Monte Carlo Field-Theoretic Simulations Applied to Block Copolymer Melts

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Carlo field-theoretic simulations (MC-FTS) are performed on melts of symmetric
diblock copolymer for invariant polymerization indexes extending down to
experimentally relevant values of N=104. The simulations are
performed with a fluctuating composition field, W-(r), and a pressure
field, W+(r),
that follows the saddle-point approximation. Our study focuses on the
disordered-state structure function, S(k),
and the order-disorder transition (ODT). Although short-wavelength fluctuations
cause an ultraviolet (UV) divergence in three dimensions, this is readily
compensated for with the use of an effective Flory-Huggins interaction
parameter, ce. The resulting S(k)
matches the predictions of renormalized one-loop (ROL) calculations over the
full range of ceN and N
examined in our study, and agrees well with Fredrickson-Helfand (F-H) theory
near the ODT. Consistent with the F-H theory, the ODT is discontinuous for
finite N and the shift in (ceN)ODT
follows the predicted N-1/3 scaling over our range of N.