Entropic segregation of short polymers to the surface of a polydisperse melt

Abstract

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.

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

“…Chain stiffness penalizes the folding of polymer chains, which violates the Silberberg assumptions and thus could contribute to the entropic segregation. 21 Here, we extend the previous SCFT for entropic segregation and its effect on surface tension to semiflexible worm-like chains. 35 Still, our study focuses on relatively flexible polymers, where the persistence length, p , is comparable to the width of the surface, ξ, but still much smaller than the total contour length of the polymer, c .…”

“…Rather than dealing with the complication of a more realistic U[φ], [39][40][41] we take the alternative approach of adjusting w(z) in order to create a specified concentration profile. 9,10,21 We specifically choose the sigmoidal profile…”

“…The field is determined with the same Anderson mixing algorithm 44 used previously. 10,21 As usual, the SCFT is unaffected by an additive constant to the field, and so for convenience, we set w(z) = 0 in the bulk. With this choice, G(z, u z , s) → 1 as z → ∞, and thus, Eq.…”

“…7 It has been shown that the finite width of the surface profile generally provides the dominant contribution to the segregation. 21,22 Excluded-volume interactions will also affect the energy of folding a polymer configuration and could, therefore, contribute to entropic segregation. However, simulations 23 have shown that this effect is relatively minor, The Journal of Chemical Physics ARTICLE scitation.org/journal/jcp presumably because hard-core interactions are, to a good approximation, screened in polymer melts.…”

“…26,27 Nevertheless, the segregation has also been detected in polydisperse melts, 32 where it causes a shift in the molecularweight distribution towards smaller N n at the surface relative to the bulk, due to the fact that shorter polymers have more ends per unit volume. 21,23,[28][29][30][31] In this case, the experiments measured the shift in N n using MALDI time-of-flight spectrometry, which does not require any labeling. Although the shift was in qualitative agreement with SCFT, the effect was considerably stronger than predicted.…”