Theory of polydisperse multiblock copolymers

We study the self-organization of a polydisperse A-B multiblock copolymer melt with repulsive interactions between the different monomers. In the framework of the one-loop (Hartree) approximation we consider the influence of the polydispersity parameter u, which is the ratio of the first two moments of the block length distribution u = ([l(2)]/[l](2)) - 1, On the condition for the order-disorder transition. At low polydispersity(u < 0.3) the system undergoes the ordinary block copolymer microphase separation transition. The value of the Flory parameter;chi on the line of the order-disorder transition increases with increasing polydispersity of the system. The transition to macrophase separation at the classical Lifshitz point u = 0.5 is precluded by a fluctuation-induced instability of the homogeneous state with respect to finite-wavelength composition fluctuations. The characteristic length scale L of these critical fluctuations above the microphase separation transition and the period of the domain structure below changes weakly with temperature as ((T - T-c)/T-c)(-1/6). In the case of an exponential block length distribution (u approximate to 1), the period of the domain structure exhibits stronger temperature dependence L approximate to ((T - T-c)/T-c)(-1/4) than that derived for this system near the Lifshitz point due to strong coupling between composition fluctuations. For values of the polydispersity parameter u > 0.4 the value of the Flory parameter on the line of the first-order order-disorder phase transition decreases with increasing polydispersity of the system.