Kinetics free-volume theories

However, because measurements are kinetically determined, this is a less accurate form of the equation. Very often it is observed that the measured shift factors, defined for different properties, are independent of the measured property. In addition, if for every polymer system, a different reference temperature is chosen, and ap is expressed as a function of T — rj, then ap turns out to be nearly universal for all polymers. Williams, Landel and Ferry believed that the universality of the shift factor was due to a dependence of relaxation rates on free volume. Although the relationship has no free volume basis, the constants and may be given significance in terms of free volume theory (Ratner, 1987). Measurements of shift factors have been carried out on crosslinked polymer electrolyte networks by measuring mechanical loss tangents (Cheradame and Le Nest, 1987). Fig. 6.3 shows values of log ap for... 

In reality, the data on isothermal contraction for many polymers6 treated according to the free-volume theory show that quantitatively the kinetics of the process does not correspond to the simplified model of a polymer with one average relaxation time. It is therefore necessary to consider the relaxation spectra and relaxation time distribution. Kastner72 made an attempt to link this distribution with the distribution of free-volume. Covacs6 concluded in this connection that, when considering the macroscopic properties of polymers (complex moduli, volume, etc.), the free-volume concept has to be coordinated with changes in molecular mobility and the different types of molecular motion. These processes include the broad distribution of the retardation times, which may be associated with the local distribution of the holes. 

There are three main groups of theories of the glass transition [28-30] (a) the free volume theory, (b) the kinetic theory, and (c) the thermodynamic theory. Although these three theories may at first appear to be different, they really examine three aspects of the same phenomenon and can be unified successfully, though only in a qualitative way. 

While the WLF equation is based on the free-volume theory of glass transition which is concerned with the introduction of free volume as a requirement for coordinated molecular motion, the equation also serves to introduce some kinetic aspects into the quantitative theory of glass transition. 

Several theories have been developed to describe glass transition, such as the thermodynamic theory [24, 25], free volume theory [26], or kinetic theory [27]. The former employs the lattice model to establish the partition function and the entropy of polymer can be calculated through this partition function. The latter takes the volume changes during the glass transition stage into account. 

The free-volume theory of the glass transition, as developed in Section 8.6.1, is concerned with the introduction of free volume as a requirement for coordinated molecular motion, leading to reptation.The WLF equation also serves to introduce some kinetic aspects. For example, if the time frame of an experiment is decreased by a factor of 10 near Tg, equations (8.47) and (8.48) indicate that the glass transition temperature should be raised by about 3°C ... 

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 kinetic based free volume theory starts with the Doolitle viscosity equation [6]... 

A crucial question for understanding a glass transition phenomenon relates to a cause of freezing molecular motion. There are three main groups of theoretical models dealing with the glass transitions kinetic theories, free-volume theories, and thermodynamic theories. 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

Diffusion Molecules of a fluid already inside a polymer at a high-concentration region compared with surrounding regions will diffuse over a finite time away from the high concentration until an equilibrium situation is achieved. If the high concentration is at the surface, diffusion occurs into the bulk. The diffusant molecules move stepwise into free volume holes as they form according to kinetic theory. 

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