Radial distribution function of freely jointed hard-sphere chains in the solid phase

Abstract

Monte Carlo simulation is used to generate the radial distribution function of freely jointed tangent-bonded hard-sphere chains in the disordered solid phase for chain lengths of three, four, six, and eight segments. The data are used to create an accurate analytical expression of the total radial distribution function of the hard-sphere chains that covers a density range from the solidification point up to a packing fraction of 0.71. It is envisioned that the correlation will help further progress toward molecular thermodynamic treatment of the solid phase in general and toward perturbed chain theories for the solid phase, in particular.

Monte Carlo Scheme for Generation and Relaxation of Dense and Nearly Jammed Random Structures of Freely Jointed Hard-Sphere Chains

“…While there have been a great number of computational studies focusing on random dense packings of monatomic hard spheres, corresponding simulation efforts on irregular assemblies of chain molecules of tangent hard spheres (“pearl-necklace” chains) are relatively quite limited and almost exclusively applied on systems characterized by packing densities quite far from the MRJ state. − In all simulations of dense systems of irregular assemblies of hard spheres one faces two major challenges: (i) the creation of the initial (random) configuration corresponding to the desired packing density and (ii) the generation of a large number of uncorrelated configurations given that, ideally, all information about packing should be obtained as an average over an extended set of different structures. For monatomic systems the first issue (construction of simulation cell) can be addressed by algorithms like the ones proposed by Jodrey and Tory 18,19 and by Tobochnik and Chapin, while in a second stage collision-driven MD algorithms undertake the task of relaxing the local intersphere packing.…”

Dense and Nearly Jammed Random Packings of Freely Jointed Chains of Tangent Hard Spheres

“…Although computationally demanding, recent algorithms can produce very dense packings with such efficiency that extremely large packings of up to a million spheres, necessary to investigate some subtle structural features, are within reach [9]. It is somewhat surprising that packings of hard-sphere chains have received little attention, although they represent a valuable departing point for perturbation work [10], in addition to having richer structure than single spheres. The main hurdle is the substantial computational difficulty associated with the generation and relaxation of packings of hard spheres which are close to the MRJ state and simultaneously satisfy the holonomic constraints defining chain connectivity.…”