Phase change of a block copolymer molecule

Abstract

The configurational statistics of a block copolymer is considered, the polymer being of the form (A-A-A...-A-)-(B-B...-B) where the AA, BB and AB interactions are different. The mathematics becomes very easy in the special case of potentials V_aa=V_bb=-V_AB, and it is shown that when V_AA(=V_BB) is attractive, V_AB repulsive a phase change can take place in the structure of the molecule. For short molecules (or weak V) the structure is that of a random flight with small local fluctuations. At a critical length (or critical V) the molecule takes up a statistical dumb-bell configuration which becomes more pronounced with increasing length (or increasing V). The theory is developed at the equivalent of a mean field theory level of accuracy. The equations are discussed for the general case V_AA not=V_BB not=V_AB, but the solution is there hampered by the intervention of an excluded volume problem.