Polymer melt near a solid wall

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Abstract
We develop a theory for the equilibrium concentration profile formed by a compressible polymer melt near a solid wall (or the mathematically equivalent incompressible polymer solution near a solid wall). The theory uses a Landau–Ginzburg free energyfunctional with a concentration dependent square gradient coefficient and an additional local contribution characterizing the influence of the wall. We introduce a mean‐field algorithm for constructing the surface free energy contribution from the expression for the bulk free energy of lattice polymers. This algorithm automatically includes both energetic and entropic contributions with no adjustable parameters for lattice systems and can be applied for branched polymers as well. Approximate analytical solutions are provided for one‐phase polymer density profiles at neutral, repulsive, and attractive walls. The approximate solutions reflect the behavior of the numerical solutions and display (only at lower polymer densities) a near wall linear variation of the polymer density which crosses over to an exponential approach to the bulk concentration. The numerically evaluated profiles for both athermal and nonathermal melts compare well with available Monte Carlo simulation data for a neutral wall. Physical arguments are presented which anticipate the existence of deviations between theory and simulations at higher densities. The use of lattice cluster theoryfree energyfunctions enables us for the first time to investigate the dependence of the density profile on the polymer architecture.