Gibbs-DiMarzio approach

The Gibbs-DiMarzio approach, as has been stated, rests on the existence of a true second-order thermodynamic transition at a temperature T2 below the observed Tg. The pressure dependence of T2 can thus be obtained by the methods of equilibrium thermodynamics. For a first-order phase transition, the pressure dependence of the transition temperature is given by the Clapeyron equation... 

There are rival theories of the glass transition the Gibbs Dimarzio theory assumes that the configurational entropy of the chains approaches zero at Tg. Other researchers prefer a mode coupling theory (MCT), based on the dynamics of density fluctuations. However, it is difficult to extract a simple physical meaning from the complex equations that describe correlations between density fluctuations. Neither theory, at its current state of development, is particularly useful in understanding the properties of glassy polymers. 

Over the past 30 years a number of theories have been developed to account for the variation in the glass transition temperature (Tg) of polymeric materials as a function of molecular weight (MW). Three of the most notable of these approaches have included the straight line technique of Fox and Flory and the statistical mechanical theories of Gibbs and Gibbs-DiMarzio (G-DM). Because of the universal applicability claimed for the latter approach, the G-DM theory has received considerable attention. " ... 

Somcynsky model differs markedly from that used by Ferry and co-workers (WLF-type), or that which can be derived from the Gibbs-DiMarzio lattice model. The Simha-Somcynsky model results in values of h=f 0.07, while the WLF empiricism and the Gibbs-DiMarzio lattice model give values of the free-volume fraction of about 0.025, as mentioned previously. The discrepancy with the WLF approach may come from the arbitrary choice of a value of unity for parameter B in the Doolittle equation. 

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

A quite different approach is adopted in the statistical mechanical theory expounded by Gibbs and DiMarzio. They considered that the rotating unit could exist in two stable conformations (which might correspond to the trans and gauche conformers discussed earher), separated by a standard state energy difference, AE°, called the flex energy. Using the techniques of statistical thermodynamics, they calculated the partition of the units between these two forms. In theory, the... 

Angell and Moynihan have used the ideas of the quasilattice model of Gibbs and DiMarzio for the glassy state to define a characteristic temperature for transport phenomena. They and Easteal have applied this approach in the low-temperature region of inorganic melts as well as to ZnClg and its solutions with pyridinium chloride, a- and )ff-picolinium hydrochloride, and quinolinium hydrochloride. 

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