NUMERICAL-ANALYTICAL CALCULATION OF MICROSCOPIC DISTRIBUTION OF COLLOID PARTICLE CENTERS IN A MACROSCOPICALLY HOMOGENEOUS AQUEOUS SOLUTION
The attempt is made to apply a two-level molecular-statistical approach to description of the structure and equilibrium thermodynamic characteristics of homogeneous colloidal aqueous solutions. This statistical method was developed for condensed molecular systems with pair interaction of molecules with each other, the latter is described, in particular, with the help of the Lennard-Jones potential for systems with a face-centered cubic lattice in the crystalline state. Taking into account the specifics of the behavior of nanoscale colloidal particles in aqueous solutions, there is a reason to describe the interaction between such particles, using the potential of SALR (Short-range Attraction and Long-range Repulsion). It takes into account strong repulsion between particles at short distances, the attraction at intermediate distances and weak repulsion at relatively large distances, which equal several effective diameters of colloidal particles. Such an unusual form of the SALR potential is a consequence of the influence of the polar solvent (water) on the colloidal particles. Therefore, the real binary fluid system, according to the previous experimental and theoretical studies, can be theoretically investigated with method of a framework of a one-component statistical model with a hexagonal lattice. The result of solving a derived closed system of integral and algebraic equations is the dependence of root-mean-square deviations of the centers of gravity of colloidal particles in water on the occupation numbers of n microcells of the modified method of conditional distributions. On the graphs of the free energy dependences, there is a bifurcation point, corresponding to the appearance of two solutions with fill numbers n > 0,5 (for n > 0,5 there is only one solution).