Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

It is investigated how figures of merits of nanocomposites are affected by structural and interaction length scales. Aside from macroscopic effects without characteristic lengths scales and atomic-scale quantum-mechanical interactions there are nanoscale interactions that reflect a competition between different energy contributions. We consider three systems, namely dielectric media, carbon-black reinforced rubbers and magnetic composites. In all cases, it is relatively easy to determine effective materials constants, which do not involve specific length scales. Nucleation and breakdown phenomena tend to occur on a nanoscale and yield a logarithmic dependence of figures of merit on the macroscopic system size. Essential system-specific differences arise because figures of merits are generally nonlinear energy integrals. Furthermore, different physical interactions yield different length scales. For example, the interaction in magnetic hardsoft composites reflects the competition between relativistic anisotropy and nonrelativistic exchange interactions, but such hierarchies of interactions are more difficult to establish in mechanical polymer composites and dielectrics.