A Dual-Phase Approach to Reveal the Presence and the Impact of the TLL Transition in Polymers Melts. Part I: Predicting the Existence of Boyer's TLL Transition from the Vogel–Fulcher Equation. Issue 10 (8th September 2021) - Ibar, Jean Pierre
Abstract: R.F. Boyer recognized the manifestations of a T > Tg transition-relaxation as early as 1963 and named it TLL, 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 > Tg transition occurring in the melt; hence, the current consensus about the existence of TLL 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 TLL transition we mathematically derive the existence and the characteristics of TLL 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 TLL 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 Mmc, approximately located at Mmc ≈ Mc /10, where Mc is the molecular weight for entanglement. A Dual-Phase interpretation of Mmc is proposed.