Systems Of Nonspherical Particles Research Articles

The scaled particle theory for mixtures of hard convex particles

The excess volume and Gibbs free energy predicted by the scaled particle theory have been calculated for five binary systems of hard spheres, cubes, tetrahedra, ellipsoids and cylinders where the particles of the mixtures have the same shape but different sizes. At a fixed pressure, the excess volume was dependent on the shape of the particles involved, the temperature, pressure and size ratio of the particle. There appeared to be no equivalent sphere which could describe the equation of state and the mixing properties of the systems of non-spherical particles. The difficulties of extending the scaled particle theory to mixtures of different shaped particles are discussed and it is shown that the scaled particle theory is not thermodynamically consistent for these systems.

The scaled particle theory for particles of arbitrary shape

The scaled particle theory of Reiss et al. has been extended to hard non-spherical particles and equations analogous to the Percus-Yevick equation have been obtained for mixtures of particles of the same shape but different sizes. The resulting equation of state produces exact second and third virial coefficients which are functions of the average radius, the surface area and the volume of the particle. The equations of state for several systems of hard non-spherical particles are compared with that for a system of hard spheres.