Critical compositions in the microphase separation transition of random copolymers

We study the microphase separation transition of random copolymers with two kinds of monomers with attraction between similar kinds. We perform a mean field analysis for nonsymmetric compositions where the total amount of the one kind of monomer exceeds that of the other. We find a critical composition ${\mathit{f}}_{\mathrm{cr}}$≊0.173. For compositions f${\mathit{f}}_{\mathrm{cr}}$ or f>1-${\mathit{f}}_{\mathrm{cr}}$ we find a first order transition of the Landau type in the presence of a cubic term in the effective Hamiltonian. For ${\mathit{f}}_{\mathrm{cr}}$f${\mathit{f}}_{\mathrm{cr}}$ our mean field analysis predicts an unusual continuous transition even in the presence of the cubic term. The effect of fluctuations is also discussed.