SIMULATION OF LAMELLAR PHASE-TRANSITIONS IN BLOCK-COPOLYMERS

Monte Carlo simulations of the lamellar phase transitions for symmetric amphiphilic chains are carried out on a cubic lattice, with the amphiphilic chain length N as large as 192 lattice sites, corresponding to lengths typical of those in experimental systems. We find that there is a qualitative change in the order-disorder transition when N exceeds about 50. For N less than or similar to 50, the compositional order parameter S at the transition is large; S almost-equal-to 0.8 on the ordered side of the transition. For N greater than or similar to 50, the jump is more modest, around 0.50 or less. Also, for N less than or similar to 50, the dominant compositional fluctuations in the disordered state near the transition have correlation lengths that are less than the lamellar spacing, while for N greater than or similar to 50, fluctuations with correlation lengths longer than this affect the transition. For 50 less than or similar to N less than or similar to 200, which is the range corresponding to many experimental diblocks, the effective value of the interaction parameter chiN at the disordering transition is around 15-17, in good agreement with the fluctuation theory of Fredrickson and Helfand but much higher than predicted by the Leibler mean-field theory. Near the disordering transition, dilation or compression of the lamellae can induce lamellar buckling or melting transitions.