Phase segregation dynamics of a chemically reactive binary mixture

Abstract

We investigate a model system of a chemically reactive binary mixture, where the simple reaction A B between the two constituents of the mixture occurs simultaneously with spinodal decomposition. The competition between the thermodynamic short-range attractive and the reactive long-range repulsive interactions leads to the formation of steady-state patterns. In the case of equal forward and backward reaction rates the steady-state average domain width, R ϱ , scales with the reaction rate, ⌫, as R ϱ ϳ(1/⌫) s , where the exponent s equals approximately 1 3 for low rates and equals exactly 1 4 for high rates. These exponent values and the variation of the maximum amplitude of the order parameter with the reaction rate can be derived by minimizing the free energy in a square wave and a single mode approximation, respectively. The phase segregation dynamics is simulated numerically using the appropriate Langevin equation. ͓S1063-651X͑96͒50509-X͔ PACS number͑s͒: 05.70.Fh, 64.60.Cn, 47.54.ϩr, 61.20.Ja

Chemical freezing of phase separation in immiscible binary mixtures

“…Over the last twenty years, several theoretical studies have investigated the idea that coupling spinodal decomposition with chemical reactions may, in the absence of hydrodynamic effects, freeze this coarsening process and stabilize a stationary inhomogeneous state characterized by an intrinsic wavelength, i. e., a wavelength determined by molecular and kinetic parameters rather than by externally imposed boundary conditions and/or geometrical constraints [2][3][4][5][6]8].…”

“…So far, the choice of these chemical terms has relied either on intuitive considerations [2,[4][5][6]8], or on a master equation derivation which exploits the kinetic similarities of some chemical reactions with spin-exchange processes [3]. This basically mean field type of approach was pioneered by Huberman [2], who predicted that the influence of chemistry on spinodal decomposition may, not only narrow the band of unstable modes, but more importantly, introduce a lower cutoff, k , below which all modes, and in particular the mode k = 0, are stable.…”

“…More than that even: in these studies, this suppression is obtained thanks to chemical processes which are considerably simpler than the one considered by Huberman, suggesting hence, that the phenomenon in question is ubiquitous in nature [5] and that the class of chemical reactions which qualify as candidates for a possible experimental demonstration, is extremely broad. A major simplification in this respect, is the fact that in none of the models studied recently, is the chemistry involved autocatalytic: typically, the reactions considered are simple isomerisation processes like A B, [3,4,8], associationdissociations reactions like A + B C [5], or standard adsorption-desorption surface reactions [6]. This apparently extremely general effect of chemistry on spinodal decomposition is however obtained through a procedure which we find thermodynamically unsatisfactory [10] because it consists in adopting chemical rate laws which, contrary to those adopted for diffusion, do not take into account the non-ideality of the systems con-sidered.…”

Modeling the Interactions between Membranes and Inclusions: Designing Self‐Cleaning Films and Resealing Pores

“…[29] In these calculations, we used a single mode approximation for the fluctuation of the order parameter around its uniform solution and defined an appropriate Greens function, [32,35] which allowed us to accounted for the contribution from the reaction term in the effective total free energy of the system. While the scenario considered here is more complex, since it involves variations in curvature of the different domains within the membrane, it can be shown that the location of the C component within the region of higher G also minimizes the total free energy of this system.…”

“…[34,35] To obtain the results presented below, we numerically integrated Equation (3)(4)(5) [26] on a lattice with lateral dimensions given by L x  L y ¼ 190  120 sites, unless specified otherwise. We assumed the membrane height to be fixed at h ¼ 0 along the edges of this simulation box.…”