Modeling the Interactions between Polymers and Clay Surfaces through Self-Consistent Field Theory

Abstract

Using numerical self-consistent field (SCF) calculations, we investigate the interactions between two closely spaced surfaces and the surrounding polymer melt. Short chains (surfactants) are terminally anchored to each of the surfaces. The coated substrates model organically modified clay crystallites (sheets). Through the calculations, we vary the characteristics of the surfactants and polymers to isolate conditions that drive the polymer to penetrate the gap between the surfaces. We also consider the effect of employing end-functionalized chains to promote the dispersion of bare clay sheets within the polymer matrix. We find that this scheme provides a robust method for exfoliating the sheets. To consider this case in greater depth, we develop an analytical SCF theory to model the interactions among the functionalized chains, nonfunctionalized polymers, and the clay sheets. The results from the numerical and analytical SCF models show good agreement on the behavior of the system. The results indicate that the optimal polymeric candidates for creating stable exfoliated composites are those that would constitute optimal steric stabilizers for colloidal suspensions.

Numerical simulation of polymer nanocomposites using self-consistent mean-field model

“…Balazs et al adopted this approach in their studies of the PNC intercalation/exfoliation processes. 6 Unlike the 1D case, the 2D formulation only averages over one lateral dimension ͑y͒, while the variation in the x and z directions is considered. Thus, every dependent variable, e.g., volume fractions, probability functions, and excess free energy, has one additional degree of freedom.…”

“…Balazs et al have extended the classical SCF approach to investigate the thermodynamic aspects of PNC. 6 The authors assumed that the clay platelets are fully covered by the intercalant; thus, the solid-solid interactions between the clay surfaces were irrelevant. The current approach assumes the presence of different interactions including solidsolid, solid-liquid, and liquid-liquid type.…”

“…[6][7][8][9] The model used in the SCF calculations consists of two infinite parallel platelets immersed in a bath of molten polymer. To incorporate the concentration effects, Ginzburg et al hybridized the SCF one-dimensional ͑1D͒ model with the density functional theory ͑DFT͒ for intercalant-grafted clay platelets, 1-nm thick and with a 30-nm diameter, dispersed in a polymer.…”

“…4,6,20 As before, 6,9 it assumes that two parallel clay platelets are placed in a reservoir of molten polymer in the x-y plane, and the distance between them in the z direction may vary. A single polymer chain is modeled as N k number of Kuhn segments, whose length is given by l k .…”

“…The grafting density of the platelets with short paraffinic intercalant chains ͑''surfactants'' in the literature 6 ͒ can vary from 0% to 100% coverage. Furthermore, the polymer melt contains different amounts of end-functionalized macromolecules of different chain lengths, comparable to that in industrial processes.…”