Amorphous stress fluctuation

Recently we have also developed a stress-fluctuation-based formalism to evaluate local elastic constants from molecular simulations. One of the assumptions implicit in continuum-level models of a pure material is that the moduh of elasticity are homogeneous throughout the system. This might not be the case, however, in glassy, amorphous polymeric systems. Figure 7 shows a cross section of a nanoscopic polymeric structure. The density distribution is shown on the left density fluctuations are relatively small (a few percent) and are distribut-... 

In the amorphous pattern we observe a spatial fluctuation of density as well as different repulsive and attractive forces. Describing the amorphous structure with (n — m)/n = x and using the 6—12-potential of Eq. (5) we obtain an internal shearing stress... 

The discussion so far assumed that the superimposed uniaxial anisotropy is perfectly uniform. This is rather the exception than the rule in reality, mostly due to internal stresses and/or surface defects. The typical fluctuation wavelengths are much larger than Zex and range from a few to about 100 pm. Such Ku fluctuations ultimately provide the limiting factor for the soft magnetic properties in amorphous and optimized crystalline (conventional or nanocrystalline) alloys. 

In a polymeric sohd conditions are more complex. There are both in-termolecular van der Waals forces and intramolecular covalent forces and, furthermore, the microscopic structure is amorphous or only partially crystalline. Microscopic fracture mechanisms are, therefore, more involved and also include chain slippage and chain scission. The latter process can occur in fully extended sequences that are anchored with their ends in crystallites or immobile entanglements, by a combined effect of mechanical stress and thermal fluctuations. Even if the situation is complicated, based on some rough knowledge of the bond energies and intermolecular forces one can still obtain some estimate of the theoretical limits of strength. Comparing it to measured... 

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