Mahmoudi P, Matsen M W
Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada.
Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada.
Eur Phys J E Soft Matter. 2017 Oct;40(10):85. doi: 10.1140/epje/i2017-11575-7. Epub 2017 Oct 6.
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 [Formula: see text]. Semi-analytical expressions for the excess concentration of short polymers, [Formula: see text], the integrated excess, [Formula: see text] , and the entropic effect on the surface tension, [Formula: see text], 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 [Formula: see text]. We illustrate how this can be used to derive a simple expression for the interfacial tension between immiscible A- and B-type polydisperse homopolymers.
已知链端对聚合物熔体表面具有熵偏好，这反过来又会导致多分散熔体中的短链偏析到表面。在此，我们使用自洽场理论（SCFT）研究短聚合物和长聚合物的双分散熔体的这种熵偏析。单个聚合物由通过统计长度为a的自由连接键连接的离散单体建模，并调整场以产生宽度为[公式：见正文]的指定表面轮廓。推导了短聚合物过量浓度[公式：见正文]、积分过量[公式：见正文]以及对表面张力的熵效应[公式：见正文]的半解析表达式，并与数值SCFT进行了对比测试。这些表达式对分子量分布具有通用依赖性，其系数取决于模型。一般来说，系数必须通过数值计算来评估，但一旦[公式：见正文]，它们就可以通过解析近似。我们说明了如何利用这一点来推导不相容的A类和B类多分散均聚物之间界面张力的简单表达式。
