Free volume models relaxation kinetics

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. 

Kinetic models of physical aging are available in the literature (Kovacs et al., 1979). During this process, volume changes are very low, typically less than 1 m3 kg but they affect a component of free volume that plays a crucial role in creep, relaxation, yielding and fracture (see Chapter 12). 

An alternative explanation of the VFT model (28) is based on the free volume concept introduced by Fox and Floury [66-68] to describe the relaxation kinetics of polystyrene. The main idea behind this approach is that the probability of movement of a polymer molecule segment is related to the free volume availability in a system. Later, Doolittle [69] and Turnbull and Cohen [70] applied the concept of free volume to a wider class of disordered solids. They suggested a similar relationship... 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

For better understanding the diverse relaxation behavior of confined polymers, researchers have utilized models or simulation tools to capture the kinetic features of the material at the molecular level, aiming to represent the results observed in experiments. The FVHD model, which has been widely employed in characterizing physical aging in bulk polymers, is reformulated to describe the relaxation behavior of polymers under nanoconfinement. A dual mechanism combines the effect of vacancy diffusion and lattice contraction, and was recently applied with time-dependent internal length scales to characterize the free volume reduction in the aging process [169]. The dual mechanism model (DMM) fits the data of thin film permeability fairly well. The potential predictive capability of the DMM model depends on the accuracy of the relationship between the internal length and time scale on the description of complex material dynamics [161]. 

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