Theortical studies of polar solvation dynamics, ionic mobility, solute diffusion and activated barrier crossing dynamicsin dense liquids

Abstract

There are several features of this chapter that are new. The self-motion of the probe solute has been incorporated here for the first time and studied systematically. The theoretical approach captures quite successfully the basic mechanisms of the complex dynamics inherent to the solvents studied here. The resulting equations, as shown here, have the structure familiar from the mode-coupling theory of atomic liquids. The theoretical predictions from the equations obtained here show that the self-motion can accelerate the process of solvation significantly. For a dipolar solute, the long-time rate of solvation can be accelerated even by 30%. The ion-dipole direct correlation function, used here, properly describes the solvent distortion at long-time limits. This is important at longer times because the solvent structure starts building up around the ion after the step-function change in charge on the solute. However, this description is still unable to take into account the nonlinearity in dynamic response of the solvent. This is an important unsolved problem that needs further attention. Comparison with Experimental Results The theoretical predictions on dipolar solvation and the comparison with recent experimental results reveal some interesting aspects of dipolar solvation dynamics. The mapping of the experimental data points onto the theoretical results suggests that the experiments seem to have missed the initial 80% of the total decay of the solvation time correlation function. The slower decay rate observed in solvation dynamics experiments on aniline in 1-propanol, compared to theoretical predictions for the same mobile dipolar solute probe, could well be explained in terms of specific solute-solvent interactions (such as H-bonding). The H-bonding between the solute and the solvent partly restricts the free motions of both the solute and the solvent molecules. This partial quenching of these motions leads to a comparatively slower relaxation. The present theory also predicts a faster solvation in propylene carbonate, which is complete within 15–20 ps.

Applications and Specific Interactions An interesting application of the present theory can be to situations where the solute’s self-motion is the primary mechanism of solvation. Such might be the case in restricted geometries, for example, in Zeolites. Recently, such a study has been carried out by Bhattacharyya and co-workers [67] in faujasite Zeolite-13X using coumarin-480 as the solute probe. This experimental study suggests that the rotational motion of the instantaneously created dipolar solute probe in the Zeolite super-cage can considerably accelerate the rate of solvation. The present theoretical study suggests an interesting role of specific solute-solvent interactions in polar solvation dynamics. Since such interactions may lead to a partial quenching of the self-motion of the solute, the rate of dipolar solvation may be significantly slower than what one would expect in the absence of these interactions. Since specific solute-solvent interactions may also quench the motions of the nearest-neighbor solvent molecules, the combined effect of these two can be significant. These specific effects are predicted to be important in the long-time limit, while the short-time dynamics may still be dominated by pure solvent dynamics. Further studies are needed to quantify these expectations.

Ion Solvation Dynamics and Simulation Insights Several aspects of ion solvation dynamics can be explained from a molecular theory. The theoretical predictions are in agreement with recent computer simulation studies [13]. The slow long-time decay observed in simulations may originate from a combined effect of non-polar solvent response and cluster formation at critical solvent density. The ultrafast solvation in supercritical water is somewhat similar to what has been observed in normal water at ambient conditions. However, the molecular mechanisms behind the ultrafast solvent response in water at these two thermodynamic conditions are dramatically different. While the intermolecular vibration of the O–H···O moiety at 193 cm?¹ is primarily responsible for the observed ultrafast dynamics in ambient water, it is the very fast single-particle rotation of water molecules that makes the solvent response ultrafast in the supercritical state. In addition, we predict that for solvation in supercritical water, the effects of molecular polarizability of water may be negligible. Thus, the simulation results here can indeed be close to experiments, unlike in the case of ambient water where simulation predicted a faster decay than what was experimentally observed later.

Non-Equilibrium vs. Equilibrium Solvation Another interesting point left untouched here: Re and Laria [13] observed a significant difference between the non-equilibrium and the equilibrium solvation time correlation function — the former was markedly slower in the long time. While such non-linear response is expected if cluster formation is involved in the late stage of solvation, a quantitative understanding of this interesting result is yet to be evolved.

Summary of Main Results A self-consistent microscopic theory is presented for the limiting ionic conductance of strong 1:1 electrolyte solutions in dipolar liquids. The theoretical predictions for the ionic conductivity at infinite dilution in water and acetonitrile are in good agreement with long-known experimental results. In particular, the theory reproduces the non-monotonic size dependence of the limiting ionic conductance accurately. The relation between the polar solvation dynamics of an ion and its mobility is clarified. The theory also explains how a dynamical version of the classical solvent-berg model can be recovered for small ions in the limit of slow liquids. The present theory also explains why the size dependence of ionic mobility is so strong while that of solvation dynamics is essentially absent. The success of the present theoretical scheme can be traced back to the following factors: 1. A self-consistent calculation of ionic conductivity, which makes the present scheme robust. 2. Inclusion of the self-motion of the ion, which was a major drawback of earlier studies. 3. An accurate treatment of the ion-dipole direct correlation function, which is non-trivial and was obtained from previous work. The approach of Chan et al. [36] requires some amount of numerical work, which was not done in any of the earlier studies. A third important ingredient is a proper translation of the dynamic response. Not only the orientational motion but also the translational motions of the solvent molecules are very important in determining the magnitude of the dielectric friction. Lastly, one must include the non-linear effect of the ionic field of the ion itself on the surrounding solvent molecules. For slow and strongly polar liquids like alcohols and formamide, the ionic field nearly immobilizes the surrounding solvent molecules. Thus, one essentially recovers the solvent-berg model, making the theoretical formalism more involved. Given the complexity of the problem, it is unlikely that a simpler theory than this can successfully explain the experimental results.

Predictive Ability and Comparison with Simulations It is interesting to note that the simple theory presented here can reproduce the experimentally observed ionic mobilities in solvents with such disparate molecular shapes, sizes, and charge distributions as water, acetonitrile, and alcohols (see Chapter 7). The present theory is largely insensitive to various subtle aspects of different solute-solvent and solvent-solvent interactions, in contrast to recent computer simulation studies by Lee and Rasaiah [56–57]. An interesting finding of Lee and Rasaiah’s work is the marked dependence of their results on the solute-solvent and solvent-solvent intermolecular potentials. The potential energy functions used in these simulation studies [56–57] are considerably more complicated than the hard-sphere plus ion-dipole and dipole-dipole potentials used to calculate static correlations such as c(110; q) and c?(q) under the mean spherical approximation (MSA) (corrected at both q = 0 and q ? ? limits). Therefore, the good predictive ability of the present theory can be attributed to the use of experimental data to describe the frequency-dependent dielectric function of the solvent together with the self-consistent scheme illustrated earlier. This suggests that for cations, mobility is determined primarily by the dynamics of the solvent, where detailed specific ion-solvent interactions are not crucial.

Anionic Conductivity and Lack of Symmetry Interestingly, the above scenario becomes more intriguing when considering anionic conductivities. At room temperature, the ionic mobilities of halide ions in aqueous solution constitute a different curve than that for cations when plotted as a function of the crystallographic radius of the ion. This experimental trend has also been reproduced semi-quantitatively by recent simulation studies of Lee and Rasaiah [57]. All these studies indicate a lack of symmetry in the static and dynamical solvent-cation and solvent-anion correlations. The present theory, however, cannot explain the distinct maximum observed for halide ions in aqueous solution because it uses MSA to obtain the ion-solvent direct correlation function, which is insensitive to the sign of the ionic charge. In principle, the present theory can be extended to explain these differences by using the proper charge representation of the solvent molecule, which means abandoning the point-dipole picture of solvent molecules. While this is certainly worthwhile, the procedure would involve extensive numerical work.

Need for Experimental Data As already mentioned, theoretical studies could not be attempted in many cases because of the lack of experimental data—not only on A? but also on dielectric relaxation. Thus, we suggest a renewed effort to obtain these data not only for common liquids but also for mixtures, which may exhibit more complex dynamical behavior.

Summary of Main Results We have presented a microscopic calculation that, for the first time, explains the anomalous temperature dependence of the limiting ionic conductivity in aqueous solutions. The strong temperature dependence is shown to arise from a collection of small effects all acting in the same direction. Thus, there is no need to invoke any unquantifiable physical concepts like the formation or breaking of a solvent-berg to explain the experimental results. The theory can also explain the significant solvent isotope effect, which has been known for a long time but was not previously explained quantitatively. The non-monotonic size dependence of limiting ionic conductivity at various temperatures has also been correctly described in terms of dielectric friction.

Broader Context In this thesis, we have studied four different but related problems of chemical dynamics in solution. These include: • Polar solvation dynamics and ionic mobility in dipolar solvents • Self-diffusion of a neutral solute • Activated barrier crossing dynamics in viscous liquids Wherever possible, we have compared the theoretical results with those from experiments and simulations, and a good agreement has been obtained in most cases. The summary of the thesis is already presented in the Preface, and therefore, we need not repeat it here. However, we take this opportunity to discuss several interesting unsolved problems that may be studied in the future.