Theoretical studies on collective orientational relaxation, solvation dynamics and electron transfer reactions in dense dipolar liquids

Abstract

In this thesis, a microscopic study of the collective orientational relaxation and its role in the dynamics of solvation and electron transfer reactions in dense dipolar liquids is presented. The origin of collective dynamics in dense liquids can be traced to the strong intermolecular correlations that are inevitably present in these liquids. In atomic liquids, the consequences of collective dynamics have been studied in great detail, and several interesting phenomena such as the propagation of shear waves at intermediate wavenumbers, de Gennes' narrowing of the dynamic structure factor, the total damping of sound waves at intermediate wavevectors, and many others have been discovered. Just as in spatial relaxation in dense atomic liquids, the collective orientational relaxation in molecular liquids is also expected to show rich and diverse dynamical behavior. Some of these, discussed in this thesis, include the slowing down of the longitudinal polarization relaxation at intermediate wavevectors in the absence of translational motion, the acceleration of the same by translational motion, the dramatic effects of intermolecular correlations in the dynamics of solvation and electron transfer reactions, the hidden role of translational modes in the long?wavelength dielectric relaxation, and several others. In this thesis, we have used an extended hydrodynamic approach to study the collective orientational dynamics in dense dipolar liquids. The advantage of this approach is that, within certain approximations, it provides a detailed quantitative theory of orientational dynamics. This extended hydrodynamic theory is a natural generalization of a similar theory used successfully in recent years for spatial relaxation, now extended to include the orientational modes. Many of the predictions of the present study are in good agreement with experiments and computer simulations, as discussed in the text. Although considerable progress has recently been made in our understanding of collective orientational relaxation and its role in various liquid?phase dynamical processes, many important problems remain unresolved. Below, we list some of the important problems that deserve careful study in the near future.

Relaxation in Hydrogen?Bonded Liquids The theoretical calculations discussed in this thesis are for dipolar liquids with no specific intermolecular interactions such as hydrogen bonding. Strictly speaking, they cannot be used to describe orientational relaxation in water and alcohols. Because of the importance of these liquids, a microscopic description of orientational relaxation in them is highly desirable. Recently, the dynamical properties of hydrogen?bonded liquids were reviewed by Bertolini et al. These authors discussed the importance of the connectivity of hydrogen?bonded liquid clusters in determining the dynamics and proposed a stochastic Liouville equation approach to treat the collective dynamics. The dynamical properties of hydrogen?bonded liquids have also been studied by Stanley and Teixeira and by others. The study of Stanley and Teixeira suggested the presence of a “patch?like” structure consisting of small clusters of molecules in water at low temperatures. These structures can have sufficiently long lifetimes to affect long?time relaxation properties, including collective orientational relaxation. In principle, the extended hydrodynamic approach developed here should be applicable to hydrogen?bonded liquids as well. The problem, however, is not trivial because the direct correlation function is not easily available for hydrogen?bonded systems. In addition to hydrogen?bonding interactions, quadrupolar interactions may also need to be treated because such liquids may have large quadrupole moments.

Orientational Relaxation of Molecules with Internal Degrees of Freedom It would be interesting to study the collective orientational relaxation of molecules possessing internal degrees of freedom. Warchol and Vaughan carried out a phenomenological analysis of orientational dynamics for molecules with free or hindered internal rotation. However, no microscopic study of this problem seems to exist. The theory discussed in this thesis can, in principle, be extended to describe orientational dynamics where molecules have one or more internal degrees of freedom. The major difficulty, however, lies in the calculation of the direct correlation function for such cases. Thus, a detailed study of the equilibrium correlation functions of molecules with internal degrees of freedom is needed for a microscopic understanding of collective orientational relaxation.

Polarizable Fluids The study of collective orientational relaxation in polarizable polar fluids is another interesting problem. All real molecules are polarizable by electric fields, with both electronic and atomic motions contributing to the polarizability tensor. The effects of polarizability on equilibrium correlations in liquids have been discussed by several authors. For equilibrium properties, Wertheim proposed that wherever the dipole moment appears in the rigid dipolar case, one must replace it by the actual dipole moment of the molecules, and wherever a function f(??) appears, one must replace it by f(??) – f(?s). This rule may not be valid for dynamics. A microscopic calculation of collective orientational relaxation in polarizable dipolar liquids has not yet been done. This is clearly an important but nontrivial problem deserving detailed study.

Orientational Relaxation in Nematic Liquid Crystals Nematic liquid crystals are characterized by long?range orientational order but no long?range translational order. They are formed by charged rod?like molecules or by ellipsoidal molecules with large aspect ratios. Because of orientational anisotropy, the dielectric function is a tensor even in the long?wavelength limit, with two components ??(?) and ??(?), corresponding to the polar response parallel and perpendicular to the axis of orientational order. A large number of experimental results are available for such systems, but few microscopic studies of collective orientational relaxation exist. The orientational dynamics in the nematic phase can be highly cooperative, as rotational motion of a molecule may require a concerted motion of its nearest neighbors. These systems present interesting theoretical problems for future study.

The above list is not exhaustive, but it gives a glimpse of the many important problems that remain unexplored in the field of orientational dynamics. We believe that this field will continue to be an exciting area of research in the coming years for both experimentalists and theoreticians, and one can look forward to significant new developments in the understanding of collective orientational relaxation and its role in various chemical processes in complex dipolar liquids.