Search

The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination of Mc by the break in the log viscosity curve against log M unequivocally differentiates un-entangled melts from entangled melts. We use reliable rheological data on monodispersed polystyrene samples from very low molecular weight (M/Mc = 0.015) to relatively high molecular weight (M/Mc = 34) to test the separation of M and T in the expression of the viscosity; we reveal that an overall illusion of the validity of the separation of T and M is mathematically comprehensible, especially at high temperature and for M > 2Mc, but that, strictly speaking, the separation of M and T is not valid, except for certain periodic values of M equal to Mc, 2Mc, 4Mc, 8Mc, 16Mc, etc. (period doubling) organized around a "pole reference" value MR = 4Mc. We also reveal, for M < Mc, the existence of a lower molecular weight limit, M'c = Mc/8 for the onset of the macromolecular behavior (macro-coil). The discrete and periodic values of M that validate the separation of the effect of M and T on the viscosity generate the fragmentation of the molecular range into three rheological ranges. Likewise, we show that the effect of temperature is also fragmented into three rheological ranges for T > Tg: Tg < T< (Tg + 23°), (Tg + 23°) < T < TLL and T > TLL' where TLL is the liquid-liquid temperature. Our conclusion is that the classical formulation of the viscosity of polymer melts is so overly simplified that it is missing important experimental facts, such as period doubling for the separation of T and M, TLL, M'c, and Mc, resulting in its inability to understand the true nature of entanglements. We present in the discussion of the paper the alternative approach to the viscoelastic behavior, "the duality and cross-duality" of the Dual-conformers, showing how this model formalism was used to test mathematically and invalidate the separation of T and M in the classical formulation of viscosity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In Part I of these 2 parts article, we derived mathematically the existence of a unique state for polymeric melts, occurring at a specific temperature above Tg, which we recognized to be the liquid–liquid transition, TLL, observed and described by Boyer and others. TLL is the temperature at which the melt is in an iso-free-volume and iso-enthalpic state independent of the molecular weight. It is a fundamental property of the material. The purpose of part II is to examine and explain the following: 1) the elusive character of TLL (at the origin of the controversy about the existence of TLL in the past), 2) the increase of free volume at TLL, and 3) the endothermal change of heat capacity on heating across TLL. Finally, our objective is to provide an explanation of TLL and emphasize its importance as an example of a self-dissipative dynamic process that converts, at TLL, into a classical thermally activated process. In this article, the experimental evidence found in the literature for TLL is critically examined to point out the often biased reviews offered by the antagonistic authors of a controversy, here the pros and cons TLL. We propose a Dual-Phase origin of the interactions in polymers to explain the weak and elusive manifestations of TLL and show, by DSC, that the TLL manifestations are made much more visible and prominent when the samples' state has been brought out of equilibrium. We analyze, in detail, the thermally activated depolarization of samples which have been submitted to a polarization stage by a voltage field. The experimental technique of thermal stimulated depolarization (TSD), and its sister derivative the thermal windowing deconvolution (TWD), are unique and powerful analytical tools that can experimentally characterize "interactive coupling", the factor that we have assumed is quantitatively responsible for the behavior of polymers and in particular of TLL. The existence and the characteristics of TLL were understood and predicted in Part I from rheological results by the use of the Thermo–Vogel–Fulcher equation whose thermo-kinetic terms, ΔH, ΔS, and T∞, could be interpreted by the interactive coupling of the local free volume and the rotational isomeric conformational state of dual-conformers belonging to the macromolecules, themselves embedded in a collective dissipative system of interactions. The statistics controlling the interactive coupling parameters was described by the Dual-Phase and Cross-Dual-Phase models. In Part II, the same models are used to explain the interactive coupling manifestations specific to the TSD and TWD results. We show that certain characteristics of the TSD and TWD results are directly related to specific parameters of the Dual-Phase model. It is the case for the transitions visible by TSD, such as Tg,ρ related to space charges and local free volume (F-conformers), and TLL marking the end of the specific impact of the Dual-Phase statistics on the properties. It is also the case when interactive coupling is analyzed by TWD: the compensation of the enthalpy and entropy of activation of the relaxations taking place at various polarization temperatures only occurs below TLL, permitting its specific determination. We conclude pointing out the perhaps crucial importance of TLL in establishing the distinct role of thermal energy in structuring or modulating the dynamics of the interactions. The Dual-Phase view of the interactions in polymers suggests that the local density difference between the b-grains and the F-conformers is "time-averaged" by the constant wiping (above Tg) of an "elastic dissipative wave" having a frequency, ωo, i.e., a function of temperature and molecular weight, and thus is different from the Brownian dissipation, i.e., the thermal fluctuation characteristic of the Boltzmann's mean field (the classical kT/h term). The elastic dissipative wave kinetically loses its collective modulation role and becomes the thermal wave at TLL. [ABSTRACT FROM AUTHOR]