Expressions for the stress and elasticity tensors for angle-dependent potentials.

The stress and elasticity tensors for interatomic potentials that depend explicitly on bond bending and dihedral angles are derived by taking strain derivatives of the free energy. The resulting expressions can be used in Monte Carlo and molecular dynamics simulations in the canonical and microcanonical ensembles. These expressions are particularly useful at low temperatures where it is difficult to obtain results using the fluctuation formula of Parrinello and Rahman [J.

Elastic constants of diamond from molecular dynamics simulations.

The elastic constants of diamond between 100 and 1100 K have been calculated for the first time using molecular dynamics and the second-generation, reactive empirical bond-order potential (REBO). This version of the REBO potential was used because it was redesigned to be able to model the elastic properties of diamond and graphite at 0 K while maintaining its original capabilities. The independent elastic constants of diamond, C(11), C(12), and C(44), and the bulk modulus were all calculated as a function of temperature, and the results from the three different methods are in excellent agreement.

Symmetry, equivalence, and molecular self-assembly.

Molecular self-assembly at equilibrium is fundamental to the fields of biological self-organization, the development of novel environmentally responsive polymeric materials, and nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements for the self-assembly of actin, tubulin, and the ubiquitous icosahedral shell structures of viral capsids. We introduce a family of simple potentials that give rise to the self-assembly of linear polymeric, random surface ("membrane"), tubular ("nanotube"), and hollow icosahedral structures that are similar in many respects to their biological counterparts.

Polymerization transitions in two-dimensional systems of dipolar spheres.

We investigate the self-organization of dipolar spheres into polymer chains as a fundamental model of the self-assembly of particles having anisotropic interparticle interactions. Our study involves a combination of modeling with vertically vibrated magnetic beads simulating a quasi-two-dimensional fluid at equilibrium and corresponding Monte Carlo simulations of hard spheres with embedded extended dipoles. We find a transition from a gas-like phase to a polymerized phase upon cooling, in accord with the analytic theory of equilibrium polymerization.

Isothermal stress and elasticity tensors for ions and point dipoles using Ewald summations.

The isothermal stress tensor and isothermal elasticity tensor for systems of point charges and of nonpolarizable point dipoles are derived from the strain derivatives of the free energy. For the case of point dipoles, it is shown that the angular dependence of the interaction potential gives rise to additional contributions to the stress and elasticity tensors not recognized previously.

Equilibrium polymerization in the Stockmayer fluid as a model of supermolecular self-organization.

A diverse range of molecular self-organization processes arises from a competition between directional and isotropic van der Waals intermolecular interactions. We conduct Monte Carlo simulations of the Stockmayer fluid (SF) with a large dipolar interaction as a minimal self-organization model and focus on basic thermodynamic properties that are needed to characterize the polymerization transition that occurs in this fluid. In particular, we determine the polymerization transition lines from the maximum in the specific heat, C(v), and the inflection point in the extent of polymerization, Phi.

Mechanical heterogeneities in model polymer glasses at small length scales.

Molecular simulations of a model, deeply quenched polymeric glass show that the elastic moduli become strongly inhomogeneous at length scales comprising several tens of monomers; these calculations reveal a broad distribution of local moduli, with regions of negative moduli coexisting within a matrix of positive moduli. It is shown that local moduli have the same physical meaning as that traditionally ascribed to moduli obtained from direct measurements of local constitutive behaviors of macroscopic samples.

Local elastic constants in thin films of an fcc crystal.

In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of finite volumes over which average elastic constants are calculated. Results for the calculation of the local elastic constants of a nearest-neighbor Lennard-Jones fcc crystal in the bulk and in a thin film are presented.

Improved simulation method for the calculation of the elastic constants of crystalline and amorphous systems using strain fluctuations.

In this paper, a method is proposed for calculating the elastic constants of arbitrarily soft or stiff systems using strain fluctuations. For stiff materials, for example, strain fluctuations may be enhanced by appropriate choice of elastic constants for the bath. Example calculations of the isothermal elastic constants of the nearest-neighbor Lennard-Jones fcc crystal demonstrate improved convergence properties over standard techniques.