首页|A Dual-Phase Approach to Reveal the Presence and the Impact of the T_(LL) Transition in Polymers Melts. Part I: Predicting the Existence of Boyer's T_(LL) Transition from the Vogel-Fulcher Equation
A Dual-Phase Approach to Reveal the Presence and the Impact of the T_(LL) Transition in Polymers Melts. Part I: Predicting the Existence of Boyer's T_(LL) Transition from the Vogel-Fulcher Equation
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NSTL
Taylor & Francis
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, unentangled 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 Mc is the molecular weight for entanglement. A Dual-Phase interpretation of M_(mc) is proposed.
NSTL
Taylor & Francis
