Molecular orientation and angular distribution probed by angle-resolved absorbance and second harmonic generation

Article abstract of DOI:10.1021/ac9912956

Second harmonic generation (SHG) and angle-resolved absorbance with photoacoustic detection were combined to evaluate both the mean orientation angle and the width of the angular distribution for two surface-bound molecular systems. Assuming a Gaussian distribution function, a physisorbed stilbene dye on fused silica exhibited a narrow distribution centered at 73° with a root-mean-square (rms) width of less than ～8°. In contrast, a covalently bound azo dye resulted in a broad orientation distribution (rms width of ～30°) centered at 60°. It was also demonstrated that the combination of nonlinear (SHG) and linear (absorbance) spectroscopic techniques provides valuable insight into molecular orientation that a combination of two linear techniques (such as fluorescence and absorbance) is unable to provide.

Full text of DOI:10.1021/ac9912956

Anal. Chem. 2000, 72, 887-898
Accelerated Articles
Mo le c u la r Orie n t a t io n a n d An g u la r Dis t rib u t io n
P ro b e d b y An g le -Re s o lve d Ab s o rb a n c e a n d S e c o n d
Ha rm o n ic Ge n e ra t io n
Ga rth J . Sim ps on, Sa ra h G. We s te rbuhr, a nd Ka thy L. Row le n*
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215
Second harmonic generation (SHG) and angle-resolved
absorbance with photoacoustic detection were combined
to evaluate both the mean orientation angle and the width
of the angular distribution for two surface-bound molec-
ular systems. Assuming a Gaussian distribution function,
a physisorbed stilbene dye on fused silica exhibited a
narrow distribution centered at 7 3 ° with a root-mean-
square (rms) width of less than ∼8 °. In contrast, a
covalently bound azo dye resulted in a broad orientation
distribution (rms width of ∼3 0 °) centered at 6 0 °. It was
also demonstrated that the combination of nonlinear
and co-workers have employed a combination of absorbance and
fluorescence in order to probe two orientation parameters for thin
surface films.6 In most spectroscopic studies, however, a narrow
distribution is assumed and a single parameter is used to evaluate
the apparent mean orientation angle. As demonstrated in refs
3-10, such an assumption is not always justified. Furthermore,
even if the molecular system is highly oriented with respect to
the local surface, surface roughness can broaden the orientation
distribution sufficiently that the assumption of a narrow distribu-
tion may not be valid.1
A classic example of an instance in which the assumption of a
narrow distribution may be misleading is that of absorbance
measurements for molecular orientation angles equal to the magic
angle of 54.7°, which is also the apparent orientation angle
obtained from a random distribution. Absorbance measurements
yielding an apparent orientation angle of 54.7° do not allow for
distinction between the case in which every molecule is oriented
in a narrow distribution centered at the magic angle and the case
in which the molecules are randomly oriented. We have recently
demonstrated that an equivalent magic angle exists for second
harmonic generation orientation measurements.19 Sufficiently
-10
1-18
(
SHG) and linear (absorbance) spectroscopic techniques
provides valuable insight into molecular orientation that
a combination of two linear techniques (such as fluores-
cence and absorbance) is unable to provide.
The ability of monolayer and multilayer films to dramatically
alter both the physical and optical properties of surfaces and
interfaces has made them interesting systems to study for both
fundamental and technological reasons.1 Orientation measure-
ments of surface-bound molecules provide valuable insight into
the 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 orientation
parameters, allowing for evaluation of the mean orientation angle
and an approximation of the orientational distribution.3-5 Saavedra
(
(
(
6) Edmiston, P. L.; Lee, J. E.; Cheng, S.-S.; Saavedra, S. S. J. Am. Chem. Soc.
1 9 9 7 , 119, 560-570.
7) Wood, L. L.; Cheng, S.-S.; Edmiston, P. L.; Saavedra, S. S. J. Am. Chem.
Soc. 1 9 9 7 , 119, 561-576.
8) Edmiston, P. L.; Saavedra, S. S. Biophys. J. 1 9 9 8 , 74, 999-1006.
(9) Edmiston, P. L.; Saavedra, S. S. J. Am. Chem. Soc. 1 9 9 8 , 120, 1665-1671.
10) Edmiston, P. L.; Lee, J. L.; Wood, L. L.; Saavedra, S. S. J. Phys. Chem. 1 9 9 6 ,
(
1
00, 775-784.
(
(
11) Piasecki, D. A.; Wirth, M. J. Langmuir 1 9 9 4 , 10, 1913-1918.
12) Piasecki, D. A.; Wirth, M. J. J. Phys. Chem. 1 9 9 3 , 97, 7700-7705.
(
(
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. 1 9 9 5 , 68, 2573-2579.
4) Yang, J.; Kleijn, J. M. Biophys. J. 1 9 9 9 , 76, 323-332.
5) Zhia, X.; Kleijn, J. M. Biophys. J. 1 9 9 7 , 72, 2651-2659.
(13) Wirth, M. J.; Burbage, J. D. J. Phys. Chem. 1 9 9 2 , 96, 9022-9025.
(14) Burbage, J. D.; Wirth, M. J. J. Phys. Chem. 1 9 9 2 , 96, 5943-5948.
(15) Simpson, G. J.; Rowlen, K. L. J. Phys. Chem. B 1 9 9 9 , 103, 1525-1531.
(16) Simpson, G. J.; Rowlen, K. L. J. Phys. Chem. B 1 9 9 9 , 103, 3800-3811.
(17) Simpson, G. J.; Rowlen, K. L. Chem. Phys. Lett. 1 9 9 9 , 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. 1 9 9 9 , 121, 2635-2636.
1
0.1021/ac9912956 CCC: $19.00 © 2000 American Chemical Society
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 887
Published on Web 02/01/2000

broad orientation distributions probed by second harmonic
generation (SHG) will yield apparent orientation angles of 39.2°,
regardless of the true distribution mean. Analogous to the magic
angle for absorbance, if a single SHG measurement yields the
SHG magic angle result, it is impossible to determine whether
the measurement represents a narrow distribution centered
around 39.2° or a broad distribution.
It is evident that the width of an orientation distribution can
be as important as the mean orientation angle. Methods that allow
for investigation of both the distribution mean and width about
that mean provide a more complete and intuitive description of
molecular orientation.3 In this report, an absorbance technique
Fig u re 1 . Definitions of relevant axes and angles. The molecular
orientation angle, θz′Z is the angle between the molecular long axis
(z′) and the surface normal (lab Z-axis). The polarization rotation angle
-10
of the incident beam, γ, is defined such that γ ) 0° is p-polarized
and γ ) 90° is s-polarized.
(
angle-resolved absorbance by photoacoustic detection, or ARAPD)
is combined with SHG to evaluate the mean molecular orientation
angle and the angular distribution about the mean for two distinct
molecular systems. In the following sections, a complete descrip-
tion of the necessary mathematical relationships for ARAPD and
SHG orientation measurements is presented.
Angle-Resolved Absorbance. ARAPD is a technique devel-
oped in our laboratory for submonolayer to multilayer absorbance
orientation measurements at dielectric surfaces.20,21 ARAPD mea-
By varying the orientation of the electric field polarization
vector with respect to the surface and tracking the resulting trend
in absorbance (and correspondingly in photoacoustic amplitude),
the ensemble-averaged orientation of a particular transition mo-
ment may be determined and from that the molecular orientation
within the surface film. Mathematically, this measurement is
described by the following expression:24
surements rely on the inherent sensitivity of photoacoustic
detection to allow for minimal-background absorbance measure-
ments with submonolayer detection limits.20 For a moderately
2
2
2
2
2
2
A
tot ) 〈(E‚f) 〉 ) |f| |E| [|e
| KfX + |e
| KfY + |e
| KfZ
] (2)
X
Y
Z
intense, unfocused pulsed laser beam, as used in these experi-
ments, the photoacoustic signal generated arises solely from heat
deposition, and not from high-intensity effects such as electro-
striction or ablation. Consequently, a model describing the
observed photoacoustic response of an optically thin sample at
the interface may be formulated by minor modifications of a simple
model previously presented by Tam et al.22,23 For a photoacoustic
wave generated from an optically thin sample at the interface
between two media (1 and 2) of different thermal and acoustic
properties, the photoacoustic amplitude generated in medium 1
is given by
where Atot is the sample absorbance, E is the incident electric
2
K ≡ 〈cos θ 〉
(3)
fi
fi
field polarization vector with components at the interface per unit
incident amplitude of e , e , and e , f is the transition moment
X
Y
Z
vector, and θ is the angle between the transition moment vector
fi
and the laboratory i-axis, with the Z-axis directed normal to the
surface. Since expectation values of squared cosines appear
frequently in discussions of angle-resolved absorbance, they are
abbreviated by the letter K, with subscripts indicating the
corresponding angle.
â1
SPAS,1 ∝ (E θσabs)
(1)
0
F (c F C + c F C )
1
1
1
p1
2 2 p2
If it is assumed for the moment that the probed transition
moment lies parallel to the long molecular axis (the z′-axis, as
shown in Figure 1) of a rodlike molecule, then KfZ may be replaced
by Kz′Z. The orientation parameter Kz′Z is experimentally deter-
mined from absorbance measurements, and describes the polar
angle between the molecular orientation axis (z′) and the surface
normal (Z). For different internal transition moment orientations
(i.e., not parallel with the long molecular axis), analogous relations
between KfZ and the orientation angles of the molecular axes have
been previously derived.16,24 Combining the law of cosines (which
states that Kz′X + Kz′Y + Kz′Z ) 1) with the relation Kz′X ) Kz′Y
(true for a random distribution within the surface plane), the
absorbance expression in eq 2 can be rewritten:
in which SPAS,1 is the photoacoustic amplitude within medium 1
some distance from the interface, E is the incident energy of the
0
excitation beam (mJ/ pulse), θ is the surface coverage (molecules/
2
cm ), σabs is the absorption cross section of the surface dye
2
molecules (cm / molecule), and â
i
i
, F , and Cpi are the thermal
expansion coefficient, density, and heat capacity at constant
pressure for medium i, respectively. The derivation of eq 1 from
the original one-medium model by Tam et al. is provided in
Appendix I. For the purposes of this study, the most important
aspect of eq 1 is that the photoacoustic amplitude is directly
proportional the absorption cross section, σabs, which itself is a
function of the molecular orientation and the orientation of the
incident electric field polarization.
2
2
2
2
2
Atot ∝ |e | + |e | + K (2|e | - |e | - |e | )
(4)
X
Y
z′Z
Z
X
Y
(
(
20) Doughty, S. K.; Rowlen, K. L. J. Phys. Chem. 1 9 9 5 , 99, 2143-2150.
21) Doughty, S. K.; Simpson, G. J.; Rowlen, K. L. J. Am. Chem. Soc. 1 9 9 8 ,
The electric field components at the interface are generated by
1
20, 7997-7998.
22) Hutchins, D. A.; Tam, A. C. IEEE Trans. Ultrason., Ferroelectr., Freq. Control
9 8 6 . UFFC-33, 429-449.
23) Patel, C. K. N.; Tam, A. C. Rev. Mod. Phys. 1 9 8 1 , 53, 517-550.
(
(
(24) Michl, J.; Thulstrup, E. K. Spectroscopy with Polarized Light: Solute Alignment
by Photoselection, in Liquid Crystals, Polymers, and Membranes; VCH
Publishers Inc.: New York, 1995; Chapter 5.
1
888 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

projection of the incident electric field onto the surface coordinate
system, with Fresnel correction factors accounting for reflection
and refraction at the interface:
oriented at the interface between two such media. Molecular
orientation may be evaluated from measurements of the intensity
and polarization of the second harmonic light generated under
various polarization conditions of the fundamental beam. Inter-
pretation of the experimental data is simplified considerably if only
one molecular hyperpolarizability tensor element is dominant
(which is often the case) and both the fundamental and second
harmonic frequencies are far from a molecular resonance (such
2
ω
2
|
e | ) |cos ϑ cosγL |
(5a)
(5b)
(5c)
X
I
XX
2
ω 2
|
e | ) |sin γL |
Y
YY
2
ω
ZZ
2
|
e | ) |sin ϑ cos γL |
25
Z
I
that Kleinman symmetry may be assumed ).
The intensity of the second harmonic light generated at an
interface, I2ω, is given by the following relation:26
I
where ϑ is the angle of incidence with respect to the surface
normal, γ is the polarization rotation angle (γ ) 0° for p-polarized
light, γ ) ( 90° for s-polarized light), and L ii are Fresnel factors
3
2
2
2ω
I2ω
)
3
2π ω sec ϑ
|e ‚ø :e e | (I )
2ω (2)
ω ω 2 ω 2
(9)
ω
3
c
that describe the electric field components at the interface per
unit field directed along the i-axis. Explicit expressions for the
Fresnel factors are presented in Appendix III for the total internal
reflection cell used in these investigations.
As can be seen in eq 5, there are two simple approaches for
altering the electric field at the interface: (1) vary the angle of
incidence for p-polarized light (γ ) 0°), or (2) rotate the plane of
polarization for a fixed angle of incidence. For the latter approach
with a constant angle of incidence, eq 4 can be rewritten:
in which the superscripts ω and 2ω indicate parameters evaluated
for either the fundamental frequency or the second harmonic,
respectively, ϑ2 is the angle between the surface normal and the
propagation direction of the second harmonic, c is the speed of
light, ω is the angular frequency of light, e is a vector describing
the fundamental electric field amplitude at the interface, e
describes the polarization state of the second harmonic, and ø(2)
is the third-ranked, second-order nonlinear polarizability tensor.
For SHG measurements with a molecular orientation distribution
that is isotropic within the surface plane (consistent with most
experiments), there are only three nonzero independent tensor
elements: øZZZ, øZXX, and øXXZ.2
ω
ω
2
ω
2
2
2
Atot ∝ a cos γ + a sin γ + K (2a cos γ -
X
Y
z′Z
Z
2
2
a cos γ - a sin γ) (6a)
X
Y
6-28
or
Atot ∝ a + (a - a ) sin γ + K [sin γ(2a - a +
The s- and p-polarized components of the second harmonic
intensity are typically measured independently, with the relation-
2
2
X
Y
X
z′Z
Z
X
ship between the measured intensities and the three independent
tensor elements given by the following expressions:26,28
a ) + a - 2a ] (6b)
Y
X
Z
ω
2
ω 2
I ) C|s sin2γ ø | (I )
(10)
where the factors a
component at the interface neglecting the dependence on the
polarization rotation angle (e.g., a
fitting coefficients, a
i
describe the electric field intensities of each
s
1
XXZ
2
ω
2
ω
2
I ) C|s ø
+ cos γ (s ø
+ s3ø + s4ø
ZXX ZZZ
- s5øZXX)|
ω 2
X
) |cosϑ
I
L
XX
| ). Since the
p
5
ZXX
2
XXZ
i
, are all known constants for a particular
(
I ) (11)
system and geometry, a fit of absorbance as a function of
polarization rotation angle yields the value of the orientation
parameter, Kz′Z. The experimentally determined orientation pa-
where I and I are the measured s- and p-polarized second
s
p
rameter is, in turn, related to the molecular orientation angle, θz′Z
,
harmonic intensities, respectively, and the s are fitting coefficients
that depend on both the fundamental and second harmonic electric
i
2
by an ensemble average of cos θz′Z
:
fields at the interface. Details of the fitting procedure used are
described in Appendix II. Explicit expressions for the fitting
coefficients for SHG measurements in the total internal reflection
geometry of this study are provided in Appendix III, including
both the linear and nonlinear Fresnel correction factors for
reflection and refraction.
π
2
2
Kz′Z ) 〈cos θ 〉 ) N
∫
cos θ P(θ ) sinθ dθ
(7)
z′Z
z′Z
z′Z
z′Z
z′Z
0
where P(θz′Z) is the distribution function for θz′Z and N is a
normalization constant. If the orientation distribution is sufficiently
narrow, such that a δ-function may be assumed for P(θz′Z), the
mean orientation angle may be approximated as follows:
Once relative values of the surface hyperpolarizability tensor
elements have been obtained from fits of the experimental data
to eqs 10 and 11, the SHG orientation parameter, Dz′Z, may be
evaluated. For rodlike molecules, Dz′Z is given by27,29
2
2
Kz′Z ) 〈cos θ 〉 ≈ cos 〈θ 〉
(8)
z′Z
z′Z
(
(
25) Kleinman, D. A. Phys. Rev. 1 9 6 2 , 126, 1977-1979.
26) Corn, R. M.; Higgins, D. A. Chem. Rev. 1 9 9 4 , 94, 107-125.
where 〈θz′Z〉 is the apparent molecular orientation angle, calculated
if 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
(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 1 9 8 5 ,
8, 107-116.
3
(29) Dick, B. Chem. Phys. 1 9 8 5 , 96, 199-215.
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 889

3
〈
cos θ 〉
øZZZ
z’Z
Dz′Z
≡
)
(12)
〈
cos θz′Z〉 øZZZ + 2øZXX
Analogous to the absorbance orientation parameter, Kz′Z, the
SHG orientation parameter depends on the angle between the
molecular long axis (z′) and the surface normal (Z) through
averages of cosine functions. Furthermore, for narrow molecular
orientation distributions in which a δ-function probability distribu-
tion is reasonably accurate, the orientation parameters measured
by SHG and ARAPD (Dz′Z and Kz′Z, respectively) should be
identical.
2
Kz′Z ≈ Dz′Z ≈ cos 〈θ 〉
(13)
z′Z
In cases for which the orientation distribution is not well-
represented by a δ-function, the two orientation parameters may
be significantly different. Combining SHG and ARAPD measure-
ments of the same system under the same conditions allows for
a convenient test of the narrow distribution assumption: if the
distribution is sufficiently narrow, both measurements will yield
identical results for the two orientation parameters, if not, both
the mean and width of the distribution may be determined.
Fig u re 2 . Experimental apparatus. (a) Schematic of the ARAPD
apparatus: DM, dichroic mirror; PD, photodiode; QF, quartz flat; GLP,
Glan laser prism; HWP, half-wave plate; (b) Schematic of the SHG
apparatus: V, visible blocking filter; L, lens (20 cm focal length); IR,
infrared blocking filter; P, polarizer (dichroic sheet); IF, 532 nm
interference filter; PMT, photomultiplier tube. (c) Blowup of the total
internal reflection flow cell. The cell consists of a 50 µm thick Teflon
spacer sandwiched between a quartz prism and a quartz microscope
slide. The piezoelectric transducer attached to the quartz slide is
acoustically coupled to the prism by the solvent in the flow cell.
EXPERIMENTAL SECTION
ARAPD experiments were conducted using the third harmonic
(
1
355 nm) of a Q-switched Nd:YAG laser (Spectra Physics GCR-
1). After separation of the third harmonic using appropriate
intensities. As with the ARAPD measurements, the incident beam
intensity was recorded in conjunction with the signal intensity by
reflecting a portion of the fundamental off a quartz window onto
a photodiode. All reported SHG data have been normalized for
the fundamental intensity.
dichroic mirrors, the 355 nm beam was passed through a quartz
window, an aperature, a Glan laser prism, a stepper motor-
controlled half-wave plate, and the total internal reflection cell (see
Figure 2a). A portion of the 355 nm beam reflected off the quartz
window was directed toward a photodoide to record the beam
intensity during data acquisition. The total internal reflection flow
cell (shown in Figure 2c) consisted of 50 µm thick Teflon spacer
Surface films of 1-docosyl-4-(4-hydroxystyrl)pyridinium bro-
mide (DPB, Aldrich) were prepared by dipping a substrate into a
chloroform (Fisher, Optima grade) solution of the dye. Prior to
film formation, substrates were cleaned by sequential sonication
in acetone, chloroform, and methanol, followed by drying under
nitrogen. The substrates were further cleaned and hydroxylated
by subsequent immersion for 5 min in a freshly prepared hot
“piranha” solution (three parts 30% hydrogen peroxide, seven parts
concentrated sulfuric acid, heated until oxygen bubbles freely
form), followed by thorough rinsing in 18.2 MΩ filtered water,
and drying under nitrogen. The substrates were then immersed
in the dye solutions for 3 min prior to slow removal (no
dependence 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 a
(
(
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 for
the flow of solvent through the cell for acoustic coupling. A
piezoelectric transducer (Panametrics) was coupled to the micro-
scope slide and spatially offset from the spot of total internal
reflection to temporally separate the photoacoustic wave from
artifacts due to scattered light. After signal amplification, the
acoustic waveforms were signal averaged on an oscilloscope, and
the amplitude was transferred to a personal computer as a function
of the excitation beam polarization rotation angle.
SHG data were acquired using the same flow cell as for the
ARAPD investigations. The Nd:YAG fundamental (1064 nm) was
passed through a visible-blocking filter, a quartz window, an
aperature, a Glan laser prism, a stepper motor-controlled half-
wave plate, a focusing lens, and the TIR flow cell. After the flow
cell, 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 in
Figure 2b. The signal-averaged PMT response was recorded on
an oscilloscope and the amplitude transferred to a personal
computer as a function of the fundamental beam polarization
rotation angle for both s- and p-polarized second harmonic
1
primarily aliphatic monolayer ). DPB monolayer films for the
ARAPD and SHG investigations were prepared directly on the
TIR prism surface, with dye removed from the non total internal
reflection (non-TIR) surfaces by wiping with a methanol-soaked
Kimwipe. Monolayer formation was confirmed both by the
ellipsometric thickness measurements and by UV-visible spectra
of dipped quartz flats, indicating the presence of the dye (acquired
with a Hewlett-Packard 8452A diode array spectrometer). The
DPB monolayer films were analyzed in contact with pure hexanes
(Fisher, Optima grade) and saturated DPB in hexanes in the flow
890 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

cell. A small signal loss was observed during data acquisition using
pure hexanes, probably due to either photochemical effects or
surface desorption, but no change in orientation resulted.
Monolayers of 4-(dimethylamino)azobenzene were covalently
bound to the fused-silica total internal reflection prisms (Melles
Griot or Esco, S1-UV). Prior to derivatization, the substrates were
cleaned and hydroxylated using the same procedure as for the
DPB substrates. For the first reaction step, the substrates were
refluxed for 2 h in a solution of dry toluene (certified ACS, Fisher
Scientific), 0.05 M pyridine (certified ACS, Fisher Scientific) and
0
.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. For
the second reaction step, the substrates were placed in a solution
of 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 and
chloroform, sonicated in acetone, chloroform, and methanol, and
dried under a flow of nitrogen. To prepare the azo dye in solution,
the same reaction procedure was used except the dye was reacted
with a 0.030 M propylamine (99+%, Aldrich) solution in toluene
rather than the aminated surface. Water contact angles were
measured before and after surface reaction on a home-built
rotating stage with droplet images acquired by an optical micro-
scope coupled to a CCD digitizing camera. Ellipsometric thickness
measurements and UV-visible measurements were made using
the same instruments as previously described. The organic layer
was removed from the non-TIR faces of the prisms by dropping
hot pirahna solution onto the horizontally positioned surfaces and
allowing the pirahna to react for 15 min, followed by thorough
rinsing with water and drying under a flow of nitrogen.
Fig u re 3 . Theoretical ARAPD response curves accounting for
reflection and refraction, including both real and imaginary contribu-
tions to the electric fields at the total internal reflection interface. The
dashed line indicates the theoretical response for a molecular
orientation normal to the surface, with each solid curve corresponding
to a 10° increment in orientation angle. The dotted curve is the
response expected from an unoriented system.
Fig u re 4 . Adsorption isotherm for DPB films prepared by substrate
dipping. The solid line is a Langmuir fit to the data, yielding a ∆G for
adsorption of -3.2 kJ/mol. For an asymptotic monolayer film thickness
of ∼12 Å and a molecular length for DPB of ∼35 Å, treating the DPB
molecule as a rigid rod suggests an orientation angle of ∼70°.
Molecular modeling calculations for both DPB and the azo dye
were performed using Hyperchem (Hypercube, release 4) with
geometry optimization performed using the AM1 semiempirical
method, and electronic structure calculations performed with the
ZINDO/ S method.
independent absorbance, γ*, will be the value of γ for which the
coefficient of Kz′Z in eq 6 is equal to zero.
RESULTS AND DISCUSSION
To extract meaningful orientation information using a TIR
2
geometry, the influence of reflection and refraction at both the
entrance and exit prism surfaces, as well as the amplitudes of the
electric field components at the total internal reflection interface,
must be known and accurate. Theoretical curves for the expected
angle-resolved photoacoustic response for several different mo-
lecular orientations accounting for these effects are shown in
Figure 3. The curves were generated using eq 6 with the Fresnel
factors and fitting coefficients described in Appendix III. For
surface-bound molecules with small orientation angles (aligned
nearly 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 with
large orientation angles (aligned nearly parallel with the surface
plane), the exact opposite trend is observed.
sin γ* ) (2a - a )/ (2a - a + a )
(14)
Z
X
Z
X
Y
For an experimental geometry with hexanes flowing through the
TIR cell and a fused-silica prism, orientation-independent absor-
bance is achieved for a polarization rotation angle of 54.73°. The
fact that the calculated value of γ* is nearly identical to the magic
angle of 54.74° is coincidental, since γ* will vary significantly with
the refractive index of both the prism and the acoustic coupling
liquid.
Case 1 . P hysisorbed Stilbene Dye Films. The adsorption
isotherm for DPB stilbene dye films is shown in Figure 4, along
with the chemical structure of the dye. Isotherm data were
acquired by dipping substrates in varying concentrations of DPB
in chloroform and recording the film thickness measured by
ellipsometry. The film thickness reaches a maximum value of ∼12
For a polarization rotation angle near 55°, all molecular
orientations yield the same photoacoustic response. This polariza-
tion angle is the equivalent of the absorbance magic angle after
correcting for reflection, refraction, and total internal reflection
surface fields. The polarization rotation angle yielding orientation-
-
4
Å for concentrations in excess of 10 M DPB, corresponding to
completed monolayer formation. Assuming the DPB molecules
may be treated as rigid, tightly packed, rodlike molecules 35 Å
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 891

Fig u re 5 . UV-visible absorbance spectra for DPB: monolayer film
-
4
-5
dipped in 8 × 10 M DPB (solid line), and 10 M DPB in chloroform
(
dashed line). The monolayer absorbance has been multiplied by 50
for comparative purposes.
Fig u re 6 . Averaged, normalized angle-resolved photoacoustic
amplitudes acquired for both monolayer films of DPB (solid triangles,
in length, a film thickness of 12 Å corresponds to a geometric
molecular tilt angle of ∼70°.
16 measurements) and multilayer films consisting of a monolayer film
UV-visible absorbance spectra are shown in Figure 5 for DPB
with surface-aggregated DPB particulates (open circles, 16 measure-
ments). The solid lines are fits to the data using eq 6b with the fitting
coefficients given in Appendix III. A representative error bar ((1σ) is
provided on each curve.
-
5
both on a quartz slide dipped in 8 × 10 M DPB and in a dilute
-
5
chloroform solution (10 M). A noticeable blue-shift is observed
in the absorbance spectrum of the surface-bound film (∼25 nm),
most likely related to the change in environment in going from a
nonpolar solvent to a polar surface. On the basis of the integrated
absorbance of the DPB film (Figure 5) in combination with the
distribution is assumed, the apparent orientation angle as ex-
pressed in eq 8 is equal to 73 ( 3°. The apparent orientation angle
of the chromophore obtained by ARAPD is remarkably close to
the calculated ellipsometry result of ∼70°.
-
4
ellipsometry results (Figure 4), dipping in ∼10 M DPB yields a
13
surface coverage for the completed monolayer of ∼9 × 10
2
molecules/ cm .
In an attempt to minimize signal losses due to DPB solvation
in hexanes, separate ARAPD measurements were conducted using
a saturated solution of DPB in hexanes as the acoustic coupling
medium. However, the photoacoustic response did not stabilize
unless the surface remained in contact with the flowing hexanes
solution for at least 1 h. ARAPD results acquired after the signal
stabilized 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 monolayer
sample. If a narrow distribution is assumed, the corresponding
mean orientation angle is 53.2° ( 0.9°. Visual inspection of the
TIR prism surface after contact with the DPB-saturated hexanes
indicated that surface agglomeration of DPB particulates had
occurred. In this set of investigations, the ARAPD response
measured after prolonged contact with DPB-saturated hexanes
is dominated by a randomly oriented particulate overlayer (or
multilayer). Note that the apparent orientation angle measured
by ARAPD of the particulate DPB is within 1.5° of the expected
magic angle response obtained for an unoriented system (cf. 53.2°
with 54.7°). This latter finding confirms the expressions used to
determine the electric field amplitudes at the interface yield results
consistent with expectations.
The transition dipole moment and hyperpolarizability for DPB
were evaluated using ZINDO/ S electronic structure calculations
in Hyperchem. The transition moment excited at 355 nm lies
parallel with the long molecular axis. Additionally, the 355 nm
long-axis transition has both the largest oscillator strength and
the lowest frequency, suggesting the hyperpolarizability at 1064
nm will be dominated by its influence. For a two-state model, the
hyperpolarizability depends on the transition moment orientation
and the change in permanent dipole between the ground and
excited states (see Appendix II.), both of which are calculated to
be parallel with the molecular z′-axis. Therefore, a dominant âz′z′z′
hyperpolarizability tensor element is expected for 1064 nm
fundamental excitation. On the basis of these modeling results,
K
fZ ) Kz′Z as per the assumption made in eq 4, and Dz′Z ) øZZZ
ZZZ + 2øZXX) consistent with eq 12.
The angle-resolved absorbance for monolayer films of DPB
acquired using the TIR cell is shown in the lower curve of Figure
/
(
ø
6
. Monolayer films were prepared by dipping the total internal
reflection prism in 10- M DPB/ CHCl
4
. The TIR cell was
3
subsequently filled and maintained with hexanes in order to
facilitate acoustic coupling to the piezoelectric transducer. Al-
though DPB is only marginally soluble in hexanes, gradual
dissolution of the surface-bound DPB into the hexanes was
observed. The loss rate was significantly less than the time
required for data acquisition, and the loss did not result in a
detectable change in molecular orientation over time. From the
ARAPD measurements, the orientation parameter, Kz′Z, was found
to be equal to 0.09 ( 0.04 (see Table 1). If a narrow orientation
Second harmonic intensities for the DPB monolayer samples
are shown in Figure 7a, while those of DPB multilayers are shown
in Figure 7b. From theoretical fits of the s-polarized curves (using
the fitting coefficients described in Appendix III), the value of the
experimental constant, C, was evaluated by setting øXXZ arbitrarily
equal to unity and fitting the data to eq 10. The relative values of
øZXX and øZZZ, normalized to øXXZ, were then obtained by fitting
892 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

Ta b le 1 . ARAP D Re s u lt s fo r t h e DP B a n d Azo Dye
Film s a
DPB monolayer
N ) 16)
DPB multilayer
azo dye
(N ) 7)
(
(N ) 16)
K
z′Z
z′Z
0.09 ( 0.04
73 ( 3°
0.36 ( 0.01
53.2 ( 0.9°
0.27 ( 0.03
58 ( 2°
b
θ
a
N equals the number of measurements made, errors are standard
deviation. b Apparent orientation angle calculated by assuming a narrow
orientation distribution.
in fact inaccurate, a different ratio between the two tensor elements
would likely result.
In contrast to the ARAPD results, little difference is observed
in the SHG response for the monolayer and multilayer films. Fits
of the monolayer data yield an orientation parameter of Dz′Z
)
0
.08 ( 0.02, indicating a mean orientation angle of 73 ( 2° if a
narrow distribution is assumed. For the multilayer data, the
extracted orientation parameter is Dz′Z ) 0.11 ( 0.03, correspond-
ing to an orientation angle of 70 ( 3° for a narrow distribution. In
both the monolayer and multilayer SHG orientation measure-
ments, the narrow-distribution orientation angle is within error
of the experimental ARAPD result, and again very close to the
orientation angle predicted by the geometric film thickness.
The striking contrast in the behavior of the ARAPD and SHG
data for the monolayer and multilayer regimes is an excellent
example of the unique information available from a combination
of nonlinear and linear spectroscopic techniques. ARAPD mea-
surements are sensitive to absorbance from all DPB within the
penetration depth of the evanescent field. Consequently, for
particulates that adsorb to the surface (over the oriented mono-
layer), the signal response is dominated by the particulates rather
than the monolayer film. In contrast, SHG arises only from
noncentrosymmetrically oriented molecules. Adsorption of cen-
trosymmetric, randomly oriented DPB particulates does not lead
to coherent surface SHG, and the SHG response is still dominated
by the nonlinear properties of the oriented surface layer. There-
fore, while the ARAPD results are greatly influenced by the
presence of the DPB particulates, no significant change is
observed in the molecular orientation measured by SHG. A
combination of absorbance and fluorescence would have yielded
the 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 was
confirmed by water contact angle, ellipsometry, and UV-visible
spectroscopy measurements. Upon reaction, the water contact
angle changed from a value below detection (complete surface
wetting) to a value of 60 ( 5°, indicating a significant alteration
in surface hydrophobicity. Ellipsometry measurements at each
step of the reaction indicate a film thickness of 5.0 ( 0.9 Å after
the first reaction step with the monofunctional aminosilane and
6.2 ( 0.8 Å after surface attachment of the azo dye. Based on the
1.2 Å increase in film thickness, and an estimated length for the
dye of 14 Å, the ellipsometry results suggest a surface coverage
of ∼9% of a monolayer. Surface coverage can also be estimated
from the UV-visible absorbance of the surface film prepared on
a quartz window. Using the azo dye molar absorptivity and the
measured film absorbance (shown in Figure 8), the surface
Fig u re 7 . Averaged, normalized SHG results acquired for both
monolayer films of DPB (a, four measurements) and multilayer films
consisting of a monolayer film with surface-accumulated DPB (b, nine
measurements). The solid lines are fits to the data using eqs 12 and
13 for the s-polarized (open circles) and p-polarized (solid triangles)
second harmonics, respectively, with the fitting coefficients given in
Appendix III. A representative error bar ((1σ) is provided on each
curve.
the p-polarized curve to eq 11 (or more precisely, eq AII.2) using
the same constant, C. Because only the magnitude of øXXZ is
retained from a fit of the s-polarized curve, the p-polarized data
are fit equally well by øXXZ and øZXX having both like and opposite
signs, leading to two possible values for øZZZ. Therefore, two sets
of possible tensor elements are generated from a single measure-
ment. Since øXXZ and øZXX are expected to be of like sign and
comparable magnitude for a dominant âz′z′z′ (see Appendix II),
orientation parameters and angles are reported only for the case
of øXXZ ) +1. It is worth noting that the values of øZXX normalized
to øXXZ are within experimental error of unity for both mono- and
multilayer DPB films (see Table 2). Equality between these two
tensor elements is predicted theoretically for molecular systems
dominated by a âz′z′z′ hyperpolarizability tensor element (see eq
AII.5). This relationship between the tensor elements supports
two important aspects of the experiments; first, calculations
indicating a dominant âz′z′z′ for DPB appear to be reliable, and
second, the expressions used to describe the both the fundamental
and second harmonic electric fields at the interface are reasonably
accurate. If either one of these experimental considerations was
coverage of the dye was estimated to be 2.2 × 10 mlcls/ cm2,
13
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 893

Ta b le 2 . S HG Re s u lt s fo r t h e DP B a n d Azo Dye Film s a
DPB monolayer (N ) 4)
DPB multilayer (N ) 9)
azo dye (N ) 6)
øXXZ
øZXX
øZZZ
Dz′Z
1
-1
0.98 ( 0.08
0.3 ( 0.1
1
-1
1.05 ( 0.09
0.40 ( 0.06
1
-1
1.1 ( 0.2
2.39 ( 0.4
0.98 ( 0.08
0.16 ( 0.12
0.08 ( 0.02
73 ( 2°
1.05 ( 0.09
0.31 ( 0.06
0.11 ( 0.03
70 ( 3°
1.1 ( 0.2
1.9 ( 0.4
0.48 ( 0.03
46 ( 2°
b
θz′Z
a
N equals the number of measurements made, errors are standard deviation. b Apparent orientation angle calculated by assuming a narrow
orientation distribution.
Fig u re 8 . UV-visible absorbance spectra for the azo dye: sub-
monolayer film prepared by surface reaction (solid line) and an 8 ×
-
4
10
M solution in toluene (dashed line). The monolayer absorbance
has been multiplied by 50 for comparative purposes.
Fig u re 9 . Corrected, averaged ARAPD results acquired for the
surface-bound azo dye (chemical structure shown in the figure, seven
measurements). During ARAPD data acquisition, the signal was
observed to decay significantly over time (representative raw data
are shown in the inset plot). Orientation measurements were made
using the raw ARAPD data, fit to a function incorporating both an
exponential decay to a constant and the polarization dependent
absorbance (shown by the solid line in the inset plot). In the main
figure itself, averaged, normalized data are shown for comparative
purposes after correcting for only the time-dependent signal loss. The
solid line is a fit to the corrected data using eq 6b with the fitting
coefficients given in Appendix III. A representative error bar ((1σ) is
provided on the upper curve.
which corresponds to ∼8% of a monolayer assuming an ap-
2
proximate molecular area of 37 Å . From both the ellipsometry
and absorbance measurements, it may be concluded that the
1
reaction procedure generates submonolayer coverages (∼ / 10 of
a monolayer) of the azo dye.
ARAPD results for the covalently bound azo dye chromophore
are shown in Figure 9 and summarized in Table 1. SHG curves
for the same system are shown in Figure 10. During ARAPD data
acquisition, the signal was observed to decay significantly over
time (representative raw data are shown in the inset plot of Figure
9
). Experimental evidence implicates cleavage of the N-S bond
as the likely photochemical loss mechanism. Orientation values
were obtained from the raw ARAPD data by fitting to a function
incorporating an exponential decay to a constant as well as the
polarization dependent absorbance described in eq 6. No signal
loss was observed over time during SHG data acquisition, as no
light was absorbed by the azo dye molecules.
Molecular modeling calculations indicate that, similar to the
DPB stilbene dye, both the transition moment of the azo dye
excited at 355 nm and the dominant hyperpolarizability tensor
element (âz′z′z′) for a 1064 nm fundamental wavelength are directed
parallel with the long molecular axis. Accordingly, the molecular
orientation of the azo dye can be evaluated using the same
SHG measurements yield an orientation parameter of Dz′Z ) 0.48
( 0.03, corresponding to an apparent tilt angle of 46 ( 2°. The
inconsistency in apparent molecular tilt angles implies that the
assumption of a narrow angular distribution is not valid.
Combining SHG and ARAP D Results. If the assumption of
a narrow molecular orientation distribution is relaxed and a
Gaussian distribution is assumed,6 a single measurement is no
longer sufficient to determine both the mean and the width of
the angular distribution. This ambiguity can be removed by
combining both ARAPD and SHG measurements of the same
molecular system. As shown in Figure 11, for a Gaussian
distribution there is range of possible solutions satisfying a single
measurement, with one extreme being an infinitely narrow
distribution and the other a potentially broad distribution. The
point at which the ARAPD and SHG curves cross indicates the
distribution width and mean which are consistent with both
measured orientation parameters (shown in Figure 11a for DPB
-10
relations as used for DPB [i.e., KfZ ) Kz′Z and Dz′Z ) øZZZ/ (øZZZ
ZXX)]. As with DPB, a dominant âz′z′z′ is supported by an
experimental ratio of øZXX/ øXXZ within error of unity (see Table
). ARAPD measurements of the azo dye long-axis orientation
+
2
ø
2
yield an orientation parameter of Kz′Z ) 0.27 ( 0.03 or an apparent
molecular tilt angle of 59 ( 2° if a narrow distribution is assumed.
894 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

that the orientation distribution for the DPB monolayers is
centered around 73° with a distribution width of less than ∼8°
(
i.e., the width at which the experimental errors no longer
overlap). In contrast, the azo dye yields a Gaussian distribution
mean of 57° with a root-mean-square (rms) width of 30°. The
distribution is shown the inset of Figure 11b. Although the
assumption of a narrow distribution has been proven accurate for
the case of DPB, it fails to reliably describe the orientation
distribution 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 by
considering the likely orienting interactions in the two cases. For
the azo dye films, dye molecules are covalently attached at specific
locations for a surface coverage of less than 1/ 10 of a monolayer,
suggesting that the predominant orienting interactions are those
of the isolated chromophore. By inspection of the surface-bound
structure of the azo dye, free rotation about the propyl chain near
the base of the chromophore may allow for a wide range of motion
of the chromophore itself. It is reasonable to propose that this
wide range of motion leads to a broad range of accessible
chromophore orientations for the azo dye. In contrast, the
dominating orienting forces for the DPB surface films are most
likely a combination of intermolecular interactions between the
chromophores and interactions between the long aliphatic hydro-
carbon chains. Assembly of neighboring molecules into highly
ordered structures would naturally lead to a high degree of
chromophore order as well, and a corresponding narrow orienta-
tion distribution.
Fig u re 1 0 . Averaged, normalized SHG results acquired for films
of the azo dye (six measurements). The solid lines are fits to the data
using eqs 12 and 13 for the s-polarized (open circles) and p-polarized
(solid triangles) second harmonics, respectively, with the fitting
coefficients given in Appendix III. A representative error bar ((1σ) is
provided on each curve.
On the basis of the azo dye and DPB results, it is tempting to
suggest general guidelines for cases in which the assumption of
a narrow distribution is expected to be reasonable and cases in
which it will most likely fail. For molecular surface systems in
which the orientation is dominated by intermolecular interactions
to form ordered assemblies, including long-chain trifunctional
silane self-assembled monolayers and tightly packed Langmuir
and Langmuir-Blodgett films, the distribution in orientation
angles in the fully assembled monolayer film may be reasonably
assumed to be narrow. In contrast, the assumption of a narrow
distribution may be quite poor for monolayer systems in which
orientation is dominated by local interactions, particularly if a
range of orientations is accessible through intramolecular reori-
entation.
Fig u re 1 1 . SHG and ARAPD molecular orientation measurements
combined to yield both the means (θo) and rms widths (σ) of the
orientation distributions for DPB (a) and the azo dye (b). Each curve
indicates the range of Gaussian distributions which can yield the
experimental orientation parameter obtained by either the SHG or
ARAPD orientation measurement alone. The point at which the
ARAPD and SHG curves cross represents the distribution mean and
width, which is consistent with both measurements. For DPB, the two
curves are within error in the limit of a narrow distribution, while for
the azo dye the distribution mean is 57° and the width is 30°. The
corresponding orientation distribution for the azo dye is shown in the
inset plot in (b) for angles from 0 to 90°.
In summary, SHG and ARAPD measurements were combined
to measure molecular orientation in a total internal reflection flow
cell. From a single measurement, an infinite number of possible
orientation distributions could be generated to satisfy the indi-
vidual orientation parameters, ranging from narrow distributions
to fairly broad distributions. However, by combining the two
linearly independent measurements, both the mean orientation
angle and the angular distribution can be evaluated. Two molec-
ular systems were investigated, one of which was demonstrated
to possess a narrow orientation distribution (rms width of less
than ∼8°) and another a fairly broad distribution (rms width of
30°). Differences in the structure of the surface films were
proposed to account for the significant difference in the angular
distributions of the two systems.
and Figure 11b for the azo dye). This crossover point is the
graphical equivalent of solving two equations with two unknowns.
For DPB films, the two spectroscopic measurements yield almost
identical orientation parameters, within experimental error of each
other in the limit of a narrow orientation distribution. Based on
the magnitudes of the experimental errors, it may be concluded
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 895

ACKNOWLEDGMENT
P ) c F ∆d / τ
L
(AI.4)
1
1
1
1
The authors gratefully acknowledge support from the National
Science Foundation.
Combining eqs AI.1-AI.4 yields the following relationship be-
tween the photoacoutic amplitude (proportional to the signal, S)
and the experimental variables:
APPENDIX I. PHOTOACOUSTIC RESPONSE FROM
AN INTERFACIAL FILM
For a laser beam radius (R
the speed of sound through the medium of interest (v) and the
s
) much larger than the product of
E θσ τ â
abs L 1
0
S ∝ P )
(AI.5)
1
2
s
F πR (c F C + c F C )
laser pulse width (τ
L
), the area of excitation may be assumed to
1
1
1
p1
2 2 p2
2
be πR
ns, vτ
s
(for quartz and organic solvents with a pulse width of 10
values will range from ∼0.01 to 0.06 mm, for a beam radius
L
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 detected
signal is directly proportional to the incident beam energy, sample
absorbance cross section, and sample coverage (for a constant
absorption cross section). Previous studies of Rose Bengal have
confirmed the linear dependence of the photoacoustic amplitude
on both the incident beam energy and the sample number
density.20
of ∼0.5 cm). Since the thickness of the surface film (a few
angstroms) will be significantly less than vτ
L
, the depth (d) of the
, and the volume to
As the source volume is essentially a flat disk, the
source volume (V) may be assumed to be vτ
L
2
22,23
s L
be πR vτ .
acoustic wave generated may be assumed to be formed via a
pistonlike expansion in thickness, with a negligible contribution
arising from the increase in circumference. Consequently, the
change in source volume, ∆V, may be approximated by eq AI.122,23
2
∆
V ) âV∆T ) πRs ∆d
(AI.1)
APPENDIX II. THEORY AND TREATMENT OF THE
SHG MEASUREMENTS
The following discussion of SHG is presented with the intention
where â is the expansion coefficient of the medium, ∆T is the
change in source temperature resulting from absorption, and ∆d
is the change in thickness of the acoustic source.
At the interface between two media, heat deposition into both
media can occur. If it is assumed that the change in temperature
of providing all the detail necessary for the reader to understand
how the data were treated. While many of the expressions may
be readily found in the literature, the complete treatment is much
less available.
Fitting P rocedure. Data were fit according to the relation in
upon excitation is identical across the interface (i.e., ∆T
1
) ∆T
2
eqs 10 and 11. In a total internal reflection geometry, the SHG
)
∆T, where the subscripts indicate the medium), then the energy
fitting coefficients will have both real and imaginary components.28
absorbed at the interface (Eabs) will be distributed to both volume
elements. This treatment is similar to descriptions of photoacous-
tics at surfaces in contact with air.30 The change in interfacial
temperature upon light absorption is given by
If the ø(2) tensor elements are assumed to be predominantly real
(
a reasonable assumption far from resonance), the data can be fit
by the following expressions:
2
2
XXZ
2
I ) C sin (2γ)ø
|s |
(AII.1)
s
1
∆
T ) Eabs/ (F V C + F V C )
(AI.2)
1
1
p1
2 2 p2
2
I ) C‚Re{[s ø
+ cos γ(s ø
+ s3øZXX + s4øZZZ -
p
5
ZXX
2
XXZ
2
2
s ø )] } + C‚Im{[s ø
+ cos γ(s ø
+ s3øZXX +
5
ZXX
5
ZXX
2
XXZ
i i
where F is the density of medium i, V is the volume element of
medium i into which the heat is deposited, and Cpi is the heat
2
s
ø
ZZZ - s
ø
ZXX)] } (AII.2)
4
5
capacity of medium i.
For an optically thin surface film, the energy absorbed (Eabs
)
where C is an experimental constant incorporating both the
constant terms in eq AII.2 and the instrument response function.
If the constant, C, is known, then measurements of the s- and
p-polarized second harmonic intensities for different fundamental
polarization rotation angles will yield the magnitudes of the
individual three independent tensor elements. If C is not known,
fits of the data to eqs AII.1 and AII.2 will yield relative values of
the tensor elements. In our experiments, only relative values of
the tensor elements were measured.
Orientation from the Molecular Hyperpolarizability. The
individual surface second-order nonlinear polarizability tensor
elements are related to the molecular second-order nonlinear
polarizability, â(2), by ensemble averages over molecular orienta-
tion:27
is equal to the incident energy (E ) multiplied by the absorption
0
cross section (σabs) and the surface coverage (θ). For an oriented
system, the absorption cross section will be a function of both
the incident wavelength and the incident polarization.
Eabs ) E θσ
(AI.3)
0
abs
Neglecting losses in the acoustic displacement associated with
damping and geometric expansion, the peak acoustic pressure in
i
medium i, P , measured at the piezoelectric detector is given by
eq AI.4. The neglect of damping can be justified for our
experimental setup, since the concomitant reduction in amplitude
is included in an instrumental response constant.22,23
λµν
(
30) Rosencwaig, A. Photoacoustics and Photoacoustic Spectroscopy; John Wiley
øijk ) Ns
∑
〈T 〉âλµν
ijk
(AII.3)
λµν
and Sons: New York, 1980; Chapters 9, 10.
896 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000

where N
s
is the surface density of molecules, T is a transformation
(i.e., when the fundamental or second harmonic is resonant with
a real state). It is worth noting that eq AII.6 is only valid for optical
frequencies far from resonance, where the molecular hyperpo-
larizability is purely real.
Molecular modeling calculations can be performed to evaluate
the orientations of relevant transition moments, as well as the
difference in permanent dipole between the ground and excited
states. With these parameters, relative magnitudes of the indi-
vidual tensor elements may be calculated. More general forms of
matrix defining the angular relations between the molecular
coordinate system (λ,µ,ν) and the surface coordinate system (i,j,k),
(
2)
and the brackets indicate an ensemble average. If â is known
and measurements are made to characterize ø(2), information
regarding molecular orientation can be determined. For nonreso-
nant SHG measurements with an orientation distribution which
is isotropic within the surface plane, the three nonzero, indepen-
dent tensor elements are given by27
the expression in eq AII.6 including contributions from multiple
transitions31 and for resonance-enhanced SHG investigations32-34
3
2
2
øZZZ ) N [〈cos θ 〉â
+ 〈cos θz′Z sin θ sin Ψ〉(â +
z′x′x′
s
z′Z z′z′z′
z′Z
2
âx′x′z′)] (AII.4a)
can be used in instances where use of eq AII.6 is not justified.
2
〈
cos θz′Z sin θ 〉â
+ 〈cos θ 〉â
APPENDIX III. FRESNEL FACTORS FOR ARAPD
AND SHG IN THE TIR CELL
1
2
z′Z z′x′x′
z′Z z′x′x′
øZXX ) N
s
2
2
[-〈cos θ
]
sin θ sin Ψ〉(â + 2âx′x′z′
z′x′x′
)
z′Z
z′Z
For the TIR cell employed in this study, the fitting coefficients
introduced in eq 6 are derived by projection onto the interfacial
coordinates:
(
AII.4b)
1
2
øXXZ ) øXZX ) N
s
2
ω
ω 2
〈
cos θz′Z sin θ 〉â
+ 〈cos θ 〉â
a ) |cosθ L |
(AIII.1a)
(AIII.1b)
(AIII.1c)
z′Z z′z′z′
z′Z x′x′z′
sin θ sin Ψ〉(â
+ 2âx′x′z′
z′x′x′
X
I
XX
(
AII.4c)
2
2
[-〈cos θ
]
)
z′Z
z′Z
ω
2
a ) |L |
Y
YY
where Ψ is the Euler rotation angle about the molecular z′-axis.
Since the X- and Y-axes in the surface plane are equivalent, øYYZ
) øYZY ) øXXZ and øZYY ) øZXX.
ω
I
ω 2
ZZ
a ) |sin θ L |
Z
For rodlike molecules with a single dominant component of
ω
the molecular hyperpolarizability tensor directed along the long
molecular axis (i.e., âz′z′z′ is dominant), the surface hyperpolariz-
ability tensor elements given by eq AII.4 simplify to
in which θI is the internal angle of incidence with respect to the
total internal reflection surface for a given frequency of light, and
ω
each
L
term is a Fresnel factor describing the interfacial
ii
electric field amplitude for the component of light directed along
the i-axis. Expressions for the Fresnel factors employed in these
investigations are given below.
3
øZZZ ) N 〈cos θ 〉â
(AII.5a)
(AII.5b)
s
z′Z z′z′z′
1
2
2
øZXX ) øXXZ
)
N 〈cos θ sin θ 〉â
s z′Z z′Z z′z′z′
ω
ω
ω
p23
L
) t (1 - r
)
(AIII.2a)
(AIII.2b)
XX
p12
From these relations, the expression reported in eq 12 is easily
derived.
ω
YY
ω
ω
s23
L
) t (1 + r
)
s12
Calculation of the Molecular Hyperpolarizability. For a
simple two-state system (i.e., ground and excited states) the
relative magnitudes of the individual components of the molecular
ω
ZZ
ω
ω
1
2
ω
2
ω 2
L
) t (1 + r ) [1 + (n / n ) ]
(AIII.2c)
p12
p23
3
(
2)
26,31
hyperpolarizability tensor, â , may be evaluated using eq AII.6,
3
ω
ω
-
e
λ
µ
ν
λ
µ
ν
where
t
ij
and
r
ij
are transmission and reflection coefficients at
âλµν(ω) )
∆d
r
r
+ r (r ∆d
+
2
2
2
ng ng ng
ng ng
ng
the ij interface for a given frequency, ω, with subscripts s and p
indicating s- and p-polarized light, and n is the refractive index of
medium i, where medium 1 is air, medium 2 is the fused-silica
prism, and medium 3 is the solvent in the flow cell (explicit
expressions for the reflection and transmission coefficients can
be found in ref 35). The transmission coefficients with subscripts
[
2
p (ω - ω )
ng
i
2
2
ωng + 2ω
µ
ν
∆
d
r )
(AII.6)
ng ng
2
2
]
ωng - (2ω)
in which ω is the optical frequency of the fundamental beam, pωng
“
12” account for reflective losses at the entrance interface, while
is the energy difference between the ground state (g) and the
the reflection coefficients with subscripts “23” describe reflection
i
excited state (n), ∆
d
is the change in permanent dipole from
ng
the ground to excited state projected along the molecular i-axis,
(32) Higgins, D. A.; Byerly, S. K.; Abrams, M. B.; Corn, R. M. J. Phys. Chem.
i
1
9 9 1 , 95, 6984-6990.
33) Higgins, D. A.; Byerly, S. K.; Abrams, M. B.; Corn, R. M. Langmuir 1 9 9 2 ,
, 1994-2000.
(34) Ward, J. F. Rev. Mod. Phys. 1 9 6 5 , 37, 1-18.
r
is the transition dipole moment projected along the molecu-
ng
(
lar i-axis, and ω is the fundamental optical frequency. Resonance
8
1
enhancement occurs both when ω ) ωng, and when ω ) /
2
ω
ng
(
35) Jenkins, F. A.; White, H. E. Fundamentals of Optics; McGraw-Hill: New
(
31) Oudar, J. L.; Zyss, J. Phys. Rev. A 1 9 8 3 , 26, 2016-2027.
York, 1957; pp 529-532.
Analytical Chemistry, Vol. 72, No. 5, March 1, 2000 897

2
zz
ω
ω
2
2
ω
2ω
at the TIR interface. For total internal reflection, the reflection
coefficients are complex.36
s ≡ L (L ) cos θ sin θ
(AIII.3c)
(AIII.3d)
(AIII.3e)
3
xx
I
R
2
zz
ω
ω
zz
2
2
ω
I
2ω
R
The Fresnel factors in eq AIII.2 follow from standard expres-
sions for the electric fields at an interface.35,36 The electric field
amplitude at a bare interface consists of two contributions, one
from the incident field and one from the reflected field, which
may interfere either constructively or destructively. In contrast
to the X- and Y- polarized components, the Z-polarized electric
field amplitude is discontinuous across the interface, changing
s ≡ L (L ) sin θ sin θ
4
2
zz
ω
ω
yy
2ω
R
s ≡ L (L ) sin θ
5
ω
ii
where
L
are the linear Fresnel coefficients previously employed
in describing the electric fields for ARAPD investigations,
are nonlinear Fresnel factors describing the detected electric field
2ω
L
ii
amplitudes of the second harmonic per unit amplitude generated
by a factor of (n
2
/ n
3
)2 from its value in the prism to its value in
at the interface, and
θ
2ω
is the reflection angle of the second
R
2ω
ω
the solvent. Rather than assuming the monolayer can be treated
as being located in either the incident or refractive medium, the
average electric field of the two media was used (as can be seen
in eq AIII.1c). The sensitivity of the calculated orientation angles
on the Z-component of the interfacial electric field was tested by
fitting the ARAPD data, assuming electric field amplitudes
representative of both the silica and the solvent. In all cases, the
different treatments yielded differences in orientation angles of
less than a few degrees from the reported values. For SHG the
fitting coefficients described in eqs 10 and 11 are given to be28,37
harmonic (neglecting dispersion, θR and θI are equal).
The linear Fresnel factors for SHG have exactly the same form
as those used for ARAPD in eq AIII.2, with the exception that the
reflection and transmission coefficients are all evaluated for a
wavelength of 1064 nm. The nonlinear Fresnel factors are given
by
2
xx
ω
2ω 2ω
L
) -(1 - r )t
(AIII.4a)
(AIII.4b)
p23 p21
2
yy
ω
2ω 2ω
L
) (1 + r )t
s23 s21
2
ZZ
ω
2ω
1
2
2ω 2ω 2 2ω
L
) (1 + r ) [1 + (n / n3 ) ]t
p21
(AIII.4c)
p23
2
The fundamental basis of the expressions in eq AIII.4 is
analogous to that used to generate the linear Fresnel factors,
described earlier.
2
yy
ω
ω
ω
ω
s1 ≡ L L L sin θ
(AIII.3a)
(AIII.3b)
yy zz
I
Received for review November 10, 1999. Accepted
January 3, 2000.
2
ω
ω
ω
ω
I
2ω
R
s2 ≡ L L L sin(2θ ) cos θ
xx
xx zz
AC9912956
(
36) Harrick. N. J. Internal Reflection Spectroscopy; Interscience Publishers: New
(37) Naujok, R. R.; Higgins, D. A.; Hanken, D. G.; Corn, R. M. J. Chem. Soc.,
Faraday Trans. 1 9 9 5 , 91, 1411-1420.
York, 1967; Chapter 2.
898 Analytical Chemistry, Vol. 72, No. 5, March 1, 2000