Molecular Orientation and Angular Distribution Probed by ...lib3.dss.go.th/fulltext/journal/analytical chemistry/2000/v72no5p... · 888 Analytical Chemistry, Vol. 72, No. 5, March

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Molecular Orientation and Angular DistributionProbed by Angle-Resolved Absorbance and SecondHarmonic Generation

Garth J. Simpson, Sarah G. Westerbuhr, and Kathy L. Rowlen*

Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215

Second harmonic generation (SHG) and angle-resolvedabsorbance with photoacoustic detection were combinedto evaluate both the mean orientation angle and the widthof the angular distribution for two surface-bound molec-ular systems. Assuming a Gaussian distribution function,a physisorbed stilbene dye on fused silica exhibited anarrow distribution centered at 73° with a root-mean-square (rms) width of less than ∼8°. In contrast, acovalently bound azo dye resulted in a broad orientationdistribution (rms width of ∼30°) centered at 60°. It wasalso demonstrated that the combination of nonlinear(SHG) and linear (absorbance) spectroscopic techniquesprovides valuable insight into molecular orientation thata combination of two linear techniques (such as fluores-cence and absorbance) is unable to provide.

The ability of monolayer and multilayer films to dramaticallyalter both the physical and optical properties of surfaces andinterfaces has made them interesting systems to study for bothfundamental and technological reasons.1 Orientation measure-ments of surface-bound molecules provide valuable insight intothe structure of thin films.1,2 From a single spectroscopic orienta-tion measurement, only a single parameter describing the orienta-tion distribution can typically be generated. In some instances,fluorescence measurements alone can yield two orientationparameters, allowing for evaluation of the mean orientation angleand an approximation of the orientational distribution.3-5 Saavedra

and co-workers have employed a combination of absorbance andfluorescence in order to probe two orientation parameters for thinsurface films.6-10 In most spectroscopic studies, however, a narrowdistribution is assumed and a single parameter is used to evaluatethe apparent mean orientation angle. As demonstrated in refs3-10, such an assumption is not always justified. Furthermore,even if the molecular system is highly oriented with respect tothe local surface, surface roughness can broaden the orientationdistribution sufficiently that the assumption of a narrow distribu-tion may not be valid.11-18

A classic example of an instance in which the assumption of anarrow distribution may be misleading is that of absorbancemeasurements for molecular orientation angles equal to the magicangle of 54.7°, which is also the apparent orientation angleobtained from a random distribution. Absorbance measurementsyielding an apparent orientation angle of 54.7° do not allow fordistinction between the case in which every molecule is orientedin a narrow distribution centered at the magic angle and the casein which the molecules are randomly oriented. We have recentlydemonstrated that an equivalent magic angle exists for secondharmonic generation orientation measurements.19 Sufficiently

(1) Ulman, A. An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-Assembly; Academic Press: New York, 1991.

(2) Ulman, A., Ed. Characterization of Organic Thin Films; Butterworth-Heinemann: Boston, 1995.

(3) Bos, J. A.; Kleijn, J. M. Biophys. J. 1995, 68, 2573-2579.(4) Yang, J.; Kleijn, J. M. Biophys. J. 1999, 76, 323-332.(5) Zhia, X.; Kleijn, J. M. Biophys. J. 1997, 72, 2651-2659.

(6) Edmiston, P. L.; Lee, J. E.; Cheng, S.-S.; Saavedra, S. S. J. Am. Chem. Soc.1997, 119, 560-570.

(7) Wood, L. L.; Cheng, S.-S.; Edmiston, P. L.; Saavedra, S. S. J. Am. Chem.Soc. 1997, 119, 561-576.

(8) Edmiston, P. L.; Saavedra, S. S. Biophys. J. 1998, 74, 999-1006.(9) Edmiston, P. L.; Saavedra, S. S. J. Am. Chem. Soc. 1998, 120, 1665-1671.

(10) Edmiston, P. L.; Lee, J. L.; Wood, L. L.; Saavedra, S. S. J. Phys. Chem. 1996,100, 775-784.

(11) Piasecki, D. A.; Wirth, M. J. Langmuir 1994, 10, 1913-1918.(12) Piasecki, D. A.; Wirth, M. J. J. Phys. Chem. 1993, 97, 7700-7705.(13) Wirth, M. J.; Burbage, J. D. J. Phys. Chem. 1992, 96, 9022-9025.(14) Burbage, J. D.; Wirth, M. J. J. Phys. Chem. 1992, 96, 5943-5948.(15) Simpson, G. J.; Rowlen, K. L. J. Phys. Chem. B 1999, 103, 1525-1531.(16) Simpson, G. J.; Rowlen, K. L. J. Phys. Chem. B 1999, 103, 3800-3811.(17) Simpson, G. J.; Rowlen, K. L. Chem. Phys. Lett. 1999, 309, 117-122.(18) Simpson, G. J.; Rowlen, K. L. Chem. Phys. Lett., in press.(19) Simpson, G. J.; Rowlen, K. L. J. Am. Chem. Soc. 1999, 121, 2635-2636.

Anal. Chem. 2000, 72, 887-898

10.1021/ac9912956 CCC: $19.00 © 2000 American Chemical Society Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 887Published on Web 02/01/2000

broad orientation distributions probed by second harmonicgeneration (SHG) will yield apparent orientation angles of 39.2°,regardless of the true distribution mean. Analogous to the magicangle for absorbance, if a single SHG measurement yields theSHG magic angle result, it is impossible to determine whetherthe measurement represents a narrow distribution centeredaround 39.2° or a broad distribution.

It is evident that the width of an orientation distribution canbe as important as the mean orientation angle. Methods that allowfor investigation of both the distribution mean and width aboutthat mean provide a more complete and intuitive description ofmolecular orientation.3-10 In this report, an absorbance technique(angle-resolved absorbance by photoacoustic detection, or ARAPD)is combined with SHG to evaluate the mean molecular orientationangle and the angular distribution about the mean for two distinctmolecular systems. In the following sections, a complete descrip-tion of the necessary mathematical relationships for ARAPD andSHG orientation measurements is presented.

Angle-Resolved Absorbance. ARAPD is a technique devel-oped in our laboratory for submonolayer to multilayer absorbanceorientation measurements at dielectric surfaces.20,21 ARAPD mea-surements rely on the inherent sensitivity of photoacousticdetection to allow for minimal-background absorbance measure-ments with submonolayer detection limits.20 For a moderatelyintense, unfocused pulsed laser beam, as used in these experi-ments, the photoacoustic signal generated arises solely from heatdeposition, and not from high-intensity effects such as electro-striction or ablation. Consequently, a model describing theobserved photoacoustic response of an optically thin sample atthe interface may be formulated by minor modifications of a simplemodel previously presented by Tam et al.22,23 For a photoacousticwave generated from an optically thin sample at the interfacebetween two media (1 and 2) of different thermal and acousticproperties, the photoacoustic amplitude generated in medium 1is given by

in which SPAS,1 is the photoacoustic amplitude within medium 1some distance from the interface, E0 is the incident energy of theexcitation beam (mJ/pulse), θ is the surface coverage (molecules/cm2), σabs is the absorption cross section of the surface dyemolecules (cm2/molecule), and �i, Fi, and Cpi are the thermalexpansion coefficient, density, and heat capacity at constantpressure for medium i, respectively. The derivation of eq 1 fromthe original one-medium model by Tam et al. is provided inAppendix I. For the purposes of this study, the most importantaspect of eq 1 is that the photoacoustic amplitude is directlyproportional the absorption cross section, σabs, which itself is afunction of the molecular orientation and the orientation of theincident electric field polarization.

By varying the orientation of the electric field polarizationvector with respect to the surface and tracking the resulting trendin absorbance (and correspondingly in photoacoustic amplitude),the ensemble-averaged orientation of a particular transition mo-ment may be determined and from that the molecular orientationwithin the surface film. Mathematically, this measurement isdescribed by the following expression:24

where Atot is the sample absorbance, E is the incident electric

field polarization vector with components at the interface per unitincident amplitude of eX, eY, and eZ, f is the transition momentvector, and θfi is the angle between the transition moment vectorand the laboratory i-axis, with the Z-axis directed normal to thesurface. Since expectation values of squared cosines appearfrequently in discussions of angle-resolved absorbance, they areabbreviated by the letter K, with subscripts indicating thecorresponding angle.

If it is assumed for the moment that the probed transitionmoment lies parallel to the long molecular axis (the z′-axis, asshown in Figure 1) of a rodlike molecule, then KfZ may be replacedby Kz′Z. The orientation parameter Kz′Z is experimentally deter-mined from absorbance measurements, and describes the polarangle between the molecular orientation axis (z′) and the surfacenormal (Z). For different internal transition moment orientations(i.e., not parallel with the long molecular axis), analogous relationsbetween KfZ and the orientation angles of the molecular axes havebeen previously derived.16,24 Combining the law of cosines (whichstates that Kz′X + Kz′Y + Kz′Z ) 1) with the relation Kz′X ) Kz′Y

(true for a random distribution within the surface plane), theabsorbance expression in eq 2 can be rewritten:

The electric field components at the interface are generated by(20) Doughty, S. K.; Rowlen, K. L. J. Phys. Chem. 1995, 99, 2143-2150.(21) Doughty, S. K.; Simpson, G. J.; Rowlen, K. L. J. Am. Chem. Soc. 1998,

120, 7997-7998.(22) Hutchins, D. A.; Tam, A. C. IEEE Trans. Ultrason., Ferroelectr., Freq. Control

1986. UFFC-33, 429-449.(23) Patel, C. K. N.; Tam, A. C. Rev. Mod. Phys. 1981, 53, 517-550.

(24) Michl, J.; Thulstrup, E. K. Spectroscopy with Polarized Light: Solute Alignmentby Photoselection, in Liquid Crystals, Polymers, and Membranes; VCHPublishers Inc.: New York, 1995; Chapter 5.

SPAS,1 ∝ (E0θσabs)�1

F1(c1F1Cp1 + c2F2Cp2)(1)

Figure 1. Definitions of relevant axes and angles. The molecularorientation angle, θz′Z is the angle between the molecular long axis(z′) and the surface normal (lab Z-axis). The polarization rotation angleof the incident beam, γ, is defined such that γ ) 0° is p-polarizedand γ ) 90° is s-polarized.

Atot ) ⟨(E‚f)2⟩ ) |f|2|E|2[|eX|2KfX + |eY|2KfY + |eZ|2KfZ] (2)

Kfi ≡ ⟨cos2 θfi⟩ (3)

Atot ∝ |eX|2 + |eY|2 + Kz′Z(2|eZ|2 - |eX|2 - |eY|2) (4)

888 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

projection of the incident electric field onto the surface coordinatesystem, with Fresnel correction factors accounting for reflectionand refraction at the interface:

where ϑI is the angle of incidence with respect to the surfacenormal, γ is the polarization rotation angle (γ ) 0° for p-polarizedlight, γ ) ( 90° for s-polarized light), and Lω

ii are Fresnel factorsthat describe the electric field components at the interface perunit field directed along the i-axis. Explicit expressions for theFresnel factors are presented in Appendix III for the total internalreflection cell used in these investigations.

As can be seen in eq 5, there are two simple approaches foraltering the electric field at the interface: (1) vary the angle ofincidence for p-polarized light (γ ) 0°), or (2) rotate the plane ofpolarization for a fixed angle of incidence. For the latter approachwith a constant angle of incidence, eq 4 can be rewritten:

or

where the factors ai describe the electric field intensities of eachcomponent at the interface neglecting the dependence on thepolarization rotation angle (e.g., aX ) |cosϑILXX

ω |2). Since thefitting coefficients, ai, are all known constants for a particularsystem and geometry, a fit of absorbance as a function ofpolarization rotation angle yields the value of the orientationparameter, Kz′Z. The experimentally determined orientation pa-rameter is, in turn, related to the molecular orientation angle, θz′Z,by an ensemble average of cos2θz′Z:

where P(θz′Z) is the distribution function for θz′Z and N is anormalization constant. If the orientation distribution is sufficientlynarrow, such that a δ-function may be assumed for P(θz′Z), themean orientation angle may be approximated as follows:

where ⟨θz′Z⟩ is the apparent molecular orientation angle, calculatedif a narrow orientation distribution is assumed.

Second Harmonic Generation. SHG is the frequency dou-bling of light and, within the electric dipole approximation for light,is symmetry forbidden in random media but allowed for molecules

oriented at the interface between two such media. Molecularorientation may be evaluated from measurements of the intensityand polarization of the second harmonic light generated undervarious polarization conditions of the fundamental beam. Inter-pretation of the experimental data is simplified considerably if onlyone molecular hyperpolarizability tensor element is dominant(which is often the case) and both the fundamental and secondharmonic frequencies are far from a molecular resonance (suchthat Kleinman symmetry may be assumed25).

The intensity of the second harmonic light generated at aninterface, I2ω, is given by the following relation:26

in which the superscripts ω and 2ω indicate parameters evaluatedfor either the fundamental frequency or the second harmonic,respectively, ϑ2ω is the angle between the surface normal and thepropagation direction of the second harmonic, c is the speed oflight, ω is the angular frequency of light, eω is a vector describingthe fundamental electric field amplitude at the interface, e2ω

describes the polarization state of the second harmonic, and �(2)

is the third-ranked, second-order nonlinear polarizability tensor.For SHG measurements with a molecular orientation distributionthat is isotropic within the surface plane (consistent with mostexperiments), there are only three nonzero independent tensorelements: �ZZZ, �ZXX, and �XXZ.26-28

The s- and p-polarized components of the second harmonicintensity are typically measured independently, with the relation-ship between the measured intensities and the three independenttensor elements given by the following expressions:26,28

where Is and Ip are the measured s- and p-polarized secondharmonic intensities, respectively, and the si are fitting coefficientsthat depend on both the fundamental and second harmonic electricfields at the interface. Details of the fitting procedure used aredescribed in Appendix II. Explicit expressions for the fittingcoefficients for SHG measurements in the total internal reflectiongeometry of this study are provided in Appendix III, includingboth the linear and nonlinear Fresnel correction factors forreflection and refraction.

Once relative values of the surface hyperpolarizability tensorelements have been obtained from fits of the experimental datato eqs 10 and 11, the SHG orientation parameter, Dz′Z, may beevaluated. For rodlike molecules, Dz′Z is given by27,29

(25) Kleinman, D. A. Phys. Rev. 1962, 126, 1977-1979.(26) Corn, R. M.; Higgins, D. A. Chem. Rev. 1994, 94, 107-125.(27) Heinz, T. F. Nonlinear Surface Electromagnetic Phenomena; North-Hol-

land: New York, 1991; pp 354-416.(28) Dick, B.; Gierulski, A.; Marowsky, G.; Reider, G. A. Appl. Phys. B 1985,

38, 107-116.(29) Dick, B. Chem. Phys. 1985, 96, 199-215.

|eX|2 ) |cos ϑI cosγLXXω |2 (5a)

|eY|2 ) |sin γLYYω |2 (5b)

|eZ|2 ) |sin ϑI cos γLZZω |2 (5c)

Atot ∝ aX cos2 γ + aY sin2 γ + Kz′Z(2aZ cos2 γ -

aX cos2 γ - aY sin2 γ) (6a)

Atot ∝ aX + (aY - aX) sin2 γ + Kz′Z[sin2 γ(2aZ - aX +

aY) + aX - 2aZ] (6b)

Kz′Z ) ⟨cos2 θz′Z⟩ ) N ∫0

πcos2 θz′Z P(θz′Z) sinθz′Zdθz′Z (7)

Kz′Z ) ⟨cos2 θz′Z⟩ ≈ cos2⟨θz′Z⟩ (8)

I2ω ) 32π3ω2 sec2ϑ

2ω

c3 |e2ω‚�(2):eωeω|2(Iω)2 (9)

Is ) C|s1 sin2γω�XXZ|2(Iω)2 (10)

Ip ) C|s5�ZXX + cos2 γω(s2�XXZ + s3�ZXX + s4�ZZZ - s5�ZXX)|2

(Iω)2 (11)

Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 889

Analogous to the absorbance orientation parameter, Kz′Z, theSHG orientation parameter depends on the angle between themolecular long axis (z′) and the surface normal (Z) throughaverages of cosine functions. Furthermore, for narrow molecularorientation distributions in which a δ-function probability distribu-tion is reasonably accurate, the orientation parameters measuredby SHG and ARAPD (Dz′Z and Kz′Z, respectively) should beidentical.

In cases for which the orientation distribution is not well-represented by a δ-function, the two orientation parameters maybe significantly different. Combining SHG and ARAPD measure-ments of the same system under the same conditions allows fora convenient test of the narrow distribution assumption: if thedistribution is sufficiently narrow, both measurements will yieldidentical results for the two orientation parameters, if not, boththe mean and width of the distribution may be determined.

EXPERIMENTAL SECTIONARAPD experiments were conducted using the third harmonic

(355 nm) of a Q-switched Nd:YAG laser (Spectra Physics GCR-11). After separation of the third harmonic using appropriatedichroic mirrors, the 355 nm beam was passed through a quartzwindow, an aperature, a Glan laser prism, a stepper motor-controlled half-wave plate, and the total internal reflection cell (seeFigure 2a). A portion of the 355 nm beam reflected off the quartzwindow was directed toward a photodoide to record the beamintensity during data acquisition. The total internal reflection flowcell (shown in Figure 2c) consisted of 50 μm thick Teflon spacer(Dupont FEP, 200CLZ) sandwiched between a fused-silica prism(Melles-Griot or Esco, S1-UV) and a UV-grade fused-silica micro-scope slide (Esco). Two holes in the microscope slide allow forthe flow of solvent through the cell for acoustic coupling. Apiezoelectric transducer (Panametrics) was coupled to the micro-scope slide and spatially offset from the spot of total internalreflection to temporally separate the photoacoustic wave fromartifacts due to scattered light. After signal amplification, theacoustic waveforms were signal averaged on an oscilloscope, andthe amplitude was transferred to a personal computer as a functionof the excitation beam polarization rotation angle.

SHG data were acquired using the same flow cell as for theARAPD investigations. The Nd:YAG fundamental (1064 nm) waspassed through a visible-blocking filter, a quartz window, anaperature, a Glan laser prism, a stepper motor-controlled half-wave plate, a focusing lens, and the TIR flow cell. After the flowcell, the second harmonic beam was directed through an IR-blocking filter, a dichroic sheet polarizer, and a 532 nm interfer-ence filter and finally to a photomultiplier tube (PMT), shown inFigure 2b. The signal-averaged PMT response was recorded onan oscilloscope and the amplitude transferred to a personalcomputer as a function of the fundamental beam polarizationrotation angle for both s- and p-polarized second harmonic

intensities. As with the ARAPD measurements, the incident beamintensity was recorded in conjunction with the signal intensity byreflecting a portion of the fundamental off a quartz window ontoa photodiode. All reported SHG data have been normalized forthe fundamental intensity.

Surface films of 1-docosyl-4-(4-hydroxystyrl)pyridinium bro-mide (DPB, Aldrich) were prepared by dipping a substrate into achloroform (Fisher, Optima grade) solution of the dye. Prior tofilm formation, substrates were cleaned by sequential sonicationin acetone, chloroform, and methanol, followed by drying undernitrogen. The substrates were further cleaned and hydroxylatedby subsequent immersion for 5 min in a freshly prepared hot“piranha” solution (three parts 30% hydrogen peroxide, seven partsconcentrated sulfuric acid, heated until oxygen bubbles freelyform), followed by thorough rinsing in 18.2 MΩ filtered water,and drying under nitrogen. The substrates were then immersedin the dye solutions for 3 min prior to slow removal (nodependence of the film thickness on dip time was observed).Ellipsometric thicknesses (AutoEL ellipsometer, Rudolph Re-search) of the DPB films were acquired on dipped silicon wafers,assuming a monolayer refractive index of 1.5 (appropriate for aprimarily aliphatic monolayer1). DPB monolayer films for theARAPD and SHG investigations were prepared directly on theTIR prism surface, with dye removed from the non total internalreflection (non-TIR) surfaces by wiping with a methanol-soakedKimwipe. Monolayer formation was confirmed both by theellipsometric thickness measurements and by UV-visible spectraof dipped quartz flats, indicating the presence of the dye (acquiredwith a Hewlett-Packard 8452A diode array spectrometer). TheDPB monolayer films were analyzed in contact with pure hexanes(Fisher, Optima grade) and saturated DPB in hexanes in the flow

Dz′Z ≡ ⟨cos3 θz’Z⟩⟨cos θz′Z⟩

)�ZZZ

�ZZZ + 2�ZXX(12)

Kz′Z ≈ Dz′Z ≈ cos2⟨θz′Z⟩ (13)

Figure 2. Experimental apparatus. (a) Schematic of the ARAPDapparatus: DM, dichroic mirror; PD, photodiode; QF, quartz flat; GLP,Glan laser prism; HWP, half-wave plate; (b) Schematic of the SHGapparatus: V, visible blocking filter; L, lens (20 cm focal length); IR,infrared blocking filter; P, polarizer (dichroic sheet); IF, 532 nminterference filter; PMT, photomultiplier tube. (c) Blowup of the totalinternal reflection flow cell. The cell consists of a 50 μm thick Teflonspacer sandwiched between a quartz prism and a quartz microscopeslide. The piezoelectric transducer attached to the quartz slide isacoustically coupled to the prism by the solvent in the flow cell.


cell. A small signal loss was observed during data acquisition usingpure hexanes, probably due to either photochemical effects orsurface desorption, but no change in orientation resulted.

Monolayers of 4-(dimethylamino)azobenzene were covalentlybound to the fused-silica total internal reflection prisms (MellesGriot or Esco, S1-UV). Prior to derivatization, the substrates werecleaned and hydroxylated using the same procedure as for theDPB substrates. For the first reaction step, the substrates wererefluxed for 2 h in a solution of dry toluene (certified ACS, FisherScientific), 0.05 M pyridine (certified ACS, Fisher Scientific) and0.02 M (3-aminopropyl)dimethylethoxysilane (Gelest). The sub-strates were then rinsed in toluene, sonicated in acetone, chlo-roform, and methanol, and dried under a flow of nitrogen. Forthe second reaction step, the substrates were placed in a solutionof dry toluene, 0.075 M N,N-diisopropylethylamine (99.5%, Ald-rich), and 0.8 mM 4-(dimethylamino)azobenzene-4′-sulfonyl chlo-ride (Fluka Chemie) at room temperature with stirring overnight.Following the reaction, the substrates were rinsed in toluene andchloroform, sonicated in acetone, chloroform, and methanol, anddried under a flow of nitrogen. To prepare the azo dye in solution,the same reaction procedure was used except the dye was reactedwith a 0.030 M propylamine (99+%, Aldrich) solution in toluenerather than the aminated surface. Water contact angles weremeasured before and after surface reaction on a home-builtrotating stage with droplet images acquired by an optical micro-scope coupled to a CCD digitizing camera. Ellipsometric thicknessmeasurements and UV-visible measurements were made usingthe same instruments as previously described. The organic layerwas removed from the non-TIR faces of the prisms by droppinghot pirahna solution onto the horizontally positioned surfaces andallowing the pirahna to react for 15 min, followed by thoroughrinsing with water and drying under a flow of nitrogen.

Molecular modeling calculations for both DPB and the azo dyewere performed using Hyperchem (Hypercube, release 4) withgeometry optimization performed using the AM1 semiempiricalmethod, and electronic structure calculations performed with theZINDO/S method.

RESULTS AND DISCUSSIONTo extract meaningful orientation information using a TIR

geometry, the influence of reflection and refraction at both theentrance and exit prism surfaces, as well as the amplitudes of theelectric field components at the total internal reflection interface,must be known and accurate. Theoretical curves for the expectedangle-resolved photoacoustic response for several different mo-lecular orientations accounting for these effects are shown inFigure 3. The curves were generated using eq 6 with the Fresnelfactors and fitting coefficients described in Appendix III. Forsurface-bound molecules with small orientation angles (alignednearly parallel with the surface normal), the maximum photoa-coustic amplitude is expected for p-polarized excitation (γ ) 0°)with a minimum for s-polarized excitation. For molecules withlarge orientation angles (aligned nearly parallel with the surfaceplane), the exact opposite trend is observed.

For a polarization rotation angle near 55°, all molecularorientations yield the same photoacoustic response. This polariza-tion angle is the equivalent of the absorbance magic angle aftercorrecting for reflection, refraction, and total internal reflectionsurface fields. The polarization rotation angle yielding orientation-

independent absorbance, γ*, will be the value of γ for which thecoefficient of Kz′Z in eq 6 is equal to zero.

For an experimental geometry with hexanes flowing through theTIR cell and a fused-silica prism, orientation-independent absor-bance is achieved for a polarization rotation angle of 54.73°. Thefact that the calculated value of γ* is nearly identical to the magicangle of 54.74° is coincidental, since γ* will vary significantly withthe refractive index of both the prism and the acoustic couplingliquid.

Case 1. Physisorbed Stilbene Dye Films. The adsorptionisotherm for DPB stilbene dye films is shown in Figure 4, alongwith the chemical structure of the dye. Isotherm data wereacquired by dipping substrates in varying concentrations of DPBin chloroform and recording the film thickness measured byellipsometry. The film thickness reaches a maximum value of ∼12Å for concentrations in excess of 10-4 M DPB, corresponding tocompleted monolayer formation. Assuming the DPB moleculesmay be treated as rigid, tightly packed, rodlike molecules 35 Å

Figure 3. Theoretical ARAPD response curves accounting forreflection and refraction, including both real and imaginary contribu-tions to the electric fields at the total internal reflection interface. Thedashed line indicates the theoretical response for a molecularorientation normal to the surface, with each solid curve correspondingto a 10° increment in orientation angle. The dotted curve is theresponse expected from an unoriented system.

Figure 4. Adsorption isotherm for DPB films prepared by substratedipping. The solid line is a Langmuir fit to the data, yielding a ΔG foradsorption of -3.2 kJ/mol. For an asymptotic monolayer film thicknessof ∼12 Å and a molecular length for DPB of ∼35 Å, treating the DPBmolecule as a rigid rod suggests an orientation angle of ∼70°.

sin2 γ* ) (2aZ - aX)/(2aZ - aX + aY) (14)


in length, a film thickness of 12 Å corresponds to a geometricmolecular tilt angle of ∼70°.

UV-visible absorbance spectra are shown in Figure 5 for DPBboth on a quartz slide dipped in 8 × 10-5 M DPB and in a dilutechloroform solution (10-5 M). A noticeable blue-shift is observedin the absorbance spectrum of the surface-bound film (∼25 nm),most likely related to the change in environment in going from anonpolar solvent to a polar surface. On the basis of the integratedabsorbance of the DPB film (Figure 5) in combination with theellipsometry results (Figure 4), dipping in ∼10-4 M DPB yields asurface coverage for the completed monolayer of ∼9 × 1013

molecules/cm2.The transition dipole moment and hyperpolarizability for DPB

were evaluated using ZINDO/S electronic structure calculationsin Hyperchem. The transition moment excited at 355 nm liesparallel with the long molecular axis. Additionally, the 355 nmlong-axis transition has both the largest oscillator strength andthe lowest frequency, suggesting the hyperpolarizability at 1064nm will be dominated by its influence. For a two-state model, thehyperpolarizability depends on the transition moment orientationand the change in permanent dipole between the ground andexcited states (see Appendix II.), both of which are calculated tobe parallel with the molecular z′-axis. Therefore, a dominant �z′z′z′

hyperpolarizability tensor element is expected for 1064 nmfundamental excitation. On the basis of these modeling results,KfZ ) Kz′Z as per the assumption made in eq 4, and Dz′Z ) �ZZZ/(�ZZZ + 2�ZXX) consistent with eq 12.

The angle-resolved absorbance for monolayer films of DPBacquired using the TIR cell is shown in the lower curve of Figure6. Monolayer films were prepared by dipping the total internalreflection prism in 10-4 M DPB/CHCl3. The TIR cell wassubsequently filled and maintained with hexanes in order tofacilitate acoustic coupling to the piezoelectric transducer. Al-though DPB is only marginally soluble in hexanes, gradualdissolution of the surface-bound DPB into the hexanes wasobserved. The loss rate was significantly less than the timerequired for data acquisition, and the loss did not result in adetectable change in molecular orientation over time. From theARAPD measurements, the orientation parameter, Kz′Z, was foundto be equal to 0.09 ( 0.04 (see Table 1). If a narrow orientation

distribution is assumed, the apparent orientation angle as ex-pressed in eq 8 is equal to 73 ( 3°. The apparent orientation angleof the chromophore obtained by ARAPD is remarkably close tothe calculated ellipsometry result of ∼70°.

In an attempt to minimize signal losses due to DPB solvationin hexanes, separate ARAPD measurements were conducted usinga saturated solution of DPB in hexanes as the acoustic couplingmedium. However, the photoacoustic response did not stabilizeunless the surface remained in contact with the flowing hexanessolution for at least 1 h. ARAPD results acquired after the signalstabilized are shown in the topmost curve in Figure 6. In this case,an orientation parameter of Kz′Z ) 0.36 ( 0.01 was obtained,significantly different from that obtained from the monolayersample. If a narrow distribution is assumed, the correspondingmean orientation angle is 53.2° ( 0.9°. Visual inspection of theTIR prism surface after contact with the DPB-saturated hexanesindicated that surface agglomeration of DPB particulates hadoccurred. In this set of investigations, the ARAPD responsemeasured after prolonged contact with DPB-saturated hexanesis dominated by a randomly oriented particulate overlayer (ormultilayer). Note that the apparent orientation angle measuredby ARAPD of the particulate DPB is within 1.5° of the expectedmagic angle response obtained for an unoriented system (cf. 53.2°with 54.7°). This latter finding confirms the expressions used todetermine the electric field amplitudes at the interface yield resultsconsistent with expectations.

Second harmonic intensities for the DPB monolayer samplesare shown in Figure 7a, while those of DPB multilayers are shownin Figure 7b. From theoretical fits of the s-polarized curves (usingthe fitting coefficients described in Appendix III), the value of theexperimental constant, C, was evaluated by setting �XXZ arbitrarilyequal to unity and fitting the data to eq 10. The relative values of�ZXX and �ZZZ, normalized to �XXZ, were then obtained by fitting

Figure 5. UV-visible absorbance spectra for DPB: monolayer filmdipped in 8 × 10-4 M DPB (solid line), and 10-5 M DPB in chloroform(dashed line). The monolayer absorbance has been multiplied by 50for comparative purposes.

Figure 6. Averaged, normalized angle-resolved photoacousticamplitudes acquired for both monolayer films of DPB (solid triangles,16 measurements) and multilayer films consisting of a monolayer filmwith surface-aggregated DPB particulates (open circles, 16 measure-ments). The solid lines are fits to the data using eq 6b with the fittingcoefficients given in Appendix III. A representative error bar ((1σ) isprovided on each curve.


the p-polarized curve to eq 11 (or more precisely, eq AII.2) usingthe same constant, C. Because only the magnitude of �XXZ isretained from a fit of the s-polarized curve, the p-polarized dataare fit equally well by �XXZ and �ZXX having both like and oppositesigns, leading to two possible values for �ZZZ. Therefore, two setsof possible tensor elements are generated from a single measure-ment. Since �XXZ and �ZXX are expected to be of like sign andcomparable magnitude for a dominant �z′z′z′ (see Appendix II),orientation parameters and angles are reported only for the caseof �XXZ ) +1. It is worth noting that the values of �ZXX normalizedto �XXZ are within experimental error of unity for both mono- andmultilayer DPB films (see Table 2). Equality between these twotensor elements is predicted theoretically for molecular systemsdominated by a �z′z′z′ hyperpolarizability tensor element (see eqAII.5). This relationship between the tensor elements supportstwo important aspects of the experiments; first, calculationsindicating a dominant �z′z′z′ for DPB appear to be reliable, andsecond, the expressions used to describe the both the fundamentaland second harmonic electric fields at the interface are reasonablyaccurate. If either one of these experimental considerations was

in fact inaccurate, a different ratio between the two tensor elementswould likely result.

In contrast to the ARAPD results, little difference is observedin the SHG response for the monolayer and multilayer films. Fitsof the monolayer data yield an orientation parameter of Dz′Z )0.08 ( 0.02, indicating a mean orientation angle of 73 ( 2° if anarrow distribution is assumed. For the multilayer data, theextracted orientation parameter is Dz′Z ) 0.11 ( 0.03, correspond-ing to an orientation angle of 70 ( 3° for a narrow distribution. Inboth the monolayer and multilayer SHG orientation measure-ments, the narrow-distribution orientation angle is within errorof the experimental ARAPD result, and again very close to theorientation angle predicted by the geometric film thickness.

The striking contrast in the behavior of the ARAPD and SHGdata for the monolayer and multilayer regimes is an excellentexample of the unique information available from a combinationof nonlinear and linear spectroscopic techniques. ARAPD mea-surements are sensitive to absorbance from all DPB within thepenetration depth of the evanescent field. Consequently, forparticulates that adsorb to the surface (over the oriented mono-layer), the signal response is dominated by the particulates ratherthan the monolayer film. In contrast, SHG arises only fromnoncentrosymmetrically oriented molecules. Adsorption of cen-trosymmetric, randomly oriented DPB particulates does not leadto coherent surface SHG, and the SHG response is still dominatedby the nonlinear properties of the oriented surface layer. There-fore, while the ARAPD results are greatly influenced by thepresence of the DPB particulates, no significant change isobserved in the molecular orientation measured by SHG. Acombination of absorbance and fluorescence would have yieldedthe unoriented response, with no surface specific information.

Case 2. Covalently Bound Azo Dye Films. Covalent attach-ment of the azo dye (see Figure 9) to the fused-silica surface wasconfirmed by water contact angle, ellipsometry, and UV-visiblespectroscopy measurements. Upon reaction, the water contactangle changed from a value below detection (complete surfacewetting) to a value of 60 ( 5°, indicating a significant alterationin surface hydrophobicity. Ellipsometry measurements at eachstep of the reaction indicate a film thickness of 5.0 ( 0.9 Å afterthe first reaction step with the monofunctional aminosilane and6.2 ( 0.8 Å after surface attachment of the azo dye. Based on the1.2 Å increase in film thickness, and an estimated length for thedye of 14 Å, the ellipsometry results suggest a surface coverageof ∼9% of a monolayer. Surface coverage can also be estimatedfrom the UV-visible absorbance of the surface film prepared ona quartz window. Using the azo dye molar absorptivity and themeasured film absorbance (shown in Figure 8), the surfacecoverage of the dye was estimated to be 2.2 × 1013 mlcls/cm2,

Figure 7. Averaged, normalized SHG results acquired for bothmonolayer films of DPB (a, four measurements) and multilayer filmsconsisting of a monolayer film with surface-accumulated DPB (b, ninemeasurements). The solid lines are fits to the data using eqs 12 and13 for the s-polarized (open circles) and p-polarized (solid triangles)second harmonics, respectively, with the fitting coefficients given inAppendix III. A representative error bar ((1σ) is provided on eachcurve.

Table 1. ARAPD Results for the DPB and Azo DyeFilmsa

DPB monolayer(N ) 16)

DPB multilayer(N ) 16)

azo dye(N ) 7)

Kz′Z 0.09 ( 0.04 0.36 ( 0.01 0.27 ( 0.03θz′Zb 73 ( 3° 53.2 ( 0.9° 58 ( 2°a N equals the number of measurements made, errors are standard

deviation. b Apparent orientation angle calculated by assuming a narroworientation distribution.


which corresponds to ∼8% of a monolayer assuming an ap-proximate molecular area of 37 Å2. From both the ellipsometryand absorbance measurements, it may be concluded that thereaction procedure generates submonolayer coverages (∼1/10 ofa monolayer) of the azo dye.

ARAPD results for the covalently bound azo dye chromophoreare shown in Figure 9 and summarized in Table 1. SHG curvesfor the same system are shown in Figure 10. During ARAPD dataacquisition, the signal was observed to decay significantly overtime (representative raw data are shown in the inset plot of Figure9). Experimental evidence implicates cleavage of the N-S bondas the likely photochemical loss mechanism. Orientation valueswere obtained from the raw ARAPD data by fitting to a functionincorporating an exponential decay to a constant as well as thepolarization dependent absorbance described in eq 6. No signalloss was observed over time during SHG data acquisition, as nolight was absorbed by the azo dye molecules.

Molecular modeling calculations indicate that, similar to theDPB stilbene dye, both the transition moment of the azo dyeexcited at 355 nm and the dominant hyperpolarizability tensorelement (�z′z′z′) for a 1064 nm fundamental wavelength are directedparallel with the long molecular axis. Accordingly, the molecularorientation of the azo dye can be evaluated using the samerelations as used for DPB [i.e., KfZ ) Kz′Z and Dz′Z ) �ZZZ/(�ZZZ +2�ZXX)]. As with DPB, a dominant �z′z′z′ is supported by anexperimental ratio of �ZXX/�XXZ within error of unity (see Table2). ARAPD measurements of the azo dye long-axis orientationyield an orientation parameter of Kz′Z ) 0.27 ( 0.03 or an apparentmolecular tilt angle of 59 ( 2° if a narrow distribution is assumed.

SHG measurements yield an orientation parameter of Dz′Z ) 0.48( 0.03, corresponding to an apparent tilt angle of 46 ( 2°. Theinconsistency in apparent molecular tilt angles implies that theassumption of a narrow angular distribution is not valid.

Combining SHG and ARAPD Results. If the assumption ofa narrow molecular orientation distribution is relaxed and aGaussian distribution is assumed,6-10 a single measurement is nolonger sufficient to determine both the mean and the width ofthe angular distribution. This ambiguity can be removed bycombining both ARAPD and SHG measurements of the samemolecular system. As shown in Figure 11, for a Gaussiandistribution there is range of possible solutions satisfying a singlemeasurement, with one extreme being an infinitely narrowdistribution and the other a potentially broad distribution. Thepoint at which the ARAPD and SHG curves cross indicates thedistribution width and mean which are consistent with bothmeasured orientation parameters (shown in Figure 11a for DPB

Table 2. SHG Results for the DPB and Azo Dye Filmsa

DPB monolayer (N ) 4) DPB multilayer (N ) 9) azo dye (N ) 6)

�XXZ 1 -1 1 -1 1 -1�ZXX 0.98 ( 0.08 0.98 ( 0.08 1.05 ( 0.09 1.05 ( 0.09 1.1 ( 0.2 1.1 ( 0.2�ZZZ 0.16 ( 0.12 0.3 ( 0.1 0.31 ( 0.06 0.40 ( 0.06 1.9 ( 0.4 2.39 ( 0.4Dz′Z 0.08 ( 0.02 0.11 ( 0.03 0.48 ( 0.03θz′Zb 73 ( 2° 70 ( 3° 46 ( 2°

a N equals the number of measurements made, errors are standard deviation. b Apparent orientation angle calculated by assuming a narroworientation distribution.

Figure 8. UV-visible absorbance spectra for the azo dye: sub-monolayer film prepared by surface reaction (solid line) and an 8 ×10-4 M solution in toluene (dashed line). The monolayer absorbancehas been multiplied by 50 for comparative purposes.

Figure 9. Corrected, averaged ARAPD results acquired for thesurface-bound azo dye (chemical structure shown in the figure, sevenmeasurements). During ARAPD data acquisition, the signal wasobserved to decay significantly over time (representative raw dataare shown in the inset plot). Orientation measurements were madeusing the raw ARAPD data, fit to a function incorporating both anexponential decay to a constant and the polarization dependentabsorbance (shown by the solid line in the inset plot). In the mainfigure itself, averaged, normalized data are shown for comparativepurposes after correcting for only the time-dependent signal loss. Thesolid line is a fit to the corrected data using eq 6b with the fittingcoefficients given in Appendix III. A representative error bar ((1σ) isprovided on the upper curve.


and Figure 11b for the azo dye). This crossover point is thegraphical equivalent of solving two equations with two unknowns.For DPB films, the two spectroscopic measurements yield almostidentical orientation parameters, within experimental error of eachother in the limit of a narrow orientation distribution. Based onthe magnitudes of the experimental errors, it may be concluded

that the orientation distribution for the DPB monolayers iscentered around 73° with a distribution width of less than ∼8°(i.e., the width at which the experimental errors no longeroverlap). In contrast, the azo dye yields a Gaussian distributionmean of 57° with a root-mean-square (rms) width of 30°. Thedistribution is shown the inset of Figure 11b. Although theassumption of a narrow distribution has been proven accurate forthe case of DPB, it fails to reliably describe the orientationdistribution for the azo dye.

A possible explanation for the significant difference in distribu-tion widths for DPB and the azo dye system may be proposed byconsidering the likely orienting interactions in the two cases. Forthe azo dye films, dye molecules are covalently attached at specificlocations for a surface coverage of less than 1/10 of a monolayer,suggesting that the predominant orienting interactions are thoseof the isolated chromophore. By inspection of the surface-boundstructure of the azo dye, free rotation about the propyl chain nearthe base of the chromophore may allow for a wide range of motionof the chromophore itself. It is reasonable to propose that thiswide range of motion leads to a broad range of accessiblechromophore orientations for the azo dye. In contrast, thedominating orienting forces for the DPB surface films are mostlikely a combination of intermolecular interactions between thechromophores and interactions between the long aliphatic hydro-carbon chains. Assembly of neighboring molecules into highlyordered structures would naturally lead to a high degree ofchromophore order as well, and a corresponding narrow orienta-tion distribution.

On the basis of the azo dye and DPB results, it is tempting tosuggest general guidelines for cases in which the assumption ofa narrow distribution is expected to be reasonable and cases inwhich it will most likely fail. For molecular surface systems inwhich the orientation is dominated by intermolecular interactionsto form ordered assemblies, including long-chain trifunctionalsilane self-assembled monolayers and tightly packed Langmuirand Langmuir-Blodgett films, the distribution in orientationangles in the fully assembled monolayer film may be reasonablyassumed to be narrow. In contrast, the assumption of a narrowdistribution may be quite poor for monolayer systems in whichorientation is dominated by local interactions, particularly if arange of orientations is accessible through intramolecular reori-entation.

In summary, SHG and ARAPD measurements were combinedto measure molecular orientation in a total internal reflection flowcell. From a single measurement, an infinite number of possibleorientation distributions could be generated to satisfy the indi-vidual orientation parameters, ranging from narrow distributionsto fairly broad distributions. However, by combining the twolinearly independent measurements, both the mean orientationangle and the angular distribution can be evaluated. Two molec-ular systems were investigated, one of which was demonstratedto possess a narrow orientation distribution (rms width of lessthan ∼8°) and another a fairly broad distribution (rms width of30°). Differences in the structure of the surface films wereproposed to account for the significant difference in the angulardistributions of the two systems.

Figure 10. Averaged, normalized SHG results acquired for filmsof the azo dye (six measurements). The solid lines are fits to the datausing eqs 12 and 13 for the s-polarized (open circles) and p-polarized(solid triangles) second harmonics, respectively, with the fittingcoefficients given in Appendix III. A representative error bar ((1σ) isprovided on each curve.

Figure 11. SHG and ARAPD molecular orientation measurementscombined to yield both the means (θo) and rms widths (σ) of theorientation distributions for DPB (a) and the azo dye (b). Each curveindicates the range of Gaussian distributions which can yield theexperimental orientation parameter obtained by either the SHG orARAPD orientation measurement alone. The point at which theARAPD and SHG curves cross represents the distribution mean andwidth, which is consistent with both measurements. For DPB, the twocurves are within error in the limit of a narrow distribution, while forthe azo dye the distribution mean is 57° and the width is 30°. Thecorresponding orientation distribution for the azo dye is shown in theinset plot in (b) for angles from 0 to 90°.


ACKNOWLEDGMENTThe authors gratefully acknowledge support from the National

Science Foundation.

APPENDIX I. PHOTOACOUSTIC RESPONSE FROMAN INTERFACIAL FILM

For a laser beam radius (Rs) much larger than the product ofthe speed of sound through the medium of interest (v) and thelaser pulse width (τL), the area of excitation may be assumed tobe πRs

2 (for quartz and organic solvents with a pulse width of 10ns, vτL values will range from ∼0.01 to 0.06 mm, for a beam radiusof ∼0.5 cm). Since the thickness of the surface film (a fewangstroms) will be significantly less than vτL, the depth (d) of thesource volume (V) may be assumed to be vτL, and the volume tobe πRs

2vτL.22,23 As the source volume is essentially a flat disk, theacoustic wave generated may be assumed to be formed via apistonlike expansion in thickness, with a negligible contributionarising from the increase in circumference. Consequently, thechange in source volume, ΔV, may be approximated by eq AI.122,23

where � is the expansion coefficient of the medium, ΔT is thechange in source temperature resulting from absorption, and Δdis the change in thickness of the acoustic source.

At the interface between two media, heat deposition into bothmedia can occur. If it is assumed that the change in temperatureupon excitation is identical across the interface (i.e., ΔT1 ) ΔT2

) ΔT, where the subscripts indicate the medium), then the energyabsorbed at the interface (Eabs) will be distributed to both volumeelements. This treatment is similar to descriptions of photoacous-tics at surfaces in contact with air.30 The change in interfacialtemperature upon light absorption is given by

where Fi is the density of medium i, Vi is the volume element ofmedium i into which the heat is deposited, and Cpi is the heatcapacity of medium i.

For an optically thin surface film, the energy absorbed (Eabs)is equal to the incident energy (E0) multiplied by the absorptioncross section (σabs) and the surface coverage (θ). For an orientedsystem, the absorption cross section will be a function of boththe incident wavelength and the incident polarization.

Neglecting losses in the acoustic displacement associated withdamping and geometric expansion, the peak acoustic pressure inmedium i, Pi, measured at the piezoelectric detector is given byeq AI.4. The neglect of damping can be justified for ourexperimental setup, since the concomitant reduction in amplitudeis included in an instrumental response constant.22,23

Combining eqs AI.1-AI.4 yields the following relationship be-tween the photoacoutic amplitude (proportional to the signal, S)and the experimental variables:

Despite the number of approximations in the proposed model,it successfully predicts the most salient features of the photo-acoustics experiments; namely, that the amplitude of the detectedsignal is directly proportional to the incident beam energy, sampleabsorbance cross section, and sample coverage (for a constantabsorption cross section). Previous studies of Rose Bengal haveconfirmed the linear dependence of the photoacoustic amplitudeon both the incident beam energy and the sample numberdensity.20

APPENDIX II. THEORY AND TREATMENT OF THESHG MEASUREMENTS

The following discussion of SHG is presented with the intentionof providing all the detail necessary for the reader to understandhow the data were treated. While many of the expressions maybe readily found in the literature, the complete treatment is muchless available.

Fitting Procedure. Data were fit according to the relation ineqs 10 and 11. In a total internal reflection geometry, the SHGfitting coefficients will have both real and imaginary components.28

If the �(2) tensor elements are assumed to be predominantly real(a reasonable assumption far from resonance), the data can be fitby the following expressions:

where C is an experimental constant incorporating both theconstant terms in eq AII.2 and the instrument response function.If the constant, C, is known, then measurements of the s- andp-polarized second harmonic intensities for different fundamentalpolarization rotation angles will yield the magnitudes of theindividual three independent tensor elements. If C is not known,fits of the data to eqs AII.1 and AII.2 will yield relative values ofthe tensor elements. In our experiments, only relative values ofthe tensor elements were measured.

Orientation from the Molecular Hyperpolarizability. Theindividual surface second-order nonlinear polarizability tensorelements are related to the molecular second-order nonlinearpolarizability, �(2), by ensemble averages over molecular orienta-tion:27

(30) Rosencwaig, A. Photoacoustics and Photoacoustic Spectroscopy; John Wileyand Sons: New York, 1980; Chapters 9, 10.

ΔV ) �VΔT ) πRs2 Δd (AI.1)

ΔT ) Eabs/(F1V1Cp1 + F2V2Cp2) (AI.2)

Eabs ) E0θσabs (AI.3)

P1 ) c1F1Δd1/τL (AI.4)

S ∝ P1 )E0θσabsτL�1

F1πRs2(c1F1Cp1 + c2F2Cp2)

(AI.5)

Is ) C sin2(2γ)�XXZ2|s1|2 (AII.1)

Ip ) C‚Re{[s5�ZXX + cos2γ(s2�XXZ + s3�ZXX + s4�ZZZ -

s5�ZXX)]2} + C‚Im{[s5�ZXX + cos2γ(s2�XXZ + s3�ZXX +

s4�ZZZ - s5�ZXX)]2} (AII.2)

�ijk ) Ns∑λμν

⟨Tijkλμν⟩�λμν (AII.3)


where Ns is the surface density of molecules, T is a transformationmatrix defining the angular relations between the molecularcoordinate system (λ,μ,ν) and the surface coordinate system (i,j,k),and the brackets indicate an ensemble average. If �(2) is knownand measurements are made to characterize �(2), informationregarding molecular orientation can be determined. For nonreso-nant SHG measurements with an orientation distribution whichis isotropic within the surface plane, the three nonzero, indepen-dent tensor elements are given by27

where Ψ is the Euler rotation angle about the molecular z′-axis.Since the X- and Y-axes in the surface plane are equivalent, �YYZ

) �YZY ) �XXZ and �ZYY ) �ZXX.For rodlike molecules with a single dominant component of

the molecular hyperpolarizability tensor directed along the longmolecular axis (i.e., �z′z′z′ is dominant), the surface hyperpolariz-ability tensor elements given by eq AII.4 simplify to

From these relations, the expression reported in eq 12 is easilyderived.

Calculation of the Molecular Hyperpolarizability. For asimple two-state system (i.e., ground and excited states) therelative magnitudes of the individual components of the molecularhyperpolarizability tensor, �(2), may be evaluated using eq AII.6,26,31

in which ω is the optical frequency of the fundamental beam, pωng

is the energy difference between the ground state (g) and theexcited state (n), Δdng

i is the change in permanent dipole fromthe ground to excited state projected along the molecular i-axis,rng

i is the transition dipole moment projected along the molecu-lar i-axis, and ω is the fundamental optical frequency. Resonanceenhancement occurs both when ω ) ωng, and when ω ) 1/2ωng

(i.e., when the fundamental or second harmonic is resonant witha real state). It is worth noting that eq AII.6 is only valid for opticalfrequencies far from resonance, where the molecular hyperpo-larizability is purely real.

Molecular modeling calculations can be performed to evaluatethe orientations of relevant transition moments, as well as thedifference in permanent dipole between the ground and excitedstates. With these parameters, relative magnitudes of the indi-vidual tensor elements may be calculated. More general forms ofthe expression in eq AII.6 including contributions from multipletransitions31 and for resonance-enhanced SHG investigations32-34

can be used in instances where use of eq AII.6 is not justified.

APPENDIX III. FRESNEL FACTORS FOR ARAPDAND SHG IN THE TIR CELL

For the TIR cell employed in this study, the fitting coefficientsintroduced in eq 6 are derived by projection onto the interfacialcoordinates:

in which θIω is the internal angle of incidence with respect to the

total internal reflection surface for a given frequency of light, andeach Lii

ω term is a Fresnel factor describing the interfacialelectric field amplitude for the component of light directed alongthe i-axis. Expressions for the Fresnel factors employed in theseinvestigations are given below.

where tijω and rij

ω are transmission and reflection coefficients atthe ij interface for a given frequency, ω, with subscripts s and pindicating s- and p-polarized light, and ni is the refractive index ofmedium i, where medium 1 is air, medium 2 is the fused-silicaprism, and medium 3 is the solvent in the flow cell (explicitexpressions for the reflection and transmission coefficients canbe found in ref 35). The transmission coefficients with subscripts“12” account for reflective losses at the entrance interface, whilethe reflection coefficients with subscripts “23” describe reflection

(31) Oudar, J. L.; Zyss, J. Phys. Rev. A 1983, 26, 2016-2027.

(32) Higgins, D. A.; Byerly, S. K.; Abrams, M. B.; Corn, R. M. J. Phys. Chem.1991, 95, 6984-6990.

(33) Higgins, D. A.; Byerly, S. K.; Abrams, M. B.; Corn, R. M. Langmuir 1992,8, 1994-2000.

(34) Ward, J. F. Rev. Mod. Phys. 1965, 37, 1-18.(35) Jenkins, F. A.; White, H. E. Fundamentals of Optics; McGraw-Hill: New

York, 1957; pp 529-532.

�ZZZ ) Ns[⟨cos3 θz′Z⟩�z′z′z′ + ⟨cos θz′Z sin2 θz′Z sin2 Ψ⟩(�z′x′x′ +

2�x′x′z′)] (AII.4a)

�ZXX ) 12Ns[⟨cos θz′Z sin2 θz′Z⟩�z′x′x′ + ⟨cos θz′Z⟩�z′x′x′

-⟨cos θz′Z sin2 θz′Z sin2 Ψ⟩(�z′x′x′ + 2�x′x′z′) ](AII.4b)

�XXZ ) �XZX ) 12Ns

[⟨cos θz′Z sin2 θz′Z⟩�z′z′z′ + ⟨cos θz′Z⟩�x′x′z′

-⟨cos θz′Z sin2 θz′Z sin2 Ψ⟩(�z′x′x′ + 2�x′x′z′) ] (AII.4c)

�ZZZ ) Ns⟨cos3 θz′Z⟩�z′z′z′ (AII.5a)

�ZXX ) �XXZ )12

Ns⟨cos θz′Z sin2 θz′Z⟩�z′z′z′ (AII.5b)

�λμν(ω) ) -e3

2p2(ωng2 - ω2)[Δdng

λ rngμ rng

ν + rngλ (rng

μ Δdngν +

Δdngμ rng

ν )ωng

2 + 2ω2

ωng2 - (2ω)2] (AII.6)

aX ) |cosθIω LXX

ω |2 (AIII.1a)

aY ) |LYYω |2 (AIII.1b)

aZ ) |sin θIω LZZ

ω |2 (AIII.1c)

LXXω ) tp12

ω (1 - rp23ω ) (AIII.2a)

LYYω ) ts12

ω (1 + rs23ω ) (AIII.2b)

LZZω ) tp12

ω (1 + rp23ω )1

2[1 + (n2

ω/n3ω)2] (AIII.2c)


at the TIR interface. For total internal reflection, the reflectioncoefficients are complex.36

The Fresnel factors in eq AIII.2 follow from standard expres-sions for the electric fields at an interface.35,36 The electric fieldamplitude at a bare interface consists of two contributions, onefrom the incident field and one from the reflected field, whichmay interfere either constructively or destructively. In contrastto the X- and Y- polarized components, the Z-polarized electricfield amplitude is discontinuous across the interface, changingby a factor of (n2/n3)2 from its value in the prism to its value inthe solvent. Rather than assuming the monolayer can be treatedas being located in either the incident or refractive medium, theaverage electric field of the two media was used (as can be seenin eq AIII.1c). The sensitivity of the calculated orientation angleson the Z-component of the interfacial electric field was tested byfitting the ARAPD data, assuming electric field amplitudesrepresentative of both the silica and the solvent. In all cases, thedifferent treatments yielded differences in orientation angles ofless than a few degrees from the reported values. For SHG thefitting coefficients described in eqs 10 and 11 are given to be28,37

where Liiω are the linear Fresnel coefficients previously employed

in describing the electric fields for ARAPD investigations, Lii2ω

are nonlinear Fresnel factors describing the detected electric fieldamplitudes of the second harmonic per unit amplitude generatedat the interface, and θR

2ω is the reflection angle of the secondharmonic (neglecting dispersion, θR

2ω and θIω are equal).

The linear Fresnel factors for SHG have exactly the same formas those used for ARAPD in eq AIII.2, with the exception that thereflection and transmission coefficients are all evaluated for awavelength of 1064 nm. The nonlinear Fresnel factors are givenby

The fundamental basis of the expressions in eq AIII.4 isanalogous to that used to generate the linear Fresnel factors,described earlier.

Received for review November 10, 1999. AcceptedJanuary 3, 2000.

AC9912956

(36) Harrick. N. J. Internal Reflection Spectroscopy; Interscience Publishers: NewYork, 1967; Chapter 2.

(37) Naujok, R. R.; Higgins, D. A.; Hanken, D. G.; Corn, R. M. J. Chem. Soc.,Faraday Trans. 1995, 91, 1411-1420.

s1 ≡ Lyy2ω Lyy

ω Lzzω sin θI

ω (AIII.3a)

s2 ≡ Lxx2ω Lxx

ω Lzzω sin(2θI

ω) cos θR2ω (AIII.3b)

s3 ≡ Lzz2ω(Lxx

ω)2 cos2 θIω sin θR

2ω (AIII.3c)

s4 ≡ Lzz2ω(Lzz

ω)2 sin2 θIω sin θR

2ω (AIII.3d)

s5 ≡ Lzz2ω(Lyy

ω) sin θR2ω (AIII.3e)

Lxx2ω ) -(1 - rp23

2ω )tp212ω (AIII.4a)

Lyy2ω ) (1 + rs23

2ω)ts212ω (AIII.4b)

LZZ2ω ) (1 + rp23

2ω )12[1 + (n2

2ω/n32ω)2]tp21

2ω (AIII.4c)


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