Effect of chain stiffness on the entropic segregation of chain ends to the surface of a polymer melt

Abstract

Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension are examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, p , is comparable to the width of the surface profile, ξ, but still much smaller than the total contour length of the polymer, c. Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k B T per chain end, which results in the usual N −1 reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N n relative to the bulk. This provides a partial explanation for recent quantitative differences between experiments and SCFT calculations for flexible polymers.

Surface Segregation in Athermal Polymer Blends Due to Conformational Asymmetry

“…The effect originates from an entropic preference for chain ends at the surface, which, in turn, favors small molecules on account of the fact that they have more ends per unit volume of material. This has been well confirmed by simulations, − theory, − and experiments. , Nevertheless, the underlying reason for ends to favor the surface is not intuitive. Silberberg showed that for an incompressible melt of flexible polymers, a hard wall acts like a reflecting boundary, which implies that the distribution of chain ends should not be affected by the surface.…”

“…37,38 One can regard the w(r) in the present simulations as a mean-field approximation for the cohesive forces missing from our model. 13 The following simulations are all performed with ϕ bulk = 0.8, w s = 4d, and L 0 = 86d. Figure 8 displays a sample configuration for κ = 4k B T, with the stiff and flexible polymers shown in red and blue, respectively.…”

“…This is done by adjusting w ( z ) so that the total polymer concentration, ϕ s ( z ) + ϕ f ( z ), adopts the gradual profile corresponding to two surfaces of width w s located at z = 0 and z = L 0 . Here, we assume a sigmoidal shape for the surface profiles as obtained from detailed simulations that include the necessary cohesive attraction among the polymers required to produce a polymer/air surface. , One can regard the w ( r ) in the present simulations as a mean-field approximation for the cohesive forces missing from our model . The following simulations are all performed with ϕ bulk = 0.8, w s = 4 d , and L 0 = 86 d .…”

“…It is, in fact, deviations from the assumptions of the Silberberg argument, such as a finite width of the surface or a limited flexibility of the polymers, that cause the segregation. 11,13 Another entropic effect is that of conformational asymmetry. It was first noticed by Sikka et al 17,18 in experiments on a series of polyolefin diblock copolymers, where the two components were chemically similar but with considerably different statistical segment lengths.…”

“…Silberberg showed that for an incompressible melt of flexible polymers, a hard wall acts like a reflecting boundary, which implies that the distribution of chain ends should not be affected by the surface. It is, in fact, deviations from the assumptions of the Silberberg argument, such as a finite width of the surface or a limited flexibility of the polymers, that cause the segregation. , …”