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Anal. Ch0m. 1984, 56, 1080-1084
Lateral Diffusion of Solutes Bound to the Alkyl Surface of C,, Reversed-Phase Liquid Chromatographic Packings Richard G. Bogar, John C. Thomas, and James B. Callis*
Department of Chemistry, BG-IO, University of Washington, Seattle, Washington 98195
When the aromatic hydrocarbon pyrene Is bound to the hydrocarbon layer of C,8 reversed-phase iiquld chromatography packings In the presence of a wetting mobile phase of composltlon 75 % methanol125% water, it exhlblts two fluorescence bands. The flrst band, In the spectral region 380-420 nm, arlses from monomeric pyrene and Is always present regardless of concentration. The second band, In the spectral region 440-560 nm, is unstructured and increases In intensity wlth increaslng concentration of added pyrene; It Is shown to a r b from excimers formed in a dmuslon ilmlted reaction. The rate constant for exclmer formation is obtained from both static and dynamlc measurements and used to estimate the diffusion coefficient for pyrene and, from thls parameter, to derive the “microvlscoslty” of the reversed phase. This later quantity (19 cP) Is approximately that of ethylene glycol. The results are Interpreted as supporting the view that the solvated reversed phase is a dynamic medium In which solutes are dissolved, rather than a static, glasslike medlum to whlch solutes are adsorbed.
Chemically bonded reversed-phase (RP) packing materials were originally introduced in an attempt to provide a stationary phase which exhibited the partitioning behavior of a liquid-liquid chromatography system while maintaining the stability of a liquid-solid system (1). Experimental (2,3) and theoretical considerations ( 4 ) have been presented to support the notion of partitioning as the mechanism for liquid chromatography using long chain alkyl bonded packings. However, a number of authors have argued that solutes are probably not dissolved in the surface layer, but merely adsorbed to it (5-9), and thus reversed-phase chromatography is actually a type of adsorption chromatography. As Colin and Guiochon (9) have noted, attempts to solve this controversy based upon experiments which draw their rationale from theories derived from equilibrium thermodynamics (e.g., relative retention times, isotherm determinations, temperature profiles) are unlikely to be definitive because adsorption and partitioning lead to very similar forms for retention as a function of a given thermodynamic variable. Clearly then, new types of experimental data are needed which can give definitive answers. We, along with other workers (10-13), believe that spectroscopic techniques are ideal for this purpose. Furthermore, these techniques have the advantage of allowing visualization at the molecular level of the reversed phase and its interactions with various solutes. For example, in a previous communication (14) we showed that infrared spectrometry gave considerable insight into the supramolecular organization of C18alkane chains of RP packing materials. Spectroscopic evidence was presented showing that the c18 chains of bonded materials, in the absence of mobile phase, were in a disordered state comparable to that of a liquid. In the presence of mobile phase, the chains became rather more ordered; we attributed this to intercalation of the organic modifier into the alkane layer. Unfortunately, infrared spectrometry is poorly suited to deducing dynamic information. Thus, we are unable to rule
out the possibility that the c18 R P is more like an amorphous, glasslike solid than a thin liquid film. In contrast to IR, fluorescence spectrometry is admirably suited to dynamic studies. In this paper, we demonstrate that excimer formation by the fluorescent solute pyrene can be used to probe the fluidity of the reversed phase. An excimer is a fluorescent excited dimer which is formed upon collision of an excited state monomer with a nearby monomer in i;ts ground state. A long series of exacting studies by Birks and colleagues (15) has led to a detailed model for excimer formation and showed it to be a diffusion-controlled process. This latter feature of excimer formation has been exploited to yield information about the fluidity of the hydrophobic interior of soap micelles (16) and model biological membranes (17). Pyrene has also been used to study chromatographic packing materials. Ware and colleagues have employed pyrene fluorescence as a probe of the intra- and intergranular motion of adsorbates on dry silica gels (1419). On the silica surface, pyrene does exhibit a red-shifted band, but this was attributed to ground-state dimers rather than excimers (20). Lochmuller and colleagues have studied the fluorescence of pyrene attached covalently to surface silanols of silica gels. Excimer formation was studied as a function of surface coverage and conclusions were drawn regarding the heterogeneity of the surface (21). In contrast, we have used free pyrene to probe the fluidity of the hydrocarbon surface of C18 reversed-phase packing materials. We reasoned that if excimers could be shown to form in the alkane layer of the RP, it should be considered to be a fluid medium which allowed two pyrene molecules to collide in a favorable orientation. On the other hand, if excimer formation could not be detected, we would have to conclude that (a) diffusion did not take place at all or (b) diffusion did take place, but it was a two-dimensional (surface) phenomenon which prevented face-to-face contact necessary for excimer formation. In either case, the R P should be considered a disordered solid or glass rather than a thin fluid layer.
THEORY Our model of excimer formation is illustrated schematically in Figure 1. We assume that the ground-state monomer pyrene, at concentration M , can be excited at rate K,, which is given by the following expression: K,, = Io [l where Io is the intensity of light incident on the sample, is the extinction coefficient of pyrene a t the wavelength of excitation, and 1 is the path length. We further assume that regardless of the wavelength of excitation, fast radiationless processes result in the formation of a vibrationally equilibrated first excited singlet monomer, at concentration M*, from which all other deexcitation processes occur. M* may return to the ground state by emission of fluorescence photons with rate constant kFMor by a radiationless process characterized by a rate constant kRM. Alternatively,M* may, during its lifetime, collide with a nearby ground-state monomer and form, with rate constant kDM,an excited-state dimer (excimer), a t concentration D*. With the excitation intensities used here, the ground-state molecules are not depleted so that M 3 Mo,where
0003-2700/84/0356-1080$01.50/00 1984 American Chemical Society
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creates a population M*(t = 0) = Mo* and that no dimers are formed at time t = 0, we obtain from eq 2 and 3 the following expressions for the monomer and excimer intensities as a function of time:
ENERGY DIAGRAM FOR PYRENE
IM(t)= kFMe-(kM+kDMMO)t
(9)
M
where we have defined
Figure 1. Excited-state diagram for excimer formation.
Mo is the initial concentration of pyrene. Under these circumstances, the excimer formation rate constant is expected to be pseudo first order and given by kDMMO. Once created, the excimer may decay by forming two ground-state molecules, either via a fluorescence process, kFD, or via a radiationless process, km. Alternatively, the excimer may dissociate with rate constant itMDforming one excited state monomer and one ground-state monomer. Because this latter process is known to be slower than all the others at room temperature and below (15,17), we will henceforth neglect it. Under the above conditions, we may write the differential equations governing the time dependence of the excited-state populations M* and D* as dM*/dt = KeH- ( k M + k D M M O ) M * (2)
dLl*/dt = kDMM&f*
- kfl*
(3)
where for convenience we have defined the following lumped constants: (4) = k F M + k& k D = kFD + kRD Under conditions of steady-state irradiation, the left-hand sides of eq 2 and 3 may be set to zero, and by use of the definitions for the fluorescence intensities of dimer IFD, and monomer, I F M kM
= kFfl*; IFM = kFMM* we can derive the following expression for the ratio: IFD
(5)
Equation 6 predicts that the ratio of dimer to monomer intensity will increase linearly with added monomer. Moreover, the slope will be directly proportional to the diffusion limited rate constant kDM, which can be obtained if the other constants kFD, kFM, and k D can be estimated or have been determined by independent experiments. Once kDM has been determined, one may obtain the diffusion coefficient D through the following relationship:
DM =
16rNDR
(7) 1000 where R is the interaction radius, D is the diffusion coefficient, and N is Avogadro’s number. We have assumed that the probability that a single collision will result in excimer formation is unity. From D we may also estimate the “microviscosity” ( q ) of the medium by assuming that the Debye-Stokes-Einstein relationship is obeyed kT
I?=GiTb where k is Boltzmann’s constant and b is the Stokes radius. Although the assumptions which go into the Debye-StokesEinstein relationship are not rigorously obeyed here, the notion of “microviscosity” is still useful as it gives an idea of the fluidity of the reversed phase. Finally, let us consider the response of the system in Figure 1 to pulsed excitation. Assuming a 6 function pulse, which
k’M
k’M
as
= kM
+ kD&.fo
(11)
Equations 9 and 10 show that while the monomer fluorescence decays exponentially to zero, the excimer fluorescence exhibits both a rise and decay, as might be expected if excimers are formed sequentially from the excited monomer states. Equation 9 is of great use in distinguishing excimers from ground-state dimers. In the later case, the fluorescence is expected to exhibit an instantaneous rise followed by a monotonic decay.
EXPERIMENTAL SECTION Materials. The CI8 bonded phase packing materials were prepared as previously described (14). We also used Partisil-10 ODs-2 packing materials from Whatman, Inc. (Clifton, NJ). Pyrene of zone refined purity was obtained from James Hinton (Valpariaso,FL). All organic solvents were of reagent grade and were shown to be fluorescence free when excited by the wavelengths of light used for pyrene. Water was glass distilled and showed no fluorescence at the wavelengths of interest. Fluorescence Measurements. Steady-state fluorescence measurements were made with a Perkin-Elmer Model 650-10 fluorescence spectrophotometer operated with a spectral bandwidth of 1.6 nm. Fluorescence data are not corrected for instrumental response. The sample of RP beads and enough mobile phase to just cover the beads were placed in a normal 1 cm X 1 cm fluorescencecuvette and mounted in a special cell holder which allowed excitation and viewing of emission from the front face. Fluorescence Lifetimes. These were obtained and analyzed as previously described (22). The excitation source was a synchronously pumped, cavity-dumped dye laser system operated at 610 nm with Rhodamine 6G as the lasing medium. Ultraviolet wavelengths were obtained by means of frequency doubling with an angle-turned KDP crystal of 12.5 mm thickness. A polarization rotator oriented the beam polarization in the vertical direction. Fluorescence wavelengths were selected by means of a Bauch and Lomb monochromator, Model 33-86-40,and detected with an RCA 31034 photomultiplier tube. Polarization effects were avoided by orienting an analyzing polarizer at the “magic angle”. Data collection was supervised by a Terak computer and transmitted by serial line at 4800 baud to the Chemistry Department’s VAX 11/780, where the decay curves were fit to sums of exponentials by using either a locally written nonlinear least squares program or a program based upon the algorithm of Provencher (23). RESULTS AND DISCUSSION Figure 2 shows the fluorescence spectrum of pyrene bound to the hydrocarbon layer of CI8 reversed-phase liquid chromatography packings in the presence of a wetting mobile phase of composition 75% methanol/25% water. The first band, in the spectral region 380-420 nm is highly structured and always present regardless of concentration; it is therefore assigned to the monomer. The second band, in the spectral region 440-560 nm, is unstructured and increases in intensity with increasing concentration of added pyrene. This band is assigned to the excimer. When the ratio of excimer to monomer fluorescence intensity was computed and plotted as a function of added pyrene, a linear relationship is obtained in agreement with eq 6. We now present results from three experiments designed to show that the putative excimer band originates from an excited-state dimer which is formed sequentially from the
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c
1250
v)
5 1000 t-
f W V
z 2
750 500
v)
w
360
400 440 480 520 E M ISSI ON WAVE LE N GT H ( n rn 1
Figure 2. Pyrene fluorescence spectrum as a function of added pyrene. For each of the five experiments, the concentrationof pyrene in the C18layer was calculated assuming a thickness of 18 A and a surface area of 350 m2/g: (A) M , = 4.4 X lo-' M; (B) M , = 4.0 X M; (C) M , = 7.9 X M; (D)Mo = 1.2 X M; (E) M, = 1.6 X lo-* M. w A
298 " K
250 3 -1
L
O
0
I i
V
0
77
O K
v)
L
W
E
360 4 0 0 4 4 0 480 520 E M I S S I ON W A V E L E N G T H ( n m )
Flgure 3. (A) Pyrene fluorescence spectrum from RP packlng materkis at room temperature. (6)Same material at 77 K. Mo = 5.3 X M. w V
200
monomer decay rate
excimer decay rate
10-5klM,s - l
1 0 - 5 h ' ~s ,- l
86.2 89.6 96.8 106.0 120.2 127.3 136.9
108.3 124.9 134.4
WAVE L E N G T H ( n m )
W
w
I50
Table I. Monomer and Excimer Decay Rates as a Function of Added Pyrene
0.44 1.3 2.6 5.7 7.5 10.6 13.2 E M I S S IO N
IO0 TIME (nsec)
Flgure 5. Fluorescence decay curves of monomer (M) and excimer (E). M , = 5.3 x 10-3 M.
concn of added pyrene 1 0 3 ~ ,M ,
V
50
6
z u W
280 320 360 400 E X C l TAT1 O N WAVELENGTH ( n m 1
Flgure 4. Fluorescence excitation spectra of monomer emission band M. (M) and excimer band (E)Mo = 5.3 X
monomer excited state, and not from a ground-state dimer. First, as Figure 3 shows, freezing of the sample to 77 K abolishes the excimer band completely. Second, when the two excitation spectra obtained by monitoring emission a t the monomer band (A = 380 nm) and the excimer band (A = 470 nm) are superimposed, they are nearly identical, as shown in Figure 4. This suggests that the state responsible for the excimer emission arises sequentially from the excited monomer state. Third, as shown in Figure 5, the fluorescence decay curves are in accord with our model of excimer formation given
in Figure 1and detailed in eq 9 and 10. Curve M shows the fluorescence decay curve of the monomer fluorescence. As expected from eq 9 the fluorescence decays monotonically to zero. In contrast, the excimer fluorescence, shown as E, exhibits both a rise time and decay in accordance with eq 10. In the case where the red-shifted emission arises from ground-state dimers, the excitation specra are not superimposable, and the decay curve of the excimer is characterized by an instantaneous rise followed by a monotonic decay to zero (20). It therefore seems safe to conclude that pyrene is capable of translational Brownian motion in the solvated RP and moreover that this motion is three dimensional in the sense that the excited state can collide with a ground state in a favorable orientation (face to face). Encouraged by these findings, we proceeded to measure monomer and excimer decay rates as a function of concentration. A typical result is shown in Figure 5. In all cases, the monomer decay curves were more satisfactorily fit by a single exponential decay than by a multiple exponential decay, thus verifying the assumptions made to arrive at eq 9 and 10. In contrast, the excimer decay rate could only be fit to a two exponential model. One of the decay rates was identical within experimental error to that obtained from the monomer. The other decay rate was much greater that the first and did not change as the concentration of pyrene was varied. Moreover, the magnitude of the intensity associated with this component was approximately equal to that of the other component, but opposite to it in sign (negative). The data for one series of decay measurements are summarized in Table I. They are quite consistent with the model presented in the theory section. We next performed experiments to rule out the possibility that the excimers originated from the small amount of pyrene present in the mobile phase. First, we observed a suspension of beads under a fluorescence microscope; the fluorescence appeared to emanate only from the beads themselves. Confirmation of this observation was made by withdrawing a small amount of mobile phase from the bead suspension and determining its fluorescence in a microcuvette. Figure 6 compares the mobile-phase spectrum with the packing material
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984 W
V 2
61
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IF
Ei2b 2
a i b-
o
W
u
360
400 440 480 520 560 EMISSION WAVELENGTH ( n r n )
u
360
400 440 480 520 560 EMISSION WAVELENGTH (nml
Figure 6. Fluorescence emission spectrum of supernatant withdrawn from the bead suspension (S) compared with that emanating from the beads (6).
Figure 7. Fluorescence spectrum of pyrene bound to dry RP material (D); fluorescence spectrum after solvation with five molecules of
spectrum. Two features are important to note. First, there is no evidence of an excimer band in the supernatant spectrum, even though the bead spectrum exhibits a pronounced band. Second, the ratio of intensities of the vibronic bands marked I and 111of the monomer spectra are quite different in both cases. Kalyansudaram and Thomas (24) showed that the ratio of these bands is quite sensitive to the polarity of the solvent. The spectrum from the beads is consistent with the pyrene being dissolved in a nonpolar environment (III/I = 1.05), while the spectrum from the mobile phase is approximately that reported for pyrene in methanol (III/I = 0.77). Having satisfied ourselves that excimer formation does indeed take place in the RP as shown in Figure 1 and eq 1-11, we feel justified in calculating the diffusion coefficient for pyrene and then the microviscosity for the RP. In order to compute these quantities, we need to obtain the concentrations of pyrene in the reversed phase. This, in turn, requires an estimate of the volume of the hydrocarbon layer, which can be determined from the known surface area (350 m2/g) and the estimated chain length for C18, under “melted” conditions. The alkane chain length was taken to be 80% of that of the all-trans form, in analogy with the known degree of shortening of C18 lipid bilayers at their gel to liquid crystal phase transition (25). We then fit the data of Table I to a straight line and obtained the quantities k M = 7.9 X lo6 s-’ from the intercept and kDM = 3.4 X lo8 M-l s-l from the slope. As an independent check, we also determined k D M from the data of Figure 2. According to eq 6 this slope is given by the quantity [ ~ F D ~ D M ] / [ ~ F M ~From D ] . this value we can determine kDM if we know kFD,kFM, and kD from other studies. Fortunately, Birks (15)has determined these quantities for us. While not under the exact conditions of our experiments, perusal of his table 7.3, pp 351-352, shows that these parameters are largely independent of solvent. Taking kFD = 1.3 x lo’s-l, kFM = 1.5 X lo6 s-l, and kD = 7.1 X lo7 s-l, we obtain kDM = 4.5 X lo8 M-’ s-’. This is in satisfactory agreement with the value (3.4 x lo8) obtained from Table I and eq 9. We believe that the former value is more accurate, because it has been directly obtained from our experiments. Now using the pyrene interaction radius R = 4.5 A and eq 6, we determine the pyrene diffusion coefficient to be approximately 2.5 X lo-’ ,ma s-l. This implies, using eq 7, a microviscosity of 19 cP, which is approximately the viscosity of ethylene glycol. The results given above show that the solvated reversed phase forms a thin fluid layer in which solutes are dissolved and can diffuse laterally. We have been particularly careful to rule out trivial phenomena such as ground-state dimers and diffusion in the mobile phase as being responsible for the observed phenomena. We are also convinced that excimers do not arise from diffusional motion where a planar molecule is translating randomly on a surface with ita planar face always oriented parallel to the surface. Pyrene molecules only form excimers when they are oriented in the face to face position. Thus, if diffusion were a surface phenomenon, one would not
expect excimers to form with high probability where only edge to edge contacts are possible. Indeed, when Ware and coworkers (1419) adsorbed pyrene to silica gel surfaces at high coverages, they were at first surprised to find that an “excimer” band formed. However, upon close examination, they noted that (a) the excitation spectra of the excimer band did not match that of the monomer, (b) the excimer fluorescence exhibited an instantaneous rise time, and (c) excimer formation was not abolished by freezing. These results are in marked contrast to those obtained by us on the bonded phase and strongly suggest that pyrene forms ground-state dimers on silica surfaces. Ware et al. (18) also showed that two-dimensional diffusion does take place on silica gel, but on a time scale many orders of magnitude longer than the lifetime of a pyrene excited state. Thus it would appear that excimer formation is an excellent probe of the nature of binding of solutes to surfaces. We have also performed experiments with dry packing materials. Under this condition we are unable to observe excimer bands, even when large amounts of pyrene are added. However, upon ”solvating”the beads with a very small amount of methanol (equivalent to =5 molecules/C18chain) we readily observe an excimer band. The data are shown in Figure 7 which gives the fluorescence spectrum of pyrene bound to the R P material with and without a small amount of methanol. Trace D, the dry material spectrum, shows only a normal monomer spectrum in the region X = 370-420 nm whereas trace S, the solvated material spectrum, exhibits a new, structureless spectral band at 470 nm consistent with an excimer emission. Moreover, the ratio of monomer to excimer did not change as more methanol was added. Apparentiy, the methanol acts to solvate the chains and greatly increases the fluidity of the system. In agreement with this finding, Sistovaris and co-workers (13) found that small amounts of methanol also markedly increased the motion of spin labels attached to alkylated silica surfaces. Combining the data from IR (10) and fluorescence studies allows US to construct a detailed description of the supramolecular structure of the long-chain bonded packing materials. In the absence of mobile phase, IR studies indicate that the chains are in a state of disorder, comparable to that expected for a liquid or a glasslike solid. In order to distinguish among these two possibilities, we used pyrene as a probe of lateral diffusion. When pyrene is incorporated into the dry reversed phase, no excimers are formed. We believe that under these circumstances, the system is in a glasslike state which prevents diffusion. More specifically, the chains are probably lying in disorder over each other, entrapping the pyrene. As a consequence of this entanglement, the rate of interconversion of rotational isomers of the chains is probably slow. Since it is this rapid rotational motion of the chains which confers fluidity to the system, the medium is frozen, at least on the time scale of excimer formation. When the reversed-phase is in contact with a solvent which wets the surface, a remarkable change occurs in the supra-
methanol per
C,,
chain (S).
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
molecular structure. First, examination of the IR spectrum in the region 1400-1300 cm-l shows that there is a sizable reduction in the number of gauche bonds in the alkane chains as judged from the decreased intensity of absorbance bands arising from molecules which exhibit “kink” and “doublegauche” defects (IO). We attribute this chain straightening phenomenon to sorption of organic modifier (in this case methanol) in the RP. A microscopic “swelling” of the system then occurs. Under these circumstances, the sorbed methanol molecules are rapidly exchanging with the bulk mobile phase. The alkane chains can now be considered as “dissolved” by the organic modifier. This solvation process implies a high rate of collision of the chains with sorbed molecules, which in turn induces rapid interconversion among rotational states, putting the chains into a melted state, which “fluidizes” the R P and allows diffusion to occur. Thus, the reversed phase is a dynamic, fluid medium in which solutes can laterally diffuse in a three-dimensional sense, as confirmed by the ability of pyrene to form excimers. However, we wish to emphasize that our results should not be taken to mean that a bonded reversed phase can be thought of as a thin film of a classical liquid with the further implication that R P chromatography is a form of classical liquid-liquid partitioning chromatography. Instead, the solvated R P should be thought of as a unique state of matter, which Flory and Dill (26,27) have called an “interfacial phase”. Such systems as the R P and aggregates of amphipathic molecules have been termed interfacial phases, or interphases, to distinguish them from other condensed phases such as liquids, crystals, and glasses, which are isotropic. In contrast, interfacial phases are remarkable for their highly anisotropic character, and properties such as solubility, order, and free energy of binding are all likely to vary strongly along an axis perpendicular to the interface. Bulk phase thermodynamic properties may not apply to interfacial systems, and widely adopted assumptions to the contrary will need reexamination.
ACKNOWLEDGMENT We are grateful to Rod Williamson for technical assistance and to Lane Sander for valuable discussion. We are indebted to John Shibata for carefully reading this manuscript and for
help with the fluorescence decay measurements. Registry No. Pyrene, 129-00-0.
LITERATURE CITED (1) Synder, L. R.; Klrkland, J. J. “Introduction to Modern Liquid Chromatography”, 2nd ed.; Wlley: New York, 1979. (2) Kirkland, J. J. J . Chromatogr. Sci. 1971, 9 , 206-214. (3) Lochmuller, C. H.; Wllder, D. R. J . Chromatogr. Sci. 1979, 17, 574-579. (4) Martlre, D. E.; Boehm, R. E. J . fhys. Chem. 1983, 8 7 , 1045-1062. (5) Boksanyl, L.; Llardon, 0.; Kovatz, E. sz. Advan. Colloid. Interface. Sci. 1978, 6 , 95-137. (6) Telepchak, M. J. Chromatographia 1973, 6 , 234-236. (7) Hemetsberger, H.; Maasfeld, W.; Rlcken, H. Chromatographia 1978, 1 , 303-310. (8) Wise, S. A.; Bonnett, W. J.; Guenther, F. R.; May, W. E. J . Chromafogr. Sci. 1981, 19, 457-465. (9) Colin, H.; Guiochon, G. J . Chromatogr. Sci. 1978, 158, 183-205. (10) Leyden, D. E.; Kendall, D. S.; Burggraff, L. W., Pern, F. J.; DeBello, M. Anal. Chem. 1982, 5 4 , 101-105. (11) Lochrnuller, C. H.; Marshall, D. 8.; Wilder, D. R. Anal. Chim. Acta 1981, 130, 31-43. (12) Sindorf, D. W.; Maclel, G. E. J . Am. Chem. SOC. 1983, 105, 1840-1851. (13) Slstovarls, N.; Rlede, W. 0.;Sillescu, H. Ber. Bunsenges. fhys. Chem. 1975, 79, 062-089. (14) Sander, L. C.; Callls, J. B.; Field, L. R. Anal. Chem. 1983, 55, 1068-1075. (15) Blrks, J. B. “Photophysics of Aromatic Molecules”; Wlley-Interscience: London, 1970; Chapter 7. (16) Thomas, J. K. Acc. Chem. Res. 1977, IO, 133-138. (17) Vanderkooi, J. M.; Callls, J. B. Blochemistry 1974, 13, 4000-4006. (18) Bauer, R. K.; Borensteln, R.; deMayo, P.; Oka, K.; Rafalska, M.; Ware, W. R.; Wu, K. C. J . Am. Chem. SOC.1982, 104, 4635-4644. (19) Hara, K.; deMayo, P.; Ware, W. R.; Weeden, A. C.; Wong, G. S. K.; Wu, K. C. Chem. fhys. Lett. 1980, 6 9 , 105-472. (20) Bauer, R. K.; deMayo, P.; Okada, K.; Ware, W. R.; Wu, K. C. J . fhys. Chem. 1983, 8 7 , 460-466. (21) Lochrnuller, C. H.;Colburn, A. S.; Hunnlcutt, M. L.; Harris, J. M. Anal. Chem. 1983, 5 5 , 1344-1348. (22) Thomas, J. C.; Allison, S. A.; Appellof, C. J.; Schurr, J. M. Biophys. Chem. 1980, 12, 177-188. (23) Provencher, S. W. J . Chem. fhys. 1976, 6 4 , 2772-2777. (24) Kalyanasundrararn, K.; Thomas, J. K. J . Am. Chem. SOC. 1977, 9 9 , 2039-2044. (25) Nagle, J. F. Annu. Rev. fhys. Chem. 1980, 3 1 , 157-195. (26) DIII, K. A.; Flory, P. J. Proc. Nati. Acad. Sci. U . S . A . 1980, 7 7 , 31 15-31 19. (27) DIII, K. A.; Flory, P. J. f r o c . Natl. Acad. Sci. U . S . A . 1981, 7 8 , 676-680.
RECEIVED for review June 20, 1984. Resubmitted February 12, 1984. Accepted February 13, 1984.
