Segregation of chain ends to the surface of a polymer melt: Effect of surface profile versus chain discreteness

Abstract

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.

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

“…Furthermore, it reproduces the simple inverse dependence on N n , first observed in the lattice SCFT of Hariharan et al [27]. In a previous study for monodisperse melts [33], we showed that the reduction in surface tension obeys…”

“…5(a) at ξ = 0, which is attributed solely to the discreteness of the chains, is a significant fraction of that for the finite widths typical of an air/polymer surface (i.e., ξ ∼ a [2,7,8]). This suggests that the importance of chain discreteness is comparable to the details of the surface profile [33], but we will demonstrate later that this is not so.…”

“…previously [33], this leads to unphysical surface profiles, particularly in the case of discrete chains. Naturally, the problem can be remedied by using a more realistic U [φ] from, for example, density functional theory [34,35], but that is beyond the scope of this paper.…”

“…The adjustment is done numerically using the Anderson-mixing [32] algorithm described in ref. [33]. Later on, we will discuss an analytical way of determining the equilibrium profile, after we derive the dependence of γ en on φ(z).…”

“…The first step is to evaluate the field w ∞ (z) and partition function G ∞ (z) for an infinitely long polymer, which turns out to be a relatively simple numerical calculation [33]. As we have shown previously [33], the excess concentration of finite chains of polymerization N in the field w ∞ (z) is…”