Model Kerner-Nielsen

Using the Kerner-Nielsen model for expressing the effect of filler concentration on Young s modulus (85) ... 

In the case of micro-composites, specific filler smface area of common fillers is usually less than the value 10 m /g. In these systems, a very small portion of polymei- molecules is in direct interaction with the filler surface. Moreover, dimensions of polymer chains and volumes chai acteristic of microscopic relaxar tion modes are orders of magnitude smaller compared to the dimensions of filler particles (see Table 6.1). Thus, continuum mechanics approaches, such as micromechauical models can be successfully used for description of their mechanical behavior. The continuum mechanics model, well usable for prediction of the mechanical contribution (i) to the modulus of elasticity of polymer composites, is the simple Kerner-Nielsen (K-N) model [66] ... 

Theory. Basic theories for the prediction of the modulus of a composite from those of the components were derived by, for example, Hashin in 1955 (I), Kerner in 1956 (2), and van der Poel in 1958 (3). Takayanagi (4, 5), and Fujino et al. (6) developed a very promising and instructive model theory which includes calculation of the loss spectra of composites, and it may easily be extended to anisotropic morphologies. Furthermore, Nielsen and coworkers may be cited for fundamental theoretical and experimental contributions (7, 8, 9,10). 

Lewis-Nielsen or modified Kerner equation [17] is one of the most successful models ... 

Nielsen developed a model for thermal conductivity, based on the Kerner equations describing the modulus of two phase systems, that provides a different response that of the SOLBM [20]. Nielsen s model added to the consideration of the relative c nductivity of the two phases the effect of the maximum packing... 

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