Modeling Physical Aging Behavior

This time-dependent behavior v ould be expected based on the model that as the network chains lose mobility during the aging process (due to the decrease in free volume), the ability to dissipate stress is reduced. The decrease in stress relaxation rate can therefore be explained on the basis of free volume collapse during physical aging. 

The C-F model has been extensively used to compare the aging behavior of polymer blends to that of the corresponding homopolymers, because of its simplicity. However, it should be noted that this model does not adequately describe all of the phenomenology associated with the glass transition, namely, its nonlinear character. The consequences of this when describing the physical aging process have been recently discussed in the literature (Li and Simon 2006 Hutchinson and Kumar 2002). 

The first comprehensive study of physical aging in a miscible blend system using enthalpy relaxation was reported by Cowie and Ferguson (1989) who followed the enthalpic relaxatirm in a series of blends of PS and poly(vinyl methyl ether), PVME. ComparisOTi of the blend behavior with that of the two components by analyzing the data oti the basis of both the P-M and C-F models led to the conclusions that the blends aged more slowly than PVME when aging was carried... 

The polymers physical aging represents itself the structure and properties change in time and is the reflection of the indicated materials thermodynamically nonequilibriiun nature [61, 62], As a rule, the physical aging results to polymer materials brittleness enhancement and therefore, the ability of structural characteristics in due course prediction is important for the period of estimation of pol5mier products safe exploitation. For cross-linked polymers the quantitative estimation of structure and properties changes in physical aging process was conducted in Refs. [63, 64] within the frameworks of fracture analysis [65] and cluster model of polymers amorphous state structure [7, 66]. The authors of Ref. [67] use the indicated theoretical models for the description of PC physical aging. Besides, for PC behavior closer definition in the indicated process such theoretical notions were drawn as structure quasiequilibrium state [68] and the thermal cluster model [69], which is one from variants of percolation theory. 

Service lifetime prediction of polymers and/or polymer based materials may be undertaken from different types of tests, such as creep behavior tests (linear and non-linear creep, physical aging, time-dependent plasticity), fatigue behavior tests (stress transfer and normalized life prediction models, empirical fatigue theories, fracture mechanics theory and strength degradation) and standard accelerated aging tests (chemical resistance, thermal stability, liquid absorption) [32]. 

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]. 

While several models have been proposed to describe accelerated aging in thin polymer films, including the diffusion of free volume and thickness-dependent lattice contraction, efforts to more fully understand the mechanisms responsible for this behavior are ongoing. Physical aging models are typically characterized by a relaxation time, which represents chain mobility, and a measure of the current deviation from the predicted equilibrium, which represents the driving force. Models commonly used to describe physical aging, or isothermal relaxation, have foundations in work by Tool, Kovacs and others. These models typically follow the form ... 

Most models developed to describe the physical aging process are based on the idea of free volume in the polymer. Some only attempt to model the observed behavior, while others take a more holistic approach and try to understand the relationship between the molecular relaxation events and the distribution of free volume in the sample. 

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