Monte Carlo simulations of phase separation in chemically reactive binary mixtures.

We present Monte Carlo simulations of a binary mixture simultaneously undergoing spinodal decomposition and the chemical reaction A — B. The competing processes give rise to novel, steady-state pattern formation with domain size scaling with reaction rate to a power, s, which equals the domain growth exponent, a, in the absence of chemical reactions. Our findings support recent numerical simulations of a Cahn-Hilliard-type model, suggesting that chemical reactions can be used to stabilize and tune patterns arising during phase separation. Simple chemical reactions have recently been suggested to dramatically afFect domain growth during spinodal decomposition in binary mixtures [1]. In ordinary spinodal decomposition [2], a binary mixture of two species of molecules A and B will become unstable with respect to long-wavelength fluctuations in concentration when the mixture is quenched to temperatures below the critical temperature. The system subsequently phase separates into two coexisting, homogeneous phases — an A-rich phase and a B-rich phase which have an interconnected morphology that coarsens with time. This process ultimately leads to macroscopic phase separation. The presence of chemical reactions alters this conventional picture. A chemical reaction such as A=8 (1) tends to spatially mix the two species, and when this reaction occurs simultaneously with spinodal decomposition , the phase separation process evolves into a steady-state pattern in which the demixing thermodynamic and mixing reactive processes balance. Understanding how these two competing processes give rise to pattern selection may have significant industrial importance in controlling the morphology of phase-separating materials [1]. The theoretical understanding of spinodal decomposition in binary mixtures is based mainly on the Cahn-Hilliard theory [2 — 4], which is readily modified to include reactions [1,5]: Here P is the local coarse-grained concentration of species A, A is the mobility of species A, I'i and I'z are the forward and backward reaction rates, respectively, and I" IP) is the Ginzburg-Landau-Wilson free energy functional , taken as the sum of the bulk free energy and the usual square-gradient approximation to the interfacial free energy [3]. A linear analysis of Eq. (2) in the absence of chemical reactions predicts the usual exponential growth of concentration Quctuations with a growth factor that has a cutofF at large wave vector k (small wavelength) [2,3]. However, it was recently shown [1] that the simultaneous occurrence of the reaction A = B decreases the growth factor. This shifts the small-wavelength cutofF to longer wavelengths, and introduces a long …