Behavior of a random heteropolymer in mixed solvents

I use a Landau theory to study the behavior of $A–B$ heteropolymers with disordered sequences immersed in a binary solvent mixture. Segments of type A are preferentially solvated in one type of solvent, and those of type B prefer the other type of solvent. At high temperatures, the behavior is qualitatively the same as that in a single solvent. As the temperature approaches the critical temperature for solvent demixing, however, the chain conformational statistics change dramatically. A phase transition occurs driven by the long-range solvent density fluctuations. The transition is one where on scales larger than a preferred length the chain is collapsed and microphase ordered. On shorter scales it is disordered and exhibits self-avoiding walk statistics. In many circumstances this domain size acquires a limiting value and the system cannot order on shorter length scales by reducing temperature. The ordering disappears when the critical point is approached too closely. Predictions are made for scattering profiles that may be observed in neutron-scattering experiments.