Analytic theory of surface segregation in compressible polymer blends

Abstract

We present an analytical theory for the competing influences of polymer-surface and polymerpolymer interactions, density and composition variations, and blend asymmetries on the surface profiles of a multicomponent polymer blend near an interacting, impenetrable interface. The theory is explicitly applied in the limit of small continuum model polymer-surface interaction parameters, a limit which still enables treating all qualitative behaviors of polymers that individually tend either to aggregate toward or to segregate from the surface. The formulation is based on an analytic combined self-consistent field-density functional theory for inhomogeneous polymer systems. The theory describes the compressible polymer system with a generic Gaussian chain-random mixing type model, which in the bulk phase reproduces a Sanchez-Lacomb-type description of the bulk thermodynamics. The analytic expressions for the density profiles, surface excesses, surface densities, and surface correlation lengths are all presented explicitly for binary compressible systems, but we note how to make the trivial extension to more components. The surface excess and surface correlation length are shown to diverge along the bulk phase spinodal, in rough accord with the increases found in recent experiments by Genzer and Composto. The relation between the continuum model interaction parameters and microscopic ͑e.g., lattice-model-type͒ interaction parameters is used to understand recent observations of a surface free energy that displays a higher than quadratic dependence on the surface composition and of the strong surface segregation exhibited by isotopic polymer blends.

Filler-induced composition waves in phase-separating polymer blends

“…The coupling constant h in the leading term plays the role of a surface field which breaks the symmetry between the two phases, i.e., attracts one of the components to the filler surface. The coupling constant g in the second term is neutral regarding the phases, and results from the modification of the interaction energy due to the missing neighbors near the surface [33] and chain connectivity [34]. For studies of surface critical phenomena [35,36] and surface dynamics [37,38] one typically keeps only these terms as a minimal model of phase separation with boundaries.…”

Simulations of Filled Polymers on Multiple Length Scales

“…The value of h can be related to the interaction energy ε mf in the previous section. The coupling constant g in the second term is neutral regarding the phases, and results from the modification of the interaction energy due to chain connectivity [57,58] and the missing neighbors near the surface when the equation is solved on a grid [59.60]. The attractive interaction between filler and polymer A causes wetting of the filler by the polymer, analogous to the density enhancement shown in Figure 4(a), which breaks the symmetry of the spinodal decomposition process, producing novel patterns.…”

Polymer melts and polymer solutions near patterned surfaces

“…Recently, Freed 3 derived a nonlocal density functional that reproduces the results of the self-consistent field methods, thereby unifying the older density functional and selfconsistent field methods and enabling the use of advantageous features of each, such as the treatment of more detailed interaction models with the former and of more realistic chain connectivity effects with the latter. This combined density functional-self-consistent field approach has been applied to describe compressible polymer melts and blends near impenetrable surfaces, 3,4 and approximate analytical solutions have been derived by introducing a reference state for which nontrivial explicitly inhomogeneous analytical solutions are possible. The simplicity of the formalism enables us to extend it to polymers near chemically heterogeneous, patterned surfaces.…”

“…They also omit the effects of the near surface depletion/ enhancement layers that arise due to the compressibility of the polymer melts and that are likewise present for the polymer profiles in incompressible polymer solutions near interfaces. 3,4,14,15 The more detailed description by Nath et al, 9 using a combination of more computationally intensive modern density functional and integral equation methods, describes the block copolymer system as compressible and thus provides nontrivial density profiles in directions orthogonal to the surface. Cahn-Hilliard model simulations 11,12 have been performed for critical composition, polymer films on a surface with striped chemical patterns, where the surface energies of the stripes is chosen to enrich one of the blend components.…”