TY - JOUR

T1 - Statistical Contact Model for Confined Molecules

AU - Santamaria, Ruben

AU - de la Paz, Antonio Alvarez

AU - Roskop, Luke

AU - Adamowicz, Ludwik

N1 - Funding Information:
The authors acknowledge the staff of El Gato, University of Arizona, for technical assistance and use of the supercomputer. RS acknowledges PASPA–DGAPA–UNAM for financial support to visit the Department of Chemistry and Biochemistry of the University of Arizona and carry out this research.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - A theory that describes in a realistic form a system of atoms under the effects of temperature and confinement is presented. The theory departs from a Lagrangian of the Zwanzig type and contains the main ingredients for describing a system of atoms immersed in a heat bath that is also formed by atoms. The equations of motion are derived according to Lagrangian mechanics. The application of statistical mechanics to describe the bulk effects greatly reduces the complexity of the equations. The resultant equations of motion are of the Langevin type with the viscosity and the temperature of the heat reservoir able to influence the trajectories of the particles. The pressure effects are introduced mechanically by using a container with an atomic structure immersed in the heat bath. The relevant variables that determine the equation of state are included in the formulation. The theory is illustrated by the derivation of the equation of state for a system with 76 atoms confined inside of a 180-atom fullerene-like cage that is immersed in fluid forming the heat bath at a temperature of 350 K and with the friction coefficient of 3.0 ps - 1. The atoms are of the type believed to form the cores of the Uranus and Neptune planets. The dynamic and the static pressures of the confined system are varied in the 3–5 KBar and 2–30 MBar ranges, respectively. The formulation can be equally used to analyze chemical reactions under specific conditions of pressure and temperature, determine the structure of clusters with their corresponding equation of state, the conditions for hydrogen storage, etc. The theory is consistent with the principles of thermodynamics and it is intrinsically ergodic, of general use, and the first of this kind.

AB - A theory that describes in a realistic form a system of atoms under the effects of temperature and confinement is presented. The theory departs from a Lagrangian of the Zwanzig type and contains the main ingredients for describing a system of atoms immersed in a heat bath that is also formed by atoms. The equations of motion are derived according to Lagrangian mechanics. The application of statistical mechanics to describe the bulk effects greatly reduces the complexity of the equations. The resultant equations of motion are of the Langevin type with the viscosity and the temperature of the heat reservoir able to influence the trajectories of the particles. The pressure effects are introduced mechanically by using a container with an atomic structure immersed in the heat bath. The relevant variables that determine the equation of state are included in the formulation. The theory is illustrated by the derivation of the equation of state for a system with 76 atoms confined inside of a 180-atom fullerene-like cage that is immersed in fluid forming the heat bath at a temperature of 350 K and with the friction coefficient of 3.0 ps - 1. The atoms are of the type believed to form the cores of the Uranus and Neptune planets. The dynamic and the static pressures of the confined system are varied in the 3–5 KBar and 2–30 MBar ranges, respectively. The formulation can be equally used to analyze chemical reactions under specific conditions of pressure and temperature, determine the structure of clusters with their corresponding equation of state, the conditions for hydrogen storage, etc. The theory is consistent with the principles of thermodynamics and it is intrinsically ergodic, of general use, and the first of this kind.

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U2 - 10.1007/s10955-016-1569-x

DO - 10.1007/s10955-016-1569-x

M3 - Article

AN - SCOPUS:84976385243

SN - 0022-4715

VL - 164

SP - 1000

EP - 1025

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -