Supercooled Liquids - American Chemical Society

Chapter 15

Multiple Time Scales in the Nonpolar Solvation Dynamics of Supercooled Liquids 1

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Downloaded by NORTH CAROLINA STATE UNIV on October 4, 2012 | http://pubs.acs.org Publication Date: September 30, 1997 | doi: 10.1021/bk-1997-0676.ch015

J . M a , John T. Fourkas , D. A. Vanden Bout , and M. Berg

3

Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208

Recent experimental and theoretical work on the dynamics of solvation in nonpolar supercooled liquids is reviewed. Transient hole burning experiments have shown that solvation dynamics occur on a wide variety of time scales. A major division into phonon-like and structural relaxation is apparent as the viscosity of the solvent increases in the supercooled region. The structural component is strongly nonexponential and extends over many decades in time. Modecoupling theory provides a consistent explanation of the structural relaxation behavior versus temperature. A continuum model links nonpolar solvation to shear relaxation of the solvent following a size change of the solute upon electronic excitation. The relationship between phonon-like and structural dynamics is examined within the continuum model, which distinguishes them as different dynamical regimes of a single coordinate, and is contrasted with "spectroscopic" models, which treat the different dynamics as arising from distinct solvent coordinates. The dynamics of supercooled liquids can be measured by a variety of different experiments, each of which measures a differently weighted average of the many coordinates present in the liquid. The majority of detailed results on short time dynamics has come from just three experiments: dielectric relaxation, light scattering and neutron scattering (/). Solvation dynamics, i e . the response of a solvent to changes in the electronic state of a solute, is a new and distinctly different type of experiment for examining liquid dynamics. Because it focuses on the short time and length scales which must underlie effects seen on all scales, it offers a unique and valuable perspective on liquid dynamics. Furthermore, solvation dynamics specifically weights the liquid coordinates by their ability to affect die electronic surfaces which control chemical reactions. It thereby creates a bridge connecting the general understanding of liquid dynamics to specific problems of solvent effects in chemistry and biology. 'Current address: Department of Chemistry, Boston College, Chestnut Hill, MA 02167 2

Current address: Department of Chemistry, University of Minnesota, Minneapolis, MN 55418

'Corresponding author. © 1997 American Chemical Society

In Supercooled Liquids; Fourkas, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

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We have been active in developing the transient hole binning experiment as a method of measuring solvation dynamics and in applying it to nonpolar solvents in the supercooled region (2-10). A large amount of information on solvation in low viscosity, polar solvents is also available (11-14% but interest in the distinctly different solvation mechanisms in nonpolar solvents has been growing (15-19). Even in polar solvents, die amount of information on solvation in supercooled liquids is limited (2024). A recurring theme in our results is the wide range of time scales which affect solvation. A primary division of the dynamics into a viscosity dependent and a viscosity independent component is made. The viscosity independent component is assigned to phonon-like dynamics within a fixed structure, and die viscosity dependent component is assigned to relaxation of that structure. The structural relaxation is found to be nonexponential and covers a wide range of time scales. In some cases, standard nonexponential treatments are strained to fit the observed range of time scales. Mode-coupling theory (MCT) (25-27) provides a consistent explanation of the temperature dependence of the structural relaxation. The a- and ^relaxation regions overlap significantly, and a global fitting to complete response functions is essential M C T also predicts that certain parameters should have the same value in different experiments. Comparison of the solvation based fits with M C T analyses of light scattering data shows that some, but not all, of these parameters are in agreement with this prediction. Although M C T makes a priori and general predictions about the form of structural relaxation data, it does not predict specific relaxation times, does not make statements about the interaction mechanism in nonpolar solvents, and does not provide any detail about the phonon-like relaxation component. We have developed a continuum model of nonpolar solvation which postulates an interaction resulting from solute size changes and successfully relates solvation data with viscosity and ultrasound measurements. The continuum theory also provides a simple model system in which the interaction of phonon and structural relaxation can be examined. In particular, it illustrates clearly die differences between theories which treat phonon and structural dynamics as different time regimes of a single dynamical process and theories which treat phonon and structural dynamics as distinct and separable processes. Transient Hole Burning Measurements of Solvation Dynamics The basic principles of the transient hole burning (THB) measurement are summarized in Figure 1. The free energy of the solute ground state and excited state vary with the arrangement of local solvent molecules, indicated in Figure 1 by a one-dimensional solvation coordinate. In equilibrium in the ground state, the solute molecules occupy a distribution of solvation configurations. Each configuration has a different transition energy to the excited state, resulting in a broad absorption spectrum (Figure la). The sample is irradiated with a short pulse of light which is resonant with only a subset of solvent configurations. A local depletion or "hole" in die ground state distribution is created (Figure lb). The resulting excited state molecules are created in a distribution which is narrower than and displaced from the equiHbrium distribution. Following the excitation, the solvent begins to relax to reestablish equiHbrium in both the ground and excited states. Both the hole and the excited state distribution increase in width o(t) and develop a Stokes' shift between their peak frequencies U(t) (Figure lc). Solvation dynamics can be monitored through either the time-dependent widths or time-dependent Stokes' shifts (8). An important advantage of this technique is that the measurements are absolute rather than relative. In the absence of any solvent movement, the Stokes shift and solvent broadening are zero. The equiHbrium values of these quantities are obtained independently from steady-state spectroscopy. Thus a



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Nonpolar Solvation Dynamics of Supercooled Liquids

Solvation Coordinate


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Figure 1. A schematic illustration of the transient hole burning experiment. (Reproduced with permission from ref 2. Copyright 1996 American Physical Society.) THB measurement, at even a single time, gives the fraction of the total relaxation to that point,

There is no need to extrapolate to or fit either long or short time values. Phonon Versus Structural Dynamics When transient hole burning was first performed over a temperature range spanning the low viscosity liquid, the supercooled region and the glass, it was immediately apparent that there were two distinct components to the relaxation (4-7). This result is illustrated in Figure 2. At room temperature, the 1.5-ps THB width is almost identical to the equilibrium absorption width. The relaxation is almost entirely complete by this time. As the temperature is lowered, the THB width becomes narrower than the absorption width, indicating that a portion of the relaxation occurs after 1.5 ps. However, as the supercooled region is traversed, a significant THB width remains at 1.5 ps. A significant fraction of the relaxation remains subpicosecond, even as the viscosity of the solution diverges. Thus, at least two relaxation components exist: one which slows down with increasing viscosity, and one which does not. The viscosity independent component can be associated with the phonon dynamics of a solid by continuing the hole burning experiments below the glass transition tenq>erature T . In the low temperature solid, permanent hole burning (PHB) is more convenient than THB. In PHB, photochemical destruction of the excited molecules allows the hole width to be measured several minutes after the initial bleaching. Below Tg, PHB and THB give the same result, indicating that there is no significant relaxation between 1.5 ps and several minutes. The widths in die solid glass fit a simple model for phonon-induced line broadening in solids (4). The curve in Figure 2 assumes a single phonon band centered at 30 enrT Extending the curve into the supercooled liquid region shows that the fast component seen in THB is simply the extension of these phonon dynamics into the liquid. At short times, the liquid appears to have an effectively static structure, about which rapid vibrational motion occurs. At higher temperatures, this simple model is not accurate, g


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both because of the changing density, and because the other relaxation component begins to affect the THB measurements.


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Figure 2. Solvent-induced widths of the electronic transition of dimethyl-stetrazine in rt-butylbenzene as measured by transient hole burning (THB), permanent hole burning (PHB) and absorption spectroscopy. (Adapted from ref 4) The second relaxation component is due to the relaxation of the temporary structure which supports the phonon dynamics. As the temperature is raised above T„, the PHB width suddenly jumps to the full absorption width. At this temperature, the second component becomes dynamic on the laboratory time scale instead of frozen. Near T , this component has little effect on the THB results. Near room temperature however, this component becomes fast enough to broaden the line at 1.5 ps, causing the THB and absorption widths to merge. In the intermediate temperature regime, the THB width was measured at various delay times in the ps to ns region, and the average relaxation time of the second component was determined. The results are plotted in Figure 3. The relaxation times are proportional to the viscosity over a range of four decades. This result contrasts g

7)(cP) Figure 3. Average relaxation time of the structural component of die solvent relaxation versus viscosity. Measured for dimethyl-s-tetrazine in «-butylbenzene. (Reproduced with permission from ref 5. Copyright 1993 American Physical Society.)



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strongly with the early, phonon-induced relaxation, which shows no evidence of slowing at high viscosity. Because die viscosity is the most common measure of the overall structural relaxation time of a liquid, the second relaxation component can be linked with structural relaxation. This conclusion is reinforced by the quantitative modeling discussed later in this paper. The same pattern illustrated here for /i-butylbenzene (4, 5) has also been seen in several other liquids (2, 3, 6, 7). Presumably the phonon-induced component seen in solvation is essentially the same as the '^microscopic" peak seen in scattering experiments, and the structural component is essentially the inelastic peak seen in low resolution scattering. The important point is that both components contribute significantly to solvation. Many theories of chemical dynamics in solution assume a single time scale for the dynamics. These theories may be plausible at sufficiently low viscosities, where the time scales of phonon and structural dynamics are comparable. However, such theories must fail at a qualitative level i f the viscosity is even moderately high, because the phonon and structural dynamics will occur on different time scales. Comparison to Mode-Coupling Theory To date, T H B experiments have focused on the structural relaxation component. Even within this single component, a wide variety of time scales are important. The most salient feature of the relaxation curves is that they are nonexponential, and the shape of the curves is temperature dependent. As the temperature is lowered and the primary structural relaxation time increases, some relaxation persists even at very early times. One approach to explaining these features is mode-coupling theory (MCT) (2527). This theory does not attempt to model details of the particular interactions involved m solvation or to predict numerical values of observed quantities. Instead it uses general features of liquid dynamics to make a priori predictions about the shapes of relaxation functions and the form of the relaxation time temperature dependence. The major predictions which can be tested with our data are: 1) The shape of the relaxation function is approximated by

(2)

R(t)««

Different approximations apply to two different time regions: the a- and )S-regions. The a-region, which covers the intermediate-to-late portion of the relaxation, obeys a simple scaling law equivalent to time-temperature superposition. This region can be approximated with a stretched exponential The /^-region, which covers the early-tointermediate portion of the structural relaxation, obeys a more complicated form based on the temperature independent function This function can be calculated for various values of A, die exponent parameter. The value of the exponent a is also determined by the value of X. Thus M C T predicts a range of relaxation times even greater than given by a simple stretched exponential. Two characteristic times, r and To, are needed to describe die relaxation function. 2) The temperature dependence of the relaxation times is given by: a

t ~c (T-T r, a

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T

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The exponents a and y are defined by the value of X in equation 2 and do not represent new adjustable parameters. Because r and rp change differently with temperature, equations 2-4 predict a relaxation shape which changes with temperature. 3) M C T does not make predictions of the various constants appearing in equations 24; these must come from a detailed treatment of the specific interactions probed by a specific experiment. However, three of the parameters, T , X and cp are predicted to be independent of the specific experiment and should be transferable between experiments. The solvation of s-tetrazine in propylene carbonate is a good example of a system which is difficult to fit into a standard analysis. The response function spreads over an increasing range of times as the temperature is lowered, strongly violating the timetemperature superposition principle. Figure 4 shows a M C T explanation of the shape. Figure 4a is an a-scaling plot generated by overlapping the lower portions of die response functions. For intermediate-to-long times, the temperature scaling does work, and a stretched exponential fit to this region is shown. At short times, the R approximation fails, but this failure is expectedfromM C T . a


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Figure 4. The solvation response function in propylene carbonate showing agreement with the a-scaling law at long time (a) and the ^-scaling law at short time (b). Fit parameters: f = 0.65, X = 0.78, J3 = 0.8. (Reproduced with permission from ref 2. Copyright 1996 American Physical Society.) p

For short to intermediate times, Rp is the appropriate approximation. A y^-scaling plot is shown in Figure 4b along with a fit to gx- The /^approximation gives a good account of the short time data for which the a-approximation fails. Similarly, the 0approximation fails at long times, but this region is accounted for by the aapproximation. Note that both the a- and /?-fits are constrained to share the same value off . Thus M C T gives good fits to the changing shape of the response function as the temperature changes. Each of the scaling plots generates a set of scaling times, r and tp The temperature dependence of these times is predicted to show a power law divergence at a critical temperature T (equations 3 and 4). Figure 5a tests this relationship. The exponents are predetermined by die value of X used in fitting g% (Figure 4b). A common value of T is required for both r and Tp hi general, the M C T fit is good. The poorer agreement at high temperatures may oe due to the anticipated failure of M C T far from T or an increase in experimental error with short relaxation times. In c

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Supercooled Liquids - American Chemical Society

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