Theory of Solvent-Mediated Long Range Force between Colloidal Particles in a Solvent

Abstract

A theory is presented for the solvent-mediated force potential between spherical colloidal particles in a solvent. The long range part of the potential Φ _ij^(sol)(r) between the i- and j-species of particles is given as Φ _ij^(sol)(r) =-k_BT∑_nK⁽ⁿ⁾d_i⁽ⁿ⁾d_j⁽ⁿ⁾ 1 over r e^-z_nr with 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 calculated from z_n and the structure of the solvent near the j-species of colloidal particle. A similar result is also obtained for the long range part of the total correlation function h_0j(r) between colloidal- and solvent-particles. It is discussed that d_j⁽ⁿ⁾ is inversely proportional to the isothermal compressibility of the solvent. The application of the theory to the solvent near its critical point gives extremely simple and universal expressions for the asymptotic behaviours of h_0j(r) and Φ _ij^(sol)(r). This Φ _ij^(sol)(r) is compared with the van der Waals potential in order to emphasize a role of Φ _ij^(sol)(r).