Dennis J. Isbister

Nonlinear effects in polar fluids: A molecular theory of electrostriction

A molecular theory of electrostriction arising from the study of dipolar adsorption at a wall in the presence of an electric field is described. The quadratic hypernetted chain (QHNC) approximation for the wall–particle closure is the first of the hierarchy of approximations generated by the hypernetted chain equation (HNC) to predict electrostriction; the mean spherical and linearized hypernetted chain fail to do so. It is found that the simplest bridge diagrams which are ignored in the HNC (and QHNC) approximations must be included if quantitative agreement with the thermodynamic theory for electrostriction as described by Kirkwood and Oppenheim is to be obtained. These bridge diagrams have been evaluated analytically resolving the above discrepancy in the term of O(E2), where E is the local electric field. The statistical mechanical approach has also been extended to evaluate a few of the contributions of O(E4) in electrostriction. Conditions under which the linear constitutive relation between the pol...

Solution of the mean spherical model for dipolar mixtures

The mean spherical model is solved analytically for mixtures of dipolar fluids. The components are identified by different but additive molecular radii and different magnitudes of the dipole moment. The direct and indirect correlation functions are found to be functionally dependent on the corresponding hard-sphere functions calculated at certain adjusted densities. Equations for the parameters concerned in calculating such densities are given. The reduction to the equal radii case follows immediately from this analysis.

Adsorption of dipolar hard spheres onto a smooth, hard wall in the presence of an electric field

Integral equations have been solved for the density profile of dipolar hard spheres against a hard, smooth wall in the presence of an electric field. This density profile was examined as a function of the bulk mediums temperature and density with different field strengths and field directions. It was found to depend primarily upon the competitive interactions of the field with the monolayer particles and the first outer shell with the monolayer particles.

The adsorption of dipoles at a wall in the presence of an electric field: The RLHNC approximation

The adsorption of dipolar hard spheres in the presence of an external electric field has previously been studied within the context of the mean spherical approximation. In order to quantify the significance of the physical trends found above, the problem is solved within the higher order closure rules afforded by the linearized hypernetted chain approximation. Exact expressions for the reduced dipole moment and the electric field strength are derived using only the asymptotic forms of the direct correlation functions. It is found that the favorable orientational correlations between the dipolar hard spheres and the wall are underestimated by the mean spherical approximation. This is emphasized in the enhanced adsorption of the dipolar species (at the wall itself) for dipoles oriented close to the direction of the field. However, the nonphysical features of the mean spherical approximation (manifested in the negativity of the density profile) are not fully rectified by the use of the linearized hypernetted...

KINETIC ENERGY CONSERVING INTEGRATORS FOR GAUSSIAN THERMOSTATTED SLLOD

A new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operator-splitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge–Kutta and Gear predictor–corrector methods.

Operator splitting algorithm for isokinetic SLLOD molecular dynamics

We apply an operator splitting method to develop a simulation algorithm that has complete analytical solutions for the Gaussian thermostated SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] for a system under shear. This leads to a homogeneous algorithm for performing both equilibrium and nonequilibrium isokinetic molecular dynamics simulation. The resulting algorithm is computationally efficient. In particular, larger integration time steps can be used compared to simulations with regular Gaussian thermostated SLLOD equations of motion. The utility and accuracy of the algorithm are demonstrated through application to the Weeks-Chandler-Anderson fluid. Although strict conservation of the kinetic energy suppresses thermal fluctuations in the system, this algorithm does not allow simulations at lower shear rates than those normally afforded by older nonequilibrium molecular dynamics simulations.

Polarization density profiles for dipoles against an electrified wall in the MS and RLHNC approximations

The polarization density profiles P(z, E) for dipoles in the vicinity of a wall, from which an electric field emerges, have been calculated using the mean spherical (MS) and renormalized linearized hypernetted chain (RLHNC) approximations. The profiles for the two approximations are significantly different. The presence of a component of the polarization density that is perpendicular to the field E, when the field is neither perpendicular nor parallel to the wall, is noted. The anisotropic response of the fluid to the electric field in the vicinity of the wall is discussed in terms of a local dielectric tensor when the relationship between the polarization density and the electric field is linear.

The solution of Ornstein-Zernike equation for hard-sphere-like mixtures

Analytic techniques of Baxter are used to solve the Ornstein-Zernike equation for the unusual closure relations c αβ(r) = 0 (r > R αβ) and h αβ(r) = -K αβ (r < R αβ). It is found taht the integral ∫ dr c αβ(r) is a simple function of the constants K αβ. This relationship is used in certain self-consistency equations arising in the solution of the mean spherical model for dipolar mixtures.

The conjugate-pairing rule for non-Hamiltonian systems

In systems that satisfy the Conjugate Pairing Rule (CPR), the spectrum of Lyapunov exponents is symmetric. The sum of each conjugate pair of exponents is identical. Since in dissipative systems the sum of all the exponents is the entropy production divided by Boltzmanns constant, the calculation of transport coefficients from the Lyapunov exponents is greatly simplified in systems that satisfy CPR. Sufficient conditions for CPR are well known: the underlying adiabatic dynamics should be symplectic. However, the necessary conditions for CPR are not known. In this paper we report on the results of computer simulations which shed light on the necessary conditions for the CPR to hold. We provide, for the first time, convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the CPR, even in the thermodynamic limit. In spite of this it appears that the sum of the maximal exponents is equal to the entropy production per degree of freedom. Thus it appears that the shear viscosity can still be calculated using the standard viscosity algorithm by summing the maximal pair of exponents.(c) 1998 American Institute of Physics.

The phase behaviour of interaction site fluids

Two simple models for polar molecular fluids, the polar hard dumb-bell (PHD) and the polar hard sphere (PHS), are shown to have a critical point for an elongation of l/σ = 0·5. The solution of the site-site Ornstein-Zernike (SSOZ) equation is used to obtain the energy as a function of density and reduced dipole moment from which the excess Helmholtz free energy ΔA is obtained analytically. The coexistence and spinodal curves are generated and the classical gas-liquid critical point for PHD located at kTσ3/μ2 = 0·106 and πρσ3/3 = 0·05. For more complex molecular fluids either the analytic solution is unknown or its use becomes impractical, so we investigate the accuracy and reliability of obtaining the free energy from numerical solutions of the SSOZ equation.