while t0 fell within ~10 ns of the laser spike time. To further verify the fit, we then calculated the measured energies of the calibration peaks using the fit parameters and Eq. 2.8. For a good fit, all four peaks could be expected to have reconstruction errors below 10 meV.

Although this technique produced consistent calibrations, it was somewhat limited as calibration of the apparatus was impossible with the microjet running. Even with the jet positioned as far out of the way as possible, the high pressure in the trap region (~10-4 Torr) effectively attenuated the ion signal more than 90%. Furthermore, the remaining signal was temporally broadened to greater than 100 ns from the ~10 ns obtainable in the absence of the jet. Unsurprisingly, we could not find photodetachment signal under these conditions. Consequently, with this calibration scheme we could not directly measure any streaming potential of the microjet. Furthermore, to achieve the low enough pressures required for good gas phase anion data (~10-6 Torr in the trap), the trap region needed to be thoroughly cleaned and pumped down at least overnight. This blinded us to any day-to-day timing variations that could introduce errors in our calibration.

2.9 Calibration with neutrals

In a significant expansion of our experimental toolkit, a Clark-MXR CPA-1000 femtosecond laser system is now available for use on the Liquid Microjet project. This laser is a second-hand system, obtained from the Femtosecond Time-Resolved Photoelectron Spectroscopy project after they upgraded to a new system, and considerable effort has gone into bringing its full capabilities online. Credit for success on this front goes to Madeline Elkins, who will doubtlessly chronicle the full saga in her upcoming thesis. The upshot is that since mid-2011 we’ve been able to deliver at least 1 μJ/pulse of ~120 fs, 266 nm light to the chamber, with a repetition rate of 1 kHz. We have been taking advantage of this new capability to calibrate by multi-photon ionization of neutral gasses.

To calibrate with neutrals, a new gas source was required. For simplicity, our gas inlet is essentially the same as our liquid microjet nozzle. A 1/4” O.D. tube is fed into the chamber, routed through the center of the einzel lens and final deflectors (n and m in Fig. 2.5) for support, ultimately

28

reaching a 1/4” to 1/16” Swagelok reducing union ~5” from the skimmer. A 1/16” O.D. tube, bent appropriately to avoid the microjet and laser completes, the gas line. It then terminates in a 100 μm I.D. nozzle constructed as per Fig. 2.2, a to c. The gas nozzle is ~5 mm behind the laser-jet interaction point, angled such that 1) it is clear of the laser and 2) the microjet and jet have clearance to pass it when moved away from the skimmer on the flight tube axis. Both a bellows valve and a metering valve are included on gas line outside of vacuum, allowing us to maintain a constant pressure by controlling the bleed-in rate. Typical operating parameters for calibration are a partial pressure of ~5×10-4 Torr of Xe or Ar, with ~4 µJ/pulse of femtosecond 266 nm light.

In our current calibration scheme, we typically ionize Xe and Ar, detaching them to their respective cationic 2P3/2 and 2P1/2 states. Unlike our previous calibration scheme, photodetachment is now multi-photon. Using 266 nm (4.66 eV), this is a three-photon process in Xe (12.13 eV to ionize) or four-photon in Ar (15.76 eV to ionize). Also, these atoms have a negligible velocity in the lab reference frame. Accounting for both of these changes, Eq. 2.15 becomes

( )1

02 ,e

e

qt n h eBE tm

υ−

= ⋅ − +

(2.16)

where n is the number of photons involved in detachment. In a complication over the old scheme, the laser wavelength is not as well-known with the femtosecond system as with the Nd:YAG. The central wavelength may change by several nanometers day-to-day, primarily determined by how much the oscillator parameters have been altered. We can measure the wavelength with a spectrometer, but it is only accurate about a nanometer in the part of the spectrum we are concerned with. In practice, we can more precisely determine the wavelength by treating it as a fit parameter on a four point calibration. By optimizing the wavelength, a good, linear fit can be obtained. The wavelength as determined by the spectrometer, the flight tube length, and the laser spike time all serve as sanity checks on the fit. Also, since we can now calibrate with the jet running, we can use the laser spike to obtain t0 to within 2 ns while taking Xe or Ar data. The resulting fits usually result in reconstructed energy errors of ~1 meV. These parameters are quite stable from day-to-day, provided the oscillator has not been adjusted significantly.

Calibration with neutrals has a number of significant advantages over the anion calibration scheme. First among them, because we can calibrate while the jet is running, we can now measure the streaming potential of the jet (see § 2.10). This has significantly improved both the accuracy and repeatability of our measurements, and the pace of progress on the project.

29

This also greatly increases our uptime as we no longer need to devote two or more full days to calibration. Uptime is also improved because of the simplicity of the technique. With only a nozzle to position before pump down, far less can go wrong now than with the anion source where there were a slew of electronics and a valve that frequently required repair or reoptimization. Finally, it allows for a much higher repetition rate while calibrating. The laser runs at 1 kHz, but the anion source was limited to a few hundred Hertz by a combination of pumping speed and valve stability, limitations that do not apply to the neutrals technique.

2.10 Streaming potentials

Electrokinetic charging of microjets is a concern for any study that aims to accurately measure electron binding energies in or near microjets. As is illustrated in Fig. 2.6, a charge double layer is present at the liquid-solid interface. Combined with the flow velocity profile, which goes to zero velocity at the walls, the charge separation gives rise to a streaming current and streaming potential.[3,21-23] Although the sign and magnitude of the streaming potential vary wildly depending on source conditions, the resulting photoelectron spectra simply shift rather than distort with a charged jet.[3] As such, it is easy to correct for a known streaming potential in energy-space.

As reported by Faubel,[3] the streaming potential of a microjet is given by

0

1 ln ,2 2

jetstrstr

jet

dIvπε

Φ = −

(2.17)

where Istr is the streaming potential, vjet is the jet velocity, and djet is the jet diameter. The streaming current then comes directly from the interaction of the velocity profile and charge distribution. For laminar flow, this is given by

Figure 2.6: Charge separation and velocity profile schematic. An exaggerated illustration of the charge double layer found at the microjet wall, and the flow velocity profile, assuming laminar flow conditions. The uneven flow in the two charge regimes gives rise to a streaming current and streaming potential.

30

( ) ( )0

,nr

strI r u r drρ= ⋅∫ (2.18)

where ρ(r) is the net ion charge distribution, u(r) is the fluid velocity profile, and rn is the nozzle radius. Considerable effort has gone into developing accurate treatments of the charge distributions, velocity profiles, and streaming currents in microchannels under various conditions, e.g Refs. [3,21-27]. From this work, it is known that streaming potentials tend to decrease with increasing salt concentration, particularly above ~10 mM, and increase with backing pressure. Depending on flow conditions, the streaming current either varies linearly (laminar flow) or nearly quadratically (turbulent flow) with the jet velocity. Overall, it appears we can minimize streaming potentials by running as small of jets as possible, at relatively high salt concentrations, and with as low of backing pressures and velocities as will produce laminar flow. However, it is also clear from this work that the accurate prediction of streaming potentials is quite challenging and we would do best to experimentally measure them. Fortunately, this is now possible thanks to the new neutrals calibration scheme detailed in § 2.9.

To determine the streaming potential of a microjet, we can measure the spectrum of calibration gas in proximity to the jet and compare to the spectrum in the absence of the jet. Unfortunately, ionization of the evaporating solvent is competitive with ionization of our calibration gas since both processes are typically three-photon at 266 nm. This means that signal from the solvent overwhelms the signal from the calibration gas when the laser is directly incident on the microjet. However, as illustrated in Fig. 2.7, we can walk the jet away from the laser interaction point and monitor the change in the arrival energy of our desired feature. We can then fit the resulting distribution of electron kinetic energies with the form[28]

Figure 2.7: Streaming potential measurement scheme. The laser is aligned to the microjet, and then the microjet is moved away from the skimmer. By observing a shift in the calibration peak, the streaming potential of the jet may be inferred.

31

.strfield free

LKE KEL x−

Φ= −

+ ∆ (2.19)

In practice, Origin requires one of the parameters to be fixed to avoid degeneracies in the fitting routing. As such, we fix L and treat the streaming potential and field-free kinetic energy as fit parameters. A resulting fit is only considered acceptable if the derived field-free kinetic energy is within ~10 meV of the measured value. A sample distribution and fit are shown in Fig. 2.8.

Figure 2.8: Jet-walk energy shift. Shift in energy of photoelectrons with jet position following three-photon photodetachment of Xe to the Xe+ (2P3/2) state, taken using the femtosecond laser at 266 nm, with 5 µJ/pulse. The form of the fit is given in Eq. 2.19.

32

2.11 Field-free collection efficiency

In our field-free spectrometer, electrons are emitted in all directions, and we only collect the small fraction of them that pass our skimmer and travel down the flight tube to our detector. For all but the 100 µm skimmer, our detected signal is limited by the size of our detector rather than our skimmer. As shown in Fig. 2.9, for a skimmer aperture radius s located distance r from the laser focus/microjet interaction point (centered in front of the simmer), the skimmer opening has an angular extent of ( )1sin .s rθ −= The detector, O.D. a, located length ℓ from the interaction point, extends to

( )1sin .aϕ −= Under our normal operating parameters, the detector extends 3.3°, the 100 µm skimmer extends 2.9°, while all other skimmers extend at least 8.5°. As such, the relevant parameter to determine the fraction of electrons collected is the solid angle subtended by the detector.

In general, the solid angle of a finite objet at distance L and angle φ is given by

cos .A L

ϕΩ = ∫ (2.20)

To apply this to our detector, detector, consider an annulus on the face of the detector at radius ρ with a width of dρ. The differential area of each annulus is then

( )2 2.dA dπ ρ ρ πρ= + − (2.21)

This can then be Taylor expanded about 0,ρ = leading to

2 .dA dπρ ρ≈ (2.22)

From the interaction point, the annulus dependent interior angle is

Figure 2.9: Calculation of the solid angle subtended by the detector.

33

1cos ,Lρρ

ϕ −

=

(2.23)

while the hypotenuse is given by

2 2 .Lρ ρ= + (2.24)

Substituting Eq. 2.22-2.24 into Eq. 2.20 leads to

( )3 2 2 22 2

0

2 2 1 .a

da

ρπ ρ πρ

Ω = = −

++ ∫

(2.25)

With a 59 cm flight length and 70 mm diameter MCPs, our detector subtends a solid angle of 11 msr. Assuming an isotropic emission of electrons, we are then collecting only 0.09% of the ejected electrons. It is this low efficiency that motivates the apparatus reconfiguration to use a magnetic bottle (see § 2.12 for details).

2.12 Magnetic bottle spectrometer

At the time of writing, the apparatus is undergoing a reconfiguration to significantly improve the collection efficiency of our photoelectrons. The new spectrometer, a magnetic bottle spectrometer of the type first described by Kruit and Read,[29] will make use of an inhomogeneous magnetic field to collect approximately 50% of the emitted photoelectrons, rather than the 0.09% collected with the original apparatus. Briefly, a strong magnetic field is generated near the point of emission, which guides electrons into a flight tube where a uniform magnetic field maintained by a solenoid. The Lorentz force, ev B×

, causes electrons to spiral around the field lines. However, the gradient in the magnetic field results in a component of the Lorentz force along the detector axis. This leads to an increase of the electron’s longitudinal velocity, and by conservation of energy, a decrease in their latitudinal velocity. Consequently, the electrons are steered into the flight tube and parallelized on their approach to the detector.

Designing a magnetic bottle spectrometer for use with liquid microjets presents a relative challenge over one designed for use with gas phase sources. Because differential pumping is required, we cannot simply slide a solenoid over the flight tube, as has been done previously in the Neumark group.[19,30] Furthermore, it is undesirable to simply put the solenoid in vacuum since virtual leaks would likely cause significant difficulties. Motivated by these considerations, the new apparatus will use a pair of concentric tubes to extend a flight tube into the differentially pumped detector region while leaving the solenoid outside vacuum. A schematic

34

Figure 2.10: Magnetic bottle photoelectron spectrometer.

a) Syringe pump b) Three-axis translation stage c) Microjet assembly d) Cryotrap e) Liquid nitrogen dewar f) Magnets g) Three-axis translation stage h) Post and platform i) Rotary motion feedthrough j) Calibration gas inlet k) Skimmer and differential pumping sheath l) Flight tube m) Detector n) Solenoid o) Magnetic shielding p) Camera

I) Trap region II) Detector region

See § 2.12 for details on the purpose and use of each component.

35

diagram of the new apparatus is presented in Fig. 2.10, while the detailed machine drawings may be found in Appendix B.

The new apparatus consists of two regions, a trap region with rare-earth magnets and the microjet source, and the detector region with the flight tube and solenoid. As shown in Fig. 2.10, these are regions I and II respectively. The trap region will be composed of two 10” CF six-way crosses, while the detector region will be on one six-way cross. Unlike the old apparatus, we no longer have a gate valve. Although it will likely have a deleterious effect on the longevity of the microchannel plate detector to sit at atmosphere much of the time, the geometry constraints of the solenoid preclude the inclusion of gate valve. As such, the separation between regions I and II is a skimmer and sheath as before, without a scheme to bypass them for pumping.

Many components of the new apparatus match the original design. Pumping in both regions will be accomplished with the same configuration of turbomolecular pumps and a liquid nitrogen dewar, e, as is outlined in sections 2.5 and 2.6. Similarly, the microjet will be generated and positioned using the same equipment previously described, a through c in Fig. 2.10. We also retain the use of each of our old skimmers. Finally, the crosses used in this version of the apparatus are entirely unmodified from the previous arrangement, simply rearranged. The changes and new components are described below.

The most important components of the new trap region are the magnet assembly and associated supports. The magnet assembly, f, consists of several 1” O.D. Samarium Cobalt permanent magnets, field strength of 1.1 T, and a soft-iron cone to shape the field and increase the gradient at the interaction point. The magnet assembly mounts on a three-axis dovetail translation stage, g, customized for use in vacuum (Siskiyou Corporation, DT3-100-VC). The stage will rest on an optics platform (Edmund NT56-929), h, supported by homemade posts that attach to the chamber bottom flange. Three rotary motion feedthroughs (Accu-Glass Products, HTR-275), i, couple to the stage with flexible drive shafts (McMaster-Carr, 3787K18) for fine adjustment of the magnet position while under vacuum. For ease of fabrication, the rotary motion feedthroughs mount on a 2.75” to 1.33” CF reducing multiplexer (Kimball Physics, MCF275-FlgMplxr-Cr1A5) that will attach to the off axis port previously used to pump behind the sheath.

Other changes to the trap region are designed to simplify operation of the apparatus. As illustrated in Fig. 2.10, the gas inlet line, j, will now couple into the chamber through an Ultra-Torr fitting (Swagelok, SS-4-UT-1-4-BT) attached to the bottom flange, a modified 10” to 4.5” zero length CF reducing flange. This will allow for limited adjustment of the gas inlet position while pumped down. The laser exit flange (not pictured, out of the page) will also be changed. Since the trap chamber needs to be opened and cleaned daily, a customized access door (Kurt J Lesker, DS-LL1000) will

36

replace the exit flange, saving at least 20 minutes per day. As with the original exit flange, the door will include a viewport for illumination of the chamber, in addition to functioning as a reducing nipple to a 4.5” CF port for attachment of the laser exit window.

Finally, the arrangement to catch the spent solvent from the microjet has been slightly modified. Rather than using a 2.75” CF connection, cryotrap d is now on a 4.5” CF connector with a 2.5” OD tube. This change was made to aid in the jet-walk studies for measurement of the jet streaming potentials, as described in section 2.10. With the old scheme, the jet would frequently hit the chamber bottom rather than actually entering the cryotrap. This resulted in higher chamber pressures than desired. Although the pressures were within our operational limits, continuing to allow the jets to miss the cryotrap is not acceptable long term. The apparatus will be used to study water again, and the formation of icicles above the point where they can be broken is clearly untenable. An additional benefit of the new cryotrap is that it will hold a larger volume at of solution, up to 800 mL compared to the original 300 mL.

The changeover to the magnetic bottle spectrometer will involve even more drastic changes to the detector region than the trap region. To meet the constraints of differential pumping between the regions and having the solenoid begin close to the interaction point rather than 10” or more away, the gate valve will be removed. This means, however, that region II will vent every day with region I and that any virtual leaks from a wire coil in vacuum would be of great concern. To engineer around this, the new flight tube flange, l, will have a pair of concentric tubes to allow the insertion of a solenoid, n, and magnetic shield, o, quite close to the interaction region but outside vacuum. As designed, the solenoid will be 26” long, matching the electron drift length. The solenoid will extend from ~2” from the interaction point to slightly past the detector. The solenoid will be wound at 10 turns per inch with 14 gauge wire. The total length of wire, including the leads at 6 and 9 feet, will be ~4200” or 107 m, with an expected total resistance 0.9 Ω. The field inside the solenoid can be found with the equation

,B nIµ= (2.26)

where μ is the relative magnetic permeability, n is the coiling density, and I is the current. From previous magnetic bottles used in the group, a field of ~20 G in the flight tube will likely be appropriate, requiring a current of 4 A and resulting in a voltage drop of 4 V. A Kepco high current power supply (ATE 6-10M) is available to power the solenoid, which can easily meet these requirements.

The detection scheme will also be significantly altered. Although data will still be collected in a time-of-flight scheme, the new detector, m, is a vendor supplied, dual MCP imaging system (Beam Imaging Solutions, BOS-25-IDA-

37

CH-MS). As demonstrated by Schultz,[31] alignment of the magnets, microjet, and laser beams is significantly expedited with an imaging setup. With the new apparatus, a video camera, p, will monitor the phosphor screen. This will be used to verify proper alignment of the magnets, the laser in front of the skimmer, and of multiple laser beams with each other. If the magnet is misaligned, distorted, oblong images from signal at the focus is expected, while round images are expected if the magnet is well aligned.[29] To align the lasers in front of the skimmer should then be rather trivial, as the skimmer should produce a shadow that the laser signal can then be centered within.[31] Time of flight signal will then be obtained by capacitively coupling either the back MCP or the phosphor screen out to the oscilloscope. Data will then be transferred to the computer and processed as described in § 2.7.

38

2.13 References

[1] M Faubel, et al, Z. Phys. D 10 (1988) 269. [2] K R Wilson, et al, Rev. Sci. Instrum. 75 (2004) 725. [3] M Faubel, et al, J. Chem. Phys. 106 (1997) 9013. [4] J D Smith, et al, J. Am. Chem. Soc. 128 (2006) 12892. [5] M J Blandamer, M F Fox, Chem. Rev. 70 (1970) 59. [6] M Fox, et al, Faraday Discuss. Chem. Soc. 64 (1977) 167. [7] M F Fox, E Hayon, J. Chem. Soc. Faraday Trans. I 73 (1977) 872. [8] M F Fox, E Hayon, J. Chem. Soc. Faraday Trans. I 73 (1977) 1003. [9] M F Fox, et al, J. Chem. Soc. Faraday Trans. I 74 (1978) 1776. [10] V H Vilchiz, et al, Radiat. Phys. Chem. 72 (2005) 159. [11] X Y Chen, S E Bradforth, Annu. Rev. Phys. Chem. 59 (2008) 203. [12] D Emfietzoglou, H Nikjoo, Radiat. Res. 163 (2005) 98. [13] N Ottosson, et al, J. Electron Spectrosc. and Rel. Phenom. 177 (2010)

60. [14] Y Itikawa, N Mason, J. Phys. Chem. Ref. Data 34 (2005) 1. [15] M Allan, J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 3531. [16] M A Khakoo, et al, Phys. Rev. A 77 (2008) 042705. [17] A Weaver, Ph.D. Thesis, University of California, Berkeley, Berkeley,

CA, 1991. [18] C Xu, et al, J. Chem. Phys. 107 (1997) 3428. [19] H Gomez, Ph.D. Thesis, University of California, Berkeley, Berkeley,

CA, 2002. [20] T A Yen, Ph.D. Thesis, University of California, Berkeley, Berkeley, CA,

2010. [21] M Faubel, B Steiner, Ber. Bunsen-Ges. Phys. Chem. 96 (1992) 1167. [22] W L Holstein, et al, J. Phys. Chem. B 103 (1999) 3035. [23] A M Duffin, R J Saykally, J. Phys. Chem. C 112 (2008) 17018. [24] S H Behrens, D G Grier, J. Chem. Phys. 115 (2001) 6716. [25] F H J van der Heyden, et al, Phys. Rev. Lett. 95 (2005) 116104. [26] F H J van der Heyden, et al, Nano Lett. 6 (2006) 2232. [27] A M Duffin, R J Saykally, J. Phys. Chem. C 111 (2007) 12031. [28] H Shen, et al, Chem. Lett. 39 (2010) 668. [29] P Kruit, F H Read, J. Phys. E 16 (1983) 313. [30] B J Greenblatt, Ph.D. Thesis, University of California, Berkeley,

Berkeley, CA, 1999. [31] F Buchner, et al, Rev. Sci. Instrum. 81 (2010) 113107.

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Chapter 3

Photoelectron Spectroscopy of Hydrated Electrons

The material contained in this chapter was previously published, and is reprinted from Chemical Physics Letters, Volume 493, Alexander T. Shreve, Terry A. Yen, Daniel M. Neumark, Photoelectron spectroscopy of hydrated electrons, Pages 216-219, Copyright 2010, with permission from Elsevier.

3.1 Abstract:

We report a systematic study of the photoelectron spectroscopy of hydrated electrons in liquid water jets using multiple precursors and photodetachment wavelengths. Hydrated electrons were generated in and detached from liquid microjets using two photons from a single nanosecond laser pulse at 266 or 213 nm. Solutions of 50 to 250 mM potassium hexacyanoferrate(II) or potassium iodide were used to provide precursor anions. All of our experimental conditions yield similar results, giving a mean vertical binding energy of 3.6±0.1 eV at a temperature of ~280 K, a slightly higher value than in recent reports.

3.2 Introduction

The hydrated electron, aqe− , an electron in aqueous solution, was discovered as a product of water radiolysis by ionizing radiation [1] and has since become a species of central interest in the physical sciences. It plays a major role in radiation chemistry and biology, because hydrated electrons can be formed by ionizing radiation in living cells, and their high reactivity leads to free radical formation with significant potential for genetic damage. From a more fundamental perspective, aqe− represents the simplest quantum mechanical solute [2], thereby motivating many experimental and theoretical studies that have focused on understanding its spectroscopy, reactivity, and relaxation dynamics subsequent to electronic excitation [3-

40

10]. A parallel experimental and theoretical effort has focused on gas phase water cluster anions, (H2O)n¯, in which an electron is bound to a known number of water molecules [11-16]. The cluster studies have provided valuable insights into the nature of aqe− , but have also raised the issue of how the properties of finite clusters can be extrapolated to bulk aqueous solutions [17,18]. For example, extrapolation of the vertical binding energies (VBE's) of water cluster anions to n→∞ yields an estimated value of 3.4±0.2 eV for the VBE of the bulk hydrated electron, based on work with clusters up to n=69 by Coe et al. [17]. Recent work by Siefermann et al. [19] on hydrated electrons in liquid water jets yielded the first actual measurement of this quantity, finding remarkable agreement (3.3 eV) with the cluster extrapolation. A similar value has been reported by Tang et al. [20].

In this paper, the properties of hydrated electrons in liquid water jets are explored using a different experimental arrangement from that of Siefermann et al. The work described here is motivated in part by some unusual aspects of their results. In their experiment, photoelectrons were created within the jet by either ionization of pure water or charge-transfer-to-solvent (CTTS) excitation of the hexacyanoferrate(II) anion (Fe(CN)6

4-) with a femtosecond laser pulse at 267 nm (4.64 eV). This was followed by photoemission using a femtosecond soft x-ray pulse at 32 nm (38.7 eV). The soft x-ray pulse results in photoelectrons with a kinetic energy around 35-37 eV, for which the electron attenuation length (EAL), the distance over which an electron signal is reduced by a factor of 1/e, is only ~2 nm [21,22]. As a result, these experiments were, in principle, much more sensitive to electrons at or very near the surface of the jet. Indeed, their experiments on pure water showed evidence for hydrated electrons with a relatively low VBE, 1.6 eV, and these were attributed to surface-bound electrons. This assignment appeared plausible since the VBE’s of water cluster anions with surface-bound electrons extrapolated to a similar value [23]. Internally-bound electrons, for which the VBE was found to be 3.3 eV, could only be seen with difficulty, even at high concentrations (0.5 M) of K4Fe(CN)6.

Here, hydrated electrons are produced by CTTS excitation and ejected using two photons from a single 35 ns laser pulse at either 266 nm (4.66 eV) or 213 nm (5.82 eV). The EAL increases dramatically at low eKE [24], so this experiment should be considerably more sensitive to electrons in the jet interior, enabling us to observe this signal at lower salt concentrations and testing the possible of effect of concentration on the measured VBE. Moreover, by varying both the photoemission energy and the anion from which CTTS excitation occurs, one obtains an important consistency check on the VBE. In fact, we find that under conditions of our experiment, the "surface-bound" electrons are not seen, and that the VBE of

41

the internally-bound electrons is 3.6±0.1 eV, close but not identical to the previously reported value.

3.3 Experiment

Experiments were conducted using dilute (50-250 mM) aqueous solutions of various salts introduced into a vacuum chamber using a liquid microjet similar to that pioneered by Faubel et al. [25,26]. A schematic drawing of our instrument is presented in Figure 3.1. The apparatus consists of a liquid jet source chamber (I), a time-of-flight (TOF) chamber (II), and a negative ion source used for calibration (not pictured). The microjet enters the chamber via a three-axis translation stage mounted on a feedthrough flange (a). The nozzle assembly is of the type developed by Saykally [27], consisting of a 9.5±0.5 mm length of 30 µm I.D. fused silica capillary (b) clamped into ~8 mm of PEEK tubing (c) by a Swagelok fitting (d). Constant flow through the nozzle is maintained by a syringe pump (Teledyne-Isco model 500D) with a 2 µm in-line filter (e) to prevent clogging. Following construction, the nozzle assembly (b-e) is coated in carbon (Acheson, Aerodag G), to reduce charge buildup on the fused silica and improve signal stability.

The experiments presented in this report used deionized and filtered liquid water (18.2 MΩ resistivity Milli-Q, Millipore), with a measured total organic content of 3-4 ppb. All chemicals were used as supplied by the vendor (potassium hexacyanoferrate(II) trihydrate, Sigma Aldrich, ≥99%; sodium chloride, Fisher, ACS; potassium iodide, Fisher, USP/FCC). Flow rates of 1 mL/min were used throughout, resulting in a jet velocity of 24 m/s. The jets typically exhibited laminar flow for 6 to 10 mm from the tip before entering the turbulent flow regime and breaking into droplets.

A pulsed laser beam intercepted the liquid jet 1 to 2 mm downstream from the tip. The jet evaporatively cools in vacuum, achieving a surface temperature between 281 and 278 K based on the temperature gradient model of Smith et al. [28]. We used a nanosecond Nd:YAG laser, (Spectra-Physics Quanta-Ray Pro 290-30) operating at 266 or 213 nm. The interaction region is denoted with an asterisk (*) in Figure 3.1. For the data at 266 nm, we typically used 10 - 35 µJ/pulse, while the 213 nm data was taken with 3 - 20 µJ/pulse. The laser polarization was parallel to the axis of the TOF spectrometer at both wavelengths.

The principle underlying this experimental configuration is to use two photons from a single ~35 ns laser pulse; the first creates a hydrated electron via CTTS excitation of the dissolved anions, and the second ejects the electron into vacuum. Hydrated electrons created by CTTS excitation equilibrate by 70 ps [29], which is considerably less than the laser pulse duration, so that the second photon will interact primarily with equilibrated

42

electrons. Furthermore, the lifetime of the hydrated electron is several hundred microseconds [30,31], much longer than our laser pulse duration.

Once in vacuum, the photoelectrons were sampled by a 500 µm diameter skimmer (f), located 0.75 to 1.5 mm from the jet, and entered the TOF chamber. The electrons then traveled through a 63 cm, field-free drift tube (g), to a chevron mounted, dual microchannel plate detector (70mm O.D., 9.7 msr acceptance angle, h in Figure 3.1). Electron flight times were collected and averaged on an oscilloscope (Tektronix, TDS3034B), passed to a computer and summed, typically for thirty thousand laser shots.

Approximately 10 cm downstream of the nozzle, the jet entered a trap (i) consisting of a 3.8×60 cm stainless steel cylinder immersed in 30 cm of liquid nitrogen. The liquid source region was further pumped by a 150 L/s turbomolecular pump (Leybold Turbovac 151), and a condensation unit made of a 15×20 cm stainless steel cylinder filled with liquid nitrogen (j). The chamber typically reached 1×10-4 Torr during operation, and could run for 2.5 h before the traps needed to be removed and cleaned. The TOF chamber was pumped by three turbomolecular pumps with a combined speed of 1000 L/s (Seiko Seiki STP 400, Leybold Turbovac 151, Leybold Turbovac 150 CSV), and typically achieved pressures of 4×10-6 Torr.

The apparatus was calibrated using gas phase I- and Br-, introduced through a gate valve (k) from our previously described ion source and mass spectrometer [32]. Briefly, appropriate precursor gases were introduced to vacuum through a pulsed piezoelectric valve. Gas pulses from a supersonic expansion passed through a pair of high voltage discharge plates pulsed to ~-900 V, and were intersected by a 1 keV electron beam for stabilization. Following collimation by a skimmer, the ions were injected into a linear reflectron mass spectrometer with a mass resolution (m/∆m) of 2000. The photodetachment laser then detached the anions just in front of the 500 µm skimmer (f) shown in Fig. 3.1. A small fraction of the photoelectrons passed through the skimmer and was collected with the TOF system used in the liquid jet measurements. The known energies for photodetachment to the 2P3/2 and 2P1/2 states of I and Br [33] were used for calibration; these energies (3-4 eV) were in the range of the binding energies found in the liquid jet studies and hence were very suitable for calibration purposes.

3.4 Results

Photoelectron spectra were first recorded at several concentrations of K4Fe(CN)6

at 266 nm. The I- CTTS band is not accessible at this wavelength [34], so we were unable to investigate precursor dependent effects here. Figure 3.2 shows raw time-of-flight photoelectron spectra at 100 mM Fe(CN)6

4- and for pure water. The signal below 500 ns is from light scattered off the jet and into the flight tube. The broad feature peaking around 1000 ns in the spectrum from the salt solution is from ejected

43

photoelectrons and is not seen in the pure water spectra. The TOF spectrum is converted into an electron kinetic energy (eKE) spectrum using the appropriate Jacobian transformation (t-3). Pure water jets can undergo significant charge buildup, a process that is largely eliminated by even a low salt concentration in the jet [24]. In light of this, background data were taking using both pure water and sodium chloride solution since Cl- does not have an accessible CTTS band at these energies [35]. Pure water and Cl- jets give very similar results, however the scattered light noise for chloride jets better matches the noise in Fe(CN)6

4- and I- data. While this does not affect the 266 nm data, it becomes relevant under the lower signal to noise conditions of the 213 nm data.

Typical background subtracted photoelectron spectra are presented in Figure 3.3, plotted versus electron binding energy (eBE) given by eBE h eKEν= − , where hν is the photon energy. As shown, we find the most probable eBE, or vertical binding energy (VBE), to be 3.6±0.1 eV at 50 mM, 3.5±0.1 eV at 100 mM, and 3.6±0.1 eV at 250 mM. We observe day-to-day variations of up to 0.1 eV with typical peak widths of 1.0±0.2 eV full width at half maximum (FWHM). The three VBE’s from Fig. 3.3 are within error bars of one another but are slightly higher than the value of 3.3 eV reported by Siefermann et al.[19] and Tang et al.[20]. We see no evidence for the previously reported peak with a VBE of 1.6 eV [19]. The 50 and 100 mM results are confirmed by repeated measurement over many days.

As a further check on these results, photoelectron spectra were recorded for several salt solutions at 213 nm, where the electron kinetic energy is higher for the same binding energy. Both Fe(CN)6

4- and I- (from KI) were used as precursor anions to check against solute-specific effects. Typical background subtracted spectra are shown in Figure 3.4. We find VBE’s of 3.6±0.1 eV using 50 mM Fe(CN)6

4-, 3.6±0.1 eV from 100 mM Fe(CN)64-, and

3.7±0.2 eV from 100 mM I-. Again, we see day-to-day variations of 0.1 eV at this wavelength and each measurement was repeated in on multiple days with the majority of our effort focused on 100 mM Fe(CN)6

4-.

3.5 Discussion

Averaged, our data give a VBE of 3.6 with a standard of deviation of 0.1 eV for the bulk hydrated electron, measured at approximately 280 K. This value appears to be independent of the precursor ion species or concentration, and it does not change over the range of laser intersection points or jet to skimmer distances used here. Moreover, the VBE does not vary with the mean electron kinetic energy at the two photodetachment wavelengths (1.1 eV at 266 nm, 2.2 eV at 213 nm). The EAL of an electron in water with 1-2 eV of kinetic energy is not precisely known, but is expected to be greater than 10 nm based on recent theoretical and experimental work [22,36]. Hence, our experiment should probe bulk hydrated electrons. In

44

contrast to our work, Siefermann et al. probed near the EAL minimum and were much more sensitive to electrons near the surface [19]. The absence of the feature at a VBE of 1.6 eV in our experiment is thus consistent with their assignment of this peak to a surface-bound electron.

The VBE obtained in our experiment is somewhat higher than the analogous feature observed at 3.3 eV by Siefermann et al, a discrepancy that could be attributed to the low signal-to-noise in their experiment associated with detection of internal electrons. However, our data also show a more tightly bound electron than recently reported by Tang et al. [20] in a femtosecond time-resolved pump probe experiment where Iˉ was detached at 240 nm and the electron ejected at 266 nm. We note that the peak in their photoelectron kinetic energy distribution shifted to lower energy, or higher VBE, as the delay between their pump and probe pulses was increased to 136 ps. Our long laser pulses imply a considerably longer delay between CTTS excitation and photoemission than in the fs pump-probe studies. Nonetheless, the 136 ps delay reported by Tang is already longer than the equilibration time for hydrated electrons (70 ps) formed via CTTS excitation [29], so it is not obvious that the longer delay time in our experiment can account for the differing VBE’s. We also note that the reported jet surface temperatures in the previous measurements are very similar to ours (278 K in Ref [19] and 280-290 K in Ref. [20]), so temperature variations among the experiments are unlikely to be an issue.

Since we are reporting a larger VBE than previous work, one obvious question to consider is whether our result reflects inelastic scattering after the electrons leave the jet. As shown by Faubel et al. [25], the effective vapor layer thickness provides a good estimate of the overall collision frequency and can be found by

Pd = P0r0 ln(r / r0 ), where

r0 is the radius of the jet,

r distance from the center of the jet to the skimmer entrance, and

P0 is the local equilibrium vapor pressure at the jet surface. Under our typical experimental conditions, with an estimate of 6.5-8.0 Torr for the equilibrium vapor pressure [37], we find our effective vapor thickness to be between 0.38 and 0.55 Torr mm. We find similar effective thicknesses that bracket our value when we repeat the calculation for the conditions in previous reports (0.25 Torr mm for Siefermann et al. and at least 0.63 Torr mm for Tang et al.). While these numbers are all slightly higher than the desired value of

Pd ≤ 0.1 Torr mm for ultraviolet photoelectron spectroscopy [38], we cannot dismiss our VBE as an artifact from inelastic scattering in the local vapor sheath.

Another possible issue to consider is the streaming potential of the jet. As has been previously demonstrated [26,39,40], liquid microjets can generate significant streaming currents with radial surface potentials up to tens of volts. The resistance, and therefore the surface potential, of the jets decreases linearly with the concentration of salt [24], so we would expect a concentration dependent VBE if this were an issue with our work. As shown

45

in Figures 3.3 and 3.4, we see no such concentration dependence and conclude that surface potentials have not skewed our results.

Previous work on water cluster anions offers evidence in support of the larger VBE found in our liquid jet study. Specifically, if the VBE’s for the largest “isomer I” cluster anions measured in our laboratory (n=50-200) are plotted vs. n-1/3 and extrapolated to n→∞, one finds a bulk VBE of ~3.6 eV [18,41], in excellent agreement with the value reported here. A similar result was seen in recent work by Ma et al [42] on very cold cluster anions (10 K); in addition, they observed a new “isomer I” cluster for which the extrapolated VBE was even higher, ~4 eV.

3.6 Conclusions

We have measured the vertical binding energy of the solvated electron in bulk water under a wide range of conditions using liquid microjets. In these experiments, two photons from a single ns laser pulse at either 266 or 213 nm were used to detach an electron from an anion is aqueous solution and then to eject the electron from the jet into vacuum. The low photon energies used here insure that we probe true bulk hydrated electrons. We find the vertical binding energy for these electrons to be 3.6±0.1 eV at ~280 K. Our results are insensitive to the laser wavelength, the choice of parent anion (I- or Fe(CN)6

4-), and the anion concentration.

3.7 Acknowledgements

Support for this work was provided by the U.S. Department of Energy (Contract # DE-AC02-05CH11231) and the American Chemical Society Petroleum Research Fund (Grant # 47852-AC6). The authors would like to thank Professor Richard Saykally, and the graduate students in his group, particularly Walter Drisdell, Dale Otten, and Craig Schwartz, for many useful discussions regarding microjets.

46

3.8 Figures

Figure 3.1. Schematic drawing of the liquid microjet photoelectron spectrometer. See text for details.

47

Figure 3.2. Typical time-of-flight spectra for water and 100 mM potassium hexacyanoferrate(II) solution. The initial spike is from laser light scattered from the jet onto the detector. The broad feature around 1000 ns in the salt solution data, but absent in the pure water data, is from electrons ejected from the jet.

48

Figure 3.3. Photoelectron spectra of aqueous solutions of K4Fe(CN)6 at concentrations of 250, 100, and 50 mM taken at 266 nm (4.66 eV). The spectra have been background subtracted using data from pure water jets and smoothed with a 10 meV gaussian.

49

Figure 3.4. Photoelectron spectra taken at 213 nm (5.82 eV) for aqueous solutions of K4Fe(CN)6 at concentrations of 50 and 100 mM and KI at 100 mM. The spectra have been background subtracted using data from pure water or sodium chloride solution jets, and smoothed with a 10 meV gaussian.

50

3.9 References

[1] E J Hart, J W Boag, J. Am. Chem. Soc. 84 (1962) 4090. [2] P J Rossky, J Schnitker, J. Phys. Chem. 92 (1988) 4277. [3] J M Wiesenfeld, E P Ippen, Chem. Phys. Lett. 73 (1980) 47. [4] A Migus, et al, Phys. Rev. Lett. 58 (1987) 1559. [5] X Shi, et al, J. Phys. Chem. 100 (1996) 11903. [6] A Hertwig, et al, Ber. Bunsen-Ges. Phys. Chem. 102 (1998) 805. [7] K Yokoyama, et al, J. Phys. Chem. A 102 (1998) 6957. [8] M Assel, et al, Chem. Phys. Lett. 317 (2000) 13. [9] M S Pshenichnikov, et al, Chem. Phys. Lett. 389 (2004) 171. [10] D Borgis, et al, J. Chem. Phys. 127 (2007) 174508. [11] J V Coe, et al, J. Chem. Phys. 92 (1990) 3980. [12] P Ayotte, M A Johnson, J. Chem. Phys. 106 (1997) 811. [13] T Tsurusawa, S Iwata, Chem. Phys. Lett. 315 (1999) 433. [14] D H Paik, et al, Science 306 (2004) 672. [15] A E Bragg, et al, J. Am. Chem. Soc. 127 (2005) 15283. [16] A Madarasz, et al, J. Chem. Phys. 130 (2009) 124319. [17] J V Coe, et al, Int. Rev. Phys. Chem. 27 (2008) 27. [18] D M Neumark, Mol. Phys. 106 (2008) 2183. [19] K R Siefermann, et al, Nat. Chem. 2 (2010) 274. [20] Y Tang, et al, Phys. Chem. Chem. Phys. 12 (2010) 3653. [21] A Jablonski, C J Powell, J. Electron Spectrosc. and Rel. Phenom. 100

(1999) 137. [22] N Ottosson, et al, J. Electron Spectrosc. and Rel. Phenom. 177 (2010)

60. [23] J R R Verlet, et al, Science 307 (2005) 93. [24] B Winter, M Faubel, Chem. Rev. 106 (2006) 1176. [25] M Faubel, et al, Z. Phys. D 10 (1988) 269. [26] M Faubel, B Steiner, Ber. Bunsen-Ges. Phys. Chem. 96 (1992) 1167. [27] K R Wilson, et al, Rev. Sci. Instrum. 75 (2004) 725. [28] J D Smith, et al, J. Am. Chem. Soc. 128 (2006) 12892. [29] J A Kloepfer, et al, J. Chem. Phys. 113 (2000) 6288. [30] E J Hart, M Anbar, The Hydrated Electron, Wiley-Interscience, New

York, NY, 1970. [31] H F Hameka, et al, J. Phys. Chem. 91 (1987) 3150. [32] R B Metz, et al, J. Phys. Chem. 94 (1990) 1377. [33] H Hotop, W C Lineberger, J. Phys. Chem. Ref. Data 14 (1985) 731. [34] M F Fox, E Hayon, J. Chem. Soc. Faraday Trans. I 73 (1977) 1003. [35] M F Fox, et al, J. Chem. Soc. Faraday Trans. I 74 (1978) 1776. [36] D Emfietzoglou, H Nikjoo, Radiat. Res. 163 (2005) 98. [37] W Wagner, A Pruss, J. Phys. Chem. Ref. Data 31 (2002) 387. [38] H Siegbahn, J. Phys. Chem. 89 (1985) 897. [39] M Faubel, et al, J. Chem. Phys. 106 (1997) 9013.

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[40] W L Holstein, et al, J. Phys. Chem. B 103 (1999) 3035. [41] A Kammrath, et al, J. Chem. Phys. 125 (2006) 076101. [42] L Ma, et al, J. Chem. Phys. 131 (2009) 144303.

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53

Chapter 4

Photoelectron Spectroscopy of Solvated Electrons in Alcohol

and Acetonitrile Microjets

The material contained in this chapter has been submitted to Chemical

Science for publication.

4.1 Abstract

Photoelectron spectra of solvated electrons in methanol, ethanol, and acetonitrile microjets are reported. Solvated electrons are generated in and detached from microjets using two photons from single nanosecond laser pulses at wavelengths ranging 266 to 213 nm. We find vertical binding energies of 3.38 ± 0.11 eV in methanol and 3.38 ± 0.10 eV in ethanol. Two features are observed in acetonitrile at 2.61 ± 0.11 eV and 3.67 ± 0.15 eV, attributed to the solvated and dimer-bound binding geometries respectively. These results are compared to previous work on solvated cluster anions and alkali-doped solvent clusters.

4.2 Introduction

Solvated electrons, 𝑒𝑠𝑜𝑙𝑣− , are among the most intriguing systems in the physical sciences, playing an important role in DNA damage,[3-5] radiation chemistry,[6,7] atmospheric aerosol chemistry,[9] and in theoretical studies as the simplest quantum mechanical solute.[10,11] Consequently, many experimental and theoretical methods have been used to study the chemistry, spectroscopy, and dynamics of solvated electrons.[12-15] However, only recently has it become possible to directly measure the

54

vertical binding energies (VBEs) of solvated electrons in bulk solution, via photoelectron spectroscopy of the liquid microjet sources developed by Faubel and co-workers.[16-18] As illustrated in Table I, several such experiments have been performed on 𝑒𝑠𝑜𝑙𝑣− in water,[2,21-23] as well as methanol and ethanol.[24,25] It is of considerable interest to compare these results to VBE’s measured for gas phase solvated electron clusters Sn‾ in order to test how or if the cluster VBEs extrapolate to the bulk values as n→∞.[26,27] While the VBEs of solvated electrons in water jets are in general agreement with extrapolated values from VBEs of water cluster anions,[28-31] recent work by Suzuki[25] finds that the VBE reported for electrons in methanol jets is 0.65 eV higher than the extrapolated value obtained from photoelectron (PE) spectra (MeOH)n¯ cluster anions[8] (see Table I). Experiments on alkali-doped solvent clusters[32-34] provide an additional point of comparison. With these considerations in mind, we have re-investigated the PE spectra of electrons in liquid jets of methanol (MeOH), ethanol (EtOH), and report first results for electrons in acetonitrile (MeCN).

Methanol and ethanol are very natural solvents in which to study electron solvation. As is the case with water, both alcohols have significant hydrogen-bonding networks that are disrupted to accommodate the excess electron.[35] Time-resolved studies of electron solvation in these solvents have been carried out in several laboratories.[36-39] Electron spin resonance (ESR) and resonance Raman (RR) spectroscopy have shown that the ground state cavity for 𝑒𝑠𝑜𝑙𝑣− in these solvents is similar to that in water, but with only four molecules in the first solvation shell rather than the six in the case of water.[40-42] This bulk solvent work is complemented by PE spectroscopy of (MeOH)n¯ clusters as large as n=460.[8] These spectra show evidence for two distinct isomers of the cluster anions, in which isomer I, the higher binding energy species, appears to be internally solvated.[8,43] In related work, photoionization measurements on Na(MeOH)n and Na(EtOH)n clusters yield extrapolated ionization potentials (IPs) which are close to, but below the solvated electron VBEs from liquid jet experiments as shown in Table I.[25,34,44]

In contrast to water or methanol, liquid acetonitrile accommodates excess electrons in two very distinct binding configurations assigned to a solvated electron within a cavity and a dimer-bound anion species stabilized by its interaction with surrounding solvent molecules.[45-47] In the dimer species, two molecules orient anti-parallel, with CCN bond angles of ~130 º and the excess electron localized by the interaction between antibonding CN orbitals.[48,49] Similarly, PE spectra of (MeCN)n¯ clusters up to n=130 show that two electron binding motifs are present: isomer I clusters with lower VBEs were attributed to the excess electron residing within a solvent cavity, while the higher VBE clusters (isomer II), which dominate the PE spectrum starting around n=13, were assigned to the dimer-bound

55

species.[19,49] Photoionization efficiency measurements on Cs(MeCN)n extrapolate to a bulk ionization potential of 2.4 eV.[33]

In light of the discrepancies in VBEs for solvated electrons in MeOH cluster anions and liquid jets, we have measured PE spectra in MeOH and EtOH jets with a somewhat different experimental configuration than that used by Suzuki. We also report the first results on excess electrons in MeCN liquid jets in order to see how the two proposed electron binding motifs in liquid phase and anion cluster experiments manifest themselves in photoelectron spectroscopy experiments.

4.3 Experimental

We generate solvated electrons in liquid jets through charge-transfer-to-solvent (CTTS) excitation of iodide in solution with one photon,[46,50,51] and then detach electrons to vacuum with a second photon. Both photons come from a single pulse from a nanosecond Nd:YAG laser, in contrast to the femtosecond pump-probe experiments carried out in other laboratories.[21,23,52] Schematically, the overall process is:

( )1 2( ) ( ) ( ) ( ) ( ) ( )

h hCTTSsolv solv solv solv solv gI I I e I e eKEν ν− −∗ − −→ → + → + .

Because this experiment is carried out with a single laser pulse, we do not control the delay between ℎ𝜈1 and ℎ𝜈2, but the equilibration time for electrons in these solutions is much less than the laser pulse duration.[47,53] As such, the majority of electrons detached are fully solvated prior to photoejection. The experiments were conducted using methanol (Fisher, optima grade), ethanol (Fisher, absolute grade), and acetonitrile (Fisher, HPLC grade). To minimize exposure to water in the MeCN experiments, fresh bottles of dry-packed acetonitrile were used each day. Low concentrations of salt were included to provide precursor anions for the generation of solvated electrons and to minimize streaming potentials.[54] Solutions variously included potassium iodide (Fisher, ≥99.0% purity), sodium iodide (Mallinckrodt, AR), tetrabutylammonium iodide (TBAI, Aldrich, ≥99.0% purity), or tetrabutylammonium chloride (TBACl, Aldrich, ≥97.0% purity).

To test for any effects of water, an ultra-dry run of acetonitrile was conducted. For this experiment, acetonitrile was dried over activated 3 Å molecular sieves for 96 hours, resulting in an expected water content below 10 ppm,[55] while the TBAI was dried by heating under vacuum overnight. All solution vessels were dried by baking at 150 °C overnight, with the solution subsequently prepared under dry nitrogen in a glove box. The syringe pump and microjet assembly were dried by purging with 4.8 pure Argon for three hours, and ultra-dry MeCN for an hour.

56

Our experimental apparatus was described in detail previously.[2] Briefly, the apparatus comprises a liquid source chamber and a time-of-flight (TOF) chamber. Bulk solutions were introduced to vacuum by applying high pressure (40-150 atm) to solution behind a 20 µm ID fused silica capillary. The resulting flow was a microjet that remained laminar for at least 1 mm, and usually for 4 mm. Flow rates of 0.250 mL/min were normally used, resulting in jet velocities of 13 m/s. The jets were collected in a liquid nitrogen cooled trap, with the liquid jet region typically achieving pressures of 2*10-4 Torr with methanol, 1*10-4 with ethanol, and 2*10-4 Torr with MeCN.

The jet was crossed with the output of a 30 Hz nanosecond Nd:YAG laser, operating at 266, 247, 231, or 213 nm, 1 mm downstream from the nozzle. Laser harmonics were produced in BBO crystals, while 247 and 231 nm pulses were produced as anti-Stokes lines of 266 nm light focused into a 65 cm long Raman cell filled with 250 psi of deuterium gas. Laser pulses were typically 8 ns long, with 0.3-1.5 µJ/pulse.

Once in vacuum, electrons were sampled by a 500 µm skimmer located 1 mm from the jet. The electrons then traveled through a 60 cm field free drift tube to a Z-stack multichannel plate detector. The resulting arrival time distributions were averaged on a digital oscilloscope, transferred to a computer, and summed, typically for 105 laser shots. Raw time-of-flight spectra were then converted to eKE spectra using the appropriate Jacobian transformation (t-3). The detector region was pumped by three turbomolecular pumps, with a combined pumping speed of 1650 L/s. The detector chamber typically achieved pressures of 4*10-6 Torr with methanol, 2*10-6 with ethanol, and 3*10-6 Torr with MeCN.

In a significant addition from our previous report,[2] the spectrometer was calibrated by three-photon ionization of Xe to the Xe+ 2P3/2 and 2P1/2 states by 150 fs laser pulses at 250 or 266 nm (4-9 µJ/pulse, 1 kHz). A Clark-MXR CPA-1000 laser system generated femtosecond pulses at 800 nm, which were either frequency-tripled to generate 266 nm light or routed into a commercial OPA (TOPAS, Light Conversion Ltd.) with light at 250 nm generated from the second harmonic of the sum-frequency signal. Trigger timing differences between the two laser systems were corrected by matching the respective time origins as measured by scattered light in the flight tube.

This new scheme allowed us to calibrate while the liquid jet was running, and directly measure the streaming potential of the jets. Following the methodology of Shen et al,[24] the liquid jet was moved away from the laser interaction point while the shift in the kinetic energy of the Xe+(2P3/2) photoelectron peak was observed. The kinetic energy of these electrons is then given by

57

( ) ( )field free strLeKE x eKE L xφ−= − + , (4.1)

where field freeeKE − is the kinetic energy of these electrons in the absence of a

field from the liquid jet, strφ is the streaming potential of the jet, L is the (fixed) distance from the skimmer to the laser, and x is the distance between the jet and laser. The field-free kinetic energy was measured each day after stopping the jet to account for day-to-day changes in the laser wavelength. The conversion of our solvated electron kinetic energy spectra to electron binding energy (eBE) is then given by

streBE h eKEν φ= − − , (4.2)

where hν is the photon energy. Temperatures for each solvent were estimated using the evaporative

cooling numerical simulation described by Faubel et al.[16] and implemented by Smith et al.[56] Jets were treated as thirty concentric annular columns of equal radial width, with distinct temperatures and heat exchange between them. The temperature dependence of the vapor pressure is explicitly accounted for, while other physical properties are treated as constant at their room temperature values. Since each annulus is significantly thicker than our probe depth, our temperatures are taken to be those of the outer annulus in each calculation. We estimate our methanol jets have cooled to 250 K, the ethanol jets to 260 K, and the acetonitrile jets to 250 K.

4.4 Results

Methanol data were recorded using 100 mM KI solutions at 213 nm, near the I(2P3/2) peak of the CTTS band.[51] A typical photoelectron spectrum, plotted versus eBE and corrected for streaming potential, is presented in Figure 4.1A. VBEs, taken as the center of a Gaussian fit to the spectra, are found to be 3.38 ± 0.11 eV, while the peak widths are 1.26 ± 0.11 eV full width at half maximum (FWHM). The streaming potentials for these jets were typically ~400 mV; uncorrected VBEs were ~3.8 eV. Ethanol data were collected using 200 mM NaI solutions at 231 nm, near the maximum of the iodide CTTS band.[50] A representative spectrum is shown in Figure 4.1B. Typical streaming potentials for ethanol jets were ~120 mV, with uncorrected VBEs of ~3.5 eV. We find a corrected VBE of 3.38 ± 0.10 eV with a FWHM of 1.03 ± 0.10 eV.

Acetonitrile data were taken at 266, 247, 231, and 213 nm with either 50 mM KI or 200 mM TBAI. Streaming potentials for acetonitrile jets were usually 0.10 eV. Typical corrected spectra from each wavelength are presented in Figure 4.1C. Two features are observed: a peak with a VBE of

58

2.61 ± 0.11 eV (~2.7 eV uncorrected), FWHM 0.70 ± 0.08 eV, that is present at all wavelengths and a peak with a higher VBE of 3.67 ± 0.15 eV (~3.8 eV uncorrected), FWHM 1.29 ± 0.16 eV, that is present at every wavelength except 266 nm. The relative signal levels and peak ratios at each wavelength are presented in Table II, normalized for laser power, number of shots, and salt concentration. All of these results were confirmed by repeated measurement over several days.

Acetonitrile is known to be hygroscopic, and one possible origin of the high VBE peak, which lies close to the VBE of hydrated electrons, is water contamination in the sample. Furthermore, it has been shown that water contamination of an acetonitrile sample can significantly alter hydrated electron dynamics following CTTS excitation, likely due to the influence of microscopic pools of water within bulk acetonitrile.[47,57-59] To test for the effects of water, data were collected at 213 nm using extra dry solution prepared as described above; these data completely agreed with our other findings.

4.5 Discussion

The VBEs for 𝑒𝑠𝑜𝑙𝑣− in both methanol and ethanol presented here are in good agreement with the findings of Horio et al.[25] Our observed peak widths and streaming potentials in methanol are larger than those reported by Horio, but agree with their findings for ethanol. The overall agreement is noteworthy because of the differences between our experiments; we generate and detach solvated electrons with two photons from the same nanosecond pulse, while Horio used two separate femtosecond pulses with a well-defined pump-probe delay. The agreement between our approaches further validates our respective approaches and underscores the importance of using a calibration obtained while the liquid jet is running. Most importantly, it shows that the VBE of solvated electrons in methanol jets is significantly higher that the extrapolated VBE from MeOH cluster anions. The general agreement between the VBE measurements in water cluster anions and water liquid jets supports the idea that it is valid to extrapolate cluster VBEs to liquid jet measurements, but the MeOH results call that conclusion into question.

In this context, the acetonitrile results are of interest as they provide an additional data point for comparing cluster and liquid jet experiments. The first point to consider is that at all excitation wavelengths except 266 nm, the liquid jet PE spectra show two peaks with VBE’s of 2.61 and 3.67 eV. As described in the Results, we have made considerable effort to show that both originate from MeCN, rather than water contaminant. Since the data taken with the ultra-dry solution match our other data and the observed wavelength dependence of both peaks match the acetonitrile CTTS curve rather than that of water,[60] we believe that effort was successful. Liquid

59

MeCN can accommodate excess electrons in two different binding motifs, cavity-solvated and dimer-bound, with the dimer-bound motif being more stable.[45-47] It is therefore reasonable to attribute the two peaks in the liquid jet PE spectra to these two solvation motifs, with the higher VBE feature corresponding to the dimer-bound motif. Such an assignment would also be consistent with the assignment of the two features in the MeCN cluster anion PE spectra, depending on how well the cluster and liquid jet VBEs match up.

Our findings in the bulk are compared to previous work on anionic solvent clusters Sn¯ in Figure 4.2. This figure shows VBEs for anion clusters of water,[1] MeOH,[8] and MeCN[19,20] are plotted vs n-1/3 and also shows VBEs obtained from liquid jet studies of the three solvents.[2] The results for water and MeOH have been discussed above. In the case of MeCN, the VBEs for isomer II cluster anions lie on a straight line in Fig. 4.2 and extrapolate to 3.66 eV, very close to the VBE of 3.67 eV for the more tightly bound liquid jet feature. This correspondence supports our proposed assignment of the 3.67 eV liquid jet feature to dimer-bound solvated electrons in MeCN. The size-dependent VBEs for isomer I clusters also lie on a straight line and extrapolate to a bulk VBE of 1.48 eV, considerably less than the low VBE peak in the liquid jet spectrum.

Comparison of the anion cluster and liquid jet VBEs with the ionization potentials of alkali-doped clusters of H2O, MeOH, EtOH, and MeCN (i.e. Na(H2O)n, etc.) are also of interest. Theoretical studies of these species indicate that the electron nominally associated with the alkali atom is actually quite diffuse and exhibits some similarities to bulk solvated electrons.[34,61-63] Experimental IP trends for these clusters are very different from the VBEs in bare cluster anions. For water and the two alcohols, the IPs drop upon addition of the first four waters or the first six alcohols, and then remain flat as more solvent molecules are added out to a maximum cluster size of 35-40.[32,34,44] The extrapolated IPs for sodium-doped water, methanol, and ethanol clusters, presented in Table I, lie close to but slightly below the corresponding liquid jet VBEs. The pattern of IPs is more complicated in Cs(MeCN)n clusters.[33] and does not flatten out until n=12, where it remains constant at 2.4 eV out to n=21, the largest cluster studied. This value lies close to but below the lower VBE feature, 2.61 eV, seen in MeCN liquid jets. Hence, the extrapolated IPs for all for cluster types exhibit the same trend with respect to the liquid jet VBEs assigned to cavity-solvated electrons. As pointed out by Liu[63] and Dauster et al,[34] the alkali-doped cluster experiments yield adiabatic rather than vertical IPs, consistent with the lower values relative to the liquid jet measurements. Aside from this relatively small discrepancy, the correspondence between the two sets of values is remarkable.

Based on the liquid jet VBEs, the extrapolated anion cluster VBEs, and the IPs of alkali-doped solvent clusters, each liquid jet VBE can be correlated

60

with at least one cluster measurement. However, the extrapolated VBEs for (MeOH)n‾ and isomer I (MeCN)n‾ clusters do not match any other measurements. In both cases, the maximum cluster size was quite large (n=450 for MeOH and 130 for MeCN), so it is unlikely that this discrepancy would be resolved by going to bigger clusters. Forck et al[44] have suggested that this situation arises for MeOH because the methanol cluster anions are solid rather than liquid. Their argument is based on a comparison of the slope of the VBE vs. n-1/3 plot with the predictions of dielectric continuum (DC) theory.[64] A similar situation may hold for isomer I acetonitrile cluster anions, too.

In DC theory, the solvated electron is treated as a spherical charge in a void, surrounded by a dielectric continuum. As such, the model is inappropriate to apply to the dimer-bound species, but presumably cluster isomers I and II come from the same cluster phase. Using DC theory, the size-dependent vertical binding energies VBE(n) for these clusters are given by

( ) ( )2

1/3

0 0

1 218 sr

eVBE n VBE nπε ε ε

−

∞

= ∞ − + −

, (4.3)

( )2

0 0

1 218 s

eVBEaπε ε ε∞

∞ = + −

. (4.4)

Here VBE(∞) is the bulk VBE, r0 is the average molecular radius, a0 is the bulk cavity radius occupied by 𝑒𝑠𝑜𝑙𝑣− , ε0 is the permittivity of free space, while ε∞ and εs are respectively the solvent optical and static dielectric constants. The molecular radius can be estimated from the bulk molar volume, while the dielectric constants are taken from literature values.[65-73] Where available, the cavity radii are estimated by moment analysis of the electron absorption spectra from 0.1 eV to 6.0 eV[74] at appropriate temperatures.[44,68,75,76]

Table III presents a quantitative comparison of DC theory and experimental findings for water and the three solvents considered here. Based on the parameters for water, the slope of the cluster VBE progression predicted by DC theory for solids and liquids can be used to assign a cluster phase. The experimental slopes for isomer I of both (MeOH)n‾ and (MeCN)n‾ clusters are in better agreement with the DC theory prediction based on parameters for the solids than the liquids.

It would be of considerable interest to investigate photoelectron spectra of MeOH and MeCN cluster anions as a function of temperature to see if higher VBE clusters are formed at higher temperatures. Several laboratories have incorporated ion trapping and cooling into anion photodetachment experiments,[30,77,78] enabling one to vary the cluster temperature systematically and test for its effect on the photoelectron spectrum.

61

However, if the cluster temperature is raised too high, extensive solvent evaporation can occur, along with ejection of the excess electron via thermionic emission, so it remains to be seen if a shift in VBE can be seen before these other effects become dominant. One would also like to understand if there is more systematic agreement between liquid jet VBEs and extrapolated IPs of alkali-doped solvent clusters than with VBEs from anion clusters. We expect these issues to be addressed in future experimental and theoretical studies on liquid jets and clusters.

4.6 Conclusions

We have measured the photoelectron spectra of solvated electrons in methanol, ethanol, and acetonitrile. We find a vertical binding energies of 3.38 ± 0.11 eV for 𝑒𝑠𝑜𝑙𝑣− in ~250 K MeOH and 3.38 ± 0.10 eV in ~260 K EtOH. Two species of excess electrons are observed in MeCN at ~250 K, with VBEs of 2.61 ± 0.11 eV and 3.67 ± 0.15 eV. These VBEs are attributed to cavity-solvated and dimer-bound motifs, respectively. This is the first reported direct measurement of electron binding energies in acetonitrile, and our alcohol VBEs are in good agreement with the recent report of Horio et al.[25]

These findings are particularly interesting in light of studies on small solvent clusters. As was observed for the bulk hydrated electron,[2,21-23] the bulk, dimer-bound excess electron in acetonitrile VBE is accurately predicted by an extrapolation of (MeCN)n‾ isomer II binding energies. Unfortunately, this predictive ability is not universally true. Extrapolations of isomer I VBEs in both (MeCN)n‾ and (MeOH)n‾ clusters predict significantly less tightly bound electrons than are observed in the bulk. We attribute this to the phase of the clusters, which based on DC theory, appears to be solid rather than liquid. Intriguingly, the adiabatic IPs of alkali-doped neutral clusters extrapolate to values slightly below the bulk VBEs assigned to cavity-bound electrons in all of four solvents. Both of these cluster trends merit further investigation.

4.7 Acknowledgements

Support for this work was provided by the National Science Foundation through Grant CHE-0649647. Thanks to Michael Lipschutz for assistance in preparation of the extra dry acetonitrile solution.

62

4.8 Figures and tables

Figure 4.1: Representative spectra of electrons solvated in A) methanol at 213 nm, B) ethanol at 231 nm, and C) acetonitrile at 266, 247, 231, and 213 nm. These spectra smoothed by convolution with a 15 meV Gaussian.

63

Figure 4.2: Vertical binding energy progressions for proposed internally solvated isomers of anionic water (Refs.[1,2]), methanol (Ref. [8]), and acetonitrile clusters (Refs.[19,20]).

64

Table I: Relevant literature values of bulk excess electron binding energies.

Solvent

Anion cluster extrapolation

(eV)a

Alkali-doped cluster

extrapolation (eV)b

Directly measured in liquid jets

(eV)c

Water 3.59 3.17 3.3-3.6 Methanol 2.54 3.19 3.36-3.38 Ethanol - 3.07 3.28-3.38

Acetonitrile (cavity-

solvated) 1.48

2.4 2.61

Acetonitrile (dimer-bound)

3.66 3.67

a Bulk binding energy extrapolations of candidate internally solvated isomers observed in anionic solvent clusters, Sn‾.[1,8,19,20]

b Bulk adiabatic ionization potentials based on the extrapolation of alkali-doped neutral solvent clusters.[32-34,44]

c Bulk vertical binding energies, measured directly with the liquid microjet technique, including the results presented in this work.[2,21,23,25]

Table II: Wavelength dependent signal level and peak ratios

Wavelength (nm) Relative intensitya Peak ratio

(low/high BE)b

266 1 -

247 7 0.6 ± 0.2

231 2 0.4 ± 0.1

213 6 0.6 ± 0.2

a Total integrated signal corrected for laser power, salt concentration, and shots collected, normalized to the signal at 266 nm.

b Ratio of integrated signals of the low and high binding energy peaks, with relative contributions determined by Gaussian two-peak fits.

65

Table III: Parameters used in dielectric continuum calculations for each solvent.

Solvent ε∞a εs

b a0(Å)c r0(Å)d

DC slope (eV)

Exp slope (eV)e

DC VBE(∞)

(eV)

Cluster VBE(∞)

(eV)e

Exp liquid

jet VBE (eV)f

Water (l) 1.78 84.2 2.45 1.93 -5.74 -6.65

4.52 3.59 3.6 Water (s) 2.01 91.5 2.35 1.98 -5.37 4.52

Methanol (l) 1.81 47.4 2.15 2.48 -4.38

-2.25

5.06

2.54 3.38 Methanol (s) 1.74 3.0 2.5 2.30 -2.84 2.61

Ethanol (l) 1.86 30 2.18 2.81 -3.77 - 4.86 - 3.38

Acetonitrile (l) 1.87 37.5 3.24 2.71 -3.96 -2.14

3.31 1.48 2.61 Acetonitrile

(s) 1.72 3.8 3.62 2.52 -3.01 2.10

a Optical dielectric constants, taken as the square of the extrapolated index of refraction from Ref. [71] (liquid H2O, MeOH, and MeCN), Ref. [69] (solid H2O and MeOH), Ref. [72] (liquid EtOH), or Ref.[73] (solid MeCN).

b Static dielectric constants, with liquid water from Ref. [67] solid water from Ref. [65], liquid ROH from Ref. [68], solid MeOH from [66], and both phases of acetonitrile from Ref. [70].

c Solvated electron cavity radius, as calculated by moment analysis of the absorption spectra from 0.1 eV to 6.0 eV[74] at appropriate phases and temperatures where available. Water from Ref. [76], liquid MeOH from Ref. [68], solid MeOH from Ref. [44], liquid EtOH from[68], and liquid MeCN from [75]. Solid MeCN is taken by approximation such that the difference between the solvated cavity radii between phases is twice the difference in molecular radii between phases, as is the case for water and methanol.

d Average molecular radii, taken from molar volumes using densities at room temperature or the freezing point.

e Experimental cluster results from Refs. [1] (water), [8] (MeOH), and [19,20] (MeCN).

f Experimental VBE as measured in liquid jets. The water value is taken from Ref. [2] others, this work.

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4.9 References

[1] A Kammrath, et al, J. Chem. Phys. 125 (2006) 076101. [2] A T Shreve, et al, Chem. Phys. Lett. 493 (2010) 216. [3] J Simons, Accts. Chem. Res. 39 (2006) 772. [4] E Alizadeh, L Sanche, Chem. Rev. 112 (2012) 5578. [5] J Gu, et al, Chem. Rev. 112 (2012) 5603. [6] C D Jonah, et al, Radiat. Phys. Chem. 34 (1989) 145. [7] J Belloni, Nukleonika 56 (2011) 203. [8] A Kammrath, et al, J. Chem. Phys. 125 (2006) 171102. [9] F Arnold, Nature 294 (1981) 732. [10] P J Rossky, J Schnitker, J. Phys. Chem. 92 (1988) 4277. [11] L Turi, P J Rossky, Chem. Rev. 112 (2012) 5641. [12] J V Coe, Int. Rev. Phys. Chem. 20 (2001) 33. [13] J M Herbert, L D Jacobson, Int. Rev. Phys. Chem. 30 (2011) 1. [14] K R Siefermann, B Abel, Angew. Chem., Int. Ed. 50 (2011) 5264. [15] B Abel, et al, Phys. Chem. Chem. Phys. 14 (2012) 22. [16] M Faubel, et al, Z. Phys. D 10 (1988) 269. [17] M Faubel, et al, J. Chem. Phys. 106 (1997) 9013. [18] B Winter, M Faubel, Chem. Rev. 106 (2006) 1176. [19] M Mitsui, et al, Phys. Rev. Lett. 91 (2003) 153002. [20] A Nakajima, private communication. [21] K R Siefermann, et al, Nat. Chem. 2 (2010) 274. [22] Y Tang, et al, Phys. Chem. Chem. Phys. 12 (2010) 3653. [23] A Lübcke, et al, Phys. Chem. Chem. Phys. 12 (2010) 14629. [24] H Shen, et al, Chem. Lett. 39 (2010) 668. [25] T Horio, et al, Chem. Phys. Lett. 535 (2012) 12. [26] D M Neumark, Mol. Phys. 106 (2008) 2183. [27] R M Young, D M Neumark, Chem. Rev. (2012) 5553. [28] J V Coe, et al, J. Chem. Phys. 92 (1990) 3980. [29] G B Griffin, et al, J. Chem. Phys. 131 (2009) 194302. [30] L Ma, et al, J. Chem. Phys. 131 (2009) 144303. [31] J R R Verlet, et al, Science 307 (2005) 93. [32] I V Hertel, et al, Phys. Rev. Lett. 67 (1991) 1767. [33] F Misaizu, et al, Chem. Phys. Lett. 188 (1992) 241. [34] I Dauster, et al, Phys. Chem. Chem. Phys. 10 (2008) 83. [35] K R Wilson, et al, J. Phys. Chem. B 109 (2005) 10194. [36] X Shi, et al, J. Phys. Chem. 99 (1995) 6917. [37] C Silva, et al, J. Phys. Chem. A 102 (1998) 5701. [38] A Thaller, et al, J. Chem. Phys. 124 (2006). [39] X Y Chen, S E Bradforth, Annu. Rev. Phys. Chem. 59 (2008) 203. [40] L Kevan, Chem. Phys. Lett. 66 (1979) 578. [41] M Narayana, L Kevan, J. Am. Chem. Soc. 103 (1981) 1618. [42] C M Stuart, et al, J. Phys. Chem. A 111 (2007) 8390.

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[43] L Mones, et al, J. Chem. Phys. 135 (2011) 084501. [44] R M Forck, et al, J. Phys. Chem. A 115 (2011) 6068. [45] I A Shkrob, M C Sauer, J. Phys. Chem. A 106 (2002) 9120. [46] C Xia, et al, J. Chem. Phys. 117 (2002) 8855. [47] S C Doan, B J Schwartz, J. Phys. Chem. B (2012) DOI:

10.1021/jp303591h. [48] I A Shkrob, et al, J. Phys. Chem. A 106 (2002) 9132. [49] T Takayanagi, et al, Chem. Phys. 324 (2006) 679. [50] M F Fox, E Hayon, J. Chem. Soc. Faraday Trans. I 72 (1976) 1990. [51] M F Fox, E Hayon, J. Chem. Soc. Faraday Trans. I 73 (1977) 1003. [52] T Suzuki, Int. Rev. Phys. Chem. 31 (2012) 265. [53] W J Chase, J W Hunt, J. Phys. Chem. 79 (1975) 2835. [54] M Faubel, B Steiner, Ber. Bunsen-Ges. Phys. Chem. 96 (1992) 1167. [55] D B G Williams, M Lawton, J. Org. Chem. 75 (2010) 8351. [56] J D Smith, et al, J. Am. Chem. Soc. 128 (2006) 12892. [57] K L Rowlen, J M Harris, Anal. Chem. 63 (1991) 964. [58] J E Bertie, Z Lan, J. Phys. Chem. B 101 (1997) 4111. [59] A E Bragg, et al, J. Phys. Chem. Lett. 2 (2011) 2797. [60] M C R Symons, S E Jackson, J. Chem. Soc. Faraday Trans. I 75 (1979)

1919. [61] R N Barnett, U Landman, Phys. Rev. Lett. 70 (1993) 1775. [62] K Hashimoto, K Morokuma, J. Am. Chem. Soc. 116 (1994) 11436. [63] B Gao, Z-F Liu, J. Chem. Phys. 126 (2007) 084501. [64] G Makov, A Nitzan, J. Phys. Chem. 98 (1994) 3459. [65] R P Auty, R H Cole, J. Chem. Phys. 20 (1952) 1309. [66] D W Davidson, Can. J. Chem. 35 (1957) 458. [67] N E Hill, J. Phys. C 3 (1970) 238. [68] K N Jha, et al, J. Phys. Chem. 76 (1972) 3876. [69] W Viehmann, A G Eubanks, Effects of Surface Contamination on the

Infrared Emissivity and Visible-Light Scattering of Highly Reflective Surfaces at Cryogenic Temperatures, Report TN D-6585, NASA, Washington D.C., 1972.

[70] A Wurflinger, Ber. Bunsen-Ges. Phys. Chem. 84 (1980) 653. [71] G Openhaim, E Grushka, J. Chromatogr. A 942 (2002) 63. [72] R Jiménez Riobóo, et al, Eur. Phys. J. E 30 (2009) 19. [73] H M Marla, et al, Astrophys. J. Suppl. Ser. 191 (2010) 96. [74] D M Bartels, J. Chem. Phys. 115 (2001) 4404. [75] I P Bell, et al, J. Chem. Soc. Faraday Trans. I 73 (1977) 315. [76] Y Du, et al, Chem. Phys. Lett. 438 (2007) 234. [77] X B Wang, L S Wang, Rev. Sci. Instrum. 79 (2008) 073108. [78] C Hock, et al, J. Chem. Phys. (submitted).

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69

Chapter 5

Photoelectron Spectroscopy of Solvated Electrons in

Tetrahydrofuran

5.1 Abstract

Efforts to measure the photoelectron spectra of solvated electrons in tetrahydrofuran are described. Highly tentative spectra are reported, and the challenges of studying this solvent are described. Although these efforts have been set aside at present, improvements to our apparatus may make this system worth revisiting.

5.2 Introduction

The behavior of solvated electrons in solution is of great interest from a variety of perspectives within chemistry, biology, and other areas of the physical sciences.[1-4] Historically, measurements of solvated electron binding energies have been confined to small anion clusters, Sn‾. By studying the electron vertical binding energy (VBE) as a function of cluster size in these systems, the bulk VBE may be estimated.[5,6] These extrapolations have proved controversial, however. It is unclear where within the cluster the excess electron localizes, and whether the clusters are representative of bulk solvation.[7-9]

Recently, it has become possible to directly measure solvated electron vertical binding energies in the liquid phase by performing photoelectron spectroscopy with microjet sources.[10-13] It is of great interest to apply the technique to new systems, particularly those that have been studied by the anion cluster technique. To date, only water,[10-13] the simple alcohols methanol and ethanol,[14,15], and acetonitrile[15] have been studied. Of these, only water, methanol, and acetonitrile have been studied with their anion cluster analogs.[5,16-18] At this point, the conclusion is that the

70

water anion clusters are liquid-like and provide an accurate estimation of the bulk VBE. On the other hand, methanol and acetonitrile cluster extrapolations significantly underestimate the bulk binding energies.[14,15] Based on a Dielectric Continuum model, it seems these clusters reflect a bulk solid behavior rather than a bulk liquid behavior.[15,19] To provide another system for comparison, the initial findings of our work with tetrahydrofuran (THF) are presented here.

Of the many systems in which excess electrons can solvate, THF is among the most interesting. In contrast to water and methanol, THF has no bulk hydrogen bonding network for solvated electrons to disrupt. As predicted by Bedard-Hearn et al.[20] and shown by Bowron et al.,[21] liquid THF is filled with naturally occurring, positively polarized voids. With transient absorption studies showing an appearance time of 380 fs for solvated in THF and no further dynamics, it appears that THF can accommodate excess electrons in these voids with minimal solvent rearrangement.[22]

Tetrahydrofuran anion clusters, (THF)nˉ, have been measured over a wide size range, up to n=100.[23] Extrapolation to the bulk limit yielded a predicted bulk binding energy of 3.1 eV. Intriguingly, these clusters are reasonably well treated within Dielectric Continuum theory by the liquid phase numbers.[23] Based on our recent findings, this implies that the bulk VBE as measured in a liquid microjet will be in reasonable agreement with the cluster prediction.[15] By measuring the VBE of solvated electrons in THF, we can test the validity of the cluster phase argument and gain new insight into the relationship between liquid properties and electron solvation.

5.3 Experimental

The work presented here was conducted using tetrahydrofuran (THF; Fisher, preservative free, submicron filtered) with low concentrations of tetrabutylammonium iodide (TBAI; 5 mM, Aldrich, ≥99.0% purity). The THF was sparged with dry, oxygen free argon for 30 minutes prior to use and throughout mixing to remove peroxides and minimize the absorption of water. Mixing was accomplished by sonication for 30 to 60 minutes, which also gently heated the solution. THF mixes were allowed to cool to room temperature before use.

The experimental arrangement used here has been described in detail elsewhere.[12,15] Briefly, the apparatus consists of a microjet source chamber and a field-free time-of-flight spectrometer. Bulk solutions were introduced to vacuum by applying high pressure (~100 atm) to solution behind a 20 µm I.D. fused silica capillary. The resulting flow was a microjet that remained laminar for 1 to 1.5 mm. Flow rates of 0.250 mL/min were used, resulting in a microjet velocity of 13 m/s.

Tetrahydrofuran was a much more challenging solvent to work with experimentally than the other solvents we have studied. Prior to any work

71

with THF, several components of our microjet system needed to be replaced. This was because THF softens or dissolves most plastics, which are used in many components of our apparatus. Most notably, our syringe pump contains plastic seals, the inline filter is held in place by a plastic ring, and PEEK (polyether ether ketone) plastic tubing is used through our assembly. For THF operation, the syringe pump seals and inline filter holder was replaced with PTFE (polytetrafluoroethylene, Teflon) plastic, which only swells mildly on contact with THF. Most of the solvent lines were replaced with stainless steel. However, that is not an option in the nozzle. Although THF induced swelling is worse for PEEK than PTFE, PTFE does not grip the nozzles strongly enough to hold it in place at pressure. As such, PEEK was still used to hold the glass capillary in the nozzle.

One millimeter downstream from the nozzle, the jet was crossed with a 30 Hz Nd:YAG operating at the fourth harmonic (266 nm). Solvated electrons were generated by photodetachment from the iodide anions in solution, via the charge-transfer-to-solvent state accessible at 266 nm.[22,24] In this way, our experiment was a two photon process, where a single 8 ns laser pulse first generated, then detached solvated electrons from the microjets. Electrons then underwent field-free flight to a Z-stack multichannel plate detector. The resulting arrival time distributions were then averaged on an oscilloscope, transferred to a computer, and summed. Raw, time-of-flight spectra were converted to kinetic energy (eKE) with the appropriate Jacobian transformation (t-3).

As detailed previously, we also made use of a femtosecond laser to calibrate our apparatus and measure streaming potentials.[15] Xenon was ionized to the Xe+ 2P3/2 and 2P1/2 states by three photons of 266 nm light with a pulse duration of ~150 fs. By walking the microjet away from the interaction point and measuring the change in arrival energy of these peaks, the streaming potential of the microjet was calculated.[15,25] Timing differences between the two systems were accounted for by a laser spike that appears on the detector, and a field-free calibration was obtained with the microjet off. Our conversion to electron binding energy (eBE) is then given by

,streBE h eKEν φ= − − (4.1)

where hν is the photon energy and strφ is the streaming potential correction.

5.4 Preliminary results and discussion

Although there is great interest in studying THF, we have made only limited progress with it because it is incredibly challenging to work with. Because of the low solubility of most salts,[22,24] we were unable to run at very high concentrations (only ~5 mM), so signal levels were consequently

72

quite low. Furthermore, these microjets are rather unstable and frequently clog before useful measurements may be made. Ultimately, however, the primary limiting factor in working with THF is the instability of the streaming potential. As illustrated in Fig. 5.1, a freshly prepared nozzle exhibited unstable charging, increasing significantly ~90 minutes after pumping down the vacuum chamber. In the recent report of Horio,[14] they discuss passivation of the jets to eliminate such issues. They experienced unstable charging conditions in their water and alcohol jets, a problem we did not encounter. They found that by flowing a salt solution through their nozzle for 24 hours before use (in air), stable operating conditions were reached. Applying the same technique, we did find that the initial test nozzle had a stable streaming potential after passivation. Unfortunately, however, that

Figure 5.1: Charging instability. A comparison of the arrival energy of a calibration peak with the jet off to two sets of running conditions with the jet on. In black squares, the stability was measured with a freshly prepared nozzle; while the red circles show the same nozzle following 24 hours of passivation (see text for details). In all cases, the nozzle was 3 mm from the laser focus.

73

nozzle clogged before we could measure any solvated electron spectra and future jets were not stabilized by equivalent passivation.

Attempts to study electrons solvated in THF are further confounded by the magnitude of charging experienced by these microjets. As shown in Fig. 5.2, we measured streaming potential corrections between -500 mV and 1.7 V. Even worse, the measurement of 1.7 V was taken with the passivated nozzle in Fig. 5.1. The final charging state of the unpassivated nozzle was not measured, but was clearly far larger. From these data it is clear that we cannot obtain reliable without frequently changing between calibration and data collection modes.

Figure 5.2: Streaming potential corrections. A comparison of streaming potential measurements taken with different nozzles. The black squares are the unpassivated nozzle from Fig. 5.1 taken before the potential built up significantly. The red circles are the same jet following 24 hours of passivation, with an apparently stable amount of charging. The other points are with a different passivated nozzle taken at immediately before and after the solvated electron spectra in Fig. 5.3.

74

Our best attempt at collecting useful data with THF is presented in Fig. 5.3. These four scans were taken in rapid succession, and required approximately 7 minutes to complete. The streaming potential was measured immediately before and after these scans, and are shown in Fig. 2 as the blue and green triangles. As evidenced by the shifting peak location, the streaming potential was clearly changing over the course of these scans. Because it takes ~10 minutes to switch laser systems, we cannot precisely say that either streaming potential corresponds to a particular peak, but it does appear that the potential changed monotonically. Uncorrected for streaming potentials, these peaks correspond to VBEs between 1.7 and 2.1 eV. If we assume that the initial and final streaming potentials are the limits of the true streaming potential for any given scan, this would put the corrected VBE at ~2 eV.

Although we have tentatively measured a VBE of ~2 eV, there are

Figure 5.3: Preliminary data. As evidenced by the shifting peak, the streaming potential was changing over the course of collecting these four scans, despite passivating the nozzle. As such, the streaming potential cannot be corrected for.

75

numerous reasons to be highly skeptical of this value. As discussed above given the low signal level, lack of averaging, and uncertainty over the streaming potential, this value must be treated as extremely tentative. Furthermore, water contamination of our THF samples from exposure to air or from moisture in the salt is a serious concern. It has been shown that any water in THF will form microscopic pools that iodide preferentially solvates in.[26] Electrons ejected from these hydrated iodide atoms initially solvate THF, but shift to the water pools on timescales of a few hundred picoseconds. Given the nanosecond duration of our laser pulses, if water is present we will preferentially sample hydrated electrons, biasing our data.

From our work thus far, it is clear that our current operating conditions are not amenable to successfully measuring the VBE of solvated electrons in THF. We clearly require the capacity to rapidly switch between measurement of the streaming potential and measurement of the solvated electron data. The femtosecond laser system is currently working well enough that the project will shortly transition away from using the Nd:YAG. This will also mean a transition from 30 Hz to 1 kHz, allowing for better averaging and rapid switching between data collection and streaming potential measurements. Finally, the transition from our field free spectrometer to our magnetic bottle spectrometer will increase our signal collection by a factor of ~500, making experiments with such low signal levels far more feasible. As such, we have set aside our efforts to study THF at the present time, but may revisit the system at a later date.

5.5 Conclusions

Although tetrahydrofuran is very interesting solution to study solvated electrons in, our present experimental conditions are ill-suited to carry out the work. We have measurements from a single day indicating the VBE is approximately 2 eV, however, there are numerous reasons to be skeptical of this value. These spectra suffer from a lack of averaging, low signal levels, and significant uncertainty over their streaming potential corrections. Furthermore, water contamination may easily have biased our data, a possibility we cannot neglect without a systematic study. Upgrades to our apparatus will soon make THF experiments more feasible; however the frequency with which these jets clog may mean the system is never revisited.

5.6 Acknowledgements

This work was funded by the National Science Foundation through Grant CHE-0649647.

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5.7 References

[1] F Arnold, Nature 294 (1981) 732. [2] P J Rossky, J Schnitker, J. Phys. Chem. 92 (1988) 4277. [3] J Simons, Accts. Chem. Res. 39 (2006) 772. [4] J Belloni, Nukleonika 56 (2011) 203. [5] J V Coe, et al, J. Chem. Phys. 92 (1990) 3980. [6] G Makov, A Nitzan, J. Phys. Chem. 98 (1994) 3459. [7] A Madarasz, et al, J. Chem. Phys. 130 (2009) 124319. [8] N I Hammer, et al, J. Phys. Chem. A 109 (2005) 7896. [9] J M Herbert, L D Jacobson, Int. Rev. Phys. Chem. 30 (2011) 1. [10] K R Siefermann, et al, Nat. Chem. 2 (2010) 274. [11] Y Tang, et al, Phys. Chem. Chem. Phys. 12 (2010) 3653. [12] A T Shreve, et al, Chem. Phys. Lett. 493 (2010) 216. [13] A Lübcke, et al, Phys. Chem. Chem. Phys. 12 (2010) 14629. [14] T Horio, et al, Chem. Phys. Lett. 535 (2012) 12. [15] A T Shreve, et al, Chemical Science (submitted). [16] A Kammrath, et al, J. Chem. Phys. 125 (2006) 076101. [17] A Kammrath, et al, J. Chem. Phys. 125 (2006) 171102. [18] R M Young, et al, Chem. Phys. Lett. 485 (2010) 59. [19] R M Forck, et al, J. Phys. Chem. A 115 (2011) 6068. [20] M J Bedard-Hearn, et al, J. Chem. Phys. 122 (2005) 134506. [21] D T Bowron, et al, J. Am. Chem. Soc. 128 (2006) 5119. [22] A E Bragg, B J Schwartz, J. Phys. Chem. B 112 (2007) 483. [23] R M Young, et al, J. Chem. Phys. 133 (2010). [24] A E Bragg, B J Schwartz, J. Phys. Chem. A 112 (2008) 3530. [25] H Shen, et al, Chem. Lett. 39 (2010) 668. [26] A E Bragg, et al, J. Phys. Chem. Lett. 2 (2011) 2797.

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Appendix A

Field-Free Spectrometer Machine Drawings

Presented here are the machine drawings for the original liquid microjet apparatus, which used a field-free spectrometer. Most of the apparatus was constructed from repurposed preexisting components, so relatively little machining was required. The microjet assembly attaches ultimately to a 6-port cross, and it is this region that was heavily customized. A ring was welded into the cross to mount magnetic shielding for the flight tube and the differential pumping sheath. The skimmer for sampling the jet, as well as the assembly to collect spent solution also required fabrication. Finally, the 10” to 4.5” conflat reducing flanges at the laser entrance and exit were modified to allow us to view the microjet to verify alignment, flow quality, and whether it has frozen.

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Figure A.1: Jet trap region side view. A machine drawing showing the assembly of the new components.

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Figure A.2: Jet trap region top view. A machine drawing showing the assembly of the new components.

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Figure A.3: Mounting ring part 1. Piece welded into a conflat cross to mount the differential pumping sheath.

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Figure A.4: Mounting ring part 2. Details of the installation of the mounting ring.

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Figure A.5: Differential pumping sheath. Attaches to the mounting ring, Figs. A.2 and A.3, and mounts the skimmer.

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Figure A.6: Skimmer – 1 mm opening. Attaches to the differential pumping sheath, Fig. A.5. The 0.1 mm skimmer is presented in Fig. A.7, other skimmers not pictured, but constructed with identical specifications aside from angles.

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Figure A.7: Skimmer – 0.1 mm opening. Attaches to the differential pumping sheath, Fig. A.5. The 1 mm skimmer is presented in Fig. A.6, other skimmers not pictured, but constructed with identical specifications aside from angles.

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Figure A.8: Jet trap top. Flange mounted to the bottom of the trap region cross. Collects spent solution and supports the liquid nitrogen cooled bottom, Fig. A.9.

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Figure A.9: Jet trap bottom. Collects spent solution and is cooled by liquid nitrogen to freeze out solution and reduce the vapor pressure.

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Figure A.10: Viewport entrance modification. Details of modifications to the 10” conflat flanges that mount the laser entrance and exit flanges. Viewports added to allow for monitoring of the jet conditions.

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Appendix B

Magnetic Bottle Spectrometer Machine Drawings

Presented here are the machine drawings for the new magnetic bottle spectrometer. As discussed in chapter 2, use of a magnetic bottle with a differentially pumped detector region, as is required for use with a microjet source, presents a significant engineering challenge. To address all of the issues, many more customized parts were required for the magnetic bottle apparatus than the original apparatus. The constraints of the detection scheme mean that all of the flight tube and detector pieces are new. Although we could have reused some of the trap components, we decided to increase the size of the pieces collecting the jet, which meant replacing all of the original trapping components. Finally, a door was added to expedite the daily vent and clean cycle, which replaces the laser exit flange from the original apparatus.

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Figure B.1: Full apparatus layout. Overview of the assembly of the full apparatus.

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Figure B.2: Dewar cross detail. Detailed view of the assembly of the cross with pumping for the Trap region, provided by a turbo and liquid nitrogen.

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Figure B.3: Jet cross detail 1. Detailed view of the assembly of the cross where the microjet nozzle mounts.

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Figure B.4: Jet cross detail 2. Detailed view of the assembly of the cross where the microjet nozzle mounts.

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Figure B.5: Detector cross detail. Detailed view of the assembly of the detector cross flange.

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Figure B.6: Liquid nitrogen dewar modification. Specifications for welding handles onto the liquid nitrogen dewar.

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Figure B.7: Detector support plate. Mounting plate for Beam Imaging detector. Numbered out of sequence because it was a last minute addition to the project after changing detector vendors.

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Figure B.8: Trap bottom. New, larger trap to catch solution from the microjet nozzle. Mounts on Trap bottom (Fig B.11).

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Figure B.9: Ice breaker. Piece used to disrupt icicle formation in the trap. Mounts on 1/4” rod and is fed into vacuum with the flange in Fig. B.10.

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Figure B.10: Ice breaker feedthrough. Mounts the ice breaker via a bored UltraTorr feedthrough. Attaches to an optional 4.5” CF tee between the trap mount flange (Fig. B.11) and the trap (Fig B.8).

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Figure B.11: Trap mount flange. Bottom piece of the jet/trap chamber. Mounts the trap (Fig B.8), magnet stand (Figs. B12-15), and feedthrough for a gas inlet line through a feedthrough in the NPT tapped hole.

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Figure B.12: Magnet platform post. Standoffs that attach to the trap mount flange (Fig. B.11) and support the breadboard (Fig. B.13).

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Figure B.13: Magnet support board. Modified optics breadboard to mount the magnet translation stage and magnet assembly.

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Figure B.14: Magnet baseplate. Piece that attaches to the translation stage in vacuum and mounds the magnet stack.

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Figure B.15: Iron cone. Soft iron cone to increase the magnetic field gradient at the laser-microjet interaction point.

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Figure B.16: Chamber door. A quick access door, modified to serve as a laser exit flange. Mounts directly on the trap region cross.

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Figure B.17: Differential pumping sheath. Mounts between the jet/trap and detector crosses, and supports the skimmer.

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Figure B.18: Flight tube flange - full assembly. Supports the solenoid and detector. Due to the complexity of the construction of this piece, details of subcomponents are presented in the following five drawings.

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Figure B.19: Flight tube flange – outer tube components. Modified 10” conflat blank to attach to the detector chamber, and a welded ring to ensure a round pipe.

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Figure B.20: Flight tube flange – outer tube. Details of the outer tube assembly. Welded support rings included as needed to fit the solenoid since pipe tolerances allow for considerable deviations from round (~0.1”).

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Figure B.21: Flight tube flange – inner tube components. Kimball Physics perimeter weld flange to mount the detector, and rings to center the solenoid assembly (Figs. B.31-35).

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Figure B.22: Flight tube flange – inner tube. Details of the inner tube. Welded rings support and center the solenoid assembly (Figs. B.31-35).

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Figure B.23: Flight tube flange – connecting plate. Final plate that attaches the inner and outer tubes.

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Figure B.24: Flight tube in vacuum support ring. Clamps onto the outer tube of the flight tube flange with three screws, with three more screws used to center the tube within the vacuum chamber.

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Figure B.25: Grid support post. Standoff to mount the grid assembly (Figs. B.26-28) using the Kimball Physics Groove Grabber system.

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Figure B.26: Grid assembly mount. Baseplates to mount the grid assembly.

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Figure B.27: Grid ring bottom. Mounts between the assembly mount, Fig. B.26, and the Grid ring top, Fig. B.28. The grid spot-welds to this piece.

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Figure B.28: Grid ring top. Detector-facing piece of the grid assembly.

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Figure B.29: Detector support rod. Standoffs for the detector to grant clearance to the electrical leads, allowing for a geometry where the bottle can slide over the detector flange.

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Figure B.30: Detector mounting flange. Machined down blank to ensure clearance for the solenoid (Figs. B.31-35), with electrical feedthroughs and a viewport for the phosphor screen for alignment purposes.

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Figure B.31: Bottle assembly – full assembly. Details of the construction of the full solenoid assembly. Individual parts described over the next four figures.

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Figure B.32: Bottle assembly – wire support tube. Plastic tube, spiral cut to support the solenoid wire.

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Figure B.33: Bottle assembly – outer plastic tube. Tube to protect the solenoid wire. A groove is cut lengthwise for the wire lead.

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Figure B.34: Bottle assembly – mu metal shield. Outermost tube in the solenoid assembly. Reduces stray magnetic fields.

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Figure B.35: Bottle assembly – retaining ring. Secures the solenoid assembly. Only one is used due to space constraints in the space within the flight tube flange where the solenoid assembly mounts.

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Figure B.36: Bottle table stand bottom. Table mounted support for the solenoid (Figs. B.31-35), designed to relieve stress on welds in the flight tube flange (Figs. B.18-23).

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Figure B.37: Bottle table stand top. Upper securement for the solenoid assembly (Figs. B.31-35). Attaches to the stand described in Fig. B.36.

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Figure B.38: Flight tube table stand bottom. Table mounted support for the inner tube of the flight tube flange (Figs. B.18-23), to relieve stress on the welds.

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Figure B.39: Flight tube table stand top. Upper securement for the inner tube of the flight tube flange (Figs. B.18-23). Attaches to the stand described in Fig. B.38.

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Figure B.40: Dewar drying rest. Stand to support the vacuum mounted liquid nitrogen dewar while it is warming up and drying between runs.

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Figure B.41: Alternative grid mount ring. After a last minute detector vendor change, there is now room for the grid assembly to attach to the detector support plate. This part is an alternate to that of Fig. B.25.

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Appendix C

Data Acquisition Software

C.1 From C++ to LabVIEW

To collect photoelectron spectra, the signals from multiple laser pulses are averaged on an oscilloscope and transferred to a computer for summation and storage. Two different versions of software were used to collect the spectra presented in this dissertation, one written in C++ and one written in LabVIEW (National Instruments). Older data were collected using a modified version of the C++ based PES 2000 program written by Harry Gomez.[1] Although this program was fully functional for our purposes, the model of oscilloscope used to collect spectra was hardcoded and it only worked with Tektronix TDS 544 oscilloscopes. When our TDS 544 stopped working near the end of 2007, the code was modified to accommodate the replacement Tektronix TDS 3034B oscilloscope. It was this version of the program that was used to collect the data presented in Chapter 3. This program remained in use for several years, until the beginnings of the transition to the femtosecond operation obsoleted the oscilloscope.

The TDS 3034B was a completely satisfactory oscilloscope when we were using a 30 Hz laser. However, when we attempted to use the newly functional femtosecond laser at 1 kHz (see § 2.9), we quickly discovered we were exceeding the limits of its processing power. While the oscilloscope can, in principle, run much faster than 1 kHz, it is effectively limited to ~33 Hz under the conditions we use for data collection. To take advantage of the improvement in the repetition rate of our laser, we acquired a Tektronix DPO 3034 oscilloscope in mid-2011. Bearing in mind that the eventual goal is to move towards time-resolved experiments, we decided against further modification of the C++ code for the newest oscilloscope. Instead, as detailed below, a new LabVIEW codebase was established. Although the new set of programs are still based on those described by Gomez,[1] and ultimately Metz,[2] the scope of ambition of the new code is far more modest. Data analysis can now easily be carried out in Origin (OriginLab), and there is no longer a need to deal with mass spectra. As such, the aim of the new code is simply the acquisition of data, in both non-

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time-resolved and time-resolved modes. At the time of writing, there are two separate data acquisition programs: a reimplementation of the PES 2000 front end for non-time-resolved data collection, and a program capable of collecting time-resolved data. The non-time-resolved data collection program works reliably, while the time-resolved collection program functions but needs more work before being used full time. Although LabVIEW code does not readily lend itself to publication in print, the design principles, main features, and limitations of each program are presented below.

C.2 Non-time-resolved data collection program

The user interface (Fig C.1) to the non-time-resolved version of the new data collection program will look very familiar to users of the C++ or older programs in our lab. It retains the same basic layout as the previous iteration of the program, while removing all options that are no longer applicable (e.g. ion mass, extraction energy, etc). This program is also much more flexible than the old program. While the choice of oscilloscope model is still hardcoded, the user can now select what hardware address the scope is at, which channel supplies the trigger, and which channel has the data supply. Also new with the LabVIEW code are the quantitative shot counter (the old program had progress bar) and the scan timers. Although many of the old inputs have been removed, it is worth noting that the save files from this program are fully backwards compatible with PES 2000.* As such, these

* All numbers are in scientific E notation with 14 digits of precision. The order of these

save file headers is: “D,” number of laser pluses in the scan, number of laser pulses averaged per transfer to the computer, number of data points collected, temporal width of each data point in ns, discrimination level in mV, time scan mode (for compatibility),

Figure C.1: GUI for the non-time-resolved data acquisition program.

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files can readily be opened and processed in the old program. It is generally easier, however, to process them within Origin; see Appendix D for two scripts that expedite the conversion from time-of-flight to energy space and the smoothing of spectra.

This version of the program is stable, and works quite reliably (the data presented in Chapters 4 and 5 were taken entirely with this program) however, there are some quirks that anyone who edits the code should be aware of. The program was designed to use the same discrimination procedure as previous data collection programs. Essentially, although the oscilloscope screens only show 8 major divisions, their internal processing includes an additional division above and below the display. The voltage at each point is tracked by an internal value that ranges from 0 at the bottom of the lower offscreen division to 65535 (216-1) at the top of the upper offscreen division. Since our data are negative voltage spikes, the baseline would be set to the very top of the uppermost division, giving a baseline of 65535, with any real signal having a smaller value. For example, a 15 mV data spike viewed on a 10 mV/div scale result in a value readout of ~55705 (~6554/div). Discrimination worked by further offsetting the baseline, to the specified value above the top of the upper, non-displayed division. The older oscilloscopes would allow for such baseline offsets well in excess of one division, apparently assigning larger values internally but still returning a maximum value of 65535 for any given point. Applying a 10 mV discrimination to the previous example would then effectively move the baseline up an additional 10 mV, meaning the signal spike would read out at 5 mV giving a value of ~62295 while all non-signal points returned 65535.

This is complicated by the degree of averaging, or the number in the “update every n shots” box. The oscilloscope averages each point over that many laser pulses before transferring data to the computer. With discrimination, the internal value of a point without signal will be above 65535 for most pulses. Discrimination is set such that the average value of a point that includes a small amount random noise will likewise exceed 65535, causing the oscilloscope return the baseline value for that point. When transferred back to the computer, these waveforms would then be inverted by subtracting each returned value from 65535 to obtain the signal retained by the program. It should be noted that this not a function of the datatype used in the C++ code; the data are transferred with the double type, which is capable of 8 bytes rather than the 2 bytes actually used.

The DPO 3034 does not function in the same way, however. Using the LabVIEW drivers and subVIs supplied by Tektronix, the output was automatically converted to voltage and shifted by an extra factor of the set

background subtraction mode (for compatibility), laser wavelength (for compatibility), ion mass (for compatibility), calibration t0 in ns, flight tube length in cm, quadratic compression factor (for compatibility), horizontal position as a percentage (hardcoded), and time offset in ns (hardcoded).

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voltage offset. The values returned also cover a slightly larger range than the 10 divisions, with points lying above the baseline reading out their actual values rather than the baseline value. To get around this, a customized version of the Get Waveform subVI, Get LPES Wave, is used, where voltages in excess of the baseline are coerced down to the baseline. While this does produce the desired functionality, it seems like an inelegant solution. It may be worth investigating this further at some point, possibly by upgrading the LabVIEW drivers, or the oscilloscope firmware. For now, however, it is satisfactorily functional.

Aside from the discrimination issue, only minimal changes have been made. Also in the Get LPES Wave subVI is a command to limit the data transferred to only the points desired, which helps expedite data collection. The final bit of customization is in the Wait for Operation to Complete subVI, which is called as part of every read operation. This was initially causing frequent timeouts, and increasing the input maximum wait-time had no effect. This was largely resolved by creating a custom version that includes a VISA command to explicitly wait for the operation to complete. It should be noted, however, that timeouts still occur if an operation takes longer than ~60 seconds to complete, so scans must finish within this timeframe. Ideally this would be longer for use with the Nd:YAG, however since the transition to kilohertz operation is imminent the issue has been left unresolved.

C.3 Time-resolved data collection program

The program for taking time-resolved data works, but only under a very narrow set of usage assumptions and should be regarded as alpha software in its current form. It is essentially the non-time-resolved program described above grafted onto the Image DAQ 2.0 program used by the Femtosecond Time-Resolved Photoelectron Imaging project. Complete details of the Image DAQ 2.0 program may be found in Appendix 4 of Ryan Young’s thesis.[3] Essentially, the goal of the program is to take a rapid series of scans at a sequence of pump-probe delays. This means that the program needs to be able to communicate with a delay stage, and a new data format is required so that bad visits to a given stage delay can be rejected during data workup. Also, to be able to correct for signal drift, a “video mode” is needed, where the oscilloscope output can be monitored with data collection paused.

As shown in Fig. C.2, all of these features have been implemented in the current version of the program. All of the input parameters from the non-time-resolved program have been carried forward, along with a table to set the desired stage delays. The video mode button pauses progress through the delays, and takes an indefinite series of scans at the current delay without saving anything. The notes box can be edited at any time, and is stored in the header file upon completion of data collection. Finally, the “load config file” allows a configuration file to be written or edited in another

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program, such as Excel, and then loaded at runtime. For backwards compatibility, the savefile header is largely preserved from the old versions of the program as well. Stored as a separate file, settings.txt, the list of scan parameters now begins with “Created with LPES alpha06” rather than “D,” followed by the remaining items detailed above, and ends with any information entered in the Notes box. The time-of-flight information is stored in separate files for each delay, named POSITION#_DELAY1_DELAY2.csv† as read from the table, e.g. 2_-100_0.csv. Because LabVIEW will append rows to a file but not columns, each visit to a stage position is appended as a new row in the file. At the completion of a data collection run all of the data files are transposed for usability and a file is generated with the summed data from each delay.

All of these features are fully implemented and work properly, however the program is limited in some ways. Primarily, these limits are:

1. The program logic assumes that the background one color scans will all happen at the end of a data collection run.

† The table only presently allows for a single stage since the project only has one

computer controlled delay stage. Since the project may need a second stage for three pulse experiments, a second stage is included in the save file names for compatibility. However, the code would require editing to actually use a second stage.

Figure C.2: GUI for the time-resolved data acquisition program.

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2. There is no way to view the data in energy space or view past scans while collection is ongoing without manually importing a data file, transposing it, and processing it as normal.

3. There is no quantitative measure of the signal level shot-to-shot, or per delay visit.

4. Although the delay table does allow for an unequal number of visits to the various stage positions, it cannot be edited once data collection starts, and the current position within the delays cannot be altered.

5. The program is written as a series of nested case statements and loops that make it very slow to respond to user input.

None of these issues actually prevent time-resolved data collection, but they do make experiments more difficult. The most limiting factor in getting good data is issue 1. The choice to collect the one color background data only at the end was based partly on the procedure of our colleagues down the hall and partly on the relative ease of only blocking lines at one point during the data run. However, it has become clear that, due to jet pointing instabilities and clogging, the program needs to allow background scans to be taken at any point during the run if we are to obtain a good subtraction. Ideally, computer controlled shutters would be implemented on each line, allowing for background collection without user intervention.

Expanding the capabilities of the program to address issues 2 and 3 should also be a high priority for future work on the program. Being able to accurately assess the quality and stability of the data with quantitative parameters would greatly benefit the project. Particularly desirable is the ability to integrate the signal over an adjustable horizontal range and track its stability, analogous to the IoPAT parameter in Image DAQ 2.0.[3] Live conversion of the data to energy space is technologically possible with the Origin plugins to LabVIEW. This should be straightforward to implement as well. The conversion script described in Appendix D could be called to generate the appropriate energy array at the beginning of the data run, with the intensity scaling occurring after each update. This would be a highly useful expansion of the program that would help to ensure that time is not wasted on bad data.

Although neither issue 4 or 5 is likely to result in reduced quality of the collected data, they do adversely affect the user friendliness of the program. It would not be unfair to describe the current version of the program as mildly user hostile. Because the program is a series of nested statements, once video mode is engaged, user actions are not processed until the completion of a round of k shots between moves. This frequently results in user frustration and could, in principle, lead to data collection with an undesirable set of parameters. Ideally the code structure should be replaced with an event structure. The interface and skeletal structure for a new

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program built around this design paradigm is largely complete, however none of the data collection, stage control, or data processing routines have been included thus far.

Ultimately, the way the program communicates with the oscilloscope may fundamentally limit the responsiveness of the program, however. Presently, the program tells the oscilloscope to begin a set of averaging and wait until that operation is complete before carrying out further instructions. The program then sends a request for the data, and waits for the response from the oscilloscope, creating a bottleneck. In principle, we would like the oscilloscope announce that it is ready to report the data without having the program explicitly delaying all other operations, allowing for more parallel operations (responding to user input, analyzing portions of the data, etc.). Unfortunately, none of the vendor supplied controls provide such a mode and, even if one can be written, the delay of activating the program may result in slower data collection.

C.4 References

[1] H Gomez, Ph.D. Thesis, University of California, Berkeley, Berkeley, CA, 2002.

[2] R B Metz, Ph.D. Thesis, University of California, Berkeley, Berkeley, CA, 1991.

[3] R M Young, Ph.D. Thesis, University of California, Berkeley, Berkeley, CA, 2011.

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Appendix D

Data Processing Routines

D.1 Overview and purpose

Data analysis is typically handled using the Origin software package (OriginLab Corporation). The following script is used to convert the raw time-of-flight (TOF) data to kinetic energy (KE) space. Oftentimes we want to smooth our data by Gaussian convolution in KE space. The built-in convolution package will not handle this operation because our even sampling in TOF space results in an uneven sampling in KE space. The following script is used to handle the conversion to KE space and process this smoothing. The routines are in the same script file, but are independently callable from within Origin.

D.2 LabTalk script

/////////////////////////////////////////////////////////////////////////////////////// Filename: PES_functions.OGS // Creation: ATS 12 October 2012 // Purpose: Useful things for microjet PES project // [ConvertMain] - Convert columns from ToF to Kinetic Energy // with t^-3 Jacobian // [SmoothMain] - Apply Gaussian smoothing to unevenly spaced // x-axis, smoothing with: // E0=sum(i)[weigh(E0-Ei)*Data(Ei)]/sum(i)[weigh(E0- // Ei)], where weigh(x,y)=exp(-y*x^2) // // Known limitations: // Prompts in both sections - could be combined to read // parameters from within a workbook, or at least check for // them. // Converting to energy: // First column is assumed to be the Time of Flight X column in ns, // with all remaining columns as data

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// Assumes initial book is at least two columns wide // Auto-updating columns remain auto-updaing/keep their formulas // Smoothing: // First column is assumed to be the Energy X column in eV, with // all remaining columns as data // Assumes initial book is at least two columns wide // Auto-updating columns remain auto-updaing/keep their formulas // Assumes first row has a valid energy and stops on // NaN/non-numerical data types // Masked points are treated as NaNs. Don't use on maked data. // Not calculating dE properly - requires time/point, length, // and tzero to do it. See calculation below. Ideally add // a check for values to do it correctly and use the current // method as a fallback. /////////////////////////////////////////////////////////////////////////////////////

[ConvertMain] double L, tz; //length and t-zero variables int convert = 0; //used to test for cancellation

L = 0; //default 0 - used as test of whether it has been set tz = 0; run.section(,getconversionparams, L tz convert); if (convert == 1 && L > 0) /*only convert if not cancelled on

parameters screen and not left at 0 length*/

run.section(,ConvertToE, L t0); return; //----------------------------------------------------------------- //Get length and t-zero //-----------------------------------------------------------------

[getconversionparams] getnumber (Tube length in cm (must be greater than 0)?) L (t_zero in ns?) tz (Enter Parameters); //end of getnumber convert = 1; //only hits this if not cancelled at dialog box return;

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[ConvertToE]

//make a new workbook, and label appropriately wcopy ow:=[<new>]<new>; //duplicate book Col(1)[L]$ = eKE; //name x Col(1)[U]$ = eV; //units Col(1)[C]$ = "$(L) cm%(LF)$(tz) ns"; /*comment with length and

t-zero used.*/ //Goto the first column, assume it is the X values, and convert to eKE range r = 1; type -a "Calculating KE values."; loop(i,1,wks.nrows) if (r[i] == 0) r[i] = 1E-50; //prevent div by 0 errors //energy[i]=284.31740*L^2/(t[i]-tzero)^2 //constants taken from old PES program /*neglects quadratic and center of mass corrections (unneeded

for liq jets)*/ r[i] = 284.31740*L^2/((r[i]-tz)^2); //Loop over the data and scale by the Jacobian loop(j,2,wks.ncols) type -a "Applying Jacobian to column $(j-1) of $(wks.ncols-1)."; range s=$(j); loop(k,1,wks.nrows) s[k]=s[k]/(r[k]^(3/2)); return; [SmoothMain] double res = 0; //resolution int smooth = 0; //used to test for cancellation run.section(,getsmoothingparams, res smooth); if (smooth == 1 && res > 0) /*only smooth if not cancelled and non-

zero resolution*/

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run.section(,smooth, res); return;

[getsmoothingparams] getnumber (Gaussian FWHM (meV) to smooth with?) res (Enter Parameters); //end of getnumber smooth = 1; //only hits this if not cancelled return;

[smooth] //variables of interest res=res/1E3; //need res in eV to match the x-axis double maxdE = (2.146/sqrt(2.773))*res; //from old PES program double totd, totw, realdE, maxj, minj, w; int energyrange, NaN; dataset tempsmoothed; //make a new workbook, and label appropriately wcopy ow:=[<new>]new; //duplicate the workbook range r = 1; //fixed ref on the energy column //This redoes the math for range many times and could probably be //more efficient, but this was faster to code. It might be possible //to make this run faster by using a second workbook instead of a //temporary dataset array. loop(i,2,wks.ncols) type -a "Smoothing column $(i-1) of $(wks.ncols-1)"; range s=$(i); loop(j,1,wks.nrows) //reset some variables minj=j; maxj=j; energyrange=1; //For each energy, calculate magnitude of the //instantaneous dE this really should be //dE=(2*[time/point]*284.31740*L^2)/((t(j)-tz)^3) //from dE/dt. To avoid requiring [time/point], //L, t(j), and tz knowledge for this subroutine,

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//just calculating it by taking the average of the //difference between this point and each adjacent point. //Stay on the workbook while calculating local slope //breaks if encounters a missing value if (r[j] == (1/0)) break; else if (j == 1) realdE=(r[j]-r[j+1]); else if (j == wks.nrows || r[j+1] == (1/0))

realdE=(r[j-1]-r[j]); else realdE=((r[j-1]-r[j+1])/2); //Includes a number of points in each direction //according to the local slope. double ratio=maxdE/realdE; /*The c ceiling function was not not working and no other

ceiling available, so it is reimplemented below*/ run.section(,ceiling, ratio energyrange); //smooth the point only if adjacent points are in range //don't try to smooth NaNs if ((energyrange > 1) && (r[j] != (1/0)) && (s[j] != (1/0))) //don't go above the top NaN=0; if (j-energyrange < 1) minj = 1; else //don't include NaNs loop(k,j,j-energyrange) if ((NaN==0)&&(r[k]==(1/0))) NaN=k; if (NaN == 0) minj = j-energyrange; else minj = NaN+1; //don't walk off the end of the workbook //don't include NaNs NaN=0; loop(m,j,j+energyrange) if ( (NaN==0)&&(r[m]==(1/0)) ||

(m>wks.nrows) ) NaN=m;

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if (NaN == 0) maxj = j+energyrange; else maxj = NaN-1; //reset variables totd=0; totw=0; //loop over the range loop(n,minj,maxj) //smooths with //E0=sum(i)[weigh(E0-

Ei)*Data(Ei)]/sum(i)[weigh(E0-Ei)] w=exp((-(2.773/res^2)*(realdE*(n-j))^2)); if(s[n]!=(1/0)) totd+=s[n]*w; totw+=w; tempsmoothed[j]=totd/totw; //point not smoothed, carry the value forward else tempsmoothed[j]=s[j]; /*Done with this column, transfer the temp buffer to the real

column and move on*/ loop(p,1,tempsmoothed.GetSize()) s[p]=tempsmoothed[p]; //convert back to meV for the label res= res*1E3; loop(z,2,wks.ncols) Col($(z))[C]$ += "%(LF)Smoothed with a $(res) meV

Gaussian"; //comment appropriately

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type -a "Done smoothing."; return;

[ceiling] //Ceiling function. int rounded; rounded=round(ratio, 0); if (rounded-1 < ratio && ratio <= rounded && ratio <= rounded && rounded < ratio+1) energyrange=rounded; else if (rounded < ratio && ratio <= rounded+1 && ratio <= rounded+1 && rounded+1 < ratio+1) energyrange=rounded+1; else if (rounded-2 < ratio && ratio <= rounded-1 && ratio <= rounded-1 && rounded+1 < ratio+1) energyrange=rounded-1; else type -a " is broken."; return;

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