Anal. Chem. 1990, 62, 22151-2256
transient infrared spectroscopy in which a dynamic thermal gradient is induced so that the spectroscopic behavior of an optically thin layer of material differs from that of the rest of the sample. Like TIRES, TIRTS overcomes the problem of high optical density in solids that previously prevented the real-time infrared analysis of most solid samples. TIRTS and TIRES are insensitive to the reflectance and optical-scattering properties of samples, and function in real time without sample preparation. Unlike TIRES, TIRTS does not involve raising sample temperature, so it can be applied where elevated temperatures cannot be used.
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(7) Jones, Roger W.; McClelland. John F. Anal. Chem. 1990, 62, 2074-2079. (8) Kember, D.;Chenery, D. H.; Sheppard, N.; Fell, J. Spectrochlm. Acta, Part A 1979. 35, 455-459. (9) Brown. R. J.; Young, 8. G. Appl. Opt. 1975, 14, 2927-2934. (10) Fredericks, Peter M.: Osborn, Paul R.; Swlnkels, Dom A. J. Anal. Chem. 1985, 57, 1947-1950. (11) Frederlcks, Peter M.; Moxon, Neville T. Fuel 1986, 65, 1531-1538. (12) Malinowski, Edmund R.; Howery, Darryl G. Factor Anawsls In Chemist ~Wiley: ; New York, 1980. (13) The Merck Index, 10th ed.;Wlndholz, Martha, Ed.; Merck: Rahway, NJ, 1983. (14) Haaland, David M.; Thomas, Edward V. Anal. Chem. 1988, 6 0 , 1193-1202. (15) Haaland, David M.; Thomas, Edward V. Anal. Chem. 1888, 6 0 , 1202- 1208.
LITERATURE CITED Grifflths, Peter R.; Fuller, Michael P. I n Advances in InfraredandRamen spectroscopy: Clark, R. J. H., Hester, R. E., Eds.; Heyden: London, 1982; Vol. 9, pp 63-129. Fraser, David J. J.; Griffihs, Peter R. Appl. Spectrosc. 1990, 4 4 , 193-199. McClelland, John F. Anal. Chem. 1983, 55, 89A-105A. Grifflths. Peter R. Appl. Spectrosc. 1972, 26, 73-76. Jones, Roger W.; McClelland, John F. Anal. Chem. 1989, 6 1 , 650-656. Jones, Roger W.; McClelland, John F. Anal. Chem. 1989, 6 1 , 1810-18 15.
RECEIVED for review May 21,1990. Accepted July 27,1990. This work was funded by the Center for Advanced Technology Development, which is operated for the U.S. Department of Commerce by Iowa State University under Grant No. ITA 87-02 and in part (J.F.M.) by Ames Laboratory, which is operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-ENG-82, supported by the Assistant Secretary for Fossil Energy.
Integrated Optical Attenuated Total Reflection Spectrometry of Aqueous Superstrates Using Prism-Coupled Polymer Waveguides S. S. Saavedra and W. M. hichert* Department of Biomedical Engineering and Center f o r Emerging Cardiovascular Technologies, Duke University, Durham, North Carolina 27706
Attenuated total reflectlon (ATR) spectrometry of aqueous solutions In contact wlth polystyrene integrated optlcai waveguides has been Investigated. The mode-dependent absorption of evanescent energy by fluorescein solutions adjacent to the waveguide sutface was measured and compared to theoretical predlctlons based on a ray optlcs approach. Although enhanced sensitlvlty was observed with increaslng mode number, the sensttivlty for the highest order mode was less than that predicted by theory.
INTRODUCTION Attenuated total reflection (ATR) spectrometry is a wellestablished technique for obtaining absorbance spectra of opaque samples and thin films and for examining interfacial phenomena (I). The major limitation of ATR spectrometry is that its sensitivity is typically 3-4 orders of magnitude less than conventional transmission measurements using a 1-cm path length cell. This lower sensitivity is due to the small penetration depth of the evanescent wave into the absorbing medium, typically around 100 nm in the UV and visible regions of the spectrum. One approach to enhancing the sensitivity of ATR spectrometry is to increase interaction of the evanescent wave with the absorbing medium by increasing the number of reflections per unit distance along the internal reflection element (IRE)/sample interface. Since the number of reflections per unit distance is inversely proportional to IRE thickness, substantial enhancements in sensitivity are observed for very 0003-2700/90/0362-2251$02.50/0
thin IRES. This mode of enhancement was recently employed by Stephens and Bohn (2), who measured the absorption of evanescent energy by monolayers bound to the surface of a 150 pm thick glass coverslip. Even greater sensitivity can be realized with integrated optical (IO) waveguides that have thicknesses comparable to the wavelength of the propagating light and therefore support hundreds to thousands of internal reflections per centimeter (3, 4 ) . IO waveguides, particularly those fabricated from thin, transparent polymer films of micron dimensions, have attracted considerable interest as a means of acquiring Raman spectra from monolayers deposited on the waveguide surface or of the waveguide material itself (5-9). In spite of the low efficiency of Raman scattering, IO waveguide Raman spectroscopy is a feasible experiment due to (1)the extremely high optical field intensities that can be generated in the guide and (2) the increased path length created by the large number of internal reflections per centimeter. The concept of integrated optical waveguide ATR (IOWATR) spectrometry was discussed from a theoretical perspective by Midwinter almost 20 years ago (3). However, the only experimental application of IOW-ATR spectrometry to date was reported by Mitchell (41, who showed that aqueous solutions of bilirubin delivered to the surface of an IO waveguide through a flow cell attenuated the guided mode intensity via absorption of the evanescent wave. A major limitation of this approach was the significant refractive index discontinuities created by placing the in- and outcoupling prisms outside of the flow cell volume. These discontinuities essentially limited efficient prism to prism propagation to the 0 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 82, NO. 20,OCTOBER 15, 1990
lowest order mode, since it is the least sensitive to changes in superstrate refractive index (Le., the higher the mode order, the greater the fraction of energy in the evanescent wave and the greater the interaction with the superstrate media). In this paper, we have investigated ATR spectrometry of aqueous solutions in contact with prism-coupled IO waveguides. In contrast to Mitchell, we utilized a flow cell that subjected guided modes to a constant superstrate/waveguide refractive index ratio, which made mode-specific ATR measurements in aqueous media possible (10, 11). The modedependent attentuation of evanescent energy was measured from absorbing solutions introduced to the surface of polystyrene waveguides. The degree of attentuation increased with mode number, as expected, but was less than that predicted by theory for the highest order mode. Calculations of absorption density for a surface excess of fluorescein a t the waveguide/solution interface were used to estimate a detection limit on the order of 1O'O molecules/cm2, which corresponds to five parts per ten thousand monolayer coverage.
THEORY The phenomenon of total internal reflection a t the solid/liquid interface is well-known. The theory and practice of ATR spectrometry has been discussed extensively by Harrick (1). Prism-coupled IO waveguides have been discussed in detail by Swalen et al. (12). In the following discussion, we draw on these sources and others (13, 14) to present the pertinent expressions for transverse electric (TE) and transverse magnetic (TM) polarized IOW-ATR spectrometry. ATR Spectrometry of Bulk Samples and Thin Films. Let A b and Af be the integrated absorbances observed from a bulk and thin-film sample, respectively, in an ATR experiment. As discussed elsewhere (1, 13), the absorption of evanescent energy, per intemal reflection, by weakly absorbing bulk solutes (Ab/N) and thin films (Af/N) at the IRE surface is given by Ab/N
=
'bC&b
Af/N = VfLf
(1)
(2)
respectively, where N is the total number of internal reflections at the IRE/sample interface and tbcb and tflf are the products of the molar absorptivity and molarity for the bulk and thin-film samples, respectively. The terms L b and Lf in eqs 1 and 2 are the evanescent path lengths in the bulk and thin-film samples, respectively, and are given by =
(le/Ii)dp
(3)
L, =
(Ie/li)df
(4)
Lb
where df is the film thickness, d, is the depth of penetration of the evanescent wave, and df/d, < 0.1. The term dpis given by d, = (h/47rn2)[sin2 8 - (nl/n2)2]-'/2 (5) where n, and n2 are the refractive indices of the bulk and IRE media, respectively, and 0 is the angle of internal reflection, while Ie/Iiin eqs 3 and 4 is the evanescent transmitted interfacial intensity per unit incident intensity. For T E and T M polarizations, Ie/Ii is given by
(le/Ii)TM
=
lncoupllng
outcowling
pr15m
prlsm
n,
Schematic illustration of light coupled into and out of an IO waveguide using a pair of high refractive index prisms. The symbols denoting the optical and physical parameters of the apparatus are defined in the text. Figure 1.
subject to assumption that the refractive index of the film, nf, is constant with respect to the interfacial normal and is equal to the bulk refractive index (which is valid for very thin films with refractive indices that vary from the bulk by only a few percent). Integrated Optical Waveguides. Figure 1is a schematic illustration of light coupled from a high refractive index prism (n,) into a thin-film waveguide (nz)sandwiched between two semiinfinite dielectrics of lower refractive index (n, and n3, where n, < n2 > n3). Light will propagate in the waveguide via total internal reflection only at the internal guiding angles 6' that represent solutions according to the following eigenvalue equation
2K2dz- 2 tan-' (K1/K2)- 2 tan-' ( K 3 / K 2 )= 2ma (8a) where d2 is the waveguide thickness and m is an integer ( m = 0, 1, 2, ...). For T E polarization, K , is given by Ki,TE
= U, = (2~/A)4-
while for TM polarization K,,TM
[l
= Ui/ni2
(84
where ni is the refractive index of the ith medium. An internal guiding angle 0 that yields a guided mode can also be expressed in terms of the accompanying prism coupling angle 4 (Figure 1) according to the expression 6' = sin-' ((n,/n,) sin [sin-' ((sin $)/n,)
+ w])
(9)
where w is the prism acute angle and np is the prism refractive index. Typically, the refractive indices of the substrate and superstrate are known and a minimum of two prism coupling angles are measured. The waveguide thickness and refractive index can then be calculated from eq 8 by using an iterative technique. Reflection Density. By use of a ray optics approximation of waveguiding in IO structures, as shown in Figure 1, the number of reflections per unit distance ( N / D )a t the waveguide/superstrate interface for a waveguide of thickness d2 is calculated from
N / D = (2d2 tan 8
+ A,, + A23)-l
(10)
where D is the distance between the right angle corners of the incoupling and outcoupling prisms and AZ1and A23 are the Goos-Hanchen shifts a t the waveguide/superstrate and waveguide/substrate interfaces, respectively. According to Hirschfeld ( 1 4 ) ,AZ1and A23 for TE and T M polarizations are given by cos 8 sin 8 A21,TE
=
(Lb)21,TE
A23,TE
=
(Lb)23,TE
n1/n2 cos 8 sin 8
(12)
n3/n2
2 sin2 8 - (nl/n2)2 (le/li)TE
(8b)
+ (nl/n2)2J sin2 6' - (nl/n2)2
b1,TM
=
(Lb)21,TM
(7)
(nl/n2)[sin 6' - (sin 8)(n1/n2)2 - sin2 8 - (nl/n2)'1
(Note: eq 7 corrects eq 18b in ref 13.) Equations 1-7 are
(cos 8)(2 sin2 8 - ( r ~ ~ / n ~ ) ~ )
(13)
ANALYTICAL CHEMISTRY, VOL. 62, NO. 20, OCTOBER 15, 1990
2253
= (Lb)23,TM (n3/n2)[sin B - (sin B)(n3/nJ2- sin2 6' - (n3/n2)2]
A23,TM
(cos 8)(2 sin2 6' - ( n 3 / n J 2 )
(14)
The terms (Lb)Pl,TE, (Lb)23,TE, (Lb)21,TM, and (Lbl23,TM in eqs 11-14 represent the TE and T M polarized evanescent path lengths a t the 21 (waveguide/superstrate) and 23 (waveguide/substrate) interfaces. The evanescent path lengths at both interfaces are calculated from eqs 3-7, except n3 must be substituted for nl in eqs 5-7 when calculating values for the waveguide/substrate interface. IOW-ATR S p e c t r o m e t r y . If both a bulk solute and a thin film are adjacent to an IRE, then the total absorption of evanescent energy per reflection (A,/N) is given by the sum of the bulk (Ab/N) and thin-film (Af/N) absorbances. Therefore, normalizing eqs 1 and 2 to D , substituting from eqs 3 and 4, and rearranging yield the expression for total absorption (A,/D) of evanescent energy by a bulk solute and thin film adjacent to an IO waveguide per unit distance between coupling prisms At/D
= Ab/D + A f / D
= (N/D)(Ie/Ii)[ebCbdp =
cbCb(N/D)Lb
+ e$&]
+ e$f(N/D)&
5 z . I
0.002
3 a II)
( 154
(D
0.001
3
(15b)
P
(15~)
i
CI
3
where Ie/Ii,d,, Lb, and Lf are calculated from eqs 3-7 and N / D is calculated from eqs 1e-14. The terms (N/D)Lb and (N/D)Lf in eq 15c represent the bulk and thin-film evanescent path lengths, respectively, per unit distance along the waveguide/superstate interface. From eq 15b, it is clear that sensitivity in IOW-ATR spectrometry is mode-dependent because variations in evanescent path length will arise from mode-dependent variations in the terms N / D , Ie/Ii, and d,. In order to demonstrate the relative impact of these terms on an ATR experiment using a multimode IO waveguide, the terms ( N / D ) m ,(Ie/IJm, and d, were calculated for the five T E guided modes supported by a 2 pm thick polystyrene waveguide with an aqueous superstrate and a glass substrate. The calculated data were normalized to the corresponding values calculated for the m = 0 mode and are plotted in Figure 2A as a function of the internal waveguiding angle (see Figure 2 caption for IO waveguide parameters). It is evident from this plot that the terms (N/D)TEand ( I e / l i ) T E increase 4- and &fold, respectively, from m = 0 to m = 4, while d, remains relatively constant. Consequently, the number of reflections per unit distance and the evanescent interfacial intensity dominate mode-dependent changes in superstate evanescent path length for multimode IO waveguides. It is interesting to note that the maximum value of ( N / D ) T E occurs a t m = 3 rather than m = 4. This results from the Goos-Hiinchen shift, which only becomes significant near the cutoff condition for the highest order mode supported by the guide. The net effect of mode-dependent variations in (Ie/Ii)TE, and d, on the respective unit bulk and thin-film evanescent path lengths in the superstrate is demonstrated in Figure 2B. The plot shows that (N/D)T&b)P1,TE and (N/D)m(Lf)21,m increase by factors of approximately 23 and 19, respectively, from m = 0 to m = 4. It is therefore evident that substantial mode-dependent variations in an TOW-ATR experiment, using a multimode IO waveguide, will result from the concomitant mode-dependent changes in the evanescent path length. Similar variations in evanescent path length are predicted for T M polarized modes. EXPERIMENTAL SECTION
Polystyrene IO waveguides were fabricated according to published methods (10, 11). A TE polarized, 488-nm laser line was coupled into and Waveguide P r e p a r a t i o n a n d Characterization.
0.003
70
73
79
76
02
internal wavegulding angle
05
00
0000
If!
=
8
Figure 2. Interfacial optical parameters as a function of the theoretical internal waveguiding angles 8, for a 2 p m thick polystyrene waveguide supporting five TE modes. The refractive n , , n 2 , and n 3 are 1.333, 1.600, and 1.510, respectively. Panel A: ( N / O h (circles), ( I J I , h in the superstrate (triangles), and d , in the superstrate (squares) are each normalized to the respective value for the m = 0 mode. Panel B: Unit bulk ((LJ2,,4N/&, rectangles) and thin-film ((L,)2,,#/Dh, triangles) evanescent path lengths in the aqueous superstrate are plotted. A value of 10 nm for the film thickness d , was assumed.
out of waveguides by using a pair of 45-45-90 LaSF5 prisms (O'Hara Optical). Incoupling angles @,,at which guided modes were launched in waveguides, were measured with a high-resolution goniometer (Picker X-Ray), as described previously (IO). From the observed &, waveguide thickness and refractive index were rlpterminpd
hv i i e p nf
R
mftwnvp nrnurim thnt mnvpruprl
been prepared and evaluated, this paper presents results derived from a single waveguide that supported five modes and had a refractive index of 1.600 and a thickness of 2.452 pm. Utilizing the convergence program in the reverse direction allowed the theoretical internal guiding angles and the number of guided modes anticipated for a waveguide of specified thickness and refractive index to be calculated. The software used in this study was developed by Ives with local modifications (15). I O W - A T R S p e c t r o m e t r y . The construction and operation of the flow cell have been described previously (10, 11). When waveguides are properly coupled in this flow cell, the mode structure established at the incoupling prism is maintained throughout the waveguiding structure. Figure 3 is a schematic of the optical configuration used to perform IOW-ATR spectrometry. The flow cell assembly was mounted on the goniometer stage with the right angle corner of the incoupling prism placed at the center of rotation. Rotation of the stage with respect to the stationary laser beam allowed the incoupling mode angle to be selected. The outcoupled mode pattern was directed onto a paper screen and photographed with a charge-coupled device (CCD) array detector cooled to -110 OC, as described previously (10, II), yielding a two-dimensional pixel image of the pattern. The CCD was binned 10-fold in the vertical direction. Attenuation of guided mode intensity due to superstrate absorbance was assessed by using solutions of fluorescein (Sigma) dissolved in distilled-deionized water. Solutions were infused into the flow cell at approximately 3 mL/min. Outcoupled mode
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 20, OCTOBER 15. 1990 liquid out I
integration
pixel image
P
band location
Flgure 3. Layout of the optical system used to record and quantitate outcoupled mode patterns from 10 waveguides. Note that tuning the waveguide to higher incoupling angles Shifts the location at which the outcoupled light Sbikes the screen to the left. This effectis manifested in a migration of the outcoupled nude patterns to lower pixel positions with increasing mode number of incoupled light
Flgure 4. Mncoupled mode patterns. integrated in the vertical direction. rexrdec from a five-modepolystyrene waveguide (2.452 Fm, n2 = 1.600) under a aqueous superstrate. The images were collected as a function of both incoupling mode angle (m = 4, 2. or 0, labeled from left to right) and bulk concentration of fluorescein in the superstrate. The fluorescein concentrations, from rear to front traw. were 0, IO*, lo-'. IO-', and M. Note the migration 01 the outcoupled mode patterns to lower pixel posRions as the incoupled light is tuned to higher order modes (i.e. increasing mode number).
A P
Table I. Theoretical TE Evanescent Path Length Parameters for a 2.452-rm Polystyrene Waveguide' mode no. parameter 8, de$
d,nm
(LllJ, (Ld~1.m. nm
m=O
m=2
m=4
86.67 44.13 0.6325 27.91 118.6
80.14 46.15 1.865 86.05 352.9
73.34 51.32 3.124 160.3 593.1
(Nlcm),, 'Refractive indices are n, = 1.333, nl = 1.600, bCalculated from 4: using np = 1.840 and w = 44.9'.
n3 =
pattern images, corrected for dark count, were recorded as a function of both incoupling mode angle and solute concentration. For statistical purposes, three mode pattem images were recorded at each incoupling angle and concentration. The position and absolute intensity of the outcoupled mode maxima were determined by averaging pixel intensities in the vertical direction of the mode pattern images, by use of Photometrics, Ltd., data analysis software. The background (stray light) intensity was estimated from the average pixel intensity in off-mode regions of the recorded images (regions where modes were not observed). Under the assumption that the stray light was constant over the entire image area, hackground-corrected mode maxima were obtained by subtracting the off-mode background intensity from the absolute (raw) intensities of the mode maxima.
[fluoresceinl Figure 5. Absorbance per centimeter at the waveguidelsuperstrate interfaceas a function of mode and fluorescein concentration fathe waveguide described in Figure 4: m = 4. triangles; m = 2, squares; m = 0, circles. Panel A: Experimentally measured A,/cm (open symbois) and calculated A,/cm (filled symbols)data are plotted. A,/Cm data were calculated as A,/cm - A,lcm. Panel E: Theweticat A&m data, computed from parameters listed in Table I, are plotted.
RESULTS AND DISCUSSION Quantitative Comparison of Mode-Dependent Evanescent Attenuation. T o quantitatively measure modedependent differences in integrated evanescent path length, experiments were performed with a polystyrene waveguide that supported five TE modes (d2 = 2.452 Fm, n2 = 1.600). From the measured incoupling angles, the parameters d,, I J I ~ , T E(L&,E, , and (NIDI, were calculated for the m = 0, m = 2, and m = 4 modes according to eqs 3,5,6,and I t 1 2 and are listed in Table I. The rear trace of Figure 4 shows the outcoupled mode patterns collected for light launched into the m = 4, m = 2, and m = 0 modes of this waveguide under a water superstrate. In all cmes, the mode of maximum intensity in the outcoupled pattern matched the excitation mode, indicating that the integrity of the mode structure was maintained throughout the waveguiding structure. Significant intermodal scattering was observed in this waveguide only for m = 4 excitation, which is consistent with our experience that intermodal
scattering typically increases with mode number. Solutions of fluorescein ranging in concentration from IO* to lW3 M were infused into the flow cell, and outcoupled mode p a t t e m were collected form = 4,m = 2, and m = 0 excitation at each solute concentration. The outcoupled mode patterns at 10-6-iO-3 M fluorescein are shown in Figure 4 and exhibit mode-dependent attenuation. At M fluorescein, t h e m = 4 outcoupled intensity excited at m = 4 was substantially attenuated from the pure water condition, while the m = 2 outcoupled intensity excited a t m = 2 exhibited moderate attenuation and the outcoupled m = 0 intensity excited a t m = 0 showed little effect. At lo4 M, m = 4 was almost completely attenuated, m = 2 was substantially attenuated, and m = 0 only moderately attenuated, while at M, m = 4 and m = 2 were extinguished to the stray light level, hut m = 0 remained detectable. From the digitized images in Figure 4, total absorbance data were calculated for the three primary outcoupled modes that corresponded to the three excitation modes. The data are
log
ANALYTICAL CHEMISTRY, VOL. 62, NO. 20, OCTOBER 15, 1990
Table 11. Comparison of Experimental and Theoretical Thin-Film Absorbance (TE Polarization) mode no. parameter
exptl slope from Af vs Cb’** correlation coeff normalized exptl thin-film path length‘ normalized theortl thin-film path lengthd
m=O m = 2 m = 4 305.8 0.992 1.00 1.00
2550 1.000 8.34 8.77
4411 0.998 14.42 24.71
Slope is given by eq 16 in the text. *For cb range 10”-104 M. cExperimental slope normalized to m = 0. dTheoretical ( N / D)(Ze/IJmcalculated from parameters listed in Table I and normalized to m = 0. plotted as A,/cm a t the waveguide/superstrate interface in Figure 5A (open symbols). Quantitative evaluation of the mode-dependent attenuation in this plot requires that the contributions of the thin-film (Af) and bulk solute (Ab) absorbances to A, be separated. The theoretical contribution of Ab/cm to A,/cm was calculated from eq 15c by using t b = 72000 M-’ cm-’ (our measurement) and the values of (Lb)pl,m and listed in Table I. The resulting data are plotted in Figure 5B. (Note that the Beer-Lambert approximation implicit in eq 15c is valid here, since the maximum value of A,/N measured was 9.4 X for lo4 M fluorescein in m = 4). Although the shapes of the A,/cm and Ab/Cm curves are similar, it is apparent from their relative magnitudes that the contribution of bulk solute absorbance to total absorbance is small. The majority of the total measured absorbance is therefore due to a surface excess of fluorescein a t the polystyrene/solution interface. The fraction of the total absorbance due to the surface excess was computed according to eq 15a as the difference between the A,/cm and theoretical Ab/cm data. The resulting Af/cm data are also plotted in Figure 5A (filled symbols). The Af/cm data (Figure 5A) were plotted against bulk solute concentration over the range 104-104 M, and a linear least-squares fit was performed for each mode (lines not shown). The experimental slope of the least-squares line and the correlation coefficient are listed in Table I1 for each mode. From eqs 15a-c, Af/cm is given by (N/D)(I,/Ii)tF&, which may be expressed in terms of the bulk concentration cb by using a proportionality function K Af/cm = K [(N/D)(Ie/Ii)etdflCb (16) where cf = Kcb relates the thin-film concentration to the bulk concentration. Therefore, according to eq 16, the slope of a least-squares fit to Af/cm vs cb is given by the expression K [(IV/D)(Ie/Ii)t,df].Since the mode-dependent variation in slope occurs only in the term (N/D)(Ie/Ii)(i.e., all other terms are constant for each mode), then the ratio of any two slopes is the ratio of the TE integrated thin-film evanescent path lengths of those two modes. Consequently, the experimental slopes of the least-squares lines were normalized to the m = 0 slope to permit comparison of the observed mode dependency in the term (N/D)TE(Ze/Ii)TEwith theoretical predictions. The normalized experimental slopes are listed in Table 11. The theoretically predicted values of (N/D)~&/li)m, also normalized to m = 0, were computed from the parameters in Table I and are also listed in Table 11. The experimental m = 2/m = 0 ratio of TE integrated thin-film evanescent path lengths is 8.34, which is in excellent agreement with the theoretical ratio of 8.77. Thus,both theory and experiment are in agreement that 8-9 times more sensitivity in IOW-ATR spectrometry of a thin film is realized by working in m = 2 than in m = 0. However, the experimental m = 4/m = 0 ratio is only 14.43, or approximately 60% of the theoretically predicted ratio of 24.71. Thus, only 60% of the theoretically predicted sensitivity was experimentally
2255
observed for m = 4 relative to m = 0. Some possible contributing factors to this discrepancy between experiment and theory are (1) the thin-film and two-phase approximations implicit in eq 2, (2) mode-dependent intermodal scattering, and (3) mode-dependent stray light. In the derivation of eq 2, the approximations were made that df < O.ld, and that Ie/Zi is not affected by the presence of the film (I,13); To assess the effect of these approximations on the measured absorbance, the mode-dependent error in Af/cm was calculated for a 10 8, thick film having a refractive index of 2.0. (Ie/Ii)TE for this three-phase interface (waveguide/fluorescein film/bulk solution) was calculated by using the stratified media technique developed by Hansen (16). The net effect of both approximations is a reduction of 3% in Af/cm for m = 4 relative to m = 0. Therefore, although the thin film and two-phase approximations should contribute to the observed discrepancy, their effect is small. If scattering occurs within a waveguide from the excitation mode to the other modes, then the reverse process is also likely. Since attenuation by an absorbing superstrate is mode-dependent, the net effect of intermodal scattering within the waveguide will be to reduce the theoretically predicted ratio of evanescent path lengths of the highest to lowest order modes. However, since intermodal scattering was significant only for m = 4 excitation, the m = 4 evanescent path length should be reduced by this effect while the m = 2 and m = 0 evanescent path lengths should be little affected. Therefore, mode-dependent intermodal scattering probably contributes to the discrepancy between the theoretical and experimental m = 4/m = 0 ratios of thin-film path lengths, although its contribution cannot be quantitiated. Finally, the contribution of stray light to outcoupled mode intensity varied with the excitation mode. By comparison of the outcoupled mode pattern images in water (Figure 4)) the stray light component for m = 4 excitation was 32% of the intensity a t the outcoupled m = 4 mode maximum, whereas for m = 2 and m = 0, the corresponding values were 11 and 14%, respectively. Since the relative stray light contribution increases with absorption, the uncertainty attributable to the stray light correction method (see Experimental Section) was substantially greater for m = 4 than for the lower order modes. It is suspected that mode-dependent stray light was a major contributor to the discrepancy in the m = 4/m = 0 ratios listed in Table 11, although like intermodal scattering, this error cannot easily be quantitated. To this point, it has been assumed that adsorption of a thin film at the waveguide/solution interface has no effect on the internal waveguiding angles. However, if the film and superstrate refractive indices are not equal, shifts in internal waveguiding angles, and hence incoupling angles, would be expected ( 3 ) . Consequently, the theoretical changes in incoupling angles expected upon adsorption of a 10 8, thick film with a refractive index of 2.0 were calculated. For the polystyrene waveguide used here, the change in incoupling angle for all modes was less than the respective standard deviation of the measurement. The absorbance data plotted in Figure 5 were therefore not measurably affected by coupling angle shifts. Adsorption Density. The adsorption density (in moles per centimeter squared) of a thin film adsorbed a t an IRE/ solution interface can be calculated from eq 15b by rearranging to solve for the term d F f . Sperline et al. (17) have demonstrated this approach for FTIR/ATR spectrometry by using the reference absorbance of a non-surface-active solute to eliminate the need for independent determination of the internal waveguiding angle (6) and the number of reflections (N). Since 8 and N are
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 20, OCTOBER 15, 1990
01
05
09
13
17
wavegulde thlckness
21
25
4 (wm)
Figure 6. Theoretical (Nlcm),.#,l,h, plotted as a function of waveguide thickness d , for ail modes supported by a polystyrene Waveguide is the mode(optical parameters given in Figure 2). (Nlcm),.&l,ll,h and d,-dependent term in the expression for integrated evanescent thin-film path length in the superstrate (eq 15b with D in centimeters) and is proportional to theoretical ATR sensitivity. Data were calculated at 0.1-pm intervals for d , 1 0.3 pm and at a higher density for d , 5 0.3 pm. The decrease in ( N l D h ( l , l I , h at thicknesses slightly less than cutoff for each mode is due to the Goos-Hanchen shift.
known in an IOW-ATR experiment, dFrvalues were calculated here directly from eq 17 by assuming that (1) the thin-film molar absorptivity was equal to the bulk value and (2) the orientation of adsorbed molecules with respect to the surface was isotropic. Good agreement was obtained among the dFf values computed for m = 0, m = 2, and m = 4 a t the bulk fluorescein concentrations that yielded appreciable thin-film absorbances for all three modes. The average absorption densities at bulk concentrations of and lo4 M were (1.8 f 0.36) x lo-'' and (1.0 f 0.24) x lo-" mol/cm2, respectively. The quantity 1000N(Ie/Il)tf in eq 17 is the sensitivity of the absorption density measurement ( I @ , from which a limit of detection for surface-adsorbed fluorescein can be estimated. Taking the detection limit to be 3 times the standard deviation of the minimum detectable absorbance and correcting for the lower sensitivity observed experimentally, a detection limit of 9.2 X mol/cm2 is estimated for the m = 4 mode. This limit would of course be correspondingly higher for a molecule with a molar absorptivity weaker than fluorescein. The detection limit can also be expressed in terms of a surface coverage by estimating the size of a fluorescein molecule. From geometric addition of the bond lengths, the dimensions of the molecule were estimated to be 9 A x 10 A X 11 A, giving a cross sectional area of about 100 A2. A complete monolayer would therefore correspond to an adsorption density of 1.7 x mol/cm2, yielding an estimated detection limit of 5.4 x monolayer fractional coverage. In the experiments described here, relatively thick, multimode waveguides were employed so that the mode-dependent variations in evanescent path length predicted by theory could easily be measured. However, since N is inversely proportional to the waveguide thickness dz,better sensitivity is predicted for thinner waveguides. In Figure 6, the term ( I V / D ) ~ ~ ( I in~ eq / Z 15b ~ ) ~(calculated for the superstrate) is plotted against d, for all T E modes supported by polystyrene
waveguides ranging in thickness from 0.15 to 2.452 pm. The plot shows that as dz is reduced to 0.2 pm, (N/D)TE(le/li)TE increases 9-fold for the highest order mode supported by the guide, which could in turn yield a 9-fold lower detection limit. However, for this enhanced sensitivity to be realized, the experimental difficulty of higher scattering losses associated with the increased internal path length in thinner waveguides would have to be addressed. This difficulty is compounded by the observation that waveguides which exhibit very low scattering losses when prism coupled in air will often show significantly more scatter in water (IO). The five-mode waveguide employed here for quantitative studies was of exceptional quality, but our success rate for fabricating waveguides of this quality and properly coupling them in water is less than 10%. Finally, since the polystyrene film was pulled off the substrate upon disassembly of the flow cell, only one experiment under an aqueous superstrate was possible per waveguide. To circumvent this limitation, we are currently investigating the use of inorganic glass-on-glass waveguides.
ACKNOWLEDGMENT Appreciation is extended to J. T. Ives of the University of Utah for providing the waveguide software, W. N. Hansen of Utah State University for providing the stratified media software, H. Z. Massoud of Duke University for use of the clean room facility, and D. S. Walker of Duke University for helpful comments. LITERATURE CITED Harrick, N. J. Infernal Reflection Spectroscopy, 2nd ed.; Harrick Scientific: New York, 1979. Stephens, D. A,; Bohn, P. W. Anal. Chem. 1989, 67,386. Midwinter, J. E. IEEE J . Quanfum Electron. 1971, QE-7, 339. Mitchell, G. L. IEEE J . Quantum Electron. 1977, QE-73, 173. Rabolt, J. F.; Santo. R.; Swalen, J. D. Appl. Specfrosc. 1980, 3 4 , 51'7. Rabott, J. F.; Schlotter, N. E.; Swalen. J. D. J . Phys. Cbem. 1981, 85, 4141
Rabott, J. F.; Santo, R.; Schlotter, N. E.; Swalen, J. D. IBM J. Res. Dev. 1982. 26. 209. Rabe, J. P:; Swaien, J. D.; Rabott, J. F. J . Cbem. Pbys. 1987, 8 6 , 1601. Miller, D. R.; Han, 0. H.; Bohn, P. W. Appl. Specfrosc . 1987, 4 7, 249. Saavedra, S.S.;Reichert, W. M. Appl. Specfrosc., in press. Saavedra. S. S.; Reichert, W. M. Appl. Specfrosc., in press. Swalen, J. D.; Santo, R.; Tacke, M.; Fischer, J. IBM J . Res. Dev. 1977, 21, 168. Reichert, W. M. Crit. Rev. Blocompat. 1989, 5 , 173. Hirschfeld, T. Appl. Specfrosc. 1977, 3 7 , 243. Ives, J. T. Ph.D. Thesis, University of Utah, 1990. Hansen, W. N. J. Opt. SOC.Am. 1988, 58,380. Speriine, R. P.; Muralidharan, S . ; Freiser, H. Langmuir 1987, 3 , 198. Strobel, H. A.; Heineman, W. R . Chemical Instrumentation: A Sysfemafic Approach, 3rd ed.; Wiley: New York, 1989; Chapter 10.
RECEIVED for review April 24, 1990. Accepted July 26, 1990. This research was funded by NIH Grant HL32132 and a biomedical research grant from the Whitaker Foundation. S.S.S. gratefully acknowledges fellowship support from the NSF Engineering Research Center for Emerging Cardiovascular Technologies.
