Electrostatic slowdown in kinetics of spinodal decomposition

We consider the kinetics of spinodal decomposition in a mixture of oppositely charged ionic species A- and C+ with a short-range Flory-Huggins incompatibility, χ > 0, between them. This represents the minimal model of systems with short-range attractions and long-range repulsions. In contrast to nonionic blends undergoing macroscopic phase separation, ionic mixtures at equilibrium form periodic phases of finite-size domains or clusters-a phenomenon known as electrostatically stabilized microphase separation. A dynamical (time-dependent Ginzburg-Landau) field theory is developed, classified as Model B plus long-range Coulomb interactions. Electrostatics generates an extra term in the resulting Cahn-Hilliard equation, which slows spinodal decomposition. Analysis of the amplification factor R(q) in the Fourier domain shows that electrostatic interactions (i) do not affect the optimal wavevector qm; (ii) slow down the optimal growth; (iii) reduce the window of positive growth, R(q) > 0, by suppressing long-wavelength modes due to the high Coulomb cost of large charged domains; and (iv) lead to a new critical scaling of the optimal growth rate with quench depth, Ropt ∼ δχ1, contrasting the exponent 2 for nonionic systems. Extension to polymer blends shows that monomer connectivity and Rouse dynamics shift qm to lower values and further decelerate growth. In dimensionless form, R(q/qm) depends on two parameters: the reduced electrostatic strength, linear in the Bjerrum length, and the reduced chain length. After rapid spinodal decay, clusters slowly coarsen to their equilibrium finite size, which exceeds the spinodal pattern scale. These results advance the understanding of the dynamics of biocondensate formation in living cells, where Coulomb interactions are ubiquitous.