Self-consistent field theory (SCFT) is used to examine the surface of an incompressible polymer melt of freely jointed chains, each consisting of N discrete monomers connected by bonds of an arbitrary potential. As a result of entropic considerations, the end monomers tend to accumulate in a narrow region next to the surface (on the monomer scale), which causes a slight depletion of ends further into the melt (on the molecular scale). Due to the reduced configurational entropy available to polymers in the vicinity of a surface, we find an entropic contribution to the surface tension that increases with the degree of polymerization, N. While many quantities are dependent on the precise bond potential connecting the monomers, the excess of ends at the surface in the limit of infinite N, the functional form of the long-range depletion of ends, and the N dependence of the surface tension turn out to be universal.

Abstract.Chain ends are known to have an entropic preference for the surface of a polymer melt, which in turn is expected to cause the short chains of a polydisperse melt to segregate to the surface. Here, we examine this entropic segregation for a bidisperse melt of short and long polymers, using self-consistent field theory (SCFT). The individual polymers are modeled by discrete monomers connected by freely-jointed bonds of statistical length a, and the field is adjusted so as to produce a specified surface profile of width ξ. Semi-analytical expressions for the excess concentration of short polymers, δφ s(z), the integrated excess, θ s, and the entropic effect on the surface tension, γen, are derived and tested against the numerical SCFT. The expressions exhibit universal dependences on the molecular-weight distribution with model-dependent coefficients. In general, the coefficients have to be evaluated numerically, but they can be approximated analytically once ξ a. We illustrate how this can be used to derive a simple expression for the interfacial tension between immiscible A-and B-type polydisperse homopolymers.

The preference for a shorter chain component at a polymer blend surface impacts surface properties key to application-specific performance. While such segregation is known for blends containing low molecular weight additives or systems with large polydispersity, it has not been reported for anionically polymerized polymers that are viewed, in practice, as monodisperse. Observations with surface layer matrix-assisted laser desorption ionization time-of-flight mass spectrometry (SL-MALDI-ToF-MS), which distinguishes surface species without labeling and provides the entire molecular weight distribution, demonstrate that entropically driven surface enrichment of shorter chains occurs even in low polydispersity materials. For 6 kDa polystyrene the number-average molecular weight (M n ) at the surface is ca. 300 Da (5%) lower than that in the bulk, and for 7 kDa poly­(methyl methacryalate) the shift is ca. 500 Da. These observations are in qualitative agreement with results from a mean-field theory that considers a homopolymer melt with a molecular-weight distribution matched to the experiments.

This study addresses entropic segregation effects at the surfaces of monodisperse and bidisperse melts. For the monodisperse melts, we focus on the segregation of chain ends to the surface, and for the bidisperse melts, we examine the segregation of short polymers to the surface. Universal shapes have been predicted for their concentration profiles, but the derivations rely on the mean-field approximation, which only treats the excluded-volume interactions in an approximate manner. To test whether or not the predictions hold up when the polymers are rigorously prevented from overlapping, we compare mean-field calculations with Monte Carlo simulations performed on the exact same model. Apart from a significant increase in the statistical segment length, the rigorous enforcement of excluded-volume interactions has a relatively small effect on the mean-field predictions. In particular, the universal profiles predicted by mean-field theory are found to be accurate.

Silberberg has argued that the surface of a polymer melt behaves like a reflecting boundary on the random-walk statistics of the polymers. Although this is approximately true, independent studies have shown that violations occur due to the finite width of the surface profile and to the discreteness of the polymer molecule, resulting in an excess of chain ends at the surface and a reduction in surface tension inversely proportional to the chain length, N . Using self-consistent field theory (SCFT), we compare the magnitude of these two effects by examining a melt of discrete polymers modeled as N monomers connected by Hookean springs of average length, a , next to a polymer surface of width [Formula: see text]. The effects of the surface width and the chain discreteness are found to be comparable for realistic profiles of [Formula: see text] ∼ a. A semi-analytical approximation is developed to help explain the behavior. The relative excess of ends at the surface is dependent on the details of the model, but in general it decreases for shorter polymers. The excess is balanced by a long-range depletion that has a universal shape independent of the molecular details. Furthermore, the approximation predicts that the reduction in surface energy equals one unit of kBT for every extra chain end at the surface.