Phase segregation dynamics of a chemically reactive binary mixture

We investigate a model system of a chemically reactive binary mixture, where the simple reaction $A\rightleftharpoons B$ 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, $R_{\infty }$, scales with the reaction rate, $\Gamma$, as $R_{\infty }\sim {\left(\frac{1}{\Gamma }\right)}^s$, where the exponent $s$ equals approximately $\frac{1}{3}$ for low rates and equals exactly ¼ 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.