Fluctuation free volume microvoid formation

The notion was developed earlier that the microhardness of glassy solids is defined by the fluctuation free volume microvoid formation (or collapse) work, ascribed to the microvoid volume unit [1]. Such an approach corresponds to the results in the present section since, as has been shown above, the fluctuation free volume is concentrated in the loosely packed matrix of polymer structure. The relative fraction of the fluctuation free volume can be estimated according to Equation 1.33. As was to be expected, the linear correlation between the values of and calculated according to Equations... 

The fluctuation free volume in crosslinking epoxy polymers has a fractal structure and the microvoids formed in the matrix are simulated by Df dimensional spheres. The size of a microvoid is considered as the volume that is necessary for its formation and is a consequence of the accumulation of thermal fluctuations. 

Simultaneously, the data of Figure 1.19 suppose a tight interconnection between the cluster model [13-15] and the fluctuation free volume theory [78, 79] separation of a segment from a cluster means formation of a free volume microvoid, whereas the addition of a segment to a cluster means its collapse . If it is correct, the entropy variation AS due to fluctuation free volume formation (Equation 1.27) must be equal to entropy change at partial decay of thermofluctuational clusters. The value of can be estimated within the frameworks of the Forsman theory [82] according to following relationship ... 

There are some problems of interest in the description of the free volume of polymers. As has already been mentioned, both fluctuation free volume and clusters have a thermofluctuational nature. It is obvious that the energy of thermal fluctuations can be expressed as kT (where k is Boltzmann s constant, T is temperature), while microvoid formation energy is equal to [80] ... 

Hence, the results stated above have shown that fluctuation free volume in epoxy polymers possesses fractal structure. Therefor a microvoid forming it should be simulated by D -dimensional sphere. The size of the microvoids is controlled by the volume which is necessary for accumulation of the thermal fluctuations enei y required for their formation. The absolute values of can serve as characteristic of polymer structure thermodynamic non-equilibrium and for quasi-equilibrium structures the value of coincides with the data obtained according to the William-Landel-Ferry equation. Microvoids of fluctuation free volume form fractal structure, which is a mirror of polymer structure [152-158]. 

Thns, the flnctnation free volume in a crosslinking epoxy polymer has a fractal structure and the microvoids, forming are simulated by Df dimensional sphere. The volume that is necessary for accnmulation of the thermal fluctuation energy, sufficient for its formation controls the size of a microvoid. 

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