J . Phys. Chem. 1987, 91, 3863-3871
3863
Intramolecular Rotational Motion in Blchromophoric Compounds. 1. Effect of Pressure on Excimer Formation in 1,3-Bis(2-naphthyl)propane in a Series of Linear Alkanes William C. Tao and Curtis W. Frank* Department of Chemical Engineering, Stanford University, Stanford, California 94305 (Received: September 1 1 , 1986; In Final Form: January 30, 1987)
Intramolecular excimer fluorescence is used as a molecular probe to study the solute-solvent-shell interactions between bichromophoric compounds and a homologous series of alkane solvents. The system investigated consists of 1,3-bis(2naphthy1)propane (BDDNP) in the solvents hexane through decane. Hydrostatic pressure as high as 380 MPa was applied to modify the overall viscosity from 0.30 to 10 cP. The rate of intramolecular excimer formation was modeled by Kramers’ theory, in which the passage of a solute particle in a potential well over an activation energy barrier is directly related to the solvent frictional coupling strength. For ppDNP in heptane through decane, the experimental results exhibit Kramers’ high-friction behavior at viscosities above 2.0 CPaccompanied by an abrupt departure from Kramers’ high-friction regime at lower viscosities. The data at viscosities below 2.0 CPcan be treated analytically by Kramers’ intermediate-friction formalism. Furthermore, the nature of the solvent-shell packing at the point of transition from the intermediate- to high-friction regimes can be characterized by a constant consisting of the ratio of the amount of inaccessiblevolume of the solvent, V,, to the amount of free volume in the solvent, Vf. The constant value of V,/Vf for heptane through decane was determined to be 2.13. The results for @DNP in hexane exhibit only Kramers’ intermediate-friction behavior, and the fitting parameters indicate that the solute-solvent-shell interactions appear to be qualitatively different than those of heptane through decane.
Introduction The influence of the solvent on the dynamics of chemical reactions has been a subject of theoretical and experimental investigation for many decades.’-’* Recently, interest has been focused on the utilization of small molecules as spectroscopic probes of solvent structure and d y n a m i c ~ . l ~ -Generally, ~~ the probes are flexible molecules that undergo unimolecular conformational changes such as threefold rotation or isomerization. The key feature is that these changes involve the passage across a potential barrier from reactant to product configurati~n.~~.~’ The rate of passage across this potential barrier is directly determined by the frictional interactions between the solute and solvent molecules. Therefore, information concerning the local solvent-shell structure and solute transport may be inferred. Many models have been proposed to describe the effect of the solvent on barrier crossing dynamics. Classical transition-state theory (TST) treated gaseous reactions with collisional probabilities in which the passage over the barrier is described by an Arrhenius form modified by a reactive frequency parameter.”
(1) Shank, C. V.; Ippen, E. P.; Teschke, 0.; Eisenthal, K. B. J. Chem. Phys. 1978, 67, 5547. (2) Rothenberger, G.; Negus, D. K.; Hochstrasser, R. M. J . Chem. Phys. 1983, 79, 5360. (3) Sundstrom, V.; Gillbro, T. Chem. Phys. Lett. 1984, 109, 538. (4) Hasha, D. L.; Eguchi, T.; Jonas, J. J . Chem. Phys. 1981, 75, 1571. (5) McCaskill, J. S . ; Gilbert, R. G. Chem. Phys. 1980, 72, 1392. (6) Larson, R. S.; Kostin, M. D. J. Chem. Phys. 1980, 72, 1392. (7) Visscher, P. B. Phys. Rev. B 1976, 14, 347. (8) Visscher, P. B. Phys. Reu. B 1976, 13, 3272. (9) Bhatnager, P. L.; Gross, E. P.; Krook, M. Phys. Reu. 1954, 94, 511. (10) Bagchi, B.; Oxtoby, D. W. J . Chem. Phys. 1983, 78, 2735. (11) Zwanzig, R.; Bixon, M. Phys. Reu. A 1970, 2, 2005. (12) Hochstrasser, R. M. Can. J . Chem. 1961, 39, 459. (13) Montgomery, J. A,; Chandler, D.; Berne, B. J. J . Chem. Phys. 1979, 70, 4056. (14) Velsko, S . P.;Fleming, G. R. Chem. Phys. 1982, 65, 59. (IS) Velsko, S. P.; Fleming, G. R. J . Chem. Phys. 1982, 76, 3553. (16) Millar, D. P.; Eisenthal, K. B. J . Chem. Phys. 1985, 83, 5076. (17) Fleming, G. R.; Waldeck, D. H.; Keery, K. M.; Velsko, S . P. Applications of Picosecond Spectroscopy to Chemistry, 1st ed.; Reidel: New York, 1984. (1 8) Frost, A. A,; Pearson, R. G. Kinetics and Mechanism, 2nd ed; Wiley: New York, 1961.
0022-3654/87/2091-3863$01.50/0
Inherent in TST are the assumptions of equilibrium in the barrier region, i.e. the transition-state complex, and a one-way flux across the barrier top. This maximum reaction rate, however, can never be fully achieved in condensed media. The early work of Kramers employed a one-dimensional Langevin equation to model the solvent dynamics in order to account for the departure from TST.I9 In this approach the solvent imposes a frictional drag force and a random fluctuating force on the solute motion which is governed by the intramolecular potential. The frictional interactions are considered to be Markovian in nature; the buffeting forces acting on the solute are spatially and temporally uncorrelated. Recent extensions of the Kramers model include non-Markovian solvent response,20,21multidimensional reaction coordinate systems,22-23 and higher friction rangesz4 Furthermore, stochastic collisional models such as the BGK model, in which the solvent affects the solute motion by impulsive collisions, have been used to perform numerical approximations of barrier crossing dynamic^.^^-^' The qualitative effects of the solvent on such barrier crossing processes are essentially the same in all these models. The solvent promotes the reaction by providing the solute with sufficient energy to overcome the barrier, but if the reaction involves large-amplitude motion the frictional forces exerted by the solvent will also impede the reaction. Several groups have studied the viscosity dependence of isomerization dynamics of small molecules in which the pendant groups undergo small-amplitude conformational changes about single and double bonds. Velsko and Fleming investigated the isomerization of diphenylbutadiene in alkane solvents and the dye DODCI in alcohol solvents.28 Hochstrasser et al. studied similar conformational changes using trans-stilbene in alkane solvents.2g The solvent homologues provided a continuous viscosity variation while maintaining the same form of solvent-solute interaction, i.e. polarity and solvation. Therefore the solvent viscosity effects can be separated from the intrinsic energy barrier by considering isoviscosity data. In all these studies the barrier crossing rate was (19) Kramers, H. A. Physica 1940, 78, 284. (20) Grote, R. F.; Hynes, J. T. J. Chem. Phys. 1980, 73, 2715. (21) Carmelli, B.; Nitzan, A. J. Chem. Phys. 1984, 80, 3569. (22) Grote, R. F.; Hynes, J. T. J. Chem. Phys. 1981, 74, 4465. (23) van der Zwan, G.; Hynes, J. T. J . Chem. Phys. 1982, 77, 1295. (24) Carmelli, B.; Nitzan, A. Phys. Reu. Lett. 1983, 51, 233. (25) Berne, 8. J.; Skinner, J. L.; Wolynes, P. G. J . Chem. Phys. 1980, 73, 4314. (26) Skinner, J. L.; Wolynes, P. G. J . Chem. Phys. 1980, 72, 4913. (27) Garrity, D. K.; Skinner, J. L. Chem. Phys. Lett. 1983, 95, 46. (28) Velsko, S. P.; Waldeck, D. H.; Fleming, G. R. J . Chem. Phys. 1983, 78, 249. (29) Hochstrasser, R. Pure Appl. Chem. 1980, 52, 2683.
0 1987 American Chemical Society
3864 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 observed to decrease monotonically as the viscosity increased, indicating possible correlation with Kramers’ high-friction regime. When analyzed with Kramers’ model in the high-frictional coupling limit, however, the data showed significant deviation from Kramers’ eq~ation.~’-~O A possible explanation of this behavior is that the solvent frictional interaction with the solute is not Markovian but rather is frequency dependent, which will cause deviations from Kramers’ equation for processes with sharply curved barriers. The amount of time spent by the reactant molecule in the transition conformation is directly determined by the curvature of the activation energy barrier. For a sharply curved barrier, the portion of the reaction coordinate which corresponds to the transition conformation is small, and momentum imparted by the solvent can cause the reactant molecule to cross and recross this region many times. Support for this explanation was later provided by Keery and Fleming who repeated the diphenylbutadiene and stilbene studies in alcohol solvents.30 The data were in good agreement with Kramers’ equation in the high-friction limit due to the reduction in barrier curvature for the alcohols relative to the alkanes. Utilizing the dimer model compound 1,3-bis(2-naphthyl)propane (DDDNP), Fitzgibbon and Frank investigated the viscosity dependence of intramolecular excimer formation in t ~ l u e n e . ~An ’ excimer is a dimeric complex formed between two adjacent aromatic chromophores sharing the same quantum of excitation energy through T-T electronic interaction^.^^ Their study differs significantly from the isomerization probe work. In cis-trans isomerization of stilbene and diphenylbutadiene, the structure of the local solvent shell around the cis and trans isomers in a homologous series of solvents at a given density is relatively the same. The solvent exerts a retarding force on the isomerization process through frictional hindrance as the density or viscosity of the solvent is increased. While the influence of the solvent on the monomeric configuration of pBDNP prior to excimer formation is qualitatively similar to that in the isomerization studies, the response of the solvent-shell structure to the rotational motion of the chromophore and the subsequent formation of a bulkier complex is quite different compared to that in cis-trans isomerization. The formation of the excimer complex requires the expulsion of solvent layers between the aromatic rings requiring extensive reorganization of the solvent-shell structure around the probe. Therefore, the nature of the solvent shell around ppDNP undergoes a transition from that of two solvated monomer rings to a single solvated excited complex. The complex relaxation and dissipative reorganization of the solvent are reflected in the monomer and excimer fluorescence. The stability of the excimer complex and the deactivation pathways are very sensitive to solvent size, density, and packing. Rather than using a series of solvents to achieve the viscosity variation, Fitzgibbon and Frank employed hydrostatic pressure to produce a continuous increase in frictional coupling between the solvent and solute. Intramolecular excimer formation is a two-step process, in which the chromophore undergoes a segmental rotation into an excimer-forming configuration followed by the 1r-r electronic attraction, while isomerization is a single-step transition. Excimer formation in ppDNP requires large-amplitude motion relative to isomerization of stilbene and diphenylbutadiene. Furthermore, the solvation of the monomer and excimer may be different due to the aromatic nature of the solvent toluene. The results agree quite well with Kramers’ intermediate-friction regime throughout the viscosity range of 0.5 to 4.0 cP. Subsequently, Tao and Frank extended the investigation of similar behavior of ppDNP to higher viscosities in trans-decalin and methylcy~lohexane.~~ Their results were consistent with those of Velsko and Fleming,” in which the data deviated from Kramers’ equation. The intermediate-friction expression of Kramers’ model cannot be used to describe the rate of excimer formation for the entire range of viscosities encountered. (30) Keery, K. M.: Fleming, G. R. Chem. Phys. Lett. 1983, 93, 322. (31) Fitzgibbon, P. D.; Frank, C. W. Macromolecules 1981, 6, 1650. (32) Frank, C. W.; Harrah, L. A. J . Chem. Phys. 1974, 61, 1526. (33) Tao, W. C.; Frank, C. W., to be submitted for publication.
Tao and Frank The use of isomerization and excimer probes have provided a fascinating picture of solvent-solute interactions and general solvent dynamics. It is clear from the foregoing discussion, however, that factors such as solventsolute size, aromaticity, and mode of frictional coupling between the solvent and the excimer complex require closer examination. In this paper we investigate the rate of intramolecular excimer formation of ppDNP in a homologous series of alkane solvents from hexane through decane. Hydrostatic pressure will continue to be used to vary the bulk viscosity of each alkane solvent at a constant temperature. Experimental Section Sample and Solvent Preparation. The compound 1,3-bis(2naphthy1)propane (PPDNP) was synthesized by a slight modification of the procedure of Chandross and D e m p ~ t e r . ~Prior ~ to purification, the materials exhibited visible fluorescence and a yellowish tint. Characterization of the compound at 298 K with a Photochemical Research Associates (PRA) Model 3000 transient lifetime spectrofluorimeter resolved three monomer decay exponentials at 340 nm upon excitation at 290 nm. The two slower decays have decay times of 5 and 67 ns, respectively, which correspond to spontaneous and delayed monomer fluorescence. The latter type of fluorescence, which accounts for about 10% of the total amplitude, is believed to be dissociation of the excimer back to monomer configuration. The third decay is a fast decay with a lifetime less than 1 ns and an amplitude equal to half of the total amplitude. This fast decay and the accompanying yellowish tint were removed by chromatography on silica gel with benzene-petroleum ether (318 K) (1:9) as the eluent. The alkane solvents hexane, heptane, octane, nonane, and decane were purchased from Aldrich in chromatographic analysis grade. Gel permeation chromatography (GPC) using a Waters Model 244 liquid chromatograph equipped with Waters 100, 500, IO3, lo4, lo5, and IO6 A r-Styragel columns yielded several impurity peah. Subsequent purification was accomplished by double vacuum distillation of the alkanes and further removal of the impurities by adsorption over activated charcoal. 2-Ethylnaphthalene (2EN) was Matheson Spectrograde and was passed through a silica gel column prior to use. The latter compound, an isolated alkyl-substituted naphthalene ring, represents the model monomer compound for PPDNP. The absorption spectrum of 2EN is very similar to that of PPDNP. High-pressure Spectroscopic Measurements. The solutions containing the monomer model and dimer compound were degassed by purging with dry nitrogen for 30 min. All solutions M in naphthalene repeat units to eliminate were kept below intermolecular excimer formation. Freshly prepared samples were stored in the dark under a partial pressure of nitrogen to minimize solution and chromophore degradation. The pressure cell has been described previou~ly.~’ In this work, the window seal was achieved by gluing the sapphire window onto a polished steel backup plug using a poly(cyanoacry1ate) adhesive. At the end of the experimental run, the adhesive was easily dissolved in acetone under ultrasonic agitation. Maximum operating pressure was 65 000 psi (450 MPa). The spectrofluorimeter has been described previo~sly.~’ The spectral response function of the spectrofluorimeter was obtained by using an Optronics Laboratories 200-W quartz-halogen Standard of Spectral Irradiance Model 220-A powered by a Model 65 constant-current power supply. The spectral correction function was then determined by the standard method described by Parker35 and stored in the microcomputer for analysis. A typical experimental run consisted of charging the pressure cell with the sample solution, applying pressure for preliminary sealing, and taking photostationary fluorescence spectra. The degassed sample solution was injected into the pressure cell while enclosed in a nitrogen-purged glovebag. Upon connection of the pressure cell to the pressure-generating system, 25000 psi of (34) Chandross, E. A,: Dempster, C. J . J. Am. Chem. Soc. 1970, 92, 3586. (35) Parker, C. A . Photoluminescence of Solutions, 2nd ed: Elsevier: Amsterdam, 1968.
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 3865
Rotational Motion in Bichromophoric Compounds WAVELENGTH ( N M ) 350
300
400
450
550
has been frequently adopted for intramolecular excimer formation. According to this scheme, the ratio of excimer to monomer quantum yields follows the expression:
6000
> I-
t:z
4500
W k
3000
0
31
34
25
28
ENERGY
22
19
(1808 C M - l )
Figure 1. Photostationary-state fluorescence spectrum of &3DNP in heptane. The dotted traces are nonlinear regression fits of the monomer and excimer fluorescence envelopes with model monomer fluorescence profile of 2EN - -) and a Gaussian function (- - - - -), respectively. (a
-
-
pressure was applied for 10 min to extrude and deform the series of washers in order to seal the window ports. The pressure was then raised to the maximum of 65000 psi. The fluorescence spectra were taken at 2500-psi intervals from 65 000 psi to atmospheric conditions. Data Analysis and Reduction. The signal from the picoammeter was sent to an ADVll-A 12-bit analog-to-digital convertor in a PDP 1 1/23 plus microcomputer. Each spectrum consisted of lo00 time-averaged points spaced 0.25 nm apart. After spectral correction using the instrumental correction function and elimination of the Raman and scattered light peaks, the excimer to monomer area quantum yield ratio, @D/@M, was extracted by a nonlinear regression analysis utilizing the Marquardt method. The corrected emission spectra were fitted to two functional forms. The first consisted of the entire vibrational envelope of the model monomer; the second consisted of a Gaussian excimer envelope. From this analysis, @D/@M, the excimer band position, v D , and the excimer band width at half-height, A Y , , ~were , calculated.
Results Emission Spectra. In ppDNP only adjacent intramolecular excimers are formed from cooperative threefold rotations over two successive energy barriers. Two rotations are required to convert from the lowest conformational energy trans-trans state of the meso dyad into the gauche-gauche excimer c o n f i g ~ r a t i o n s . A ~~ typical fluorescence spectrum of &3DNP in heptane, representative of all the photostationary-state experimental results, is illustrated in Figure 1. The solid trace represents time-averaged fluorescence intensities which have been corrected for the instrumental response of the spectrofluorimeter. The monomer emission consists of a vibronically structured envelope extending from 32 000 to 26 000 cm-l, while the emission of the excimer is a broad structureless Gaussian band red-shifted approximately 6000 cm-I with respect to the 0-0 transition of the monomer and superimposed on the tail end of the monomer fluorescence. Integrated monomer and excimer fluorescence over the entire emission envelope are extracted from nonlinear regression fitting of model monomer fluorescence from 2-ethylnaphthalene in combination with a Gaussian function. As noted from the dotted traces in Figure 1, 2-ethylnaphthalene is an excellent monomer model for /3pDNP and provides a good estimation of the integrated excimer to monomer fluorescence quantum yield ratio, @,/aM. Thermodynamic Regimes. The standard steady-state kinetic analysis due to Birks?’ which was originally developed to interpret the rate of intermolecular excimer formation in pyrene systems,
where k , and k F M are fluorescence decay rate constants for the excimer and monomer, kIDis the rate constant for deactivation of the excimer complex by internal conversion, and k M D is the rate constant for dissociation of the excimer to excited- and groundstate monomers. The rate of formation of the excimer is denoted by k,,, to emphasize the rotational diffusion process. Equation 1 is expected to be valid for systems where there exists only one type of excimer overlap configuration and a single pathway toward excimer formation. In a separate investigation, Tao and Frank3* determined the photophysical kinetic scheme for /3/3DNP in cisdecalin and methybyclohexane in which they found two distinct types of excimer overlap configuration having similar energies but different decay times. At 298 K, the fluorescence lifetime profile at 420 nm, which corresponds to the peak of the excimer Gaussian fluorescence envelope, exhibits a 5-11s rise time accompanied by a biexponential decay with lifetimes of 62 and 85 ns. Although this transient response suggests the existence of two types of excimers at 420 nm, the relative contribution of the faster decaying excimer decreases from 12% at 298 K to less than 2% at 173 K. The two types of excimer overlap configuration can be readily visualized from molecular models of /3/3DNP. The configuration with the longer lifetime is the regular parallel sandwich formed by the two chromophores with a separation distance of 3 A. The shorter lifetime excimer consists of a similar sandwich formation with one of the chromophore rotated 180’ along the connecting bond to the propane linkage. The separation distance of the latter type of excimer configuration is increased slightly while the extent of overlap between the two chromophores is decreased. At equilibrium conditions, however, we cannot resolve more than one Gaussian from the excimer fluorescence envelope. The simplified steady-state kinetic scheme of eq 1 must be modified to account for two excimer complexes, which leads to the following:
where the added subscripts 1 and 2 correspond to the two different excimer configurations, and kD, = k F D l k l D , , i = 1, 2. Two limiting conditions, denoted a and /3 by Selinger et al., encompass the thermodynamic behavior of excimer formation for all aromatic molecules as a function of pressure and t e m p e r a t ~ r e . ~ ~ In the a regime, also termed the high-temperature dynamic equilibrium region by Birk~,~’ the rate of excimer dissociation back to the excited-state monomer configuration is much greater than the deactivation of the excimer by fluorescence and internal conversion, k M D , >> k F D l + kID,, i = 1,2. Equation 2 therefore reduces to
+
\‘I
where the observed quantum yield ratio is now proportional to the sum of the two molar equilibrium constants consisting of the ratio of the rate of formation of the excimers k,,, to the respective rate of dissociation of the two types of excimer. The ratios k F D l / k F M , i = 1, 2, are usually independent of pressure and only slightly dependent on solvent and t e m p e r a t ~ r e . ~The ~ molar equilibrium constants, however, increase as the pressure increases due to a negative activation volume for excimer formation.41 ~
~~
~~
~
(36) Nishijima, Y . ;Yamamoto, M. Polym. Prepr., A m . Chem. SOC.,Diu. Polym. Chem. 1979, 20, 391. (37) Birks, J. B. Photophysics of Aromatic Molecules, 1st ed; Wiley-Interscience: New York, 1970.
~
(38) Tao,W. C.; Frank, C . W., to be submitted for publication. (39) Speed, R.; Selinger, B. Aust. J . Chem. 1969, 22, 9. (40) Johnson, G. E. J . Chem. Phys. 1975, 63, 4047. (41) Johnson, P. C.; Offen, H. W. J . Chem. Phys. 1972, 56, 1638. J . Chem. Phys. 1973, 59, 801.
Tao and Frank
3866 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 WRVELENGTH 300
350
408
(NM) 450
550
6500
>
TABLE I: Summary of Empirical Viscosity Parameters for the Modified Tait Eauation solvents D,MPa E A?,' CP hexane 110 1.173 0.30-1.70
heptane octane nonane decane
7 0 MPQ
5200
Lo
140
z
3900
z
143 175 182 195
1.477 1.840 2.055 2.263
0.39-2.65 0.5 1-4.25 0.65-6.84 0.87-9.96
"The viscosity range corrsponds to hydrostatic pressures from 0.1 to MPa.
H
380
TABLE 11: Summary of Photostationary-State Fluorescence Parameters at 0.1 and 380 MPa 0
0.1 34
31
28
ENERGY
25
22
19
(1806 CM-')
Figure 2. @pDNPmonomer and excimer fluorescence in heptane as a function of hydrostatic pressure. The labels of increasing pressure values
correspond to the decreasing excimer envelope. Note the isoemissive point at 27 250 cm-'. Higher pressures serve to compress the excimer complex leading to a further decrease in the inter-ring separation, thus stabilizing the excimer. The /? regime, also denoted the diffusion-controlled regime, occurs when the excimer dissociation rate is much slower than the combined rates of radiative and nonradiative deactivation. Equation 2 then takes the form
I?=[?][
k F D l kD2
Solvent hexane heptane octane nonane decane
MPa
380
MPa
@D/@M
YD
YDI/~
A~'D~ A~DI/Z
3.0 1.3 2.8 6.2 8.5
25031 24814 24855 24731 24764
4515 4634 4627 4718 4750
731 636 621 595 610
142 319 293 282 290
"All excimer band positions and widths are given in cm-'. *AuD and cumulative decreases of the excimer band position and half-width at half-height upon compression up to 380 MPa relative to those at 0.1 MPa AuDIj2 are
--I
f
00DNP
+ kFD2kDl C
U-3EXANE
kDlkD2
Since the segmental rotational rate, which depends directly upon the viscosity of the solvent, will decrease as the viscosity increases with increasing hydrostatic pressure, the observed quantum yield ratio will also decrease. It is important to note that the thermodynamic state of the excimer formation process, whether it is in the a or @ regime, depends strictly on the state variables temperature and pressure. Crossover between the regimes has been observed for intermolecular excimer formation in 1,2-benzanthracene and ~ y r e n e . ~ * A transition from the dynamic equilibrium regime a to the diffusion-controlled regime /3 may occur when the viscosity of the solvent is increased, such as with the application of hydrostatic pressure. The reverse transition from @ to a may also take place as a result of an increase in temperature at constant pressure. In order to study the influence of the solvent shell on excimer formation in ppDNP and to infer the degree of frictional coupling between the solvent and the solute from the rate of intramolecular excimer formation, the segmental reorientation event should be diffusive in nature and the thermodynamic state should favor excimer deactivation by radiative fluorescence over dissociation back to monomer (Le., the thermodynamic state should be in the @ regime). Increasing hydrostatic pressure modifies intramolecular excimer formation in two ways: higher viscosity retards the rate of excimer formation while a tighter solvent shell can provide stability with respect to excimer dissociation. Figure 2 shows the effect of pressure on @@DNPfluorescence. In general, the excimer to monomer fluorescence quantum yield ratio decreases with increasing pressure for experiments performed at 298 K. An additional feature observed in Figure 2 is the existence of an isoemissive point at 27 250 cm-I. An experimental indication that the thermodynamic conditions are appropriate for either the a or @ regime is the existence of an isoemissive point in the fluorescence spectra.43 The appearance of the isoemissive point requires that either k M D , >> k r D , + k l ~ , or k M D ,
