Computer simulation studies of orientational relaxation in strongly correlated dipolar systems

Abstract

In the preceding three chapters of this thesis, computer simulation and theoretical studies of orientational relaxation in dipolar liquids and solids have been presented. The primary objective has been to understand the role of intermolecular correlation in orientational and dielectric relaxation in dipolar systems. Because of these correlations, orientational relaxation in a dense dipolar (and obviously molecular) liquid is a complicated process. Not only does the orientational motion derive contributions from many different kinds of molecular motions, but the relative weights of these contributions are complex functions of molecular arrangements. The situation is further complicated for dipolar liquids because the long-range and anisotropic nature of dipolar interactions introduces nontrivial static and dynamic correlations that need to be treated consistently. As long as one is satisfied with a continuum-hydrodynamic description, these complications do not arise. However, as soon as a microscopic description is attempted, the enormity of the problem becomes obvious.

Theoretical Approaches and Challenges In such a situation, theoretical studies have naturally focused on the simplest molecular models-dipolar lattices, polar hard spheres, and Stockmayer liquids. Still, progress has been rather slow. An appropriate example of this difficulty is provided by the calculation of dielectric friction. Even when approximated by Kirkwood’s formula for friction on a fixed dipole, a time-dependent mean-field calculation cannot be carried out rigorously because no accurate expression for the wavevector- and frequency-dependent memory function, Tf(k,z)T_f(k, z)Tf(k,z), is yet available. When one approximates this memory function by the single-particle limit (that is, the k??k \to \inftyk?? limit of Tf(k,z)T_f(k, z)Tf(k,z)), too small an effect of dipolar interactions is predicted. In the opposite limit, replacing Tf(k,z)T_f(k, z)Tf(k,z) by its Tf(k=0,z)T_f(k = 0, z)Tf(k=0,z) value leads to a much better effect-but the justification of this approximation remains unclear.

Main Results of This Thesis In this thesis, detailed studies of orientational relaxation in three such simple systems have been presented. The systems studied include: • Brownian and molecular dynamics of dipolar lattices • Molecular dynamics of dipolar soft-sphere liquids • Stockmayer liquids The main results include: • The first explicit demonstration of the rank dependence of dielectric friction • The first explicit demonstration of the difference between single-particle and collective friction • The discovery of the exotic time dependence of orientational relaxation in a random dipolar lattice These results highlight the important role of intermolecular correlations in dense dipolar liquids. In fact, the main theme of the present thesis has been that all the seemingly different problems in the field of dynamics of dense dipolar liquids are strongly affected by the presence of intermolecular correlations. Any microscopic theory must pay proper attention to these correlations. The situation is further complicated by the different dissipative mechanisms present in a dense dipolar liquid.

Current Understanding and Future Directions Finally, we return to the question often asked in this thesis: How much do we really understand the role of correlations in the dynamics of dipolar liquids? To put this question in perspective, let us recall that even a few years ago, the main theoretical framework available was the continuum model. Although it was widely recognized that the continuum model is inadequate and should be discarded, the real thrust for doing so has come only recently. The microscopic description developed by Chandra and Bagchi [1, 2] and others [3, 4] includes correlations properly and appears to be far more successful than the continuum model in describing detailed dynamics. An example is the single-particle correlation function C1(t)C_1(t)C1(t) of a Brownian dipolar lattice, where the microscopic theory fares substantially better than the continuum models of Nee and Zwanzig [5] and Hubbard and Wolynes [6]. However, further advances have been hindered by the lack of reliable equilibrium orientational correlation functions, which unfortunately have yet to be measured experimentally. Regarding the dissipative kernels (or memory functions), some progress has been made, but a detailed picture has yet to emerge. Thus, to answer the question on the extent of our understanding of the effects of intermolecular correlations on dynamics, our answer is that it is still rather poor. A lot more effort is needed in this field to obtain a satisfactory understanding. Given the importance of this field in chemistry, such an effort will certainly be worthwhile.

Recent Focus: Dipolar Soft-Sphere Systems The system of dipolar soft-spheres has been the focus of much study in recent years [7, 8]. The attractiveness of this system lies in the ability to study in detail the role of translational modes of the molecules. The hidden role of translation and the dynamic translational-rotational coupling in a strongly polar liquid has been studied here using the above liquid model and also the conventional Stockmayer liquid model. Another motivation to study this problem comes from the suggestion made by Zhou and Bagchi [9] that the study of wavevector-dependent dielectric relaxation will be useful to understand orientational relaxation more clearly. They also added that the random lattice would resemble a liquid even more than the cubic lattice mentioned earlier. The studies presented here justify this suggestion. Future Directions and Open Problems The static and dynamic properties, as well as the frequency-dependent dielectric response, are studied in Chapter 4 of this thesis. We conclude this thesis by discussing a few specific problems for future study. The statistical mechanical studies of phase transitions in dipolar cubic lattices shall be of great importance and interest for the following reasons: (a) These models have been used to represent plastic crystal phases. (b) The types of phase transitions that these systems exhibit are intriguing and thought-provoking. Cubic lattices have been found to undergo a low-temperature transition to a ferroelectric state (in body-centered and face-centered cubic lattices) or to an antiferroelectric state (in the simple cubic lattice). These have been proposed as models for hydrogen halides. Several Monte Carlo studies have been reported using this type of cubic lattice [10–12] to study phase transition behavior. However, the study of phase transitions using molecular dynamics techniques has not yet been attempted. We suggest this as an important future problem.

From the discussions presented in Chapters 2 and 3, it is clear that the theoretical development and understanding of rank dependence is still rather poor. This thesis shows that both the Hubbard–Wolynes [6] and Madden–Kivelson [13] theories break down at high polarities, particularly for l>2l > 2l>2. To understand the role of rank dependence in orientational relaxation, microscopic theories such as molecular hydrodynamic theory or the projection operator technique need to be developed. As far as we know, such studies have not been carried out yet. On the computational side, having studied simple systems like the dipolar cubic lattice using Brownian dynamics and molecular dynamics simulations, it would be worthwhile to carry out Langevin dynamics simulations with a local friction term to estimate the relative importance of the effects predicted in this thesis.

On the theoretical side, a quantitative description of the wavevector- and frequency-dependent memory function is required. This is necessary to understand the observed significant difference between the memory functions for single-particle and collective correlation functions, as described in Chapter 3. There is also a need to understand why the simulated memory function for the mobile solute fails to describe the single-particle orientational dynamics. Fortunately, the microscopic description of C1(t)C_1(t)C1(t) has been rather satisfactory. This may indicate that, in this particular case, the approximation of replacing the wavevector- and frequency-dependent memory function by its long-wavelength limit (k = 0) is not serious. However, this requires further verification.

The study shows that the single-particle orientational correlation functions computed for the model polar liquids (dipolar soft-sphere and Stockmayer liquids) exhibit sub-diffusive behavior at longer times. The reason for this type of decay is not yet understood. It would be appropriate to obtain the frequency-dependent friction from a mode-coupling theory and use it to understand more about this decay nature. Since no phase transition is observed as the system is quenched, the non-exponential decay of the single-particle reorientational correlation function must be understood in terms of intermolecular correlations. This is a challenging problem for theoreticians. Finally, it will be interesting to perform a phase transition study of orientational dynamics in a random lattice, because, as suggested earlier by Zhou and Bagchi [9], a random lattice is not expected to show an antiferroelectric phase transition. The main advantage of this delayed phase transition is that the study of dynamics can be extended to much higher polarities than possible in the dipolar cubic lattice [9].

There is, of course, the need to understand polar effects on the orientation of real molecules, especially charged organic dye molecules, which are often used as probes to test theories. A step toward this goal has already been taken by Alavi and Waldeck [14–16], who considered a realistic charge distribution instead of treating them as a point charge or a point dipole at the center of a sphere. A microscopic study of this problem will be worthwhile. A more ambitious project would be to consider protic liquids. Here, a treatment similar to the one developed by Raineri, Friedman, and co-workers [4, 17, 18] can be a useful starting point. On the computational side, there is a need to simulate at least a few more model systems, such as face-centered and body-centered dipolar lattices, to check the generality of the results obtained here. On the experimental side, one would like to see systematic studies aimed primarily at understanding the effects of polarity. Although systematic studies of orientational relaxation exist for non-polar liquids [19], similar studies for dipolar liquids do not seem to exist.

Conclusion We conclude this thesis by noting that the field of orientational relaxation in dipolar systems still offers a large number of interesting problems, which should keep the field active for many years to come.