Abstract

R.F. Boyer recognized the manifestations of a T > T_g transition-relaxation as early as 1963 and named it T_LL, the liquid-liquid transition. He suggested that it was due to the melting of “local order”, a controversial issue conflicting with the dominant theories at the time, led by P. Flory, which asserted a structure-less liquid state for melts. At the same time as this controversy unrolled, de Gennes published his reptation model of polymer physics which, after some modifications and ramifications, quickly became the new paradigm to describe the dynamic properties of polymer flow. The new model of reptation has no theoretical arguments to account for a T > T_g transition occurring in the melt; hence, the current consensus about the existence of T_LL is still what it was already in 1979, that it is probably an artifact only existing in the imagination of Boyer. In part I of this paper on the T_LL transition we mathematically derive the existence and the characteristics of T_LL from a dual-phase description of the free volume using a modification of the Vogel-Fulcher equation (VF), a well-known formulation of the temperature dependence of the viscosity of polymer melts. This new expression of the VF formula, that we call the TVF equation, permits to determine that T_LL is in an iso-free volume and iso-enthalpic state when M, the molecular weight, varies. The data analyzed by the TVF equation are the dynamic rheological results for a series of monodispersed, un-entangled polystyrene samples taken from the work of Majesté. The new analysis also permits to put in evidence the existence of a new transition, which we call M_mc, approximately located at M_mc ≈ M_c/10, where M_c is the molecular weight for entanglement. A Dual-Phase interpretation of M_mc is proposed.

摘要

RF Boyer早在 1963 年就认识到 T > T _g转变松弛的表现，并将其命名为 T _LL，即液-液转变。他认为这是由于“局部秩序”的熔化，这是一个有争议的问题，与当时由 P. Flory 领导的主流理论相冲突，该理论断言熔体是无结构的液态。在这场争论展开的同时，德热内斯发表了他的高分子物理学爬行模型，经过一些修改和衍生，迅速成为描述聚合物流动动态特性的新范式。新的蠕动模型没有理论论据来解释熔体中发生的 T > T _g转变；因此，目前关于 T 存在的共识_LL还是1979年的样子，大概是只存在于博耶想象中的神器。在本文中在T I的一部分_LL过渡我们数学推导的存在和T的特征_LL从自由体积的双相描述使用沃格尔-富尔彻方程（VF）的变形例，公知的制剂聚合物熔体粘度的温度依赖性。VF 公式的这个新表达式，我们称之为 TVF 方程，允许确定 T _LL当分子量 M 变化时，它处于等量自由体积和等焓状态。TVF 方程分析的数据是一系列单分散、未缠结的聚苯乙烯样品的动态流变结果，这些样品取自 Majesté 的工作。新的分析也证明了新跃迁的存在，我们称之为 M _mc，大约位于 M _mc ≈ M _c /10，其中 M _c是纠缠的分子量。提出了 M _mc的双相解释。