Theory of solvent-mediated long range force between colloidal particles ina solvent

A theory is presented for the solvent-mediated force potential between sphe rical colloidal particles in a solvent. The long range part of the potentia l Phi(ij)((sol))(r) between the i- and j-species of particles is given as P hi(ij)((sol)) (r) = -k(B)T Sigma(n) K((n))d(i)((n)) d(j)((n)) 1/r e(-2nr) w ith the temperature T and the Boltzmann constant k(B), where K(n) and z(n) are determined by the bulk structure of the solvent and d(j)((n)) is calcul ated from z(n) and the structure of the solvent near the j-species of collo idal particle, A similar result is also obtained for the long range part of the total correlation function h(0j) (r) between colloidal- and solvent-pa rticles. It is discussed that d(j)((n)) is inversely proportional to the is othermal compressibility of the solvent. The application of the theory to t he solvent near its critical point gives extremely, simple and universal ex pressions for the asymptotic behaviours of h(0j) (r) and Phi(ij)((sol)) (r) . This Phi(ij)((sol)) (r) is compared with the van der TT Waals potential i n order to emphasize a role of Phi(ij)((sol)) (r).