Theory of non-equilibrium critical phenomena in three-dimensional condensed systems of charged mobile nanoparticles

Abstract

A study of 3d electrostatic self-assembly (SA) in systems of charged nanoparticles (NPs) is one of the most difficult theoretical problems. In particular, the limiting case of negligible or very low polar media (e.g. salt) concentration, where the long-range NP interactions cannot be reduced to commonly used effective short-range (Yukawa) potentials, remains unstudied. Moreover, the present study has demonstrated that unlike the Debye-Hückel theory, a complete screening of the charges in SA kinetics (dynamic SA) is not always possible. Generally speaking, one has to take into account implicitly how each NP interacts with all other NPs (the true long-range interactions). Traditional theoretical methods allow us to monitor such electrostatic 3d system kinetics only for very short times, which is far from sufficient for understanding the dynamic SA. In this paper, combining an integrated analytical approach (the non-linear integro-differential kinetic equation for correlation functions) and reverse Monte Carlo in the 3d case, we have obtained a self-consistent solution of this challenging problem. We demonstrate, in particular, the existence of critical points and critical phenomena in the non-equilibrium kinetics in a 3d system of oppositely charged mobile NPs.

Kinetics of dimer F type center annealing in MgF2 crystals

“…and chemical (reactions) properties was introduced and discussed by us in Refs. [51][52][53][54][55][56][57][58][59]. In particular, recently we developed phenomenological theory describing the diffusion-controlled kinetics of radiation defect annealing in ionic solids [9,15] and demonstrated how its fitting to the experimental curves allows one to extract two control parameters: the migration energy of the interstitial ions Ea and the pre-exponent X=N0RD0/β, where N0 is initial defect concentration, R recombination radius, D0 diffusion pre-exponent, and β heating rate.…”

Static and dynamic screening effects in the electrostatic self-assembly of nano-particles

“…This equation is nothing else but the so-called linearized Poisson-Boltzmann equation, 2 where, however, the statistical characteristics are used for the description of dynamic screening effects, r NP = r NP [F(r,t)], similar to ref. 1. Note that in the limiting case of a very low density of NPs, e.g.…”

“…Moreover, SA is characterized by a fundamentally different spectrum of fluctuations, with strongly developed long-range correlations, responsible for the aggregation. 1 The general problem of NP screening has been formulated by us recently, 1,12-14 but it was not solved properly: we took into account the dynamic screening effects but neglected the static effects. This is valid only for the absence of salt solution (formally, k 0).…”

“…1 and 12-14 the new approach was formulated, the basic ideas of which are listed below, Section 2.1. The kinetics of twodimensional (2d) [12][13][14] and three-dimensional (3d) 1 systems of NPs were considered in detail.…”

“…We consider the realistic 3d case, for better understanding the results, it is desirable prior acquaintance with the recent study. 1 We use essentially the same model for electrostatic dynamic SA as in previous ref. 1 and 12-16 taking into account the competition of long-range, Section 2.2, and short-range, Section 2.3, particle interactions.…”