Backward (B) Sample Soft Matter and Forward (F) Chemical

Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada Propriété d’un consortium d’universités canadiennes, géré en co-entreprise à partir d’une contribution administrée par le Conseil national de recherches Canada

Canada’s national laboratory for particle and nuclear physics Laboratoire national canadien pour la recherche en physique nucléaire

et en physique des particules

Accelerating Science for Canada Un accélérateur de la démarche scientifique canadienne

0.5 1.0 1.5 2.0-0.3

-0.2

-0.1

0.0

10 K

Cor

rect

ed In

tegr

al A

sym

met

ry (%

)

Magnetic Field (T)

290 K

µSR and βNMR of Soft Matter and

Chemical Systems

Iain McKenzie TRIUMF Centre for Molecular and Materials Science

Department of Chemistry, Simon Fraser University

Electronic clock

Muon detector

y

+e

Backward (B) positron detector

P( = 0)t µ+

Sample

x

z

Forward (F) positron detector

Muons and Chemistry

September 8, 2016 µSR and βNMR of Soft Matter and Chemical Systems 2

Mu+ •  Can’t resolve chemical shifts

so no structural information about diamagnetic muonated molecules.

•  Mu+ diffusion in materials.

Muonium •  Mu reaction kinetics in gases

and liquids (isotope effect) •  Interaction with environment

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

ln(µ

s/T 2µ

)

1000/[T(K)]

Tg = 215 K

150 200 250 3000.0

0.1

0.2

0.3

1/T 2µ

(µs-1

)

Temperature (K)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

-0.15

-0.10

-0.05

0.00

0.05

Asymmetry

Time (µs)

0 1 2 3-0.2

-0.1

0.0

Asymmetry

Time (µs)

Mu+ hopping in PEO

Relaxation in WTF: Good for pulsed source

Relaxation in WTF: Good for pulsed source Mu in H2O

Muons and Chemistry


Muoniated Radicals •  Structure •  Molecular dynamics •  Reaction kinetics •  Spin labels

Mu

H

Mu

MuC C

R

R

R

R

C CR

R

R

R

Mu

C O

R

R

MuC O

R

R

Mu

a)

b)

c)

C C O

R

R

C

C OR

R Mu

-COC Mu

R

R

Mu

d)

e)

C

R

R

MuC Mu

R

R

Identification of Muoniated Radicals


TF-µSR Precession frequencies (requires CW source)

ALC-µSR Resonance fields

Hyperfine Coupling Constants

Temperature Dependence of HFCs

Muon hfcc (Aµ)

Distribution of unpaired electron

Nuclear hfccs (H, D, 13C, 14N….)

•  3D structure •  Intramolecular motion

Solid

Level Crossing Resonance


Electronic clock

Muon detector

y

+e

Backward (B) positron detector

P( = 0)t µ+

Sample

x

z

Forward (F) positron detector

A B( ) = NF − NB

NF + NB

∝Pz B( )

Magnetic Field (B)

Time integral measurement RATE IS CRITICAL!

Level Crossing Resonance

December 19, 2012 Muoniated Radicals 1

Ene

rgy

Pol

ariz

atio

n

Magnetic Field

αeβµβk

αeβµαk

αeαµβk

αeαµαk

muon-nucleus spin flip-flop ΔM = 0

muon spin flip ΔM = ±1

muon-nucleus spin flip-flip ΔM = ±2

BresΔ0 ≈

12Aµ − Akγµ −γ k

BresΔ0 ≈

Aµ2γµ

HiFi @ ISIS: ~100 Mevents/hr Helios @ TRIUMF: ~1800 Mevents/hr

Why Rate is Important


0.5 1.0 1.5 2.0-0.3

-0.2

-0.1

0.0

10 K

Cor

rect

ed In

tegr

al A

sym

met

ry (%

)

Magnetic Field (T)

290 K

•  Ability to scan over wider field range. Find all resonances.

of the ALCs and the eSR, this points to a thermallyactivated, SOI-based spin relaxation mechanism.

Such an increase of the eSR with the Z of the substituentatom, the so-called heavy atom effect, is expected for aSOI-based spin relaxation mechanism. However, we do notexpect a simple relationship between these two quantities,for the following reasons. First of all, although the atomicSO coupling constant is predicted to increase as Z2 basedon simplifying assumptions [39], its actual value varies in acomplex way with Z [40]. Second, the effect of the SOI dueto the substituted atom compared to that from all the otheratoms in the molecule depends on the weight of the wavefunction at the substituent site, and this is molecule specific[20]. To overcome these difficulties, and estimate indepen-dently the strength of the SOI along the series in order torelate it with the eSR rate, we have measured the excitonsinglet to triplet conversion rate, known as the intersystemcrossing rate (kISC), via time-resolved photoluminescence.An estimation of kISC has been possible in Alq3, Gaq3,and Inq3 where singlet and triplet emissions can be bothclearly singled out by time-resolved luminescence measure-ments (details of these measurements are shown in theSupplemental Material [25]). This was not possible in Biq3and in the TES series due to their different optical properties.

The kISC is proportional to the square of the matrixelement of the SOI Hamiltonian between the singlet andtriplet states [41], so kISC can be used as a reliable mea-surement of the strength of the molecular SOI. Thisapproach is solidly founded on the widespread understand-ing of the physics behind the singlet-to-triplet conversion[41–44], and allows us to bypass the fact that the preciseform of the underlying dependence of the eSR on theatomic number of the substituents is unknown.

Figure 3(a) shows the eSR as measured through !SRas a function of kISC, which is proportional to the SOIstrength, in the Xq3 series. It reveals a clear relationshipbetween the eSR and the strength of the SOI. This depen-dence suggests the existence of a SOI-driven mechanismfor spin relaxation. We also plot, in Fig. 3(b) the same eSRdata versus the Z of the substituent atom. The expectedincrease of the eSR with Z is indeed observed in Fig. 3(b).

In the following, we will show that an alternative inter-pretation in terms of a HFI-based mechanism does notprovide a consistent explanation of the observed changeof eSR with Z.Given that the only change we made to the molecule was

the central atom, with the number and location of hydrogenatoms remaining unaltered, there should not be any directeffect of the HFI between the electron and hydrogen in thechanges observed here.An effect of the HFI due to changes to the spin and

nuclear magnetic moment of the central atom is also veryunlikely. Table I shows that the magnitude of the spin andthe nuclear moment of the substituent atoms does notcorrelate with the observed increase of the eSR. Instead,for the case of Alq3 and Gaq3, where the eSR roughlydoubles, both the nuclear moment and spin of Al aresignificantly larger than those of Ga. Finally, one mightargue that changing the central atoms may still bear anindirect effect on the HFI that could influence the observedresults. Changing the mass of an atom in the molecule canimply a change in the bond lengths and angles or, moregenerally, a modification of the energy and population ofvibrational modes. Both of these effects could result in a

0.8

0.6

0.4

0.2

eSR

(MH

z)

3.53.02.52.01.5

ISC rate (MHz)

Xq3

(a)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

eSR

(MH

z)

806040200

Z

Xq3 TES

(b)

FIG. 3 (color online). (a) Electron spin relaxation rate as afunction of the intersystem crossing rate in the Xq3 series at300 K. The electron spin relaxation rate shows a dependence onthe intersystem crossing rate, which is used here as a measure-ment of the strength of the spin-orbit interaction. (b) eSR for theXq3 and TES series as a function of the atomic number of thesubstituent atom, Z.

Magnetic Field (T)

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

Pola

riza

tion

1.61.41.21.00.8

10K 300K

(a)Alq3

1.61.41.21.00.8

Gaq3 (b)1.61.41.21.00.8

Inq3 (c)

1.61.41.21.00.8

Biq3 (d)

FIG. 2 (color online). Muon spin polarization around the ALCs in (a) Alq3, (b) Gaq3, (c) Inq3, and (d) Biq3 at 10 K (blue triangles)and 300 K (red circles). Modelling for these ALCs is indicated by the black lines and is used to determine the electron spin relaxationrate, which is essentially proportional to the amplitude of the ALC curves (see text).

PRL 110, 216602 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending24 MAY 2013

216602-3

of the ALCs and the eSR, this points to a thermallyactivated, SOI-based spin relaxation mechanism.

Such an increase of the eSR with the Z of the substituentatom, the so-called heavy atom effect, is expected for aSOI-based spin relaxation mechanism. However, we do notexpect a simple relationship between these two quantities,for the following reasons. First of all, although the atomicSO coupling constant is predicted to increase as Z2 basedon simplifying assumptions [39], its actual value varies in acomplex way with Z [40]. Second, the effect of the SOI dueto the substituted atom compared to that from all the otheratoms in the molecule depends on the weight of the wavefunction at the substituent site, and this is molecule specific[20]. To overcome these difficulties, and estimate indepen-dently the strength of the SOI along the series in order torelate it with the eSR rate, we have measured the excitonsinglet to triplet conversion rate, known as the intersystemcrossing rate (kISC), via time-resolved photoluminescence.An estimation of kISC has been possible in Alq3, Gaq3,and Inq3 where singlet and triplet emissions can be bothclearly singled out by time-resolved luminescence measure-ments (details of these measurements are shown in theSupplemental Material [25]). This was not possible in Biq3and in the TES series due to their different optical properties.

The kISC is proportional to the square of the matrixelement of the SOI Hamiltonian between the singlet andtriplet states [41], so kISC can be used as a reliable mea-surement of the strength of the molecular SOI. Thisapproach is solidly founded on the widespread understand-ing of the physics behind the singlet-to-triplet conversion[41–44], and allows us to bypass the fact that the preciseform of the underlying dependence of the eSR on theatomic number of the substituents is unknown.

Figure 3(a) shows the eSR as measured through !SRas a function of kISC, which is proportional to the SOIstrength, in the Xq3 series. It reveals a clear relationshipbetween the eSR and the strength of the SOI. This depen-dence suggests the existence of a SOI-driven mechanismfor spin relaxation. We also plot, in Fig. 3(b) the same eSRdata versus the Z of the substituent atom. The expectedincrease of the eSR with Z is indeed observed in Fig. 3(b).

In the following, we will show that an alternative inter-pretation in terms of a HFI-based mechanism does notprovide a consistent explanation of the observed changeof eSR with Z.Given that the only change we made to the molecule was

the central atom, with the number and location of hydrogenatoms remaining unaltered, there should not be any directeffect of the HFI between the electron and hydrogen in thechanges observed here.An effect of the HFI due to changes to the spin and

nuclear magnetic moment of the central atom is also veryunlikely. Table I shows that the magnitude of the spin andthe nuclear moment of the substituent atoms does notcorrelate with the observed increase of the eSR. Instead,for the case of Alq3 and Gaq3, where the eSR roughlydoubles, both the nuclear moment and spin of Al aresignificantly larger than those of Ga. Finally, one mightargue that changing the central atoms may still bear anindirect effect on the HFI that could influence the observedresults. Changing the mass of an atom in the molecule canimply a change in the bond lengths and angles or, moregenerally, a modification of the energy and population ofvibrational modes. Both of these effects could result in a

0.8

0.6

0.4

0.2

eSR

(M

Hz)

3.53.02.52.01.5

ISC rate (MHz)

Xq3

(a)

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

eSR

(M

Hz)

806040200

Z

Xq3 TES

(b)

FIG. 3 (color online). (a) Electron spin relaxation rate as afunction of the intersystem crossing rate in the Xq3 series at300 K. The electron spin relaxation rate shows a dependence onthe intersystem crossing rate, which is used here as a measure-ment of the strength of the spin-orbit interaction. (b) eSR for theXq3 and TES series as a function of the atomic number of thesubstituent atom, Z.

Magnetic Field (T)

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

Pola

riza

tion

1.61.41.21.00.8

10K 300K

(a)Alq3

1.61.41.21.00.8

Gaq3 (b)1.61.41.21.00.8

Inq3 (c)

1.61.41.21.00.8

Biq3 (d)

FIG. 2 (color online). Muon spin polarization around the ALCs in (a) Alq3, (b) Gaq3, (c) Inq3, and (d) Biq3 at 10 K (blue triangles)and 300 K (red circles). Modelling for these ALCs is indicated by the black lines and is used to determine the electron spin relaxationrate, which is essentially proportional to the amplitude of the ALC curves (see text).

PRL 110, 216602 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending24 MAY 2013

216602-3

Alq3

•  Measure more samples, temperatures, field points, etc. •  Stability of beam over day. Can distort long ALC sweeps.

Nuccio et al. PRL 2013, 110, 216602

Probing Reactivity of Biradical


M1497 Result�LCR Measurement in Solid State�

0.0 0.1 0.2 0.3 0.4 0.5

-0.8

-0.6

-0.4

-0.2

0.0

Biradical Mes*H

Cor

rect

ed In

tegr

al A

sym

met

ry (%

)

Magnetic Field (T)0.5 1.0 1.5 2.0 2.5

-1.5

-1.0

-0.5

0.0

Biradical Mes*H

Cor

rect

ed In

tegr

al A

sym

met

ry (%

)

Magnetic Field (T)

Biradical�

P

P

tBu

H2C

tBu

tBu

tBu

tBu

tBu

tBu

Mes*H�

tBu tBu

tBu

Ito et al. M1497 TRIUMF

Aµ = 46.2(3) MHz

Biradical Mes*H

Probing Reactivity of Biradical


Muonium Addition: DFT Study�

Possible Muonium Addition�

ΔEDFT (Kcal/mol) 0.0� 20.0�

(UBP86-D/TZ2P)�

C-attack� P-attack1�

P

P

tBu

Bn

tBu

tBu

tBu

tBu

tBu

tBuMu

Aµ (MHz)�

P

P

tBu

Bn

tBu

tBu

tBu

tBu

tBu

tBu

MuP

PtBu

Bn

tBu

tBu

tBu

tBu

tBu

tBu

Mu

P-attack2�15.3�

6.4� 394.4� 51.5�

Ito et al. M1497 TRIUMF

Muoniated Probes in Soft Matter


•  Introduce spin label in soft matter system (liquid crystal, polymer)

•  Similar to spin labeling with stable nitroxides except smaller perturbation.

•  Radical sensitive to: •  Orientation of probe •  Polarity of local

environment •  Fluctuations on the ns

to µs timescale

O

O O

O

O O

O O

O O

O O

O O

O

O O

O O

OO

O O

O

O

O O

O O

O O

O O

O

O

O O

MuH

Cosurfactants in Bilayers and Micelles


1.80 1.85 1.90

Cor

rect

ed A

sym

met

ry

Magnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K

1.80 1.85 1.90

Cor

rect

ed A

sym

met

ry

Magnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K278K

288K

1.80 1.85 1.90

Corr

ecte

d A

sym

metr

y

Magnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K

298K

Rotation of micelles

L1Bilayers

LαOH

Mu H

HO

O

O

O

O

HO

O

O

O

O

OH

O

O

O

O

OH

O

O

O

O

1.8 1.9 2.0 2.1

∆0

Cor

rect

ed A

sym

met

ry

Magnetic Field (T)

278 K

283 K

288 K

∆1

293 K

298 K

308 K

O P M O P M

hydrophobic

hydrophilic

L1

C12E4

Lα

Cosurfactants in Bilayers and Micelles


1.80 1.85 1.90

Cor

rect

ed A

sym

met

ry

Magnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K

1.80 1.85 1.90

Cor

rect

ed A

sym

met

ryMagnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K278K

288K

1.80 1.85 1.90

Corr

ecte

d A

sym

metr

y

Magnetic FIeld (T)

308 K

298 K

293 K

288 K

283 K

278 K

298K

Rotation of micelles

L1Bilayers

LαOH

Mu H

HO

O

O

O

O

HO

O

O

O

O

OH

O

O

O

O

OH

O

O

O

O

1.75 1.80 1.85 1.90 1.950.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

MetaPara

0.1 µs

1 µsPolarization

Magnetic Field (T)

10 µs

10 ns

1 ns

τRot

Ortho

Slow rotation of micelle broadens Δ1

Bilayer doesn’t rotate. Rapid uniaxial rotation.

τRot > 10 µs

τRot ~ 0.1 µs

τRot ~ 1 µs

Cholesterolic Liquid Crystal


O

H

H HO

Cholesteryl

nonanoate

McKenzie et al. JPCB 2011, 115, 9360

P/2

Aµ = 441.9 MHz Bres(Δ1) = 1.62 T

UB3LYP/6-31G(d,p)//UPBE0/EPR-II

Aµ = 71.7 MHz Bres(Δ1) = 0.26 T

Cholesterolic Liquid Crystal


1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80

Cor

rect

ed A

sym

met

ry

Magnetic Field / T

382.9 K

376.4 K

368.6 K

363.8 K

357.1 K

349.2 K

40

60

80

100

350 355 360 365 370 375 380 38520

40

60

80

100

Δ1

FW

HM

/ m

TΔ

0 F

WH

M /

mT

Temperature / K

N* I

Isotropic phase Slow isotropic reorientation broadens Δ1

N* phase Wobbling within a

cone averages dipolar hyperfine

coupling Narrows Δ1

ϕc

Discotic Liquid Crystals


X C6H13XC6H13

X

C6H13

X

C6H13

X

C6H13

X

C6H13

1

23

4

4a 12b

5

6

7 8

8a 8b

9 10

11

124b 12a

(b)(a)

25

30

35

40

45

0.5 1.0 1.5 2.0 2.5

-5

-4

-3

-2

-1

0

Asy

mm

etry

[%]

302 K 352 K 332 K 362 K 337 K 372 K 342 K 377 K

Cor

rect

ed A

sym

met

ry [%

]

Magnetic Field [T]25

30

35

40

45

0.5 1.0 1.5 2.0 2.5

-5

-4

-3

-2

-1

0

Asy

mm

etry

[%]

302 K 352 K 332 K 362 K 337 K 372 K 342 K 377 K

Cor

rect

ed A

sym

met

ry [%

]

Magnetic Field [T]

Ap = -35.73 MHz Bres = 2.336 T !"#

Ap = 9.39 MHz Bres = 2.092 T !"#

Ap = 98.37 MHz Bp = -3.17; 0.06; 3.11 MHz

Bres = 1.612 T !"#

Aµ = 399.70 MHz Bµ = -12.87; 0.23; 12.65 MHz

Bres = 1.467 T !$#

(a)$

(b)$

•  Formation of 1D “molecular wires” in Colh and H phases.

•  λe ~ 100’s of µs-1 in Colh and H phases of HHTT. Mechanism unknown.

McKenzie et al. PRE 2013, 87, 012504

Polymer Electrolytes


Load

Electrons Current

Anode Cathode Separator

Solid Polymer Electrolyte

Polyethylene oxide (PEO) or (CH2-CH2-O)n is used as electrolyte in lithium-ion

batteries.

Understanding microscopic dynamics of Li+ in polymer

electrolyte essential to optimize materials.

Li+

Bulk Measurements Versus Local Probes?


(>3 nm) dynamics. Above q! 0:2 !A"1, the scatteringintensities are dominated by the incoherent backgroundfrom the protonated monomers. Therefore, the self-correlation functions of monomers are measured by NSE,in other words, segmental motions of monomers. In thishigh-q region, !R of pure PEO is consistent with thepreviously reported values by Brodeck et al. [20] usingincoherent intermediate scattering techniques, which coverhigher q values (0:2 !A"1 # q # 2:0 !A"1).

While, in NSE, the observed relaxation features arisefrom mixtures of local segmental motions and chainnormal modes, the segmental relaxation behavior wasindependently investigated using dielectric measurements.Dielectric measurements directly couple to both the dipo-lar degrees of freedom and the Li-ion transport in PEO,whose dynamics can be investigated in a wide frequencyand temperature range. For the present work, we havestudied the sample with a PEO:LiTFSI ratio of 10:1 atfrequencies from 1 Hz to 1 GHz and at temperatures from150 to 350 K [19]. Figure 2 shows the " and # relaxationtimes obtained from the fits to the measured dielectricconstant and conductivity data, significantly extendingthe temperature range of the relaxation time data reportedin Ref. [17]. In addition, the dc resistivity $dc, deducedfrom the dielectric measurements, is shown (crosses).It reasonably agrees with the results of the independentlymeasured dc conductivity [19]. In literature, often a closecorrelation of segmental motion and ionic charge transportis assumed [3,17,23]. Thus, the $dcðTÞ plot (right scale ofFig. 2) was scaled to achieve the same number of decadesper cm as for the !ðTÞ plots (left scale) and verticallyshifted to match the !"ðTÞ curve. Obviously, $dcðTÞ and!"ðTÞ exhibit nearly identical temperature dependence.The solid line in Fig. 2 represents a fit of !"ðTÞ withthe phenomenological Vogel-Fulcher-Tammann (VFT)equation [24–26],

! ¼ !0 exp!

DTVF

T " TVF

": (2)

Here !0 is an inverse attempt frequency, D is the so-calledstrength parameter, and TVF is the Vogel-Fulcher tempera-ture. The obtained fit curve (!0 ¼ 3:8' 10"13 s, D ¼ 8:0,and TVF ¼ 177 K) provides a good description of therelaxation-time data and, moreover, a reasonable matchof the dc resistivity data is achieved. Thus, these resultsindicate that the ionic charge transport in PEO-LiTFSI isindeed strongly coupled to the " process (which in poly-mers corresponds to the segmental motion), as also oftenfound for electrolyte solutions and dipolar glass-formingliquids [27] and as also predicted by the Debye-Stokes-Einstein relation. This can be easily rationalized if regard-ing the ionic charge transport as the motion of spheresthrough a viscous medium and if having in mind that it isthe" relaxation that determines the viscosity. However, therigidity of the polymer chain also has to be accounted for as

it was recently shown for a series of PEO-related polymerelectrolytes [28]. Figure 2 also shows the relaxation time!R from the present NSE measurements at the lowestand highest of q values, measured at two temperatures(squares). They are several decades larger than those ofthe segmental " relaxation, fully consistent with theirinterpretation as normal modes. Comparison of theobtained normal-mode time scales with those associatedwith the ionic charge transport at corresponding lengthscales of NSE indicates that this relaxational process isalso correlated with the ionic charge transport in PEO atmacroscopic length scales [19]. The dielectric data alsorevealed the presence of a secondary# process that followsan Arrhenius law with activation energy of 0.29 eV (Fig. 2,open circles and dashed line). In Ref. [23], the # relaxationin PEO:LiTFSI was proposed to arise from the local reor-ientation of the C-O bond dipoles in the polymer chain.However, it should be noted that secondary relaxationsin polymers are also often identified with the so-calledJohari-Goldstein relaxation [29], which was shown to arise

FIG. 2 (color). Arrhenius diagram showing the relaxation timemap (left scale) and the dc resistivity (right scale). The relaxationtime constants fromNSE (squares) are shown for the lowest (upperdata point) and highest values of q (lower point). The " (closedcircles) and # relaxation times (open circles) were determinedfrom fits of the dielectric spectra [19]. The solid line shows a fit ofthe " relaxation time with the VFT equation. The dashed line is afit of !#ðTÞ with an Arrhenius law revealing an energy barrier of0.29 eV. The dc resistivity curve is vertically shifted tomatch the"relaxation times, demonstrating a perfect agreement of the tem-perature dependences of both quantities (note the same decades/cmscaling of both ordinates). The stars denote the relaxation timesreported in thework byMao et al. [10] for anEO=Li ratio of 7:5=1(we show an approximate q-averaged value, read off from thedashed lines in Fig. 3 of Ref. [10]).

PRL 111, 018301 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending5 JULY 2013

018301-3

C. Do et al. PRL. 2013, 111, 018301

•  α-relaxation (main chain motion) and DC conductivity have identical temperature dependence (VFT).

•  Implication is that the α-relaxation plays an important role in long range Li+ transport.

VFT

Arrhenius 28 kJ/mol

β-NMR of Lithium Diffusion in PEO


0.0 0.2 0.4 0.6 0.8 1.05

10

15

20

25

PE

O:L

iTF

A PE

O:L

iOT

f

PE

O:T

FS

I

EA

τ0-1(X)/τ0

-1(PEO:LiTFA)

EA (

kJ m

ol-1)

Ionicity

PE

O

100

101

102

103

τ 0-1(X

)/τ 0-1

(PE

O:L

iTF

A)

3.0 3.5 4.0 4.5 5.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

PEO PEO:LiTFSI PEO:LiOTf PEO:LiTFA

ln(T

1/s)

1000/[T(K)]0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

PEO:LiTFA

200 K 240 K 260 K 272 K 291 K 317 K

Nor

mal

ized

Pol

ariz

atio

n

Time (s)

PEO:LiTFSI

198 K 247 K 317 K

Time (s)

•  Hopping of 8Li+ appears to be an Arrhenius process.

•  Diffusion parameters depend strongly on the ionicity of the lithium salt.

through the z dependence of R. It is only when we restrict thethermal expansion to have one of two discrete values, αm or αg,that a layer model naturally results. The temperature-dependentthermal expansivity of the entire film is then given as

α α α= * + − *z h z h[ ( )]/m g (3)

For a dilatometric measurement of Tg, the temperature is variedand typically the transition is taken as the midpoint where α =(αg + αm)/2. Thus, at the measured dilatometric glasstransition, the system satisfies the condition that z*(T) = h/2. Note that replacing the word expansivity by heat capacitywould allow the same argument to be made for calorimetricmeasurements carried out at the same cooling rate as typicaldilatometric studies.At the thin film glass transition Tg(h), and making use of eq

2,

ξ =−

−−

⎛⎝⎜⎜

⎞⎠⎟⎟h

Tf

T T hR T h2 ( )

(bulk) ( )

( )1 g g

s g (4)

which simplifies to

ξ= +

−− ⎡⎣ ⎤⎦

T h RT R

f h T h( )

(bulk)

1 /2 ( ( ))g s

g s

g (5)

We note that this expression is still completely general, and inorder to calculate Tg(h), we need to specify the function f thatdescribes the spatial extent of the enhanced surface dynamics.We consider the simple example where f decreases exponen-tially as z increases, f(z/ξ(T)) = exp(−z/ξ(T)). We stress thatthe qualitative results obtained here do not depend on thischoice of functional form. Using eq 5, if we include thesimplifying assumption that ξ(T) = ξ0 (i.e., temperature-independent), we can now write an explicit expression forTg(h)

ξ−

− = −T h T

R T h( ) (bulk)

(bulk)1

1 exp( /2 )g g

s g 0 (6)

Figure 2 is a plot of the functional form of eq 6 and showsthat if the rheological temperature of the free surface is higherthan that of the bulk (i.e., Rs − Tg(bulk) > 0), then themeasured glass transition of a thin supported film decreaseswith decreasing film thickness, consistent with the vast majorityof experiments. Figure 2 is notable in that it describes anapparent reduction in the dilatometric Tg value at a particular hvalue even though only a layer with vanishingly small thicknesswould actually have it’s dynamics described by that Tg value.This idea is consistent with the layer-by-layer Tg studies of ref12, though we have not calculated layer-by-layer Tg values fordirect comparisons with those measurements. In other words,the measured Tg value is essentially uncoupled from the filmdynamics. At Tg, a bulk sample would be near equilibrium in itsentirety on the time scale of the experiment, but in our modelat Tg for a thin film, only half of the film is in equilibrium, whilethe remainder is in the glassy state. This demonstrates that thesame dilatometric measure leads to different dynamicalscenarios in thin films and bulk materials.Figure 3 shows data that represents a large body of the

thickness-dependent Tg values in the literature for supportedpolystyrene films.1,3 This data shows a great deal of scatter, andit is not clear that fitting to data with such large scatter is thebest approach. As an alternative, we fit to a subset of Tg data

where the annealing conditions and atmosphere have beencarefully controlled and documented.23 These data are shownas the solid squares in Figure 3. Also shown as lines in thisfigure are calculations based on eq 6 for two cases of ξ(T). Inthe first case (solid line), we use a constant value of ξ0 and Rsand fit the equation to the data to obtain Rs = 435 K and ξ0 =3.6 nm. We can see from Figure 3 that this very simpleapproach provides an excellent description of not only the datafrom ref 23, but the entire body of literature data shown.Despite this agreement, we need to examine other

possibilities. In particular, we have assumed that Rs isindependent of temperature. This means that the relaxationtime of segments at the free surface is independent oftemperature. This is rather unphysical, as there must be someslowing down with decreasing temperature. To obtain a morephysically reasonable temperature-dependent expression for Rsrequires an expression for the temperature-dependentrelaxation time in bulk materials near the bulk Tg value. Sincethere are studies that suggest a high surface mobility in thetemperature range of interest,16,22 a reasonable approach wouldbe to use the bulk Vogel−Fulcher−Tamman (VFT) expressionfor the relaxation times near the bulk Tg to get a temperature-dependent rheological surface temperature. The VFT equationis given by τ ∼ exp[B/(T − T0)], with B the activationtemperature and T0 the Vogel temperature. In the simplest casethat the surface relaxation can be described as a simple activatedprocess14,15 τ ∼ exp(Es/T), where Es is an activation barrier

Figure 2. Normalized change in the glass transition as a function of thenormalized film thickness as given by eq 6.

Figure 3. Tg(h) using the model described in the text with bothconstant (solid line) and variable (dashed line) values for Rs and ξ.Best fit parameters are given in the text.

ACS Macro Letters Letter

dx.doi.org/10.1021/mz4006217 | ACS Macro Lett. 2014, 3, 310−314312

Glass Transition in Polystyrene Thin Films


•  Reduction of Tg for thin, supported PS films

•  Results suggest region near the surface with enhanced dynamics

J.A. Forrest and K. Dalnoki-Veress Adv. Colloid Interface Sci. 2001, 94, 167

Free surface

Bulk

Sub

stra

te

s

h

Evidence for Lower Tg Near the Surface


Neutron reflectometry on 100 nm thick

multilayer film

R. Inoue et al. Phys. Rev. E 2011, 83, 021801

Substrate

355

> 410

365 373 372

1

5 4 3 2

Tg / K

d-PS h-PS d-PS h-PS d-PS

β-NMR of Polystyrene


10 100

0.0

0.2

0.4

0.6

0.8

1.0 317 K 300 K 280 K 240 K

1/T 1av

g (s-1)

Mean Implantation Depth (nm)

Li+

•  Spin relaxation due to torsional motion of phenyl rings.

•  Enhanced dynamics and lower torsional barrier within ~10 nm of free surface.

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Pol

ariz

atio

n

Time (s)

8Li+ pulse Polystyrene Surface 2.5 nm Bulk 79 nm

PEO:LiTFSI Surface 1.9 nm Bulk 49 nm Bulk 69 nm

3.2 3.4 3.6 3.80

1

2

3

4

5

Bulk

ln(T

1avg /s)

1000/[T(K)]

Surface

EA = 0.39(2) eV

EA = 0.25(1) eV

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