Fluctuation correction for the critical transition of symmetric homopolymer blends

Monte Carlo simulations are performed on structurally symmetric binary homopolymer blends over a wide range of invariant polymerization indices, N¯. A finite-size scaling analysis reveals that certain critical exponents deviate from the expected 3D-Ising values as N¯ increases. However, the deviations are consistent with previous simulations and can be attributed to the fact that the system crosses over to mean-field behavior when the molecules become too large relative to the size of the simulation box. Nevertheless, the finite-size scaling techniques provide precise predictions for the position of the critical transition. Using a previous calibration of the Flory-Huggins interaction parameter, χ, we confirm that the critical point scales as (χN)_c=2+cN¯^-1∕2 for large N¯, and more importantly we are able to extract a reliable estimate, c≈1.5, for the universal constant.