Theories for the glass transition

A complete theoretical understanding of the glass transition phenomenon is not yet available. The current theories can be divided into three groups free volume theories, kinetic theories and thermodynamic theories. 

The free volume theories state that the glass transition is characterized by an iso-free volume state, i.e. they consider that the glass temperature is the temperature at which the polymers have a certain universal free volume. The starting point of the theory is that the internal mobility of the system expressed as viscosity is related to the fractional free volume. This empirical relationship is referred to as the Doolittle equation. It is a consequence of the universal William-Landel-Ferry (WLF) equation and the Doolittle equation that the glass transition is indeed an iso-free volume state. The WLF equation, expressed in general terms, is  

The WLF equation was originally based purely on empirical observations. It can, however, be derived from free volume theory starting from the empirical Doolittle viscosity equation  

The kinetic theories are dealt with in section 5.3.2. According to these theories there is no true thermodynamic glass transition. The kinetic theories predict that the glass transition is a purely kinetic phenomenon and that it appears when the response time for the system to reach equilibrium is of the same size as the time-scale of the experiment. The theory predicts that a lowering of the cooling rate will lead to a decrease in the kinetic glass transition temperature. 

The Gibbs-DiMarzio theory is based on a lattice of coordination number 2 filled with polymer molecules ( J each with a degree of polymerization X, and holes (no). The intramolecular energy is given by xfAs, where / is the number of bonds in the high-energy state (state 2) and Ae = 2 is the 

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The only currently existing theory for the glass transition is the mode coupling theory (MCT) (see, e.g. [95, 96, 106]). MCT is an approach based on a rather microscopic description of the dynamics of density fluctuations and correlations among them. Although the theory was only formulated originally for simple (monatomic) fluids, it is believed to be of much wider applicability. In this review we will only briefly summarize the main basis and predictions of this theory, focusing on those that can be directly checked by NSE measurements. 

A Generalized Theory for the Glass Transition Temperature of Grosslinked and Uncrosshnked Polymers, Journal of Polymer Science, Part B Polym. Phys. 28 (1990), P. 1483 - 1498... 

Stutz H., Illers H., and Mertes J., A Generalized Theory for The Glass Transition Temperature of Crosslinked and Uncrosslinked Polymers , Journal of Polymer Science Part B Polymer Physic, Vol. 28 (1990), pp. 1483-1498. 

The segmental mobility can be related to the T -Tg difference using a theory of the glass transition. For example, if the reac-... 

As early as 1950 Fox and Fiery19 put forward the idea that the glass temperature corresponds to the iso-free-volume state. This hypothesis was developed by other authors20 21 and has won wide acceptance. It has been used with minor modifications as the basis for a number of sophisticated theories of the glass-transition... 

A theoretical derivation based on the Gibbs-Di Marzio (1958) theory of the glass transition leads to the conclusion that for the series of poly(alkyl methacrylates)... 

Major open questions where landscape-based ideas should prove helpful include the possible thermodynamic basis for the glass transition (Debenedetti et al., 1999), the relationship between kinetics and thermodynamics of deeply supercooled liquids and glasses (Adam and Gibbs, 1965 Wolynes, 1988), and translation-rotation decoupling and the breakdown of the Stokes-Einstein relationship in supercooled liquids (Fujara et al., 1992). In addition, the reformulation of the thermodynamics of hquids embodied in Eqs. (16), (52), (55), (56), (61), and (62) suggests that understanding basic topological features of a landscape s density-dependent statistics could lead to improved theories of simple and complex liquids. As explained in Section V, landscape statistics can be obtained from experiments, theory, and simulations. 

The entropy theory of the glass transition was developed by Gibbs and DiMarzio and by Adams and Gibbs to describe polymeric systems. By mixing the polymer links with holes or missing sites on a lattice to account for thermal expansion as in a lattice gas model, they could determine the entropy of mixing and the configurational entropy of the polymer. They found a second-order transition at a temperature They then pointed... 

The theories of the glass transition should account for observed effects below and above the main glass transition. 

Free-volume theories of the glass transition assume that, if conformational changes of the backbone are to take place, there must be space available for molecular segments to move into. The total amount of free space per unit volume of the polymer is called the fractional free volume Vf. As the temperature is lowered from a temperature well above Jg, the volume of the polymer falls because the molecules are able to rearrange locally to reduce the free volume. When the temperature approaches Tg the molecular motions become so slow (see e.g. fig. 5.27) that the molecules cannot rearrange within the time-scale of the experiment and the volume of the material then contracts like that of a solid, with a coefficient of expansion that is generally about half that observed above Tg. 

For these polymers the following equation for Tg (absolute) can be deduced from the free-volume theory of the glass transition (see section 7.5.3) ... 

Fletcher, S., V. J. Black, I. Kirkpatrick, and T. S. Varley. 2013. Quantum design of ionic liquids for extreme chemical inertness and a new theory of the glass transition. Journal of Solid State Electrochemistry lT.321-331. 

QUANTITATIVE EVALUATION OF THE GIBBS-DIMARZIO THEORY OF THE GLASS TRANSITION FOR POLYSTYRENE... 

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