Computer Simulation of Polymer Blends in Thin Films

Computer Simulation of Polymer Blends in Thin Films 

The first Monte Carlo study of phase transitions in thin films of symmetric binary polymer mixtures confined between two neutral hard walls (to which neither component is preferred energetically) was presented by Kumar et al. [39]. 

Here we do not give any details on simulation methodologies, since these have been reviewed recently elsewhere [186,198], and just reproduce typical results on the change of the phase diagram due to confinement (Fig. 19 [39]). A note- 

Since in Fig. 19 critical temperatures have been estimated by a rough extrapolation only, this study [39] could not make too definitive statements about the shift of the critical temperature due to confinement. A more extensive study has been possible for the bond fluctuation model [55], extracting both critical temperatures and the coexistence curves by use of the finite size scaling technique [236-239,280]. Figs.21, 22 present the results for chain length N=32. While mean field theory Eqs. (36) and (37) in Sect. 2.1 has predicted a crossover from 

A more complete description of the crossover from two- to three-dimensional critical behavior, that incorporates the shift of Tc, Eq. (129), can be written down in terms of crossover scaling functions M for the order parameter M, Eq. (130) and S for the collective scattering intensity Scoll for scattering wavenumber q— 0, which can be accessed by small angle scattering techniques [186]. Defining =1—T/Tc (D- °o) we can write 

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