Weakening of Solvation-Induced Ordering by Composition Fluctuation in Salt-Doped Block Polymers

The spontaneous ordering of block polymers doped with ions is affected by both selective solvation and long-range Coulombic interaction. The mean-field treatment was recently shown to overestimate the solvation-induced ordering, requiring a large solvation radius to fit experimental phase diagrams, which may be relieved by including composition fluctuations. Treating the composition fluctuations in such systems is challenging because of the need of resolving heterogeneous dielectric profile that couples with the ordering itself. Starting from a minimal model, we develop a Landau-Brazovskiĭ expansion for the free energy of salt-doped block polymer near the ordering transition. It is found that the wavelength for typical composition fluctuations first decreases with salt doping, due to Coulombic interaction, then increases due to ionic solvation. Two mechanisms that weaken the solvation-enhanced ordering are identified: the Brazovskiĭ-type composition fluctuation that stabilizes disordered phase, and the coupling between mismatch in dispersion interaction and the dielectric permittivity through monomeric polarizability.