Globules of annealed amphiphilic copolymers: surface structure and interactions

A mean-field theory of globules of random amphiphilic copolymers in selective solvents is developed for the case of an annealed copolymer sequence: each unit can be in one of two states, H (insoluble) or P (soluble or less insoluble). The study is focussed on the regime when H and P units tend to form long blocks, and when P units dominate in the dilute phase, but are rare in the globule core. A first-order coil-to-globule transition is predicted at some T = T(cg). The globule core density at the transition point increases as the affinity of P units to the solvent, epsilon, is increased. Two collapse transitions, coil --> "loose" globule and "loose" globule --> "dense" globule, are predicted if epsilon is high enough and P units are marginally soluble or weakly insoluble. H and P concentration profiles near the globule surface are obtained and analyzed in detail. It is shown that the surface excess of P units rises as epsilon is increased. The surface tension decreases in parallel. Considering the interaction between close enough surfaces of two globules, we show that they always attract each other at a complete equilibrium. It is pointed out, however, that such equilibrium may be difficult to reach, so that partially equilibrium structures (defined by the condition that a chain forming one globule does not penetrate into the core of the other globule) are relevant. It is shown that at such partial equilibrium the interaction is repulsive, so the globules may be stabilized from aggregation. The strongest repulsion is predicted at the coil-to-globule transition point T(cg): the repulsion force decreases with the distance between the surfaces according to a power law. In the general case (apart from T(cg)) the force vs. distance decay becomes exponential; the decay length xi diverges as T --> T(cg). The developed theory explains certain anomalous properties observed for globules of amphiphilic homopolymers.