Anal. Chem. 1989, 6 1 , 656-660
856
LITERATURE CITED (1) Griffiths, Peter R. Appl. Spectrosc. 1072, 26, 73-76. (21 Lin. L. T.: Archibald. D. D.:Honlas. D. E. A,m . / . Soectrosc. 1088. 42. 477-483. (3) Chase, D. B. Appl. Spectrosc. 1981, 3 5 , 77-81. (4) Kember, D.;Chenery, D H.; Sheppard, N.; Fell, J. Specb-ochim. Acta, Part A 1070, 35A, 4551459. (5) Handke, M.; Harrlck, N. J. Appl. Spectrosc. 1986, 4 0 , 401-405. (6) Chen, Inan; Lee, Sanboh J . Appl. Phys. 1083, 5 4 , 1062-1066. (7) Hill, James M.; Dewynne, Jeffrey N. Heat Conduction; Blackwell SCIentific: Oxford, U.K., 1987; pp 8-1 1. (8)Chang, Shu-Sing In Thermal Analysis in Polymer Characterization; Turi. E. A.. Ed.: Hevden and Son: Philadelahia. PA. 1981: DO 98-113. (9) Erk, S.; Keller, A.;*Poltz, H. Phys. 2. 1937, 38, 394-402: 1
.
(10) Handbook of Chemistryand Physics, 62nd ed.;Weast, Robert C.. Ed.; Chemical Rubber: Cleveland, OH, 1981; p C-753.
RECEIVED for review August 16, 1988. Accepted December 22, 1988* This work was funded in part by the Center for New Industrial Materials, which is operated for the U.S.Department of Commerce by Iowa State University under Grant No. ITA 87-02, and in part by AmeS Laboratory, which iS Operated for the U.S. Department of Energy by Iowa State University under Contract No* supported by the Assistant Secretary for Fossil Energy. W-7405-ENG-829
Silver-Coated Fumed Silica as a Substrate Material for Surface-Enhanced Raman Scattering A. M. Alak’ and T. Vo-Dinh* Advanced Monitoring Development Group, Health and Safety Research Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6101
A new and simple type of substrate for surface-enhanced raman scatterlng (SERS) was lnvestlgated. This new substrate Is based upon sliver-coated fumed slllca on surfaces such as glass plates or microscopic slides. Fumed slllca, which has submkrometer size structure provides the surface roughness necessary for SERS process. The effects of several experlmental factors, lncludlng the type of fumed siilca, the concentratlon of the mlcropartlcles, and the sllver layer thickness were Investlgated. The SERS spectra of various organk species were used to demonstrate the efficiency and applicabHity of the new substrate. Fumed-slllca-based substrates offer many advantages, since they are slmple to prepare and easy to handle. The bask material, fumed slllca, Is also commercially avallable at very low cost.
INTRODUCTION Raman spectroscopy has proved its usefulness as a practical tool for organic analysis (1,2). A major disadvantage of the Raman technique, however, is the small scattering cross section that often requires the use of powerful and costly laser sources for excitation. Recently, a renewed interest has developed in Raman spectroscopy as a result of discoveries of “giant enhancement” in the Raman scattering efficiency when an analyte molecule is adsorbed on metal surfaces or metal particles in solutions (3-8). Many theoretical models have been developed to explain the large Raman enhancement and to account for both the physical and chemical effects associated with the surfaceenhanced Raman scattering (SERS) (5). More than one mechanism appears to contribute to the SERS phenomenon. One major contribution to Raman enhancement is associated with amplified local electromagnetic fields a t the surface. These fields originate from roughness-induced excitation of surface plasmons (5)and from the concentration of the electric field lines near high-curvature points of the surface (8,9). If the adsorbate molecule is relatively close to the surface, image ’Present address: M e r r e l l Dow Pharmaceuticals, Inc., 2110 Galbraith Rd.,Cincinnati, OH 45215.
E.
dipole and the modulated reflectance mechanism may also contribute to Raman enhancement (5). This electromagnetic enhancement contribution is not molecule-specific and does not require physical contact between adsorbate molecule and metal surface. Enhancement is also attributed to the modification of molecular polarizability and, hence, the Raman cross section. This modification of the molecular polarizability is caused by interaction of molecules and metal surface through chemisorption, a process that consists of the formation of a complex between analyte molecules and the atoms of the metal surface (10). The chemical mechanism implies the presence of “active sites” or structures on the surface capable of forming particular molecular configurations. In contrast to the electromagnetic model, in which the enhancement mechanism has a long-range character, the “active site” model involves an enhancement mechanism limited to the molecular layer in direct contact with the metal surface. Another chemical concept called “adaatom”, which involves chemical adsorption between the analyte molecule and the substrate ( I l ) , may also be involved in the surface enhancement process. Generally, the observation of SERS of molecules adsorbed on metal surfaces requires that the metal surface be roughened. The specific nature of this roughness, and its exact role in the enhancement, has been a subject of considerable debate (5). The three common types of substrates used in SERS were chemical electrodes, colloidal sols, and island films prepared by vacuum deposition of silver. Repeated oxidation-reduction cycles were used to dissolve and redeposit silver to provide a rough surface. The repeated oxidation-reduction process gives a rough surface, which will induce enhanced Raman scattering via the electromagnetic enhancement mechanism ( 4 , 5 ) . The use of silver sol for obtaining SERS has attracted considerable interest among analytical chemists because of its experimental simplicity. Other types of SERS-active solid substrates involving metal-covered surfaces having submicrometer structures, such as microspheres, quartz post, etc., have been reported (12-1 6). Previous studies in this and other laboratories (12-20) have demonstrated the effectiveness and potential of SERS as a powerful spectrochemical technique to identify and quantify different compounds such as nitropolyaromatic hydrocarbons, drugs, organophosphorus chemicals, and pesticides using
0003-2700/89/0361-0656$01.50/00 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 7, APRIL 1, 1989
SERS-active substrates based on silver-coated microspheres. In this study a new and useful type of substrate for SERS is investigated. This new substrate involves evaporating silver onto solid surfaces, such as glass slides, covered with fumed silica. The fumed silica materials have submicrometer structure which provides the surface roughness necessary to the S E W process. Fumed silica offers many advantages since it is easy to handle and commercially available at very low cost. The results demonstrate that the fumed-silica-based substrates are very efficient and produce large SERS enhancements. Different types of fumed-silica materials having different particle diameters were investigated. Measurements with a variety of organic chemicals demonstrated the usefulness of this new type of SERS substrate.
657
Table I. SERS Intensity as a Function of Fumed Silica Size"
fumed silica typeb L-90 LM-5 M-5 EH-5
nominal
SERS intensity
surface area,b
particle
(photon
diameter,b
m2/g
Pm
counts) X IO3
re1 std dev: %
100 f 15
0.027 0.017 0.014 0.007
4.59 2.93 1.35 1.47
22 20 18 24
160 f 15 200 f 25 380 f 30
Fumed-silica materials were suspended in aqueous solution to give 3% solution. bData supplied by vendor. cAverage of five measurements. The silver thickness used was 70 nm.
EXPERIMENTAL SECTION Instrumentation. SERS measurements were conducted with a SPEX (Model 1403, SPEX Industries, Metuchen, NJ) double-grating spectrometer equipped with a gallium arsenide photomultiplier (RCA, Model C31034) used in the single-photon counting mode. The slit widths of the monochromators were set at 0.8 mm, providing a spectral resolution of 0.4 nm. Data storage and treatment were performed on a SPEX Datamate DMI processor. The laser line used for excitation was the 647.1-nm line from a krypton ion laser (Innova Model WK,Coherent, Palo Alto, CA). Approximately 40 mW of laser light was used to irradiate the sample. A 60° angle geometry was used for excitation and detection. The scan rate of the monochromator was 200 cm-'/min. No background substraction was performed. A five data point smoothing procedure was used. Photographs of the substrate shown in this work were obtained with a Novascan 30 scanning electron microscope. Procedure. Fumed silica materials were provided by Cab-0-Sil (Cabot Corp., Tuscola, E)and used as received. The fumed-silica materials were suspended in aqueous solution to give the desired concentration. The substrate preparation involved two steps. The first step was the deposition of fumed silica on a glass microscope slide. This deposition was accomplished by placing a glass slide on a spin-coating device. A few drops of the aqueous fumed-silica solution were placed on the glass slide, which was then spun at 2200 rpm for 20 s. The second step involved coating of silicacoated glass slide with silver. The silica-coated glass slide was attached to a motor mount and placed inside a vacuum evaporator. The rate of deposition was 2 nm/s. The substrate was then rotated at a 65O angle over the silver source during silver evaporation, which occurred at a pressure below 2 X lo4 Torr. The rate of silver deposition was measured with a Kronos Model QM-311 quartz crystal thickness monitor. The substrates were removed from the evaporator after silver deposition and used directly. For most studies the substrates were freshly prepared and used on the same day for SERS measurements. When they could not be used on the same day, the substrates were stored under nitrogen atmosphere to minimize contamination and/or oxidation. Benzoic acid, phthalic acid, and anthracene were purchased from Aldrich Chemical Co. (Milwaukee, WI). Dinoseb was provided by the Environmental Protection Agency, Environmental Monitoring Systems Laboratory (Las Vegas, NV). Sample solutions (104-10-6 M) were prepared in spectroscopic grade ethanol (Aagar Chemicals).
RESULTS AND DISCUSSION The experimental parameters investigated in preparing the silver-coated fumed-silica substrates included the type of fumed-silica materials, the concentration of the fumed silica, and the silver layer thickness. The effect of these parameters on the SERS intensity was determined by using benzoic acid as the model compound. The effectiveness of the SERS process has been found experimentally to be related to surfaces possessing some form of roughness. As a result, there have been various experimental studies investigating microstructures that can be correlated with theoretical electromagnetic models (24-27). In general, it is difficult to produce microstructures with
morphologies and defined surface roughness that can be readily compared with electromagnetic calculations. For analytical purposes, the control of surface roughness is a critical factor that can strongly affect the SERS process. From this viewpoint, fumed-silica materials provide a simple way to control and determine the surface roughness of the substrates by selecting the appropriate silica particle size and particle suspension concentrations. The results of surface roughness and SERS dependence studies are given in Table
I. Fumed-silica materials are available a t different grades depending on the surface areas and nominal particle diameters. Different fumed-silica materials, with surface areas ranging from 100 to 380 m2/g and nominal particle diameters from 0.007 to 0.027 pm were investigated in this study. The intensity of the 1004-cm-' vibration of the SERS spectra of a 3-pL sample of IO-' M benzoic acid was used as the measured signal. Table I gives physical properties of different fumedsilica materials and the SERS intensity as a function of the silica particle diameters. According to the experimental data, the maximum SERS intensity is produced by the substrates having the fumed silica (L-90 type) which have the largest nominal particle diameter (0.027 pm). The lowest SERS intensity is exhibited by the smallest silica sizes, 0.014 and 0.007 pm. The fumed silica particles that produced the largest SERS enhancement (L-90) were used as a substrate to induce SERS spectra in the remaining measurements of this study. Silver was used in this study as the surface coating material, because silver had shown the best results in inducing SERS (5, 11). We have investigated the effect of using different thicknesses of silver coatings on the SERS process. Various silver deposits having a thickness between 10 and 200 nm were investigated. The SERS signals observed for adsorbed benzoic acid increased with increasing silver thickness, reaching a maximum with 60-100 nm of deposited silver. With a silver thickness above 100 nm, the SERS signal sharply decreased due to the fact that a layer of silver that is too thick will smooth the surface and therefore decrease the SERS effects. On the other hand, a film of silver that is too thin can be destroyed by the sample spotting. No noticeable change in the SERS intensity was observed in the region between 60 and 100 nm. Most of the measurements in this study were made on silver films of 70 nm thickness. Comparative measurements were made by using different concentrations of L-90 fumed silica in aqueous solutions. Figure 1 shows the variation in the SERS intensities as a function of fumed-silica concentrations. The 1004-cm-' vibration of benzoic acid (3-pL sample, loT4M) was used again as the reference signal. The fumed-silica concentration investigated ranged between 1%and 10% (w/w). Use of higher concentrations was limited by the aggregate formation of the fumed-silica particles. Lower concentrations of fumed silica did not form a uniform layer when deposited over the glass
058
ANALYTICAL CHEMISTRY, VOL. 61. NO, 7. APRIL 1. 1989
2
4
6
S
10
%FUMED SILICA
Flgure 1. SERS signals as a function of the concentration of fumed silica in suspensions used lo produce SERSactive substrates. (The lumed silica used was L-90 which has a surface area of 100 15 m'lg and a nominal parlicie diameter of 0.027 pm. The SERS signal
*
the 1006cm-' band of adsorbed benzoic acid is used as the reference.) 01
Figure2
\ ; : , , F n i i ~ ~ ~ . i ~ n ~ . . . ~ ; *r r. -. ,i ~. - ;
I
C.l-;
n a . q 3 0 . L..Jc~.".eas ' ~ j , C O i l t W , . n a g e s ~ 2 - ! Tr ~ PCF lnc*-ess *as 50 nm
:-vi,te .,,or
.P,
suhstrates. A fumed silica of 090 concentration gave the best SERS enhancement. Figure 2 shows a phokwaph of a fumed silica surface prepared with a 390 solution of L-90 silica obtained by a scanning electron microscope (SEMIafter deposition of silver having a thickness of d , = XJnm using an evaporation angle, R- = 6 5 O . The photopaph shows that the siher particles are welheparated from one another and the surface is uniformly covered by the silver particles deposited on the top of the fumed silica. This indicates that the 3% solution of fumed silica gives a well-defined roughness and the structures needed for the giant Raman enhanrement.
nSre 3. (A) Surfaw-mhanced Raman scattering spectrum of a 3-pL sample of IO-' M benzoic acid. (E) Conventional Raman spectra of pure benzoic acid. The ktypton laser excitation line was 647.1 nm. Several advantages associated with fumed silica are the ease of handling and the low cost of the fumed silica which is
commercially available in various types and sizes. The simplicity of the sample preparation is the main advantage of these substrates. The fumed-silica-based substrates do not require elaborate and time-consuming etching procedures. In order to compare the fumed-silica substrates with the previously used microsphere substrates, we selected microspheres of 0.364 pm, which gave the best SERS enhancement (15) for comparative measurements. Two types of substrates, fumed silica and 0.364-pm microspheres, were prepared under the m e experimental conditions (Le.. angle of evaporation, silver layer thickness, laser power, and angle of excitation). In all these measurements, silver-covered fumed-silica substrates gave better SERS signals than the microsphere particles. The SERS signal, for example, of the 1004-cm-' vibration peaks of benzoic acid using microsphere substrates was 2.97 X lo3 photon counts compared to 4.59 X loTphoton counts for the 3% (L-90) fumed-silica substrate. Figure 3 shows a SERS spectrum of benzoic acid on fumed silica (390, L-90). Benzoic acid was selected as the model compound because the SERS spectrum of this compound has been extensively investigated (3, 12, 16,24). Only 3 pL of a lo4 M solution of benzoic acid in ethanol was spotted on the substrate. It is of interest to compare the Raman spectrum obtained with pure benzoic acid (Figure 3R) to the SERS spectrum of 10.' M benzoic acid. Whereas the major peaks at 1004 and 1600 cm-' are similar to those of pure benzoic acid obtained by conventional Raman measurements. the hands at 1630 and 1288 cm-' attributed to the C=O stretching mode obtained by using conventional Raman measurements are not present in the SERS spectrum. The interactions between the analyte molecules and the SERS-active substrate surface cause spectral shifts in the SERS hands at 420,616, 794,1820, and 1442 cm-'. These shifts can range from a few reciprocal
ANALYTICAL CHEMISTRY, VOL. 61, NO. 7, APRIL 1, 1989
-
t
1l24
VI
52
659
1 00 -
4 U
E E
8 -
I
4 >
VI
a Y 2
I
I 200, 200
400
600
800
1000
1200
1400
1600
1800
200
400
BOO
800
RAMAN SHIFT (crn”)
1WO
1200
1400
1600
1800
RAMAN SHIFT (crn”)
Flgure 4. Surface-enhanced Raman scattering spectrum of a 3-pL sample of lo-‘ M dinoseb.
Figure 6. Surface-enhanced Raman scattering spectrum of a 3-pL sample of lo-‘ M anthracene. Table 11. Surface-Enhanced Raman Bands of Dinoseb, Phthalic Acid, Anthracene, and Benzoic Acid on Silver-Coated Fumed Silica dinoseb, cm-’
200
400
600
800
1000
1200
1400
1600
la00
RAMAN SHIFT (cm‘’)
Figure 5. Surface-enhanced Raman scatterlng spectrum of a 3-pL sample of lo4 M phthalic acid.
centimeters as in the case of the band at 1120 cm-’, to tens of reciprocal centimeters as in the case of the bands at 616 and 794 cm-’. Figures 4,5, and 6 show the SEW spectra of various organic compounds (anthracene, phthalic acid, and dinoseb) measured with silver-coated fumed silica (3% of L-90). The main vibrational features in the spectral region 200-1800 cm-’ are summarized in Table 11. In general, the results of SERS measurements with fumed silica demonstrate that each individual SERS spectrum can be used as a “fingerprint” for each compound. Fumed-silica substrates offer well-resolved and sharp Raman bands. The success in detecting the above four molecules at very low concentrations demonstrates that the new substrate can be used as a practical substrate for SERS study of various chemicals. Measurements were conducted to evaluate the analytical figure of merit of SERS using silver-coated fumed-silica-based substrates. The minimum detectable quantity per sample spot for the compounds investigated were in the nanogram levels, benzoic acid (12.2 ng) at 1004 cm-’, anthracene (17.8 ng) at 1232 cm-’, phthalic acid (16.6 ng) at 1036 cm-’, and dinoseb (24.2 ng) at 1324 cm-l. The minimum detectable amounts are given per sample spot, i.e. quantity of analyte spotted on the substrate, and do not account for the laser/sample illumination ratio. Since the quantity of sample actually illuminated by the laser beam is only l/lw of the total sample spot, the actual limits of detection are in the picogram levels. The results of multiple measurements conducted on samples prepared identically gave a relative standard deviation of about 20%. This reproducibility, which is associated not only
1606 1568 1510 1406 1324 1260 1070 1000 834 612 368 238
phthalic acid, cm-’
1614 1572 1232 1160 1152 1036 846 824 800 782 650
benzoic anthracene, ern-’
acid, cm-’
1732 1590 1390 1344 1232 1164 1148 932 852 824 810 642
1598 1156 1138 1024 1004 876 836 616 440
with the spectroscopic measurements but also with substrate preparation, silver coating, and sample spotting, would be quite satisfactory for most analytical studies. The dynamic ranges were approximately 102-103 for the compounds studied. CONCLUSION Several conclusions can be drawn from this present study: (1)Silver-coatedfumed silica provides an efficient material €or a new type of SERS-active substrate. (2) Fumed-silica materials should have great potential for practical applications since they are easy to handle and are commercially available at low costs. (3) The surface roughness of the substrate can be controlled by the size of the fumed silica used to prepare the substrates. (4) The data obtained in this study with various types of organic species, including simple organic compounds, polynuclear aromatic hydrocarbons, and pesticides, indicate that fumed-silica substrates produce SERS signals that are more intense than those obtained with microsphere substrates. ACKNOWLEDGMENT We gratefully acknowledge the generosity of Mr. R. F. Geiger, Jr., of Cab-0-Si1 for supplying the fumed-silica materials. LITERATURE CITED (1) Chemical Appllcations of Non-Linear Raman Spectroscopy; Harvey, A. B., Ed.; Academic Press: New York, 1981. (2) Lord, R. C. Appl. Spectrosc. 1977, 3 1 , 187. (3) Fleischmann, M.; Hendra. P. J.; McQuiilan, A. J. Chem. Phys. Left. 1974, 26, 123. (4) Jeanmaire, D. L.; Van Duyne, R. P. J. Electroanal. Chem. 1977, 8 4 , 1. (5) Surface-Enhanced Raman Scattering; Chang, R. K., Furtak. T. E., Eds.; Plenum Press: New York, 1982. (6) Kertak, M.; Wang, D. S.; Chew, H. Appl. Opt. 1980. 9 , 3373.
880
Anal. Chem. 1989, 61, 660-665
(7) Furtak, T. E.; Reyes, J. Surf. Sci. 1080,93, 351. (8) Gersten, J. I. J . Cbem. Phys. 1080, 72, 5779. (9) Liao, P. F.; Wokaun, A. J . Chem. Phys. 1082, 76, 751. (10) Furtak, T. E. J. Electroanal. Chem. Interfaciel€lectrochem.1083, 150, 375. (11) Otto, A. Appl. Surf. Sci. 1080,6,309. (12) Vo-Dlnh, T.; Hiromoto. M. Y. K.; Begun, G. M.; Moody, R. L. Anal. Chem. 1084,56, 1667. (13)Enlow, P. D.; Bunclck, M.; Warmack, R. J.; Vo-Dinh, T. Anal. Chem. 1086,58, 1119. (14) Alak, A. M.; Vo-Dlnh, T. Anal. Chem. 1087,59, 2149. ( 1 5 ) Moody, R. L.; Vo-Dlnh, T.; Fletcher, W. Appl. Spectrosc. 1087, 6 , 966. (16) Vo-Dinh, T.; Meler, M.; Wokaun, A. Anal. Chim. Acta 1086, 18, 1843. (17)Alak, A. M.; Vo-Dlnh, T. Anal. Chim. Acta, In press. (18) Buncick, M. C.; Warmack, R. J.; Little, J. W. and Ferreil, T. L. Bull. Am. Phys. Soc. 1084,2 9 , 129. (19)Meiec, M.; Wokaun, A.; Vo-Dlnh, T. J. Phys. Chem. lS85,89, 1843. (20)Vo-Dinh, T.; Aiak, A. M.; Moody, R. L. Spectrochlm. Acta, Part 8 1088,438, 605. (21)Tran, C. D. Anal. Chem. 1084,56, 824. (22)Sheng, R. S. S.; Zhu, L.; Morris, M. D. Anal. Chem. 1086,58, 1116. (23)Jennlngs, C.; Avoca, R.; Hor, A.; Lonfyt, R. Y. Anal. Chem. 1084,56, 2033.
(24) Rowe, J. E.; Shank, C. V.; Zwemer, D. A.; Murray, C. A. Phys. Rev. Lett. 1080,4 4 , 1770. (25) Barber, P. W.; Chang, R. K.; Massoull, H. Phys. Rev. 8 : Condens. Matter 1083,27, 7251. (26) Kerker, M.; Blatchford, G. G. Phys. Rev. B : Condens. Matter 1082, 26, 4052. (27) hkier, M.;Wokaun, A. Opt. Lett. 1083,8 , 581. (28) Goudonnet, J. P.; Begun. G. M.; Arakawa, E. T. Chem. Phys. Lett. 1982,92, 197.
RECEIVED for review February 16, 1988. Resubmitted December 12,1988. Accepted December 15,1988. This research is sponsored by the Office of Health and Environmental Research, U.S.Department of Energy, under Contract DEAC05-840R21400 with Martin Marietta Energy Systems, Inc. This research also was supported in part by an appointment (of A.M.A.) to the postgraduate Research Training Program under Contract DE-AC05-760R00033 between the U.S.Department of Energy and Oak Ridge Associated Universities.
Statistical Considerations in the Analysis of Dispersive Kinetics Data as Discrete or Continuous Distributions of Rate Constants David B. Marshall Department of Chemistry and Biochemistry, Utah State Uniiuersity, Logan, Utah 84322-0300
Slngte-exponentlal, multlexponenllal, and stretched-exponentlal test data were analyzed as either a discrete (multlcomponent) or a contlrwoug dlsMbrdlon of rate (decay) constants. Various statistical tests were applied to try to determine the model thd was most consistent wlth the data. The results Indicate that typical statistical and Informath theoretic tests faH to dbtkrguldr reHab#y between a contkwous and a discrete model unless the maximum noise In the data Is lower than about 0.5% of the maxlmum slgnal amplltude, or a slgnalto-nolse ratb of about 400. Thls findlng has serious hnpllcatlons for the analysls of klnetk or lumlnescence decay data from dlsperslve or energetically heterogeneous systems.
INTRODUCTION This paper addresses the analysis of exponential-like decay data that are commonly observed in luminescence decay and kinetics experiments. In order to establish a consistent terminology for this report, conventional single-exponentialdata will be referred to as “SE” data, and curves resulting from the sum of several discrete single exponentials will be called multiple-exponential or “ME” data. Curves that arise from underlying continuous distributions of lifetimes or rate constants will be referred to as continuous-exponential or “CE” data. Nonexponential behavior is sometimes observed in situations where SE or ME data are expected, due to the unwanted convolution of the SE or ME process with some other physical effect. Data arising from this type of situation will be called nonexponential or “NE”data. Finally, SE, ME, CE, and NE data will be referred to in aggregate as exponential-like or “EL” data. This study addresses statistical considerations concerning the problem of deciding which of the SE, ME, or CE models applies when EL data are observed. Origins of EL Data. EL data can arise as an artifact due, for example, to the convolution of the excitation light profile 0003-2700/89/0361-0660$01.50/0
with the luminescence decay. Here, the data is clearly NE in nature but can be corrected by using standard deconvolution methods to yield the pure chemical SE or ME response (1). (The deconvolution procedure is not without danger (2), and more recent methods such as experimental referencing (3),a least-squares approach ( 4 ) ,and phase plane analysis (5) have also been proposed.) NE behavior also occurs due to physical effects such as the influence of diffusion-controlled quenching on excimer or exciplex photophysics (6). This type of phenomenon is an example of the broader topic of time(or frequency-) dependent transport coefficients (7). The treatment of NE data arising from instrumental artifacts or inherently nonexponential physical processes will not be discussed further here, since proper analysis depends on a recognition of the physical nature (and mathematical form) of the effect and not on statistical considerations. Here, we are concerned with statistical grounds for choosing between models when the data have already been corrected (or were never corrupted) by these types of instrumental or physical effects. EL data can arise from true chemical (or photophysical) factors in a variety of experiments. In fluorescence decay measurements, EL decays can occur simply from solutions containing different fluorophores, or from more complicated mechanisms such as the convolution of fiit-order decays from a number of rotational conformers when the excited-state lifetime depends on conformation (8). In the first case, the data are logically considered as ME in nature. In the second, considerable controversy surrounds the choice of either an ME or a CE model to explain the data (see ref 8-10 and references contained therein). In chemical kinetics, there is growing interest in dispersive kinetics systems, where the chemical reaction rate depends on various factors such as reaction partner distance in rigid glasses (1I ) , diffusion-controlled reactions in membranes with fractal geometries (12),catalysis on fractal surfaces (13),and adsorption-desorption kinetics @ 1989 American Chemical Society
