Simulation of Lamellar Phase Transitions in Block Copolymers and Surfactants

Abstract

Simulations of the lamellar phase transitions of symmetric amphiphilic chains are carried out on a cubic lattice, with the amphiphilic chain length N varied from 6 to 48 lattice sites, corresponding to lengths ranging from surfactants to short block copolymers. We find that the effective interaction energy parameter χN (which incorporates the effect of added solvant) at which the transition from the lamellar ordered state to the disordered state occurs is roughly equal to 18-21. While this result is consistent with an extrapolation of the Fredrickson-Helfand weak-segragation theory to N values in the range of the simulations, the amplitude of the sinusoidal compositional wave in the ordered state near the transition is large for all N studied, in disagreement with the weak segregation theories. Thus, for values of N up to 48, the transition occurs in a “moderate,” rather than weak-segregation regime. Near the disordering transition, fluctuating “bridge” or “hole” defects in the lamellae spontaneously appear; with heating these proliferate and lead to the disordering transition. These fluctuating bridges might help explain anomalous diffusion and rheological behavior observed near the disordering transition. We also find that in the ordered state near the transition, the orientational order parameter, which is proportional to the intrinsic birefringence, falls rapidly with increasing N, roughly as 1.5 N^-2.