Fluorescence Spectroscopy of 2-Amino-7-nitrofluorene
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978 2415
Time-Resolved Fluorescence Spectroscopy of 2-Amino-7-nitrofluorene in Two-Solvent Solutions Leslle A. Haliidy and Michael R. Topp" Department of Chemist/y, University of Pennsylvania, Philadelphia, Pennsylvania 19 104 (Received March 13, 1978; Revised Manuscript Received June 30, 1978) Publicatlon costs assisted by the National Science Foundation
Picosecond time-resolved spectroscopy has been used to reveal new features of the microscopic environmental relaxation about a polar solute molecule by selective interaction with a polar component of a binary solvent solution. The rates of the Stokes shift and quenching by hydrogen-bonded interactions are seen to vary linearly with mole fraction of 2-propanol in benzene solution. The shift of the fluorescence spectrum is attributed to the selective affinity of the highly polar excited state for polar solvent molecules, increasing the microscopic dielectric constant above the macroscopic value.
1. Introduction The molecule 2-amino-7-nitrofluorene (ANF) exhibits a large change in dipole moment on excitation to the first excited electronic singlet state. The relaxation of the environmental Franck-Condon state formed on excitation in solution results in a largely red-shifted fluorescence spectrum, the position of which can be related to the dielectric properties of the solvent, according to the modified Lippert e q ~ a t i o n l - ~
where ?jabs and lUfl refer to the 0-0 transition bands of the absorption and fluorescence spectra. For solution spectra, it is experimentally difficult to determine where the 0-0 bands are located, so eq 1is more useful if it is expressed in terms of spectral maxima. It has been ~ h o w n lthat , ~ eq 1 can be rewritten as A&bkes
= >absmax - ?jflmax =
(6?,bs
-
hca3
+ 6Cfl) +
TABLE I: Fluorescence Properties of 2-Amino-'7-nitrofluorene in Various Solvents h-,"
absorp tion
nm fluorescence
A; T' P m-
cyclohexane 375 benzene 51 gblc 0.64 388 diethyl 532 0.66 394 ether 0.73 386 538 n-butyl chloride 0.67 542 dioxane 398 o-dichloro0.75 398 567 benzene ethyl 0.82 367 59 2 acetate acetone 64 1 407 0.9 pyridine 421 662 0.86 dimethyl425 680 0.88 f ormamide 1-propanol 400 687 1.04 1.05 4OOc 2-propanol 69OC methanol 1.19 397 752 a See ref 1 except where indicated. Reference 5. This work.
-1 -1 [ =G (2) I E
n2
where Tabsmax and Zflmax refer to the spectral maxima, and and 65, are the wavenumber differences between the 0-0 bands and the peaks in the fluorescence and absorption spectra, respectively. For a single solute, the (6'u,b + 63fl) term is constant as long as there is no significant solvent effect on the band shape; thus, the shift in spectral maxima is a linear function of the solvent dielectric properties. Typical literature data for ANF in various solvents are listed in Table I. If the values from Table I are displayed graphically, it is seen that the agreement with eq 2 is not g 0 0 d ; ~ like - ~ many general theories, this one attempts to use a simple equation to describe a complex phenomenon. To improve our understanding of the Stokes shift, we have undertaken a study of the details of particular examples of solvent-shifted fluorescence. In the study of local molecular interactions in solution, it is necessary to use a molecular probe sensitive to changes in molecular environment. Early theories of the dipolar properties of molecules in solution were based on experimental observations of fluorescence Stokes shifts as a function of solvent polarity, using the above equation. However, we find that the shapes of the spectra and the fluorescence quantum yields also depend on the solvent indicating the presence of some dynamic processes, the 0022-365417812082-2415$01 .OO/O
effects of which are lost in the standard nanosecond fluorescence experiment. In order to obtain the fluorescence time profiles and the emission spectra of the molecule in different states of solvation, special techniques are necessary.'OJ1 We have recently shown12,13that the Stokes shift of ANF can be time-resolved in a picosecond laser experiment and that this type of measurement gives us direct information about the rate of solvent polarization by the excited state dipole. We have shown in preliminary experiments that this rate is faster in both 2-propanol and o-dichlorobenzene than the calculated spontaneous T z relaxation time measured by microwave absorption. In fact, it was necessary to reduce the temperature in the 2-propanol solutions to slow down the relaxation rate to within the time resolution of our 10-ps resolution sampling technique. Reducing the temperature of the o-dichlorobenzene solutions to just above the freezing point of that solvent was insufficient for direct time resolution of the relaxation rate, but indirect measurements were p0ssib1e.l~ Picosecond time-resolved fluorescence measurements on solutions thus allow access to information fundamental to the understanding of molecular motion and interactions. Apart from measurements of fluorescence depolarization, 0 1978 American Chemical Society
2416
L. A. Hallidy and M. R. Topp
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
which convey important dimensional information about molecular solvation, fluorescence spectral measurements allow sensitive analysis of the molecular environment. Thus, it is possible to detect solvent orientation in the presence of a polar solute molecule and more generally the influence of selective solvation in mixed solvents. In solution, the selective affinity for polar solvent molecules by polar solute species is well known, and varies from nonspecific dielectric interaction~l~ to specific exciplex formation.15 However, little in detail is known about the molecular aspects of this type of phenomenon. Additional information is needed from studies based on the following considerations: (a) In a single solvent no really good information is available about the extent and energy of solvation of a particular molecule. Stokes shift measurements measure differences in behavior between ground and excited states. Therefore, it is necessary to measure the fluorescence spectra of both environmental Franck-Condon states and states which are environmentally relaxed.16 (b) It is clear that a dynamic equilibrium exists between solvent molecules under the influence of a solute dipole and those solvent molecules remote from such a nucleus, but the rate and mechanism of this process remain obscure. (c) It is not known how the magnitude of the Stokes shift between absorption and fluoresence spectra is representative of a measurable dielectric constant, especially in two-component solvents. (d) In alcoholic solutions, the fluorescence of ANF is strongly quenched, and in mixed solvents, where the alcohol is diluted out by nonpolar solvent such as benzene, two diffusion-related processes should operate; the rotational diffusion of the polar solvent about the solute and the translational diffusion of the polar component of the solvent when in the vicinity of the solute. We need to know their relative rates. (e) Lippert has made observations of the fluorescence shift as a function of temperature and solvent composit i ~ n , ~and J ~ has concluded that the position of the fluorescence spectrum is determined by a balance between the rates of fluorescence decay, on one hand, and the Stokes shift on the other. This latter quantity has been equated to the spontaneous dielectric relaxation rate in the absence of better data. Our recent work12J3 has prompted a reexamination of this problem through experiments on two-solvent solutions. The present paper presents new information for which the following have been measured: (a) fluorescence spectra of ANF in solutions of binary solvents, time integrated over about 40 ns; (b) dielectric constants and viscosities of binary solutions of benzene/2-propanol; (c) picosecond time-resolved fluorescence profiles of solutions of ANF in binary solvents over the wavelength range 490-680 nm. 2. Time-Integrated Fluorescence Spectra As a first approach toward studying selective solvation, we measured the fluorescence spectra, with -40-11s time resolution. Since the fluorescence spectrum predominantly occurs in the low-frequency end of the visible spectrum we found it convenient to construct a special spectrometer, using a pulsed laser and a single-shot red-sensitive video recording system. The optical arrangement is shown in Figure 1. The pulse from a frequency-doubled &-switched ruby laser was incident on sample solution after suitable attenuation. The sample cell was placed in front of a slit orifice (150 pm), which was imaged through a constant deviation prism by achromatic lenses onto a silicon-target TV camera. The resulting single-shot fluorescence spectra
a
CON STANT DEVIATION PRISM
ACHROMATIC LENS
,SLIT
ORIFICE
u CAMERA
MONITOR
VIDEO OSCILLOSCOPE
Figure 1. Apparatus for obtaining single-shot fluorescence spectra in the low-frequency end of visible region.
TABLE 11: Fluorescence Spectral Data for 2-Amino-7-nitrofluorene in Mixed Solutions of Benzene/l-Propanol vol % 2PrOH 0 1 5 10 50 100
ATfwhy
hwx,nm 515k 4
536 k 4 560 ?r 6 570k 1 0 650+ 10 6 9 0 * 10
Av"stok?s,'
Pm-
mi
0.38 0.4
0.64 0.7 1 0.79
0.41
0.46 0.51
0.59
0.81 1.00 1.05
a Absorption maximum varied only 1 3 nm over entire concentration range (from 387 nm at 0% 2-propanol to 400 n,m at 100% 2-propanol). For simplicity in calculating AuStokes, it was assumed that the absorption maximum varied linearly with concentration.
were stored on a video disk recorder and displayed simultaneously on a monitor and an oscilloscope. Single video lines were photographed, the spectra were traced and the intensity was corrected for both the wavelength dependent frequency dispersion of the prism and for the spectral response of the TV camera. The fluorescence data are shown in Table 11, from which we note both an increasing red shift and an increasing width with increasing concentration of 2-propanol. We were satisfied that the fluorescence spectra were not significantly perturbed by either stimulated emission or reabsorption. This set of data shows distinctly the effects of a selective interaction between the alcohol and the polar solute molecule. 3. Dielectric Constant Measurements From eq 2, we would expect that the macroscopic dielectric constant of a single component solvent is the greatest contributing factor to the Stokes shift. However, in a mixed solvent, this concept has less meaning. In a single-solvent solution, the microscopie dielectric constant should be very close to that of the bulk liquid, but in mixed solution, the long-range and short-range dielectric constants should not be the same because of inhomogeneous solvent molecular distributions induced by selective solvation. In order to pursue this, we have measured the macroscoDic dielectric constants for various compositions of benzeie/2-propanol mixtures, and these are shown in Table 111. From these values, we observe that small additions of 2-propanol to benzene yield disproportionately small increases in dielectric constant. Figure 2 shows a plot of the measured dielectric constant function E-1
n2-1
The Journal of Physjcal Chemistry, Vol. 82, No. 22, 1978 2417
Fluorescence Spectroscopy of 2-Amino-7-nitrofluorene
TABLE 111: Measured Dielectric Constants for Benzene-2-Propanol Mixtures vol % 2PrOH Elneas fcalcda 0 2.27 2.27 1.0 2.33 3.01 2.24 2.39 3.39 5.57 2.54 4.17 11.1 2.85 5.11 21.9 3.75 7.77 32.6 5.2 9.54 100 18.3b 18.3 a From eq 2 and Figure 2. Value taken from the “International Critical Tables”.
O7
t
d20
TI 4 W
U
L
I
6
7
8 AV
9
IO
(kK)
Figure 2. Relationship between the magnitude of the Stokes fluorescence shift and macroscopic physical properties of a benzene/2-propanol solution of ANF. The concentration of 2-propanol is increasing from left to right.
against observed frequency shift (from Table 11). The values for the refractive index were obtained from linear interpolation of the extreme values (from the “International Critical Tables”, n = 1.501for pure benzene, and n = 1.378 for pure 2-propanol). Since the variation in n was small over the entire concentration range compared to other variables, this procedure should cause minimal error in the calculations. It is seen in Figure 2 that the data do not obey the linear eq 222even in the region of low 2-propanol concentrations where the spectral shape does not change significantly. For reference, a straight line is drawn between the extreme values for the pure liquids, and effective dielectric constant values calculated from this linear graph are compared with measured values in Table 111. From the results in Table I11 it can be deduced qualitatively that the effective dielectric constant seen by the excited solute molecule for all intermediate concentrations of polar solvent exceeds the macroscopic value. We view this as evidence for the displacement of the local solvation equilibrium from the average concentration in bulk. Thus, the observations appear to be consistent with a model based on selective interaction between the polar solute molecule and the polar solvent component, which immediately introduces dynamic considerations into the picture since we have two electronic states of radically different dipole moments about which the degree of selective solvation should be different. The lower state is dipolar because of the remote groups of different electron affinity, but the upper state is almost zwitterionic in character. It is therefore expected that, on excitation, at least two molecular diffusion processes should ensue: (1)
TABLE IV: Viscosity Data and Diffusion-Limited and Experimental Rate Constantsa for Benzene/2-Propanol Mixtures at 296 K vol % 109~ cp ~101OkII ~ 1, 0 9 h k 109h, (hd - hfo) 2PrOH Q 0 0.59 1.11 0 0.8 0 1.4 1.3 1 0.59 1.11 2.9 2 0.59 1.11 5 0.59 1.11 7.2 5.0 1.1 6.4 2.9 1.09 14.4 10 0.60 20 2.9 20 0.66 0.99 26.0 37 6.6 0.89 34.7 30 0.74 10.9 43.6 51 50 0.98 0.67 100 2.18 0.30 39.3 92 18.2 a Errors in determination of the relaxation rate constants were typically < 20%.
reorientation of the near neighbors, a process that should occur within the laser pulse duration, according to our process due published m e a ~ u r e m e n t s ; l(2) ~ * a~ relaxation ~ to diffusion of polar material toward the fluorescent dipolar center from bulk solution, this should be slower than the reorientation. Within our simplified picture, the extent to which process 1 is detectable depends on several factors: (a) The actual number of near neighbor 2-propanol molecules is determined by the degree of solvation of the ground state. (b) A small population of 2-propanol near neighbors will result in a small shift in the spectrum which may not be readily detectable. (c) A small number of 2-propanol near neighbors are essentially in an environment of benzene, which has a viscosity coefficient about 1/4 that of pure 2-propanol. Thus, the actual rotation time of the 2-propanol molecules could be 1-2 ps (based on our measurements reported in ref 13) and therefore beneath our time resolution. Temperature variation may resolve this problem. (d) It is not clear that the relaxation process can be broken down into two simple exponentials. 4. Viscosity Measurements Since diffusion and molecular rotation are certainly involved in the relaxation of molecular excited levels, we have measured the viscosity coefficients for all of the solutions used. An Ostwald viscometer was used and the measured relative viscosity coefficients were referenced to those of the pure solvents found in the literature (corrected to 296 K). These results appear in Table IV. From the viscosity data and the simplified form of the Debye equation
k11 = 8RT/30007
(3)
we calculated a series of diffusion-limited second-order rate constants. From each of these was calculated an effective pseudo-first-order rate constant, k,,,,, according to the relationship
k,,,, = kI~[2-PrOH]
(4) therefore allowing for the concentration of 2-propanol. These also appear in Table IV. Errors in determination of the viscosity coefficients were smoothed out graphically before using the Debye relation, but the original data are presented in Figure 2, where the Stokes shift is plotted against viscosity coefficient. As with the fluorescence data, we notice a disproportionate effect on the viscosity of small amounts of added material. Unlike the fluorescence spectrum, however, the viscosity is sensitive to small amounts of nonpolar soluent
L. A. Hallidy and M. R. Topp
The Journal of Physical Chemistty, Vol. 82, No. 22, 1978 I
I
I
I
I
1
I
I
I
200
300
400
500
600
700
SO0
/ / 0
100
TIME ( p s )
Figure 3. Fluorescence profiles of a solution of ANF in 10% 2propanoV90% benzene solution.
in the alcohol. Thus, while the initial large drop in fluorescence energy occurs at low concentrations of propanol, the viscosity drops rapidly for small amounts of benzene in propanol. Inspection of the “International Critical Tables” shows this viscosity behavior to be a general phenomenon of binary solvents which has been treated more recently in the literature in relation to dielectric relaxation p r o c e s s e ~ . The ~ ~ ~effect ~ ~ is more pronounced with the viscous alcohols, and thus is probably correlated with the breakdown of long range structure. However, the important conclusion is that for the concentration range of 2-propanol over which long range diffusion may be important, i.e., 0-lo%, the diffusionlimited rate constant should be independent of concentration. Thus, over this range kvisc should be directly proportional to the concentration of 2-propanol. The relaxation times measured below depend similarly on concentration of 2-propanol, and we wish to relate these two processes. 5. Fluorescence Relaxation Times Our laser experiments were designed to measure the fluorescence time profiles a t different places in the fluorescence spectrum of ANF, varying the relative concentrations of benzene and 2-propanol in mixed solution. The apparatus used has been described elsewhere by us.12313 The method involved frequency-conversion gating of the fluorescence excited by picosecond laser pulses at 354 nm. The experimental resolution was about 10 ps and the high signal-to-noise ratio allowed sensitive detection of fluorescent signals over the range 1-1000 ps. Within the limits of experimental accuracy, we ascertained that the decay profiles measured at both 490 and 680 nm were exponential for all our determinations. We suppressed the effects of fluorescence depolarization on the fluorescence profiles by appropriate selection of the excitation polarization in relation to the preferred axis of the gating c r y ~ t a l . Complete ~ ~ ! ~ ~ removal of depolarization effects was confirmed by monitoring the fluorescence profile of ANF either in pure benzene or in benzene/ propanol solutions a t an isoemissive point, where the Stokes shift phenomena were not dete~tab1e.l~ Our experimental results are listed in Table IV and sample profiles appear in Figure 3. As before,12 we have concentrated on analysis at two wavelengths representative of the high-frequency and low-frequency components of the fluorescence spectra. The important results are as follows.
0
IO
5 [Z-PrOH]
15
(M)
Figure 4. Experimentally derived values of k, and kd compared to the calculated pseudo-first-orderdiff usion-limitedrate constant as a function of 2-propanol concentration in benzene solutions of ANF.
(a) The quenching of both sets of states was found to be accurately proportional to the concentration of alcohol up to and including pure alcohol. (b) The efficiency of population of the relaxed states from the environmental Franck-Condon states was calculated to be constant at -84%. The remainder was lost to nonfluorescent levels. (The actual fate of this excitation So and SI energy (Le., the distributions between S1 T1 relaxation and other nonradiative processes) remains to be studied.) (c) The deactivation of the two states obeys the equations k , = 7.0 X 1Og[2PrOH] = k, - k d
-
-
hd = 1.5 x 109[2PrOH] + kfo
where k,( is the total first-order rate constant for decay at 487 nm, k, is the part of k,, due to the Stokes shift process, k d is the total first-order rate constant for decay at 680 nm, and kfo is the fluorescence decay rate constant at zero concentration of 2-propanol. The measurements of the efficiency of conversion of environmental Franck-Condon states to relaxed fluorescent states are based on the assumption that the solvation does not alter the molecular electronic structure of the state and therefore the two sets of states should be deactivated at a similar rate by radiative and radiationless processes, with the exception that the upper states can also relax by solvent reorientation to the lower states. In Figure 4 we have plotted three curves illustrating the behavior of the functions k, and k d against concentration of 2-propanol together with kviso the calculated pseudo first-order rate constant predicted by the Debye equation. At low concentrations, the relaxation of Franck-Condon states appears to have a rate about 70% of the calculated diffusion limit, but at high concentrations eq 3 and 4 fail to account for the continued linear dependence of the measured rate constants on Concentration. 6. Discussion
In solution, the fluorescence Stokes shift is considered to occur through a dielectric polarization mechanism. In a hydrogen-bonded solvent such as 2-propanol, this process is fast enough that, at room temperature, we cannot resolve
Fluorescence Spectroscopy of 2-Amino-7-nitrofluorene
The Journal of Pbysical Chemistty, Vol. 82, No. 22, 1978 2419
the shift from our pulse duration. However, it is interviscosity approach17J8 where the effective diffusion coefficient of one component of a liquid mixture is calesting to note that when we dilute the 2-propanol by culated with respect to the other component, over the adding benzene, the rate of the shift decreases proporrange when the two concentrations are comparable. tionately, and the extent of the shift can no longer be However, it is unclear at present how this approach must explained by the bulk dielectric properties of the solvent. Therefore, the reduced rate of the Stokes shift is prebe modified in the vicinity of the solute ANF molecule. sumed to result from a diffusional process, the end product Continuing studies of the details of the Stokes shift of which is a greater effective dielectric constant in the phenomena will rapidly improve our knowledge of imvicinity of the solute molecule. Since the observed profiles portant solvent-solute interactions, specifically, the interaction of a polar molecule with its environment. Up to corresponding to decay of the higher-energy states appear to be single exponentials, it is presumed that the extent the present, the location of polar molecules in complex of relaxation by near neighbors prior to diffusion is relenvironments have been studied by the intensity of the atively small and therefore that the extent of selective time-integrated fluorescence spectral maximum, but we have now demonstrated the importance of dynamic solvation in the ground state is quite small. In order to considerations in these interactions. Therefore, in a theory measure this in a quantitative fashion, it will be necessary of solvent-solute interactions, the nature of the envito measure full fluorescence spectra immediately following ronment and its diffusional properties must be considered, the laser pulse and a t different stages of the primary and the concept of a static dielectric constant must be relaxation process.21 abandoned. We have shown that the environmental Franck-Condon relaxation is complete before fluorescence decay occurs, Acknowledgment. We gratefully acknowledge the the differential in rates being about one order of magsupport given to this project by the National Science nitude. This proves that the actual position of the Foundation through the Materials Research Program fluorescence spectrum observed by time-integrated (DMR-76-00678). We also thank Mr. A. Passen for measurements does not result from a competition between measuring viscosities and dielectric constants. the two processes as suggested previously by L i ~ p e r t . ~ J ~ Since the excited molecule relaxes completely with respect References and Notes to its environment well before it is electronically deactiE. Lippert, 2.Elektrocbem., 61, 962 (1957). vated, it is clear that we are observing in the fluorescence A. T. Amos and B. L. Burrows, Adv. Quant. Cbem., 7, 289 (1973). shift a shift in the solvation equilibrium of the polar E. Lippert and F. Moll, Z . Elektrochem., 58, 718 (1954). molecule, which becomes complete after a short-range N. Mataga, Y. Kaifu, and M. Koizumi, Bull. Cbem. Soc. Jpn., 29, 465 (1956). diffusional process. The position of the fluorescence B. Gronau, E. Lippert, and W. Rapp, Ber. Bunsenges. Pbys. Cbem., maximum closely represents the true energy of an envi76, 432 (1972). ronmentally relaxed state rather than some average value E. G. McRae, J. Pbys. Cbem., 61, 562 (1957). M. B. Ledger and P. Suppan, Spectrocbim. Acta, Part A , 23, 641 resulting from competitive relaxation processes. (1967). The final point to be made concerns the linearity of the F. J. Kampas, Cbem. Phys. Lett., 26, 334 (1974). relaxation rate constants with concentration of 2-propanol D. Grasso and E. Bellio, Cbem. Pbys. Left., 30, 421 (1975). W. S.Struve and P. M. Rentzepis, Cbem. Phys. Left., 29, 23 (1974). over the entire range &loo%. The diffusion-limited rate H. E. Lessing and M. Reichert, Cbem. Pbys. Lett., 46, 111 (1977). constant given by eq 3 and 4 can account for this trend 1. A. Hallldy and M. R. Topp, Chem. Phys. Lett., 48, 40 (1977). only if the value of TJ is constant over the given range of L. A. Hallidy and M. R. Topp, submitted for publlcation. concentrations. In order to explain this observation, it is E. Lippert in “Organic Molecular Photophysics”, Vol. 2, J. B. Birks, Ed., Wiley, New York, N.Y., 1975, p 1. necessary to postulate a similarity between the viscosity K. Egawa, N. Nakashima, N. Mataga, and C. Yamanaka, Cbem. phys. and dielectric constant behavior. That is, these quantities Lett., 8 , 108 (1971). exhibit both short-range and long-range components and G. Fischer, G. Seger, K. A. Muszkat, and E. Flscher, J. Cbem. SOC. Perkin Trans. 2 , 1569 (1975). there is no reason to expect the viscosity of the solvent in N. E. Hill, Proc. Pbys. SOC. London, Ser. B , 67, 149 (1954). the immediate vicinity of the polar dye molecule to corP. P. Ho, W. Yu, and R. R. Alfano, Cbem. Pbys. Lett., 37, 91 (1976). respond to the bulk average. In this model, long-range L. A. Hallidy and M. R. Topp, Cbem. Pbys. Lett., 46, 8 (1977). G. R. Fleming, J. M. Morris, and G. W. Robinson, Cbem. Pbys., 17, diffusion provides an appropriate description of the ob81 (1976). served behavior at low concentrations, but at high conW. R. Ware, S. K. Lee, G. J. Brant, and P. P. Chow, J. Cbem. Pbys., centrations, the extent of molecular motion amounts only 54, 4729 (1971). Strictly, in plotting agalnst the dielectric constant function, to one or two layers of solvent around the solute molecule. one should use values of the fluorescence maxima which correspond We note (from the viscosity data) that small quantities of to the totally environmentally relaxed excited states. In the absence benzene are sufficient to break the structure of 2-propanol, of this information, we have used the observed time-Integrated and therefore it may be justified to assume that a similar maxima. The extent to which this approxirnatlon is valld can be deduced from the time-resolvedmeasurementspresented in section situation exists around a large solute molecule, resulting 5. The required maxima should In all cases be slightly further red in a short-range viscosity that is smaller than the bulk shifted from those listed in Table I1 and the “local” dielectric constants value. It may also be possible to consider the “mutual” (.ecalcd) will be slightly underestimated.
