### Molecular Dynamics Methods in Studying Phase Equilibria

Tahir Cagin

Computer Aided Innovation of New Materials II, pp 255-259

Invited Paper presented in CAMSE'92, September 22-25, 1992, Yokohama, Japan

Eds. M. Doyama, J. Kihara, M. Tanaka, R. Yamamoto, North Holland:1993.
## ABSTRACT

Two molecular dynamics methods which are useful in studying phase equilibria
are presented. Both are based on the extended system Hamiltonian formalism.
With the first method, Grand Canonical Molecular Dynamics (GCMD), the
physical system is coupled to a chemical potential reservoir. The number of
molecules or concentration of species in the physical system varies
continously. In order to accomodate a continuous variation in the number
of molecules, a real number variable is used. The variation in the number
variable is determined from a dynamical equation of motion which depends on
a prespecified chemical potential. The number of molecules is determined by
taking the integer part of number variable, nu. The remainder of nu
represents a fractional mlecule and is used to scale the interactions of
the fractional particle with the rest of the system under study.
The second method, Gibbs Ensemble Molecular Dynamics, combines the essential
features of the GCMD method with the two subsytem approach used in the
Gibbs Ensemble Monte Carlo (GEMC) method. As in the GEMC, the model system
is composed of two subsystems in thermal, material and if desired in
mechanical equilibrium. Material equilibrium is facilitated through a
transfer equation which is derived from the microscopic expression for the
chemical potential of a closed system. In addition to the phenomenological
foundations for these methods, examples of applications to a homogeneous
simple fluid and to a molecular liquid are presented.