Computer simulation of highly polar liquids: The hard sphere plus point dipole potential

Real space electrostatics for multipoles. III. Dielectric properties

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids.

Ferroelectric domain formation in discotic liquid crystals: Monte Carlo study on the influence of boundary conditions

The realization of a spontaneous macroscopic ferroelectric order in fluids of anisotropic mesogens is a topic of both fundamental and technological interest. Recently we demonstrated that a system of dipolar achiral disklike ellipsoids can exhibit long-searched ferroelectric liquid crystalline phases of dipolar origin. In the present work, extensive off-lattice Monte Carlo simulations are used to investigate the phase behavior of the system under the influences of the electrostatic boundary conditions that restrict any global polarization. We find that the system develops strongly ferroelectric slablike domains periodically arranged in an antiferroelectric fashion. Exploring the phase behavior at different dipole strengths, we find existence of the ferroelectric nematic and ferroelectric columnar order inside the domains. For higher dipole strengths, a biaxial phase is also obtained with a similar periodic array of ferroelectric slabs of antiparallel polarizations. We have studied the depolarizing effects by using both the Ewald summation and the spherical cutoff techniques. We present and compare the results of the two different approaches of considering the depolarizing effects in this anisotropic system. It is explicitly shown that the domain size increases with the system size as a result of considering a longer range of dipolar interactions. The system exhibits pronounced system size effects for stronger dipolar interactions. The results provide strong evidence to the novel understanding that the dipolar interactions are indeed sufficient to produce long-range ferroelectric order in anisotropic fluids.

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

Dielectric constants of simple liquids: stockmayer and ellipsoidal fluids

Coarse-grained models of molecular interactions are of interest because they convey the essence of molecular interactions in simple and easy to understand form. However, coarse-grained models fail to adequately predict some material properties, such as the failure of the Stockmayer model to reproduce the dielectric behavior of highly polar liquids. We examine the behavior of the Stockmayer fluid over a range of dipole densities that covers known organic solvents, as well as that of an ellipsoidal Stockmayer-like fluid, using NVT rigid-body Monte Carlo simulations. Both fluids are examined under different electrostatic boundary conditions and ensemble sizes. While the Stockmayer model predicts that liquids of similar dipole density to acetonitrile would be ferroelectric and have a dielectric constant far higher than shown by experiment, the ellipsoidal model provides a better accounting of dielectric behavior. This result bodes well for the use of coarse-grained solvent models for large-scale simulations.

Formation of Ferroelectric Domains Observed in Simulation of Droplets of Dipolar Particles

In this work it is shown that domains of ordered dipoles are formed in large droplets made from dipolar particles provided that the dipole-dipole interaction between nearest neighbors is larger than the thermal energy. The size of the domains grows almost linearly with the size of the droplets for droplets containing 1000-30 000 particles. The largest domains occupy around 25-35% of the droplet volume. The total dipole moment of a domain is of the order of 3-10% of the maximum dipole moment possible if all dipoles in the domain were parallel. The finding offers an explanation to the observation that different boundary conditions yield different long-range order for dipolar liquids and challenges the present view of a short-range dipolar order in polar solvents.

Computer Simulation study of polar liquids: static and dynamic properties

The Berne-Pechukas-Kushick potential for linear molecules, together with a central electric point dipole, has been used as the model for polar liquids in a series of molecular dynamics computer simulations. Different simulations used Ewald summation, spherical cut off and spherical cut off with reaction field correction to sum the dipole-dipole interactions, and the relative merits of these methods are discussed. Results for thermodynamic properties and the distribution function h ∆ ( r ) are presented. Results for the autocorrelation functions for dipole orientation and angular velocity are also presented, and discussed in terms of memory functions, particularly with regard to the Steele perturbation theory. The complex, frequency-dependent dielectric constant has been calculated from the memory function of the autocorrelation function of the periodic cube dipole moment, and results are presented in the form of Cole-Cole plots. The ‘dielectric friction’ approach to polar liquids is examined against the evidence of the molecular dynamics data. Attention is drawn to the behaviour of the cross correlations between dipole orientations and their importance to the problem of dielectric relaxation is emphasized.

Calculations of electrostatic interactions in biological systems and in solutions

Correlating the structure and action of biological molecules requires knowledge of the corresponding relation between structure and energy. Probably the most important factors in such a structure– energy correlation are associated with electrostatic interactions. Thus the key requirement for quantative understanding of the action of biological molecules is the ability to correlate electrostatic interactions with structural information. To appreciate this point it is useful to compare the electrostatic energy of a charged amino acid in a polar solvent to the corresponding van der Waals energy. The electrostatic free energy, ΔGel, can be approximated (as will be shown in Section II) by the Born formula (ΔGel= –(166Q2/ā) (I – I/E)). Where ΔGelis given in kcal/mol,Qis the charge of the given group, in units of electron charge,āis the effective radius of the group, andEis the dielectric constant of the solvent. With an effective radius of charged amino acids of approximately 2 Å, Born's formula gives about – 80 kcal/mol for their energy in polar solvents whereEis larger than 10. This energy is two orders of magnitude larger than the van der Waals interaction of such groups and their surroundings.