Static Correlations in the Ordered Colloidal Systems

Abstract

The macroion-macroion correlation function and structure factor are studied within the Ornstein-Zernike (OZ) integral equation closed by hypernetted-chain approximation using the method of critical modes. Developing the results which have recently been received in [1][2][3] for a case of a model system consisting of a mixture of charged hard spheres, the role of detalization in describing the compound characters is investigated. In particular, it is shown that adding the uncharged particles to the model of the solution of macroparticles and counterions significantly affects the structural parameter of ordering extracted within the critical modes method providing close theoretical and relating experimental results.

Kinetic Model of Compaction in Granular Materials

“…It was found experimentally that the kinetic phase diagram describing the compaction demonstrates an asymptotic saturation to quasiequilibrium states, which correspond to the maximum packing density or close to it. In the general case of the simplest systems (hard spheres), the relaxation law reproduces, with a sufficient accuracy, the known homogeneous Kolmogorov-Vogel-Fulcher scenario [6,7]. Theoretical approaches to the packing kinetics -among them, it is enough to mention the kinetic model of free volume [7-9, 11, 12] -satisfactorily describe the asymptotic behavior of the corresponding order parameter in general.…”

“…where Γ is a kinetic coefficient. The analysis of the expression obtained for 𝐹 demonstrates that the functions, which were obtained by confining series (6) to the quadratic terms inclusive, have one extreme point (namely, a minimum) in the physical region of the values of packing parameter 𝜂. In a vicinity of those states, we may expect a deceleration of the relaxation processes in the model system.…”

“…As an example, let us consider Eq. ( 7) with regard for series (6) confined to the quadratic contribution inclusive. The corresponding kinetic equation in the approximation described above reads…”

“…For instance, the compaction in granular materials under the action of external impacts, which has the efficient direct practical application, was studied in a number of works (see, e.g., works [5][6][7][8][9][10][11][12]) in detail. It was found experimentally that the kinetic phase diagram describing the compaction demonstrates an asymptotic saturation to quasiequilibrium states, which correspond to the maximum packing density or close to it.…”