Abstract
By integrating all degrees of freedom of the electric field and small ions with an ensemble averaging, we construct thermodynamic quantities for colloid dispersions. The unoccupied volume is accepted as the proper thermodynamic variable to describe the chemical and thermal equilibrium of the small ions in the region outside of all the particles. Using the electric potential of the dispersion which satisfies a set of equations derived by linearizing the inhomogeneous Poisson-Boltzmann equation, we calculate the electric part of the internal energy and obtain that of the Helmholtz free energy by applying the Legendre transformation with respect to temperature. The electric part of the Gibbs free energy can be deduced from that of the Helmholtz free energy by the two means of the total sum of chemical potentials and the Legendre transformation with respect to the unoccupied volume. Thus the thermodynamic theory has been successfully formulated for the colloid dispersion. The pair potential derived from the Gibbs free energy possesses a medium-range strong repulsive part and a long-range weak attractive tail being additionally affected by the fraction of the unoccupied volume.
