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Statistical distribution of bonding distances in a unidimensional solid

Author

Listed:
  • Belousov, Roman
  • De Gregorio, Paolo
  • Rondoni, Lamberto
  • Conti, Livia

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.

Suggested Citation

  • Belousov, Roman & De Gregorio, Paolo & Rondoni, Lamberto & Conti, Livia, 2014. "Statistical distribution of bonding distances in a unidimensional solid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 19-31.
    • Handle: RePEc:eee:phsmap:v:412:y:2014:i:c:p:19-31
    DOI: 10.1016/j.physa.2014.06.006
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