Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs)...

A self-consistent field (SCF) theoretic approach, using a general excess Helmholtz energy density functional that includes a square gradient term, is derived for polymer melt surfaces and implemented for linear polyethylene films over a variety of temperatures and chain lengths. The formulation of the SCF plus square gradient approximation (SGA) developed is generic and can be applied with any equation of state (EoS) suitable for the estimation of the excess Helmholtz energy. As a case study, the approach is combined with the Sanchez−Lacombe (SL) EoS to predict reduced density profiles, chain conformational properties, and interfacial free energies, yielding very favorable agreement with atomistic simulation results and noticeable improvement relative to simpler SCF and SGA approaches. The reduced influence parameter invoked in the SGA to achieve accurate density profiles and interfacial free energies is consistent with the definition of Poser and Sanchez, J. Colloid Interface Sci. 1979, 69, 539−548. The new SCF_SL + SGA approach is used to quantify the dominance of chain end segments compared to that of middle segments at free polyethylene surfaces. Schemes are developed to distinguish surface adsorbed from free chains and to decompose the surface density profiles into contributions from trains, loops, and tails; the results for molten polyethylene are compared with the observables of atomistic simulations. Reduced chain shape profiles indicate flattening of the chains in the surface region as compared to the bulk chains. The range of this transitional region is approximately 1.6 radii of gyration (R g ). The inclusion of chain conformational entropy effects, as described by the modified Edwards diffusion equation of the SCF, in addition to the square gradient term in density, provides more accurate predictions of the surface tension, in good match with experimental measurements on a variety of polymer melts and with atomistic simulation findings.

We investigate single and opposing silica plates, either bare of grafted, in contact with vacuum or melt phases, using self-consistent field theory. Solid–polymer and solid–solid nonbonded interactions are described by means of a Hamaker potential, in conjunction with a ramp potential. The cohesive nonbonded interactions are described by the Sanchez-Lacombe or the Helfand free energy densities. We first build our thermodynamic reference by examining single surfaces, either bare or grafted, under various wetting conditions in terms of the corresponding contact angles, the macroscopic wetting functions (i.e., the work of cohesion, adhesion, spreading and immersion), the interfacial free energies and brush thickness. Subsequently, we derive the potential of mean force (PMF) of two approaching bare plates with melt between them, each time varying the wetting conditions. We then determine the PMF between two grafted silica plates separated by a molten polystyrene film. Allowing the grafting density and the molecular weight of grafted chains to vary between the two plates, we test how asymmetries existing in a real system could affect steric stabilization induced by the grafted chains. Additionally, we derive the PMF between two grafted surfaces in vacuum and determine how the equilibrium distance between the two grafted plates is influenced by their grafting density and the molecular weight of grafted chains. Finally, we provide design rules for the steric stabilization of opposing grafted surfaces (or fine nanoparticles) by taking account of the grafting density, the chain length of the grafted and matrix chains, and the asymmetry among the opposing surfaces.

A mesoscopic simulation approach is developed for liquid–gas interfaces of weakly and strongly entangled polymer melts and implemented for linear polyethylene at 450 K. A combined particle and field-theoretic treatment is adopted based on aggressive coarse-graining, each polymer bead representing ∼50 carbon atoms, with effective bonded interactions extracted from atomistic simulations. Nonbonded interactions in the mesoscopic model are dictated by an equation of state (here the Sanchez–Lacombe) in conjunction with a variant of gradient theorythe discrete square gradient theory. The dynamics of free films is examined in the presence and in the absence of topological constraints (modeled by slip-springs) to unveil the impact of the latter on chain self-diffusion, to assess their contribution to the interfacial free energy, and to explore how this contribution can be removed by invoking a compensating potential. The molar mass dependence of surface tensionwhich arises from bonded contributions among beads in the mesoscopic chainsis extracted over a broad range of molar masses (103–106 g/mol), in excellent agreement with experiment. Two approaches for computing the surface tension are adopted, based on stress profiles and based on changes in free energy with interfacial area, leading to consistent results. The predicted density profiles, conformations, and orientational tendencies of the mesoscopic chains are retrieved from the simulations and shown to reproduce very well the corresponding results from atomistic simulations. An annealing scheme is developed with the purpose of accelerating transitions of metastable states into more stable biphasic states such as spherical and cylindrical droplets, free films, and spherical and cylindrical bubbles, which minimize the free energy of the periodic model system. Results for the phase diagram as a function of polymer volume fraction conform to the predictions of atomistic simulations of simpler systems.

No abstract