The low-temperature dynamics of ultraviscous liquids hold the key to understanding the nature of glass transition and relaxation phenomena, including the potential existence of an ideal thermodynamic glass transition. Unfortunately, existing viscosity models, such as the Vogel–Fulcher–Tammann (VFT) and Avramov–Milchev (AM) equations, exhibit systematic error when extrapolating to low temperatures. We present a model offering an improved description of the viscosity–temperature relationship for both inorganic and organic liquids using the same number of parameters as VFT and AM. The model has a clear physical foundation based on the temperature dependence of configurational entropy, and it offers an accurate prediction of low-temperature isokoms without any singularity at finite temperature. Our results cast doubt on the existence of a Kauzmann entropy catastrophe and associated ideal glass transition.

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Viscosity of glass-forming liquids.

The rheological behavior of polymer blends is compared with that reported for emulsions, block polymers and homologous polymer blends. It has been shown that the properties of polymer alloys frequently differ from those of these “model” systems—the principal difference being the lowering of at least one rheological function below the value predicted In the log-additivity rule. Primarily, the most recent (post 1977) results are reviewed. The data obtained by the authors on the flow of poly(ethylene terephthalate)/Polyamide-6,6 are discussed in detail.

Melt rheology of polymer blends

The production of polymer blends increases at a rate of about 13 percent/y. Most of the commercial blends are multiphase systems of complex morphology, determined by the thermodynamic properties of the components and the rheology. Since the diffusion rates are relatively low, the blends are seldom at equilibrium. In most cases, the blend products have properties imposed by the morphology, created by a particular combination of the thermal and deformational history. There are three main reasons for studying the melt flow of blends: optimization of the processing conditions, search for the appropriate means to generate the desired morphology, and the interest in the basic study of the rheology of these complex systems.



In this paper the results published during the last five years are reviewed. The data for polymer blends are compared with those obtained for simpler model systems: liquid mixtures, emulsions, and polymer blends. From the rheological point of view, the blends are divided into three groups: those where viscosity shows positive deviation from the log-additivity rule, PDB, those where the opposite effect is observed, NDB, and the remaining mixed-behavior systems, PNDB. To PDB belong the miscible blends and those with strong inter-domain interactions. To NDB belong those where the interactions are weak. To PNDB belong the blends in which there is a concentration-dependent transition of structure. The shear dependent properties of blends are also discussed.

Melt flow of polymer blends

As one of the most important properties of glass-forming liquids, viscosity has drawn significant attention in both glass manufacturing and fundamental research. We review the recent scientific progress in viscosity of glass-forming systems, including both the liquid and glassy states. After the Vogel-Fulcher-Tammann (VFT) equation was introduced, many more efforts have been made to develop more accurate models to describe the temperature dependence of viscosity. In addition to the VFT equation, we also discuss three other viscosity models, viz., the Adam-Gibbs, Avramov-Milchev, and Mauro-Yue-Ellison-Gupta-Allan models. We compare the four viscosity models in terms of their theoretical underpinnings and ability to fit measured viscosity curves. The concept of fragility and the universality of the high-temperature viscosity limit are also discussed. Temperature-dependent constraint theory is introduced in detail as a powerful tool for predicting the composition dependence of viscosity. Some examples of the application of this approach to predict the glass transition temperature and fragility of various glass systems are shown. Topological constraint theory is not only of scientific interest, but also has important industrial applicability. We also discuss the thermal history dependence of viscosity in the glassy state. Some phenomenological models are briefly reviewed, while the main focus is given to the modified Mauro-Allan-Potuzak model, which can accurately predict the nonequilibrium viscosity as a function of temperature, thermal history, and composition. The correlation of viscosity with elasticity is described in terms of the shoving model. Some theoretical implications of the various viscosity models are discussed, including the concepts of the Kauzmann paradox and the ideal glass transition. Some of the evidence against the existence of these phenomena are discussed. We also review the link between glass relaxation and viscosity, that is, emphasizing that the viscosity equations presented in this review can also be used to model different types of relaxation effects based on the Maxwell relation.

Viscosity of glass-forming systems

The liquid state behavior of the following atactic polymers has been reviewed: the alkyl and cycloalkyl methacrylates; polyisobutylene; polybutadiene, its random copolymers with styrene and acrylonitrile, and S-B diblocks; polystyrene; and the poly-α-olefins C3, C5, and C6. Just as Tg manifests itself through time-dependent (relaxational) and thermodynamic (transition) effects, so also does a T Tg or Tβ relaxation. With increasing syndiotactic content, PMMA's reveal strengthening Tβ and Tl processes. Relaxation maps plotting log frequency-T−1 are presented for PBD and PIB, showing both Tg and Tl. The latter exhibits non-Arrhenius behavior with an activation enthalpy about half that at T...

Dynamics and thermodynamics of the liquid state (T < Tg) of amorphous polymers

Least squares programs were used to evaluate the correlation between recent experimental results and theoretical, semi-theoretical, or empirical relations between liquid viscosity and temperature. It was found that none of these describes the experimental dependence in the whole range of temperature. A new dependence based on the free volume concept and cell-hole liquid theory is proposed. The theory permits linearization of the viscosity-temperature data in the range (Ti, Ti+1), where the Ti's are the liquid-liquid transition temperatures. It was demonstrated that these transitions, both in small molecular and in polymeric liquids, occur in discrete steps: Ti = aiTg, where Tg is the glass transition temperature and the ai's are numerical parameters. Not all the transitions Ti were apparent in all liquids. Transition T2 = 1.26Tg was observed for most polymeric liquids. On the basis of thermal analysis it was demonstrated that the Ti's coincide with the temperatures at which small changes in the a...

L. A. Utracki

Papers

Temperature dependence of liquid viscosity