Solvation dynamics in alcoholic solution in the temperature interval 90

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.

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 . describes solvent," and the longitudinal relaxational time, T ~ T~ 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.

0022-3654188 12092-3679$01 SO10

repolarization of the solvent.' can be e m p l ~ y e d : ' ~ . ' ~

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

3680 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988

Barigelletti

213-273 K, approaching rL at the higher temperature. In this work we employ the luminescent 2-aminophenyl phenyl sulfone (OAPS; dipole moments for ground and excited states are

OAPS

1.4 and 6.5 D, r e s p e c t i ~ e l y ~to~probe ) the solvent dynamics of EtOH-MeOH (1 :4 v/v) in the 90-1 90 K interval, which includes the glass-to-fluid transition region of the solvent. The reasons for this choice are as explained in the following. Two models can be employed to describe phenomenologically the X , nm effect of solvent relaxation on the luminescence spectra of a Figure 1. Room-temperature absorption spectrum of 1.06 X IO-' M molecular namely, the above-mentioned continuous shift OAPS in EtOH-MeOH (a) and normalized emission spectra at 90 (b) and 190 K (c). of the emission and the two-state models. According to the first model,27*28 the emission maximum v,(t) is expected to shift to lower c I energy in an exponential fashion with time (eq 2). The two-state describes the relaxation as an equilibrium between two levels of solute-solvent origin, and there is no continuous shift between the initially excited and the relaxed levels. The latter type of relaxation is presumably connected with the presence of two interconverting emitting states of different nature.29 The -* 2 4 1 solute-solvent relaxation of excited OAPS takes place according '5 to the former model. This is shown by the regular shift of the emission maximum in steady-state spectra taken at different temperatures; see below. To obtain the required fluorescence data at low temperature, one must use glass-forming solvents. As neat MeOH (melting point = 179 K) and EtOH (melting point = 156 K) are frequently 70 150 230 310 found to crack around a certain low temperature, an EtOHT, K MeOH mixture has been e m p l ~ y e d . ~The ' solvation dynamics Figure 2. Temperature dependence of the emission maximum, v,, of in neat MeOH are reported to be the simplest in the series of OAPS, in EtOH-MeOH (0). The full line results from numerical alcohols, lacking cooperative effects due to aggregate formation treatment of the experimental points. Also shown is the same parameter of the type found in higher alcohols.17 Similar conclusions are derived from studies of the dielectric properties of a l ~ o h o l s ~ ~ . ~ in ~ -the ~ ~same solvent for rhodamine 101 ( 0 ) . showing that while higher alcohols are characterized by three to the solvent repolarization process. dispersion regions, the behavior of MeOH and EtOH is somewhat For a complete picture of solvent dynamics, molecular Experimental Section aspects of solvation (related to the size of the solvent molecule 2-Aminophenyl phenyl sulfone, OAPS, and rhodamine 101 were as compared to that of the solute), should be taken into a c c o ~ n t . ~ ~ . ' ~obtained from Aldrich (99%) and Eastman Kodak, respectively. The aim of this work is to investigate the relaxational dynamics The solvents employed were of-the best grade commercially of the alcoholic solution, extending the range of the explored available. Absorption and emission spectra of OAPS (af N temperature toward the freezing point of the solvent, about 1 IO 0.20-0.6 depending on t e m ~ e r a t u r e ~and ~ ) rhodamine 101 (af = K. It is shown that the slowed-down solvent dynamics at low 139)were obtained with a Perkin-Elmer 555 spectrophotometer temperature allows a combined use2*of steady-state fluorescence and a Perkin-Elmer MPF-44B spectrofluorimeter equipped with spectra and fluorescence lifetimes to extract parameters pertaining a DCSU-2 differential corrected spectral unit, respectively. The uncertainties in the spectral measurements are estimated to be f 50c~-].~O (25) Barieelletti. F. J. Chem. SOC..Faradav Trans. 2 1987, 83, 1567. The temperature-dependent measurements were carried out by (26j LakGwicz, J. R. Principles of Fluoresrknce Spectroscopy: Plenum: M for OAPS) degassed by repeated using samples (about New York, 1983; p 217. (27) Bakhshiev, N. G.: Mazurenko, Y.T.; Piterskaya, I. V. Opt. Spectrosc. freeze-pumpthaw cycles. The samples were thermostated inside 1966, 21, 307. a modified C 600 Thor temperature controller. The uncertainty (28) Mazurenko, Y.T.: Bakhshiev, N. G. Opt. Spectrosc. 1970, 28,490. in temperature is estimated to be f 2 K. The emission lifetimes (29) A two-state relaxation behaviorz6 is likely involved in some Ru(I1) were measured by a modified Applied Photophysics single-photon polypyridine complexes.30 (30) Barigelletti, F.; Juris, A,; Balzani, V.; Belser, P.: von Zelewsky, A. apparatus. Pulsed excitation was provided by a Thyratron gated J . Phys. Chem. 1987, 91, 1095. Barigelletti, F.; Juris, A.; Balzani, V.; Belser, lamp (operating frequency 20-25 kHz) filled with deuterium. The P.; von Zelewsky, A. J . Phys. Chem. 1986, 90, 5190. Juris, A,; Barigelletti, pulse width at half-maximum was 2.5 ns. The samples were F.; Balzani, V.; Belser, P.:von Zelewsky, A. J . Chem. S o t . . Faraday Trans. excited at the lowest energy absorption band, and the decay was 2 1987, 83, 2295. (31) Herkstroeter, W. G. In Creation and Detection of the Excited State; observed at the maximum of the emission band. The reported Lamola, A. A,, Ed.: Marcel Dekker: New York. 1971; Vol IA, p 1. lifetimes were obtained by numerical treatment of the measured (32) Grant, E. H. Proc. Phys. SOC.,London Sect. B 1957, 70, 937. flash and decay curves with least-squares nonlinear iterative re(33) Hassion, F. X.; Cole, R. H. J . Chem. Phys. 1955, 23, 1756. convolution p r o g r a m ~ . ~ The ] quality of the fit was assessed by (34) Bertolini, D.; Cassettari, M.; Salvetti, G. J . Chem. Phys. 1983, 78. 363. (35) Saxton, J. A.; Bond, R . A,; Coats, J. T.;Dickinson, R. M. J . Chem. Phys. 1962, 37, 2131. (36) Denney, D. J.; Cole, R. H. J . Chem. Phys. 1955, 23, 1767. (37) Dannhauser, W.: Cole, R. H. J . Chem. Phys. 1955, 23, 1762 (38) Reference 11, p 351

(39) Eaton, D. F. U . S . Enuiron. Protect. Agency, Newslett. 1986, 28, 21. Karstens, T.;Kobs, K. J . Phys. Chem. 1980, 84, 1871. (40) For a pertinent discussion about errors introduced by the spectral measurements, see ref 19.

The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3681

Solvation Dynamics in Alcoholic Solution

TABLE I: Temperature Dependence of the Relaxation Time, T ~ for , the EtOH-MeOH Solvent T, K T , , ns T, K T , , ns T, K T., ns

3-

115 120 125 130 135

2-

OTemperature for which

1-

'-

140 145 150" 155 160 if

39 22 11 6.4 4.2

165 170 175 180

2.6 1.6 1.1 0.8

7%.

,

'

+3.0

E

650 390 190 94 75

0

'

-3.0 1

I

I 128

0

'

I

256

time axis, channels

Figure 3. Emission decay of excited OAPS in EtOH-MeOH, T = 90 K. Upper graph: flash (a) and decay (b) profiles; the full line for the decay results from the fitting procedure. Lower graph: distribution of the residuals, R, = (y, -f;)/yt'I2 along the time axis. y i and1; are the experimental and calculated points, respectively; channel width = 0.404 ns; T~ = 8.6 ns; x 2 = 1.102. I

I

I

4

6

h 8

1000/ T, K - '

Figure 5. Arrhenius plot for the rate of solvent relaxation, k, (+), in the EtOH-MeOH mixture: intercept = 32.9, slope = -2.18, T/1000, and r = 0.994. k , and k , data for neat EtOH and MeOH, closed and open points, respectively, are also reported as derived from the original works: ref 12 (A),ref 33 (M), ref 34 ( 0 ) and (0),and ref 36 ( A ) . For neat EtOH and MeOH the full lines are drawn only to show linearity, Dashed lines point to deviations from linear behavior.43 The melting point, mp, for neat EtOH and MeOH is indicated.

t

70

I

I

I

150

230

310

T, K Figure 4. Temperature dependence of the emission lifetime,

Tf, of OAPS in EtOH-MeOH (0).The full line results from numerical treatment of the experimental points. Also shown is the same parameter in the same solvent for rhodamine 101 ( 0 ) .

the reduced x2 value close to unity and a regular distribution of the residuals along the time axis. Single-exponential analysis gave satisfactory results over the full temperature range explored. The uncertainty in lifetime measurements is estimated to be 17%. The emission spectra and lifetimes of OAPS did not show detectable excitation dependence, even if for a certain temperature, Le., 150 K (see below), one should expect such effects due to time-dependent (nanosecond time scale) distribution of emitting levels of solutesolvent origin. The excited state of OAPS responsible for the emission is of a charge-transfer nature, corresponding to electron promotion from the amino group to the nearby ring.25

Results and Discussion Figure 1 shows the room-temperature (298 K) absorption spectrum and the emission spectra of OAPS taken at 90 and 190 K. Figure 2 reports the change of the emission maximum as a function of temperature. At 90 K the emission maximum centers at 25 750 cm-I. Increasing the temperature in the range 100-185 K results in a red-shift of the emission from 27 750 to 23 500 cm-'. Further warming results in a smooth blue-shift. The last effect can be ascribed to a decrease of the static dielectric constant of (41) Bevington, P.R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969. Barigelletti, F.; Dellonte, S.; Flamigni, L. Gazz. Chim. I t a l . 1982, 112, 543.

the solvent with increasing t e m p e r a t ~ r e . ~ ~ Figure 3 shows the time evolution of the emission intensity of excited OAPS, taken at 90 K. Figure 4 reports the change of the emission lifetime, rf,as a function of temperature. From 90 to 150 K the emission lifetime changes from 8.6 to 10 ns, respectively, while further warming brings about a gradual shortening of the lifetime until at room temperature Tf = 1.3 ns. For comparison purposes in Figures 2 and 4 is also reported the behavior of 2, and T f , respectively for 3 X M rhodamine 101 in the same solvent. Rhodamine 101 is a fluorescence standard (aPf = 139) whose ground and excited states exhibit similar polarity.42 As a consequence, no solvent repolarization takes place after light excitation, and J, and T f are expected-and found-to be practically unaffected by temperature. The temperature dependence of the emission data for OAPS (Figures 2 and 4) can be discussed on the basis of the model for continuous relaxation of the solvent.26-28 Upon light excitation an emissive charge-transfer excited state with moderate charge separation is obtained. At high temperature ( T > 185 K), the needed repolarization of the solvent occurs in a time interval much shorter than the emission lifetime, and the emission takes place from a solvent-stabilized energy level, 2, = 23 500 cm-' as taken at 185 K (Figure 2). For T < 100 K the solvent is frozen, and the emission takes place from an unrelaxed (solvent destabilized) level, v0 = 27 750 cm-', as taken at 90 K. In the temperature interval 115-180 K the rearrangement of the solvent and the emission are processes taking place at comparable rates, so that the emission comes from partly relaxed energy levels. The changes of the steady-state emission maximum with temperature are described byZ8 (42) Drexhage, K. H. In Topics in Applied Physics. Dye Lasers; Schaefer, F. P., Ed.; Springer: Berlin, 1973; Vol. 1, p 144.

J . Phys. Chem. 1988, 92, 3682-3686

3682 8,

= 8,

+ (8, - 8 , ) T , / ( T , +

Tf)

1/ T behavior of the separate alcohols,43approaching that for kD of EtOH. The obtained result seems of value because it indicates that the solvent relaxation of EtOH-MeOH solvent, as obtained through eq 3,28 obeys a simple activated law, apparently approaching a Debye-type behavior.” Making use of the linear fitting parameters of Figure 5 , one obtains T~ = 10 ps at room temperature, while TD and T L are 58 and 3.7 ps, respectively, for MeOH and 175 and 9.8 ps, respectively, for EtOH.44 This discrepancy suggests that for T > 190 K the actual relaxational process of the solvent departs from the simple description holding at lower temperatures.

(3)

According to eq 3 and with use of the data of Figures 2 and 4 for the 90-1 90 K interval, one obtains the temperature dependence of k, ( = 1 / ~ , ) . In Figures 2 and 4 the full line shows the result of a numerical treatment of the experimental points, according to a fitting procedure outlined in a previous paper.25 This enables one to compare interpolated 3, and Tf data along with temperature. Table I reports the obtained temperature dependence of T~ at 5 K intervals. Figure 5 shows the plot of the In k, versus 1/T data of Table I. The plot is linear, and an Arrhenius-type process for the solvent relaxation can be assumed, the slope corresponding to the pertinent activation energy, E , = 1520 cm-’. For comparison purposes, literature data for kL ( k L = 1/71) and kD (kD = ~ / T D )for neat MeOH and EtOH are also displayed in the figure. These data were either previously reportedI2 or derived from dielectric data taken at the lowest frequency dispersion region investigated in the original ~ o r k s . ~As~one - ~ sees, ~ the slope for the reported k, versus 1 / T behavior is steeper than that for kl or kD versus

Acknowledgment. Work was done within the Programma Strategico Dinamica Molecolare of the National Research Council (CNR) Technical assistance by L. Minghetti is acknowledged. Registry No. OAPS, 4273-98-7; EtOH, 64-17-5; MeOH, 67-56-1. I

(43) Deviations from the linear behavior of In k versus i / T plots are expected at T < melting point.37 ( 4 4 ) Kosower, E. M. J . A m . Cbem. SOC.1985, 107, 1114.

Computer Simulation of the Separation of a Two-Component Mixture in Preparative Scale Liquid Chromatography Georges Guiochon* and Samir Ghodbane Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996- 1600, and Analytical Chemistry Division, P.O. Box X , Oak Ridge National Laboratories, Oak Ridge, Tennessee 37831 (Received: August 27, 1987; In Final Form: December 14, 1987)

A model describing the propagation of a binary mixture at finite concentration in nonlinear liquid chromatography is discussed. This model consists of two mass balance equations, one for each solute. A finite difference method is used to derive numerical solutions of this set of nonlinear partial differential equations with boundary conditions corresponding to the elution of large concentration bands. These solutions describe the shape of the elution profiles of partially resolved compounds. Although the model used corresponds to ideal chromatography (constant equilibrium between the mobile and stationary phase, Le., infinite column efficiency), it is possible to simulate the smoothing effect of a finite column efficiency by properly selecting the differential space element in the numerical integration. The numerical solutions appear to converge satisfactorily toward a stable solution of the system of equations provided the Courant-Friedrichs-Lewy (CFL) criterion is met in the choice of the integration parameters. The profiles obtained are very realistic and fare quite well with experimental results retrieved from the literature. Some of the results obtained are discussed in detail.

differential equations obtained, with the boundary conditions defined by the injection characteristics (Le., the profile of the input band). Although such a complete set of equations is untractable at the present stage,’ a good understanding of the chromatographic phenomenon can be achieved with a simplified model. The heat balance equation is usually dropped by assuming that the column is athermal, the heat generated by sorption of the band front being adsorbed when the tail of the band desorbs. Although approximate, this assumption appears quite satisfactory in practice. If it is considered that the kinetics of radial mass transfer is infinitely fast while axial diffusion is negligibly slow (Le., that the height equivalent to a theoretical plate (HETP) is equal to zero), the system of partial differential equations becomes hyperbolic. These assumptions lead to the ideal model of chromatography which has been widely used to investigate the propagation of finite concentration bands in chromatography.2-8 In so doing,

Introduction In preparative scale chromatography, columns are overloaded and operated under conditions where equilibrium isotherms are no longer linear. Accordingly, the retention times of the peaks maximum vary with increasing sample size, and the peaks broaden and become more and more unsymmetrical. Thus, it is virtually impossible to make any accurate prediction of the peak profiles from simple linear chromatographic theory. A general theory which takes all of the effects of finite concentration into account is needed to predict the elution profiles of each component of a partially resolved band and to calculate the performance of a given column and the influence of the sample size injected and of the other experimental conditions. This would be most useful in the optimization of the column operating conditions for maximum production.’ Such a general theoretical framework could be obtained by writing the mass balance and the kinetic equations for each component of the sample and for the mobile phase in a given slice of the column, the heat balance equation, and a set of mixed adsorption isotherms and by integrating the system of partial

(2) De Vault, D. J . A m . Cbem. SOC.1943, 65, 532. ( 3 ) Glueckauf, E. Proc. R. SOC.1946, A186, 35. ( 4 ) Rhee, H. K.; Ark, R.; Amundson, N. Trans. R. SOC.1970, A267.419. (5) Jacob, L.; Valentin, P.; Guiochon, G. J . Chim. Phys. 1969, 66, 1097. (6) Jacob, L.; Valentin, P.; Guiochon, G . Chromatographia, 1971, 4 , 6 . (7) Guiochon, G.; Jacob, L. Cbromatogr. Reu. 1971, 14, 7 7 . (8) Valentin, P.; Guiochon, G. Sep. Sci. 1976, 10, 245.

( 1 ) Guiochon, G. In New Directions in Chemical Analysis; Shapiro, B. L., Ed., Texas A&M University Press: College Station, TX, 1985; p 84.

0022-3654,I 8 8,12092-3682$01.50/0 I

0 1988 American Chemical Societv -