Anal. Chem. 2000, 72, 3407-3411
Orientation-Insensitive Methodology for Second Harmonic Generation. 2. Application to Adsorption Isotherm and Kinetics Measurements Garth J. Simpson and Kathy L. Rowlen*
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309
In this work, the theory presented in part 1 for an experimental configuration that provides a means to isolate surface coverage measurements by SHG from coverage-dependent molecular orientation changes was tested. The adsorption isotherm for disperse red 1 on glass was found to be quite sensitive to the choice of excitation polarization rotation angle due to a coveragedependent change in molecular orientation. Appropriate selection of the polarization rotation angle, as dictated by the theory presented in part 1, yielded reliable adsorption isotherm results that were essentially independent of changes in molecular orientation. Use of a standard experimental approach (e.g., probing the intensity of p-polarized second harmonic for p-polarized fundamental), resulted in large error (nearly 100%) in the calculated equilibrium constant. The adsorption isotherm for rhodamine 6G on glass was found to be relatively insensitive to the choice of polarization rotation angle since its apparent orientation angle did not change significantly as a function of coverage. Although nonlinear optical techniques such as second harmonic generation (SHG) can be powerful probes for submonolayer and monolayer films at surfaces and interfaces, the coveragedependent nonlinear response is typically a function of both the number density at the interface and molecular orientation. In part 1 of this study, a theoretical method was proposed to generate SHG measurements insensitive to changes in orientation, allowing for isolation of the SHG signal contribution associated solely with the change in surface number density. In part 2 of this study, the method introduced in part 1 was applied to adsorption isotherm measurements and compared with more traditional methods in which a single polarization combination is measured. EXPERIMENTAL METHODS All SHG measurements were acquired using an instrument described in detail elsewhere.1 In brief, a total internal reflection flow cell consisted of a 50-µm-thick Teflon spacer (Dupont FEP, 200CLZ) sandwiched between a BK-7 glass prism (Melles-Griot) and a UV-grade fused-silica microscope slide (Esco). An inlet/ outlet system in the microscope slide allowed for the flow of dye solution through the cell. Prior to assembly of the cell, the cell was cleaned thoroughly by rinsing/sonicating in acetone, chloroform, and methanol followed by drying under nitrogen. Solutions * Corresponding author: (e-mail)
[email protected]; (phone) (303) 492-5033; (fax) (303) 492-5894. (1) Simpson, G. J.; Westerbuhr, S. G.; Rowlen, K. L. Anal. Chem. 2000, 72, 887-8. 10.1021/ac000347k CCC: $19.00 Published on Web 07/07/2000
© 2000 American Chemical Society
of disperse red 1 (DR-1, Aldrich, ∼95%) and rhodamine 6G (R6G, Aldrich, ∼95%) were prepared in methylene chloride (Fisher) which had been first passed through a silica gel column to remove any surface-active impurities. All solutions were used within a week of preparation. For measurement of the SHG polarization response curves, the fundamental of a Q-switched Nd:YAG laser (1064 nm, 10 ns) was passed through a visible-blocking filter, a quartz window, an aperture, a Glan laser prism, a stepper-motor-controlled half-wave plate, and the TIR flow cell. A small portion of the fundamental beam was reflected off the quartz window and directed toward a photodiode. Focusing of the beam was not required. After the flow cell, the second harmonic beam was directed through an IRblocking filter, a dichroic sheet polarizer, a 532-nm interference filter, and finally a photomultiplier tube (PMT). Both the signalaveraged PMT response and the photodiode response were recorded on an oscilloscope and the amplitudes transferred to a personal computer as a function of the fundamental beam polarization rotation angle for both s- and p-polarized second harmonic intensities. The same beam path was employed for SHG adsorption isotherm measurements. The appropriate dye solution was introduced in the flow cell via a syringe pump and allowed to equilibrate prior to intensity measurements. Each measurement consisted of the signal-averaged PMT amplitude for 64 pulses. On average, six measurements were recorded (i.e., two measurements for each polarization combination, and the process repeated three times) at each concentration for each polarization condition (i.e., for Ipp, Ips, Is45, and the appropriate orientation-insensitive polarization combination). The fundamental intensity was set between 3 and 6 mJ/pulse for 10-ns pulses, with minimal drift during data acquisition. All measurements were normalized for the fundamental intensity prior to analysis. Molecular modeling calculations were performed using Hypercube v4.0, with the AM1 semiempirical method used for geometry optimization and the ZINDO/S semiempirical method used for electronic structure calculations. RESULTS AND DISCUSSION For surface adsorption according to a Langmuir model, the relationship between the surface number density, Ns, and the concentration in solution at equilibrium is given by2,3 (2) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice-Hall: Upper Saddle River, NJ, 1989; Chapter 5. (3) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; WileyInterscience: New York, 1994; Chapter 3.
Analytical Chemistry, Vol. 72, No. 15, August 1, 2000 3407
Ns ) Nmax
Kads[dye] 1 + Kads[dye]
(1)
where Nmax is the surface number density at saturation, Kads is the adsorption equilibrium constant, and [dye] is the concentration of dye in solution. Through eq 1, SHG measurements of the surface number density as a function of dye concentration can be used to determine the equilibrium constant for adsorption, Kads (and from that the change in Gibbs free energy, ∆Gads). The Langmuir model assumes only one type of surface site and a coverage-independent adsorption energy. While such a simple adsorption model may not be justified, it is expected to be reasonably successful for the evaluation of Kads by nature of the general insensitivity of macroscopic adsorption measurements to the molecular details of adsorption.3 DR-1 Adsorption Isotherm. The polarization-dependent SHG response curves and molecular structure for DR-1 are shown in Figure 1 for a 10-3 M dye solution in methylene chloride. From the combined fits of the s- and p-polarized second harmonic intensities to expressions provided in part 1 (eq 1 of part 1), the values of the three independent χ(2) tensor elements were determined, and are given in Table 1. Two sets of χ(2) tensor elements were obtained from each fit, one in which χZXX and χXXZ are of like sign and one in which they are of opposite sign. Molecular modeling calculations performed on DR-1 suggested the molecular hyperpolarizability tensor for DR-1 should be dominated by the βz′z′z′ element, for which χZXX and χXXZ should be equal (see eq 7a in part 1). From the experimental fits, the ratio of χZXX to χXXZ is near unity as predicted, suggesting that the modeling calculations are reliable and that the treatment of the linear and nonlinear electric fields at the total internal reflection interface employed are reasonably accurate (if either of these conditions did not hold, it is very likely that a different ratio would be observed experimentally). Consequently, the SHG orientation parameter, D ) 〈cos3(θ)〉/〈cos(θ)〉, can be evaluated using eq 5 from part 1. Assuming a narrow orientation distribution yields an apparent orientation angle of 44° ( 1°. Adsorption isotherms for solutions of DR-1 measured under several polarization conditions are shown in Figure 2. Of the four adsorption isotherms measured for DR-1, three were acquired using traditional polarization combinations, Ipp, Ips, and Is45, in which the first subscript describes the polarization state of the second harmonic and the second subscript designates the polarization state of the fundamental (e.g., the subscript “s45” corresponds to the s-polarized second harmonic generated for a fundamental polarization rotation angle of γ ) 45°). For the remaining adsorption isotherm, second harmonic intensities were measured under the appropriate orientation-insensitive polarization conditions described theoretically in part 1. For the case of DR-1 (i.e., for a βz′z′z′ dominated molecular hyperpolarizability), the orientation-insensitive polarization condition for the TIR cell employed is achieved for p-polarized second harmonic detection with a fundamental polarization rotation angle, γ, of 63° (i.e., Ip63; see Figures 2 and 3 of part 1). Fits of each data set to a Langmuir adsorption isotherm, without correcting for changes in orientation, yielded different values for the experimental constants, as summarized in Table 1. For example, the equilibrium constants 3408 Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
Figure 1. SHG response curves for DR-1 on glass (from a 10-3 M solution in methylene chloride). Open triangles are the p-polarized intensities; solid circles are the s-polarized intensities. Solid lines are fits to the data (see part 1). The structure of DR-1 is shown in the inset. The tensor elements determined from the fits are compiled in Table 1. The fits yield an apparent orientation angle of 44° ((1°). Table 1. Summary of Regressions to SHG Response Curves (Figures 1 and 4) DR-1 (N ) 3) χXXZ χZXX χZZZ Dz′Z
1 0.92 ( 0.06 2.10 ( 0.03 0.53 ( 0.02
θz′Z*d
44° ( 1°
-1 0.92 ( 0.06 2.19 ( 0.03
R-6G (N ) 2) 1 -0.33 ( 0.04 0.68 ( 0.02 0.75 ( 0.02b 0.87 ( 0.03c 30° ( 2° b 21° ( 3° c
-1 -0.33 ( 0.04 0.77 ( 0.02
a N equals the number of measurements made, errors are one standard deviation. b Assuming uniform distribution about the orientation axis (i.e., ψ ) random). c Assuming the x′-axis lies out of the surface plane (i.e., ψ ) 90°). d Asterisk indicates apparent orientation angle calculated by assuming a narrow orientation distribution.
evaluated from Ips and Is45 measurements were similar, but differed by a factor of ∼2 from the constant obtained from measurements of Ipp. The three independent tensor elements may be evaluated from fits to the entire polarization response curves as in Figure 1 or, alternatively, from the combined measurements of Ipp, Ips, and Is45. The relationships between the tensor elements and the detected intensities may be found in eq 2 of part 1. From these combined measurements, apparent orientation angles for DR-1 were evaluated at each concentration and are shown in the inset of Figure 2. The orientation distribution does not remain constant as a function of surface coverage, changing from an apparent orientation angle of ∼42° at low coverages to ∼50° at high coverages. However, for all concentrations probed, the apparent orientation angle for DR-1 is within the range of validity for the proposed method from part 1 (i.e., between 0° and ∼50°). If the SHG intensities Ipp, Ips, and Is45 are rescaled at each concentration for the apparent orientation angle (i.e., via the orientation angle correction, or OAC, approach described in eq 6 of part 1), a fit of the entire corrected data set, shown in Figure 3, yields an adsorption equilibrium constant of 0.050 ((0.004). Thus, the equilibrium constant obtained by correcting for the
Figure 2. Adsorption isotherms for DR-1 on glass (from methylene chloride solutions) measured under different polarization conditions: Ipp, solid dots; Ip63, open triangles; Is45, solid triangles; and Ips, open dots. Errors are (1σ from six measurements. The solid lines are Langmuir fits to the data according to eq 1. Results from the fits are compiled in Table 2. The apparent orientation angle, θ*, as a function of concentration is shown in the inset, evaluated from the combined intensity measurements. For all reported orientation angles, the measured values of χZXX/χXXZ were between 0.8 and 1.2.
Figure 3. Adsorption isotherm for DR-1 after correcting the measured intensities for the change in orientation angle via the OAC approach: Ipp, solid dots; Is45, solid triangles; and Ips, open dots. The solid line is a Langmuir fit to the entire corrected data set. From the fit, the adsorption equilibrium constant was found to be Kads ) 0.050 ((0.004).
change in orientation angle using the OAC method was within the error of the value obtained using the orientation-insensitive geometry (cf. 0.050 with 0.054) and quite different than the value obtained from measurement of Ipp alone (0.094). The change in apparent orientation angle with coverage provides an explanation for the observed differences in equilibrium constants from isotherm measurements acquired under different polarization conditions. For example, it is not surprising that Ips
and Is45 measurements yield similar equilibrium constants, as they both scale identically with the molecular orientation angle for a dominant βz′z′z′ tensor element (i.e., with 〈sin2 θ cos θ〉2). In contrast, Ipp measurements depend on a squared combination of both 〈sin2 θ cos θ〉 and 〈cos3 θ〉 functions. The values for Kads and ∆Gads measured for Ips and Is45 detection were also similar to those obtained both by the OAC approach and by the orientation-insensitive geometry. The SHG response for Ips and Is45 detection scale with 〈sin2 θ cos θ〉, which is fairly constant from about 45° to 60° (see Figure 1 of part 1). Over this very limited range of orientation angles, the SHG response for Ips and Is45 is not expected to depend greatly on changes in orientation. The fact that similar results were obtained for Ips, Is45, and Ip63, and from the OAC approach, all of which were significantly different that the results from Ipp measurements, correlates well with the predicted response given the detected change in apparent orientation angle. The observed change in apparent orientation angle for DR-1 as a function of concentration may result from a variety of effects. The most obvious explanation is that the mean orientation angle changed from a value of 42° to a value around 50° as the surface number density increases. However, intuition would suggest that an increase in surface density would more likely lead to a change in orientation favoring alignment toward the surface normal, in contrast to experimental observation. Recent investigations in our laboratory have demonstrated that the width of the orientation distribution can often be as important as the mean when interpreting SHG orientation measurements of surface systems.1,4 Since the apparent orientation angle of DR-1 at low concentrations is within a few degrees of the SHG magic angle of 39.2°,4 the initial orientation distribution is potentially quite broad. Therefore, an equally plausible explanation for the observed trend in apparent orientation angle is that the mean orientation angle changed minimally as a function of surface coverage (e.g., ∼50°), but the distribution width about that mean narrowed as the surface coverage increases. While it is not especially important for the purposes of this investigation which of the two explanations better describes the actual orientation distribution, it is worth mentioning that changes in the apparent orientation angle can result not only from changes in the mean tilt angle but also from changes in the width about that mean. As a final note, use of the OAC approach is only strictly justified for narrow orientation distributions, an assumption that has not been confirmed for DR-1. If surfaceadsorbed DR-1 does indeed exhibit a fairly broad orientation distribution at one or more concentrations (leading to a potential for errors using the OAC approach), such behavior may provide a possible explanation for the subtle differences observed between the equilibrium constants and adsorption energies obtained using the two methodologies. R-6G Adsorption Isotherm. The polarization-dependent SHG response curves for a 5 × 10-5 M solution of R-6G in methylene chloride are shown in Figure 4 and are clearly very different from the analogous response curves for DR-1 (Figure 1). The relative tensor elements evaluated from fits of the polarization response curves in Figure 4 are compiled in Table 1. Molecular modeling calculations for a fundamental frequency of 1064 nm predict a dominant βx′x′z′ molecular hyperpolarizability (4) Simpson, G. J. Rowlen, K. L. J. Am. Chem. Soc. 1999, 120, 7997-8.
Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
3409
Figure 4. SHG response curves for R-6G on glass (from a 5 × 10-5 M solution in methylene chloride). Open triangles are the p-polarized intensities; solid circles are the s-polarized intensities. Solid lines are fits of the data (see part 1). The structure of R-6G is shown in the inset. The tensor elements determined from the fits are compiled in Table 1. The fits yield an apparent orientation angle of 30° ((2°), if a uniform distribution about the orientation axis is assumed. The null observed around 56° in the p-polarized response is in agreement with the predicted behavior from part 1.
tensor element for R-6G by nature of a strong resonance enhancement from an absorbance maximum centered around 532 nm. As a consequence, a ratio of χZZZ/χZXX equal to -2 is predicted (see eq 19a of part 1), in excellent agreement with the experimental ratio of -2.1 ( 0.3. Additionally, the minimum in the p-polarized SHG response observed at 56° is consistent with the value of 55.8° predicted in part 1 for a dominant βx′x′z′ tensor element. These combined results indicate that the molecular hyperpolarizability is indeed dominated by the βx′x′z′ tensor element for our experimental conditions. Apparent orientation angles for R-6G are summarized in Table 1. The observed orientation angles are generally consistent with previous SHG studies of R-6G orientation.5-9 In the case of a dominant βx′x′z′ tensor element, the calculated polarization rotation angle for which there is minimal dependence on molecular orientation is ∼56° (from eq 23 of part 1). However, this polarization rotation angle also corresponds to a minimum in signal (see Figure 5 in part 1). The problem of minimal signal can be avoided if the total second harmonic intensity (i.e., the sum of both s- and p-polarized second harmonics) is used (see Figure 6 in part 1). From an analysis of the polarization dependence of the signal, a polarization rotation angle of 27° was (5) Slyadneva, O. N.; Slyadnev, M. N.; Tsukanova, V. M.; Inoue, T.; Harata, A.; Ogawa, T. Langmuir 1999, 15, 8651-8. (6) Kikteva, T.; Star, D.; Zhao, Z.; Baisley, T. L.; Leach, G. W. J. Phys. Chem. B 1999, 103, 1124-33. (7) Morgenthaler, M. J. E.; Meech, S. R. J. Phys. Chem. 1996, 100, 3323-9. (8) DiLazzaro, P.; Mataloni, P.; DeMartini, F. Chem. Phys. Lett. 1985, 114, 103-8. (9) Heinz, T. F.; Chen, C. K.; Ricard, D.; Shen, Y. R. Phys. Rev. Lett. 1982, 48, 478-81.
3410 Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
Figure 5. Adsorption isotherms for R-6G in methylene chloride measured under different polarization conditions: Ipp, solid dots; I(p+s)27, open triangles,; Is45, solid triangles; and Ips, open dots. Errors are (1σ from six measurements. The solid lines are Langmuir fits to the data according to eq 1. Results from the fits are compiled in Table 2.
predicted to yield a good signal and to be insensitive to changes in molecular orientation. Adsorption isotherms for R-6G on glass acquired under different polarization conditions are shown in Figure 5, with apparent orientation angles reported above the corresponding concentrations. Langmuir-type behavior was observed for concentrations of e10-4 M. At higher concentrations, deviation in the ratio of χZZZ/χZXX from the expected value of -2 toward a value closer to -1 was observed. Similar trends in the SHG response at high surface densities have been reported in previous measurements of rhodamine dyes5,10 and can be attributed to dimerization/ aggregation of R-6G monomers.5-7,10-13 Therefore, the polarization dependence of the adsorption isotherm was investigated for dye concentrations less than 7.5 × 10-5 M (i.e., for concentrations below the onset of significant aggregation). Results from Langmuir fits to the data are summarized in Table 2. In general, the experimental constants obtained from the fits were comparable regardless of the polarization condition under which they were measured, including the values obtained using the orientationinsensitive polarization rotation angle (27°) and from the OAC approach. The uniformity of the experimental constants Kads and ∆Gads measured under the different polarization conditions can be understood by considering how little the molecular orientation changed as a function of concentration. Throughout the R-6G adsorption isotherm, the apparent orientation angle changed by only ∼3°. Since this change in orientation is comparable to the error in the orientation measurements, it is not surprising that little difference was observed in the constants evaluated under different experimental geometries. R6G Desorption Kinetics. The use of an orientation-insensitive experimental geometry has applications in kinetics measure(10) Inoue, T.; Moriguchi, M.; Ogawa, T. Thin Solid Films 1999, 350, 238-44. (11) Inoue, T.; Moriguchi, M.; Ogawa, T. Anal. Chim. Acta 1996, 330, 11721. (12) Tsukanova, V.; Slyadneva, O.; Inoue, T.; Harata, A.; Ogawa, T. Chem. Phys. 1999, 250, 207-15. (13) Peterson, E. S.; Harris, C. B. J. Chem. Phys. 1989, 91, 2683-8.
Table 2. Experimental Constants Obtained from Langmuir Fits to Adsorption Isothermsa.b
DR-1 R-6G
Kads ∆Gads (kJ/mol) Kads ∆Gads (kJ/mol)
Ipp
Ips
Is45
Iγ*c
OAC
0.094 ( 0.004 5.9 ( 0.1 9(1 -5.4 ( 0.3
0.041 ( 0.004 7.9 ( 0.2 8(2 -5.2 ( 0.8
0.047 ( 0.005 7.6 ( 0.3 14 ( 1 -6.5 ( 0.2
0.054 ( 0.006 7.2 ( 0.2 15 ( 2 -6.7 ( 0.3
0.050 ( 0.004 7.4 ( 0.2 11.0 ( 0.8 -5.9 ( 0.2
a Raw data shown in Figures 2, 3, and 5. b Errors are standard errors from nonlinear regression. c Ι acquired using the orientation-insensitive γ* experimental configuration, described in part 1.
Figure 6. Desorption kinetics for R-6G from glass (10-3 M in methylene chloride): (a) raw data; (b) ln plot of the data. The solid line in the bottom figure is a biexponential fit to the data. From the fit, the two decay constants are given to be k1 ) 0.59 min-1 ((0.03 min-1) and k2 ) 0.0105 min-1 ((0.0006 min-1).
ments as well as in measurements of adsorption isotherms. In fact, the orientation-insensitive geometry is probably more useful in kinetics measurements because of the difficulty associated with acquiring SHG responses for multiple polarization combinations at each data point as a function of time (required by the alternative OAC approach). Shown in Figure 6a is the time-dependent SHG intensity during R6G desorption from the surface of BK7 glass. After allowing for surface equilibration of 10-3 M R-6G in methylene chloride, pure methylene chloride was introduced into the flow cell and the SHG response recorded as a function of time. Data were acquired using the orientation-insensitive polarization rotation angle of 27°. The final rapid drop to near zero after 30 min (indicative of rapid desorption of the remaining R-6G) occurred after switching to methanol as the solvent. Desorption data acquired prior to changing the solvent were reasonably fit to a biexponential decay, shown in Figure 6b. The rate constant for the initial rapid decay, k1, was found to be 0.59 min-1 ((0.03 min-1) and the rate constant for the slower loss, k2, was found to be 0.0105 min-1 ((0.0006 min-1), almost 2 orders of magnitude smaller. For the second, slower loss mechanism, the room-temperature lifetime of R-6G
on the glass surface in contact with pure methylene chloride was a surprising 1.6 h. While this example is presented only for illustrative purposes, it is interesting to speculate on the origins of the decay curve. There are several potential explanations for the observation of a biexponential decay for R-6G desorption. First, the initial R-6G concentration was 10-3 M, an order of magnitude in excess of the limit in which the SHG response is well-behaved. Consequently, the observed decay in SHG intensity could be due to changes in surface coverage and/or changes in β(2) related to aggregation. Another possible explanation for the observed biexponential desorption kinetics is the presence of both strongly bound and weakly bound surface species. Fluorescence experiments support the hypothesis that multiple types of adsorption sites exist at a silica surface.14-16 If it is assumed for the moment that the rapid initial decay in Figure 6 can be attributed to desorption of species only present at high surface concentrations, the slower loss rate may be correlated with the equilibrium process interrogated in the isotherm measurements. From the combined knowledge of the equilibrium constant and the rate of desorption, the adsorption rate constant for R-6G onto glass was calculated to be ∼0.1 min-1. While the above treatment is undoubtedly an oversimplification of the true surface dynamics, it does serve to demonstrate the potential application of the orientation-insensitive geometry for kinetics measurements by SHG. For comparable accuracy, similar experiments using the alternative methodology (i.e., the OAC approach) would require multiple measurements under different polarization conditions to correct each time point for the apparent orientation angle. For SHG signals that change as a function of time, measurement of all three polarization combinations at each point becomes nontrivial. Conversely, traditional measurements that neglect concentration-dependent changes in molecular orientation entirely could result in inaccurate results. ACKNOWLEDGMENT The authors gratefully acknowledge funding from the National Science Foundation.
Received for review March 23, 2000. Accepted June 14, 2000. AC000347K (14) Wirth, M. J.; Ludes, M. D.; Swinton, D. J. Anal. Chem. 1999, 71, 3911-7. (15) deMello, A. J.; Elliott, J. A.; Rumbles, G. J. Chem. Soc., Faraday Trans. 1997, 93, 4723-31. (16) Kemnitz, K.; Tamai, N.; Yamazaki, I.; Nakashima, N.; Yoshihara, K. J. Phys. Chem. 1987, 91, 1423-30.
Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
3411
