Statistical distribution of bonding distances in a unidimensional solid

Roman Belousov, Paolo De Gregorio, Lamberto Rondoni and Livia Conti

Physica A: Statistical Mechanics and its Applications, 2014, vol. 412, issue C, 19-31

Abstract: We study a Fermi–Pasta–Ulam-like chain with Lennard-Jones potentials to model a unidimensional solid in contact with heat baths at a given temperature. We formulate an explicit analytical expression for the probability density of bonding distances between neighboring particles, which depends on temperature similarly to the distribution of velocities. For a finite number of particles, its validity is verified with high accuracy through molecular dynamics simulations. We also provide a theoretical framework which is consistent with the numerical findings. We give an analytic expression of the mean bond distance and elastic constant in the case of the square-well and harmonic interparticle potentials: we outline the role played by the hard-core repulsion. We also calculate the same quantities in the case of series expansions of Lennard-Jones potential truncated at different, even series power.

Keywords: Probability distribution; Phase space; Bond length; Fermi–Pasta–Ulam chain (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:412:y:2014:i:c:p:19-31

DOI: 10.1016/j.physa.2014.06.006

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