Microvoid formation energy

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] ... 

Since the value of / < 0.159 [120] and T < then it is apparent that in the case of glassy polymers energy of the thermal oscillations of order kT is not sufficient for microvoid formation kT < ej. The second problem requiring explanation and repeatedly discussed [48, 80, 147,148] is the absolute value of f, which within the frameworks of the kinetic theory is estimated according to Equation 1.33. The values 0.050-0.100 were obtained for different polymers [157], which is much more than the generally accepted value of = 0.025 0.003 for most polymers within the frameworks of the Williams, Landel and Ferry concept (WLF) [8, 145,146]. 

Figure 8.9 illustrates the TEM images of the PP/EPR blend with 20 wt% of EPR impacted by different energy (from 5 to 20 J). These images clearly exhibited the microfracture deformation through the formation of craze and voids, which was responsible for the brittle-ductile transition observed during mechanical deformation. The origin of the ductile fracture could be attributed to the relaxation of strain constraint by the microvoids in the craze. 

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. 

Now we shall consider the energetic criterion for formation of the microvoid with volume V. For this purpose the concept of solids free fracture was used [167], which postulates that it is possible to accumulate a restricted amount of potential energy with density Ain a restricted volume V, and it is necessary to carry out work equal to the product of surface area S on a specific surface energy to form a new surface. The limiting case of free fracture takes place at the condition [167] ... 

---