J . Phys. Chem. 1988, 92, 3675-3679
3675
Self-Diffusion in the Compressed, Highly Viscous Liquid 2-Ethylhexyl Benzoate N. A. Walker, D. M. Lamb, S . T. Adamy, J. Jonas,* School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801
and M. P. Dare-Edwards Shell Research (U.K.) Ltd., Thornton Research Centre, P.O. Box 1 , Chester CH1 3SH, U.K. (Received: October 23, 1987)
The self-diffusion coefficients,densities, and viscosities of liquid 2-ethylhexyl benzoate are reported as a function of pressure from 1 to 4500 bar within the temperature range from -20 to +lo0 O C . The rough hard sphere (RHS) model and the Stokes-Einstein equation are used to analyze the data. The RHS model indicates a high degree of rotational-translational coupling which increases as density increases. The nonspherical shape and conformational flexibility of the molecule are proposed as the cause of this behavior. The Stokes-Einstein equation is found to hold over 5 order of magnitude changes in self-diffusion and viscosity.
Introduction In a previous paper,’ we presented the results of a ’ H N M R study of self-diffusion in 2-ethylhexyl benzoate (2-EHB) (C6H5COOCH2CH(CHzCH3)(CH2)3CH3) over a wide range of temperatures (-20 to +lo0 “C) and pressures (1 to 4500 bar). The results were of intrinsic interest as the study utilized two different N M R methods to obtain self-diffusiondata over the wide range of fluid viscosities accessible (1 to approximately 90 000 cP). The resultant diffusion coefficients (D)of the system ranged from around 1C5to cmz s-l, which to the best of our knowledge is an unprecedented range to be directly measured for a single fluid system. These data, combined with the corresponding density and viscosity values, present the opportunity to analyze the transport properties of this fluid by using available theories of diffusion in liquids over a very wide range of fluid states. Characterization of the degree of the coupling between the rotational and translational motions in 2-EHB and the behavior of this coupling with density provides the motivation for the use of the rough hard sphere (RHS) model for diffusion as developed by Chandler.2 In addition, the wide range of fluidity covered in this study enables a test of the Stokes-Einstein relationship over 5 orders of magnitude. This diffusion study is part of a wider multidisciplinary (NMR, Raman, and IR) program ongoing in several laboratories to study the molecular dynamics of 2-EHB at high pressure. Interest in this fluid is prompted by a lack of understanding of the relationship, between the molecular properties and bulk fluid properties of elastohydrodynamic (ehd) lubricants, which operate under conditions of high pressure. In this respect 2-EHB has been chosen as a model synthetic hydrocarbon based ehd lubricant, its molecular structure being complex enough to represent a real ehd fluid, while still being simple enough to allow spectroscopicprobing of its molecular dynamics. Indeed, the wide range of fluid viscosities readily accessible by using the pressure and temperature capabilities in our laboratory4 is indicative of the fluid’s suitability as a model lubricant. Studies of self-diffusion in hydrocarbon based liquids under pressure have, in the past, concentrated mainly on fairly simple molecules such as short alkane^,^ cyclohexane,6 methylcyclohexane,’ and methanol.* Data from such systems have been (1) Walker, N. A.; Lamb, D. M.; Jonas, J.; Dare-Edwards, M. P. J . Magn. Reson. 1987, 74, 580. (2) Chandler, D. J . Chem. Phys. 1975, 62, 1358. (3) Edward, J. T. J . Chem. Educ. 1970, 74, 261. (4) Jonas, J. Reu. Phys. Chem. Jpn. 1980, 50, 19. (5) Bachl, F.; Ludemann, H. L. Physica B+C 1986, 139 & 140, 100. (6) Jonas, J.; Hasha, D.; Huang, S. G. J . Phys. Chem. 1980, 84, 109. (7) Jonas, J.; Hasha, D.; Huang, S. G. J . Chem. Phys. 1979, 71, 3996. (8) Jonas, J.; Akai, J. A. J . Chem. Phys. 1977, 66, 4946.
0022-3654/88/2092-3675$01.50/0
successfully interpreted in terms of the R H S and Stokes-Einstein models of self-diffusion. The significance of the present study relative to previous systems studied results from (i) the molecular complexity and size of 2-EHB and (ii) the wide range of diffusivities accessible in 2-EHB due to its pressure-viscosity and temperature-viscosity behavior.
Experimental Section Materials. The sample of 2-EHB (purity 199.8%) was synthesized by Palmer Research Ltd. (U.K.). N M R Measurements. Measurement of self-diffusion coefficients was achieved using ‘H N M R at 60 M H z in a wide-gap Varian electromagnet and required two different techniques in order to cover the full range. Diffusivities greater than 3 X cm2 s-l were measured by using the spin-echo Bessel analysis method developed by Lamb et aL9 Diffusivities less than 3 X lo-* cm2 s-’ were obtained by measuring the H I field dependence of the rotating frame proton spin-lattice relaxation time ( T1,) according to the method developed by Burnett and Harmon.” Full experimental details of the applicability and limitations of the N M R techniques are given in our previous paper.’ Table I lists the diffusion coefficients. Gaps in the data in the -20, 0, 20, and 40 O C isotherms occur where the diffusion coefficient fell outside the constraints of both the spin-echo and TI, methods (see ref 1 for full details). Accuracies in the measured values of D range from &3% at the largest D to &IO% for the lowest D for the spin-echo-derived data and &30% for the T!,-derived data. Densities. Density measurements were carried out using a high-pressure, variable-temperature densitometer.” Calibration of the instrument for each isotherm was achieved by using the I-bar densities which were measured with a commercially available Mettler/Paar DMA45 digital density meter. The experimental densities as a function of pressure were fit to the Tait equation (1/Pr
- l/pp)pr = C log [ ( B + P ) / B + Pill
where pp is the density in g cm-3 at pressure P , p, is the density at the reference pressure ( P , = 1 bar), and B and C a r e the Tait parameters for each isotherm. The fitted densities for each isotherm are listed in Table I, and the Tait parameters are given in Table 11. An accuracy of f5% is assigned to the density measurements. Viscosities. High-pressure viscosities were obtained by using a high-pressure falling slug viscometer described previously.I2 (9) Lamb, D. M.; Grandinetti, P. J.; Jonas, J. J . Magn. Reson. 1987, 72, 532. (10) Burnett, L. J.; Harmon, J. F. J . Chem. Phys. 1972, 57, 1293. (11) Akai, J. A. Ph.D. Thesis, University of Illinois, 1974. (12) Artaki, 1.; Jonas, J . J . Chem. Phys. 1985, 82, 3360.
0 1988 American Chemical Society
3676 The Journal of Physical Chemistry, Vol. 92, No. 1 2 , 1988 TABLE I: Experimental Self-Diffusion Coefficients, Viscosities, and Densities D x 109, T. O C P . bar n, CP p . g cm-) cm2 s-' -20
0
20
1 500 1000 1500 2000 2500 3000
70.3 250 945 2950 9190 20800b 88500
0.9960 1.0214 1.0425 1.0605 1.0764 1.0906 1.1035
165 53.8 9.36 2.73 1.19 0.455 0.154
1 500 1000 1500 2000 2500 3000 3500 4000 4500
16.9 44.4 119 293 714 1690 3850 9800 24500 57200
0.9805 1.0076 1.0300 1.0493 1.0662 1.0814 1.0952 1.1079 1.1 197 1.1306
609 244 95.2 37.5
6.77 13.0 27.9 56.9 112 240 437 950 1790 3680
0.9650 0.9940 1.0175 1.0376 1.055 1 1.0707 1.0848 1.0977 1.1097 1.1208
1540 719 346 166 89.3 42.4
2500 3000 3500 4000 4500
3.62 6.60 11.7 21.0 38.8 73.0 128 234 427 735
0.9495 0.9814 1.0066 1.0277 1.0459 1.0620 1.0765 1.0897 1.1019 1.1132
2980 1640 878 460 263 171 91.9 45.7
1 500 1000 1500 2000 2500 3000 3500 4000 4500
2.27 3.88 5.82 8.94 14.6 24.3 37.4 61.8 103 165
0.9340 0.9687 0.9958 1.0182 1.0375 1.0545 1.0698 1.0837 1.0964 1.1083
4230 2740 1600 1070 717 402 254 159 96.1 61.6
1500 2000 2500 3000 3500 4000 4500
1.58 2.34" 3.45" 5.20 7.63 11.1 16.7 24.9 36.4 54.3
0.9185 0.9562 0.9562 1.0085 1.0286 1.0462 1.0620 1.0763 1.0894 1.1016
6500 4310 2710 1910 1280 882 582 38 1 255 172
1 500 1000 1500 2000 2500 3000 3500 4000 4500
1.16 1.61" 2.23" 2.99 4.25 5.81 8.49 11.9 15.2 20.8
0.9030 0.9436 0.9740 0.9987 1.0196 1.0379 1.0542 1.0690 1.0826 1.0951
9220 6260 4230 2900 2060 1490 1080 795 530 387
1 500
1000 1500 2000 2500 3000 3500 4000 4500 40
1 500 1000 1500
2000
60
80
1 500
1000
100
Extrapolated values (see text).
4.97 1.94 0.937 0.41 0.148
3.08 1.61
Interpolated values.
Ambient pressure viscosities, for use as calibration points, were measured from 20 to 100 'C with a Cannon semimicro glass
Walker et al. TABLE 11: Parameters of the Tait Equation T, O C B , bar C T, O C -20
0 20 40
1633 1606 1447 1237
0.2153 0.2291 0.2266 0.2208
60
80 100
B, bar
C
1127 1004 910.8
0.2254 0.2251 0.2269
viscometer. Due to the large range of viscosities covered in any one isotherm, nonlinearity was observed in the fall times at the lower pressure regions and thus extrapolation was necessary in some cases. Here, the linear (higher pressure) portions of the fall time isotherms were extrapolated back to I-bar pressure, permitting the viscometer calibration using the known 1-bar viscosities. Table I lists the experimental viscosities and indicates those which are extrapolations of the higher pressure data. An accuracy of f10% is assigned to the viscosity measurements.
Results and Discussion Experimental Results. Table I lists the diffusion coefficients, viscosities, and densities at each pressure and temperature. Figures 1 and 2 display the diffusion coefficients and viscosities, respectively, along each isotherm. The most striking feature of the data is the range of diffusivities and viscosities measured, each covering nearly 5 orders of magnitude. RHS Model Analysis. This model, based on molecular dynamics simulation^'^ for hard sphere liquid, was originally developed by Chandler.2 Although the model is strictly applicable to only spherical molecules, it has been successfully applied to several nonspherical systems,&*and it is obviously of interest here, because the analysis of the diffusion data in terms of this R H S model yields information on the degree of the coupling between the rotational and translational motions in the liquid. In addition, it is interesting to test whether its applicability can be extended to a large irregularly shaped flexible molecule such as 2-EHB. The RHS theory allows calculation of a theoretical diffusion coefficient of a smooth hard sphere (DSHS) liquid of known molecular diameter and density according to
where a is the hard-sphere diameter, p is the number density, and the other symbols have their usual meaning. The experimental diffusion coefficient Dexptl is considered to be approximately equal to the rough hard sphere diffusion coefficient (DRHs), which in turn is proportional to DsHs by a factor A , i.e.
Dexpti DRHS= ADSHS
(2)
The factor A can range from 0 to 1 and is considered a measure of the rotational-translational coupling of the system; the smaller the value of A , the stronger the coupling is considered to be (Le., the fluid is diffusing less rapidly than would a smooth hard sphere). Values of the hard sphere diameter ( u ) can be determined independently of the self-diffusion data if one uses the fluidity analysis method of Hilderbrand et a1.I4 One plots fluidity (4 = 1/ v ) vs molar volume (V) for each isotherm, and the volume axis intercept of the extrapolated linear low-density region of the plot yields the molecular diameter according to Dymond'sls definition, I = 1.384v0and Vo= Nu3/2'/*.This method has been successfully ~ 3 shows this used for a number of previous s t ~ d i e s . ~ , ' , 'Figure analysis for the 100 OC isotherm which yielded a molecular diameter of 7.18 A. The 80,60, and 40 'C isotherms yielded values of 7.23,1.30,and 1.34 A, showing an increase in u with decreasing temperature in accordance with previous studies. The 20,0, and -20 OC isotherms exhibited strong curvature even at low densities, negating the calculation of u for these isotherms. However, the (13) Alder, B. J.; Gass, D. M.;Wainwright, T. E. J. Chem. Phys. 1970, 53, 3813. (14) Hildebrand, J. H.; Lamoreaux, R. H. Proc. Nutl. Acad. Sci. U S A .
1972, 69,3428.
(15) Dymond, J. H. J . Chem. Phys. 1974, 60, 969. (16) Fury, M.; Munie, G.; Jonas, J. J . Chem. Phys. 1979, 70, 1260.
The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3617
Self-Diffusion in 2-Ethylhexyl Benzoate
0.9
I
0.0
0.7 0.6
7 ;
-> 0
0.5
'
0.4
3
0.3
E LL
0.2 0. I n "
210
220
230
240
250
260
MOLAR VOLUME ( c m 3 m o ~ i ' )
Figure 3. Volume dependence of fluidity at 100 OC.
TABLE III: Calculated Smooth Hard Sphere Diffusion Coefficients, Packing Fractions, and Values of A packing DsHs X IO5, P,bar T, O C fraction cm2 s-' A0
do 0
1000
2000 3000 4000 Pressure ( b a r )
5000
Figure 1. Self-diffusion coefficients for 2-EHB as a function of tem-
perature and pressure. The solid symbols represent data derived from the spin-echo Bessel analysis technique; the open symbols were obtained by using the To relaxation method.
1000
2000
3000 4000 5000 6000 PRESSURE (bor)
Figure 2. Experimental viscosities for 2-EHB as a function of tempera-
ture and pressure. data for these isotherms fall beyond the range of applicability of eq 1 (as clarified below). Evidence of the validity of the fluidity analysis approach is apparent when one also calculates u using Bondi's method of additive molecular group volume increment^.'^ This method yields a value of 7.7 A (assuming a spherical shape), which given the (17) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968; p 450.
40
0.506
1.26
0.24
1 500
60
0.490 0.508
1.95 1.23
0.22 0.22
1 500 1000
80
0.468 0.487 0.502
3.03 2.1 1 1.49
0.21
1 500
100
0.450 0.47 1 0.486 0.498 0.509
4.05 2.94 2.21 1.66 1.25
0.23 0.21 0.19 0.17 0.17
1000 1500 2000 a
'
1
A =
0.20 0.18
Dsxptl/DSHS.
approximate nature of Bondi's method is in remarkable agreement with the values derived by means of the fluidity analysis. According to Chandler,2 u is not expected to be density dependent and only a weak function of temperature. Thus, we use the values of u at each temperature to determine DsHs along each isotherm according to eq 1. The A factors are then determined via eq 2. It is important to note at this point that eq 1 is only strictly valid for a certain range of densities such that 0.70 5 pa3 5 0 . 9 4 , although Chandler has assumed that eq 1 can be extrapolated to pu3 = 0.97. Unfortunately, much of our data are such that pu3 > 0.97; Table I11 shows the values of DsHs and A for the applicable temperatures and pressures. Several qualitative conclusions may be drawn from the results presented in Table 111. Firstly, the values of A are much less than 1, indicating strong rotational-translational coupling between 2-EHB molecules. Such behavior is physically reasonable considering the irregular shape of 2-EHB. A similar value of A was found for methylcyclohexane at -70 O C 7 and was also attributed to strong rotational-translational coupling as a consequence of the nonspherical shape of molecules studied. It is somewhat surprising to find a similar value of A for our system given the much more irregular shape of the 2-EHB molecule. However, one must also consider the flexibility of the side chains which may play an important role in determining the value of A . Secondly, A exhibits a pronounced decrease as density increases at 80 and 100 OC. The two values which fall away from the main data range (40 OC, 1 bar and 60 OC, 500 bar) appear spurious; however, the limited amount of data at these temperatures is insufficient for any trends to be discerned. In any case, these data are for liquid states where pu3 is very close to the limiting value of 0.97 and may indicate that these states are in fact beyond the range of applicability of the RHS analysis. It is not surprising that the observed dependence of A on density at 80 and 100 "C is at variance with Chandler's stipulation2 that A should be rigorously density independent. Most previous studies of self-diffusion have concluded that A is not dependent at all on density. It would seem likely that the
3678
The Journal of Physical Chemistry, Vol. 92, No. I,?, I988
low values of A for our system are consequences of the irregular shape and conformational flexibility of 2-EHB which also results in increases in the magnitude of rotational-translational coupling as density increases. More recent R H S analysis of self-diffusion data for some simple polyatomic systems such as benzene, CC14, and 1,2-dichloroethane’*has also revealed A factors that decrease with increasing density by as much as 50%. Dymond” has commented that such behavior may be accounted for if one considers LT to be density dependent. This, however, would be contrary to Chandler’s assertion that r is likely to be independent of density;*indeed CT would have to increase with increasing density, which one might consider a physically unreasonable trend. It would seem qualitatively more likely that the magnitude of the rotational-translational coupling is really increasing as a function of density. Unfortunately, the range of densities over which the RHS theory is applicable is insufficient to allow us to analyze our full range of data, but the trend in A with increasing density is readily discernible, particularly for the 100 ‘C isotherm. Stokes-Einstein Analysis. The availability of a wide range of diffusion coefficients and viscosities enables us to provide a rigorous test of the Stokes-Einstein equation at the molecular level for 2-EHB. This hydrodynamic theory relates the diffusion coefficient to the viscosity ( a ) and molecular radius ( r ) according to
D = kT/(Craq)
Walker et al.
40‘C
IO-’
-
3500
I
(18) Easteal, A. J.; Wool!’, L. A. Physica B+C 1984, 124, 182. (19) Dymond, J. H. Chem. SOC.Rev. 1985. 14, 317. (20) Tyrell. H. J. V.; Harris, K . R. Diffusion in Liquids; Butterworths:
London, 1984; p 259. (21) Parkhurst. Jr., H. J.; Jonas, J. J . Chem. Phys. 1975, 63. 2698. (22) (a) Sperol, A , ; Wirtz, K. Z . Nafurforxh., A 1953, 8, 522. (b) A,: Wirtz. K. Z . Naturforsch.. A 1953, 8 , 532. (23) Vogel, H.; Weiss, A. Ber. Bunsen-Ges. Phys. Chem. 1981. 85. S39. (24) Chen, H.: Chen. S . J . Phi,$. Chem. 1984, 88. 5118.
4500
P R E S S U R E (bo,)
l-
STOKES-EINSTEIN TEST A EXP E R I M ENTAL ENTAL PER S L I P LIMIT (C.41 --STICK L I M I T (C.61
(3)
where C is a constant equal to 4 in the “slip” limit and 6 in the “stick” limit. Equation 3 is derived for a macroscopic sphere moving in a continuum and thus should theoretically only apply to solute-solvent systems where the solute is a large compared with the solvent; in this case the stock condition (C = 6) should apply. It has been suggested20that the slip condition (C = 4) may be approached when the solute and solvent are of similar size (Le., self-diffusion). Interestingly, several studies have shown that eq 3 provides a reasonable estimate of self-diffusion for a number of simple molecules such as cyclohexane,6 methylcyclohexane,’ and benzene.2’ Our data provide the opportunity to test the relationship over a much wider range of viscosity than these previous studies. Figure 4 allows comparison of the experimental data and the calculated diffusion coefficients at the stick and slip limits for each isotherm. The uncertainty in the values of the calculated values is estimated at 3~10%.Table IV lists the values of C calculated from the experimental diffusion coefficients and viscosities. The molecular radius used in each case is the average hard sphere diameter of 7.26 A determined by using the fluidity method for the R H S analysis. The uncertainties in C are f30% for the TI,-derived data and f14R for the spin-echo-derived data. The prominent feature apparent from Table IV and Figure 4 is that the Stokes-Einstein equation generally provides a good description of self-diffusion in 2-EHB over a 5 order of magnitude data range. The -20, 0. 20. and 40 ‘C isotherms mainly fall slightly below the C = 4 limit; the only exceptions to this are the 4000- and 4500-bar data at 20 OC (which are derived from the T I , measurement) which appear spurious. Low values of C have also been observed for methylcyclohexane‘ and pyridine,16 where an average value of 2.9 was reported. Interestingly, many of the i,alues of C for these isotherms fall close to the value of 3.36 predicted by Wirti et al.?’ These authors modified the Stokes-Einstein relationship to take into account the molecular structure of the medium by introducing a “microfriction” factor. This relationship has been found to be closely obeyed for several fluids, both neat and solutions.24 For the 60 and 80 O C isotherms, the Cvalues fall (within error) close to the slip limit, indicating that eq 3 is correctly describing the diffusive behavior
I
J
500
2500
1500
3500
4500
PRESSURE ( b a r )
Figure 4. Comparison of the experimental and predicted (Stokes-Ein-
stein) self-diffusion coefficients. The symbols A represent the experimental data; the solid and broken lines represent the slip (C = 4) and stick (C = 6) limits, respectively, of eq 3. TABLE IV: Stokes-Einstein Constants C = kT/(naDq) p, bar -20 O C 0 O C 20 OC 4 0 O C 60 O 1
500 1000
1500 2000 2500 3000 3500 4000 4500
2.6 2.3 3.5 3.8 2.8 3.2 2.2
3.2 3.1 2.9 3.0 3.9 4.4 3.6 3.3 3.9
3.4 3.8 3.7 3.8 3.5 3.5
3.5 3.5 3.7 3.9 3.7
3.0 3.2 3.6
6.4 6.0
4.2 3.8 4.3 4.2 3.8 4.1 4.2 4.1 4.1 4.0
C
80 O C
100 OC
4.2 4.2 4.6 4.3 4.4 4.4 4.4 4.5 4.6 4.6
4.2 4.5 4.8 5.2 5.2 5.2 4.9 4.8 5.6 5.6
of 2-EHB. At 100 O C , the values of Call fall within the stick-slip boundary conditions. It is interesting to examine in more detail the behavior of the C coefficient for the 100 ‘C isotherm (see Table IV). One notes a definite trend in C as a function of pressure from the value of 4.2 close to the slip condition at 1 bar to the C value of 5.6 at 4500 bar, Le., approaching the stick boundary condition. Obviously, one may conclude that the increase in pressure changes the boundary condition from slip to stick, reflecting the increase in the degree of the coupling between rotational and translational motions as deduced from the pressure behavior of .4 for the 100 OC isotherm (see Table 111). In addition, we want to point out the low value of C (C < 4.0) for lower temperature isotherms, which suggests that Gierer and Wirtz’s22 microviscosity concept (C = 3.36) perhaps warrants some additional theoretical work. At the present time, a detailed investigation of the rotational correlation times for 2-EHB over the range of temperatures and pressures is in progress. W e hope that the availability of transport and relaxation data for selected liquids will stimulate theoretical work. Most importantly, however, considering the irregular (nonspherical) shape and conformational flexibility of 2-EHB, it is somewhat surprising that the StokesEinstein equation can describe reasonably well the diffusive behavior over such a wide range of viscosity. Interestingly, a previous variable-temperature NMR study25of o-terphenyl, in the liquid (25) McCall, D. W.; Douglass, D. C.; Falcone, D. R. J . Chem. Phys. 1969. 50. 3839.
J . Phys. Chem. 1988, 92, 3679-3682
3679
spherical shape and conformational flexibility of 2-EHB. In addition, we have found that the Stokes-Einstein theory provides a generally good description of self-diffusion in 2-EHB over an extremely wide viscosity range.
and glassy states, also found that the Stokes-Einstein constant variedlittle (by a factor of 2) over a very wide range of viscosity.
Conclusion In conclusion, we have analyzed self-diffusion data in 2-EHB over a wide range of temperatures and pressures in terms of the R H S and Stokes-Einstein theories. Over the limited range of applicability of the R H S model, we find that this model gives a rotational-translational coupling parameter that is density-dependent. This result is not surprising in view of the highly non-
Acknowledgment. This research was partially supported by the Department of Energy under Grant 22-85 PC850503, by AFOSR under Grant AFOSR 85-0345, and by Shell Research (U.K.) Ltd. Registry No. 2-EHB, 5444-75-7.
Solvation Dynamics in Alcoholic Solution in the Temperature Interval 90-190 K Francesco Barigelletti Istituto FRAEICNR, via dei Castagnoli 1 . 40126 Bologna, Italy (Received: September 4, 1987;
In Final Form: December 12, 1987)
Solvation dynamics in EtOH-MeOH (1 :4 v/v) has been studied by combined steady-state and nanosecond time-resolved emission data employing 2-aminophenyl phenyl sulfone as a luminescent probe. The temperature range explored was 90-1 90 K. It has been found that the solvent relaxational process follows an Arrhenius-type activated behavior, the determined activation energy being E, = 1520 cm-'. The nature of the relaxation is briefly discussed.
repolarization of the solvent.' can be e m p l ~ y e d : ' ~ . ' ~
Introduction Solvation dynamics is currently under study because of its key role in chemical reactions, namely, electron-transfer reactions.'-'0 For intramolecular electron transfer two relaxational times for solvent motion can be employed, the Debye relaxational time, T ~ derived in the frame of the dielectric continuum theory for the solvent," and the longitudinal relaxational time, T ~ T~ . describes the relaxation of the solvent polarization for a dielectric continuum subjected to constant charge perturbation' ( T =~ [ t m / t o ] T D , where t- and co are the high- and low-frequency dielectric constants, respectively). Recent studies have pointed out that a range of relaxation times between T~ and T~ could provide a better description of the actual dynamics of the solvation p r o ~ e s s . ~This ~'~ seems particularly true for alcohols in view of specific effects and, for linear alcohols, of relaxational movements concerned with molecular rotation as well as rotation of the C-OH group.I3 The relaxational dynamics of the solvent can be experimentally observed by using a luminescent molecular probe whose optical excitation leads to Franck-Condon (nonequilibrated) solutesolvent arrangements. In this case the temporal shift of the luminescent energy level is related to the rate constant for the
(1) Sumi, H.; Marcus, R. A . J . Chem. Phys. 1986, 84, 4272. (2) Brunschwig, B. S.; Ehrenson, S.; Sutin, N. J . Phys. Chem. 1986, 90, 3657. (3) Rips, I.; Jortner, J . Chem. Phys. Lett. 1987, 133, 411. (4) Kosower, E. M.; Huppert, D. Annu. Reo. Phys. Chem. 1986, 37, 127. (5) Pasman, P.;Mes, G. F.; Koper, N. W.; Verhoeven, J. W. J . Am. Chem. SOC.1985, 107, 5839. ( 6 ) McGuire, M.; McLendon, G. J . Phys. Chem. 1986, 90, 2549. (7) Gennett, T.; Milner, D. F.; Weaver, M. J. J . Phys. Chem. 1985, 89, 2787. (8) Kakitani, T.; Mataga, N. Chem. Phys. 1985, 83, 381. (9) Spears, K. G.; Gray, T. H..; Huang, D. J . Phys. Chem. 1986, 90, 779. (10) Heitele, H.; Michel-Beyerle, M. E. Chem. Phys. Left. 1987, 138, 237. (1 1) Davies, M. In Dielectric Properties and Molecular Behaoior; Sugden, T. M., Ed.; Van Nostrand Reinhold: London, 1969; p 280. (12) Su, S. G.; Simon, J. D. J . Phys. Chem. 1987, 91, 2693. (13) Garg, S. K.; Smyth, C. P. J . Phys. Chem. 1965, 69, 1294.
0022-365418812092-3679$01 SO10
J
~
A- correlation ~ ~ function, A ( t ) ,
A ( t ) = (Vm(t) - V m ) / ( n o - J m ) ,
(1)
where n,(t), v,, and no are the time-dependent shift of the emission maximum and the fully relaxed and initially excited emission maxima,23 respectively. If a single relaxation process is present, the rate for solvent relaxation, k, ( k , = 1 / =~ 1 / ~~ ~ ' ~ 9 ' ' ) , is obtained on the basis of the following equation: V,(t)
= nm + (no - v-) exp(-k,t)
(2)
The activation energy for solvent relaxation, E,, can then be obtained by plotting In k, versus 1/T. Molecular probes giving charge-separated excited states are likely candidate for such s t ~ d i e s . ' ~ ~ 'For ' - ~ ~instance, monitoring the luminescence of the emitting TICT (twisted intramolecular charge transfer) state of bis(4-methy1amino)phenyl sulfone,24 DMAPS, Su and Simon12 found that the actual solvent relaxational time, T,, lies between T~ and T~ in the temperature interval (14) van der Zwan, G.; Hynes, J. T. J . Phys. Chem. 1985, 89, 4181. ( 1 5 ) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 86, 257. (16) Calef, D. F.; Wolynes, P. G. J . Chem. Phys. 1983, 78, 470. (17) Declemy, A,; Rulliere, C.; Kottis, Ph. Chem. Phys. Lett. 1987, 133, 448. (18) Castner, E. W., Jr.; Maroncelli, M.; Fleming, G. R. J . Chem. Phys.
.--,
1987 i - - - ~ r insn
(19) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 6221. (20) Nagarajan, V.; Brearley, A. M.; Kang, T.-J.; Barbara, P. J . Chem. Phys. 1987, 86, 3183. (21) Anthon, D. W.; Clark, J . H. J . Phys. Chem. 1987, 91, 3530. (22) An extended review of studies dealing with solvation dynamics as well as comprehensive presentation of the subject can be found in ref 19 and 20. (23) As discussed by Maroncelli and Fleming,I9 taking the peak frequency is only one of the ways of using spectral data. A more detailed analysis of the spectral features should include the width and asymmetry of the emission band. (24) Rettig, W.; Chandross, E. A. J . Am. Chem. SOC.1985, 107, 5617.
0 1988 American Chemical Societv
