Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin-film geometry: A Monte Carlo simulation

Abstract

The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte-Carlo simulations of the bond fluctuation model of symmetric polymer mixtures, using chains containing N A = N B = N = 32 effective monomers connected by effective bonds with an attractive interaction between monomers of the same type and a repulsive interaction between different types. We use short range potentials at the walls, the right wall favoring A monomers and the left wall B monomers. Periodic boundary conditions are applied in the directions parallel to the walls. Both the canonical and semi-grand-canonical ensemble are studied. We argue that the latter case is appropriate for experiments with a lateral resolution L much less than the actual lateral sample size, in thermal equilibrium. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the "intrinsic profile") like w ∝ √ D, before a crossover to a saturation value w max (w 2 max ∝ ln L) sets in. In the semi-grand-canonical ensemble, however, one finds the same widths w ∝ √ D as in the canonical ensemble for not too large L, while for large L the interfacial profile is smeared out over a finite fraction of the film thickness (w ∝ D for D → ∞). We discuss the implications of these findings for the interpretation of both simulations and experiments.

Symmetric diblock copolymers in thin films. II. Comparison of profiles between self-consistent field calculations and Monte Carlo simulations

“…We investigate the fluctuations of the local interfacial position in more detail for the parallel lamellar phases L 2 and L 4 . In the MC simulations we have measured the local interfacial position via a block analysis [28]. This is illustrated schematically in Fig.4(a).…”

Equation of state for macromolecules of variable flexibility in good solvents: A comparison of techniques for Monte Carlo simulations of lattice models

“…These effects prevent an exact localization of the values of density and order parameter at the isotropic-nematic transition by the SE method. The rounding of the transition is unavoidable and mainly due to the presence of capillary wave excitations of the interface 46 , which would even increase in magnitude upon an increase of the lateral dimension of the simulation box 47,48 , in contrast to the grand canonical bulk simulations where one can reduce finite size effects by increasing the system size. The slight shift of the transition in the order parameter profile as opposed to the density profile is an indication of a precursor of a nematic wetting layer at the hard wall.…”

Incorporating Fluctuations and Dynamics in Self-Consistent Field Theories for Polymer Blends

“…Quantitatively comparing dynamical calculations to computer simulations of the bond fluctuation model [103], we investigate the relation between the dynamics of collective composition fluctuations and the underlaying dynamics of single chains, which is encoded in the Onsager coefficient Λ. The parameters of the bond fluctuation model can be related to the coarse-grained parameters, χN , R e andN , of the standard SCF model and the static properties of the bond fluctuation model (e. g., the bulk phase behavior [44,50] and interface properties [43,45,54,55]) have been quantitatively compared to SCF theory. Note that the mapping between the particle-based simulation model and the SCF model does not involve any adjustable parameter: the Flory-Huggins parameter χN is identified via the energy of mixing, the length scale is set by R e and the time scale is determined by the self-diffusion constant of a single polymer chain in a dense melt.…”