Equivalence of chain conformations in the surface region of a polymer melt and a single Gaussian chain nder critical conditions

In the melt polymer conformations are nearly ideal according to Flory's ideality hypothesis. Silberberg generalized this statement for chains in the interfacial region. We check the Silberberg argument by analyzing the conformations of a probe chain end-grafted at a solid surface in a sea of floating free chains of concentration f by the self-consistent field (SCF) method. Apart from the grafting, probe chain and floating chains are identical. Most of the results were obtained for a standard SCF model with freely jointed chains on a six-choice lattice, where immediate step reversals are allowed. A few data were generated for a five-choice lattice, where such step reversals are forbidden. These coarse-grained models describe the equilibrium properties of flexible atactic polymer chains at the scale of the segment length. The concentration was varied over the whole range from f = 0 (single grafted chain) to f = 1 (probe chain in the melt). The number of contacts with the surface, average height of the free end and its dispersion, average loop and train length, tail size distribution, end-point and overall segment distributions were calculated for a grafted probe chain as a function of f, for several chain lengths and substrate/polymer interactions, which were varied from strong repulsion to strong adsorption. The computations show that the conformations of the probe chain in the melt do not depend on substrate/polymer interactions and are very similar to the conformations of a single end-grafted chain under critical conditions, and can thus be described analytically. When the substrate/polymer interaction is fixed at the value corresponding to critical conditions, all equilibrium properties of a probe chain are independent of f, over the whole range from a dilute solution to the melt. We believe that the conformations of all flexible chains in the surface region of the melt are close to those of an appropriate single chain in critical conditions, provided that one end of the single chain is fixed at the same point as a chain in the melt.