For a compact binary composite material, thus with null porosity, we may consider the following correlation to predict (estimate) its density (ρ) after that of its components: 1/ρ ≈ g1·w1/ρ1 + g2·w2/ρ2; where g1 and g2 are empirical fitting coefficients to the available experimental data which can be taken as the unit (g1 = g2 = 1) if no such data is available; w1 and w2 stand for mass fractions of the filler and matrix (w1 + w2 = 1). It can be noticed that the electrical conductivity (σ) has SI units of siemens per meter (S/m); what makes those of its cube, σ3 (S3/m3) comparable to those of density (kg/m3). Hence, the following correlation seems dimensionally appealing: 1/σ ≈ [f1·w1/σ13 + f2·w2/σ23]1/3. Here f1 and f2 are empirical fitting coefficients to experimental conductivity (or resistivity) data, taken as the unit if such data is unknown (f1 = f2 = 1), while σ1 and σ2 stand for the electrical conductivity of the considered components. Hopefully, that may allow us to, rather roughly, estimate the electrical conductivity of the composite, taken as non porous and isotropic. Note that the proposed compositional-based empirical approach is deprived of thermodynamic support; while does not account for microstructural aspects ― such as the filler particles shape ― that should notoriously affect the composite conductivity. Percolation effects, which may lead to a sharp conductivity change at a narrow composition range, were also disregarded.
As for the glass transition temperature (Tg) ― generally speaking, it is not to be properly understood as a bulk property of the composite, being rather a property of its glass (or polymer) component(s).
We have done several works on fillers including nanoclay, nanometal and metal oxide particles and found the change is very small except for Ag-Cu where we found a tremendous increase in Tg. However, we have not studied electrical conductivity.
Dear Ningaraju Subramanya,
the answer to your question depends on the specific system you are looking at. if it is nonhomogeneous on atomic scale (mixture of the matrix and filler "particles"), then I believe, there is no fundamental answer and understanding and one uses only some phenomenological correlations.
If the system is atomically homogeneous, the answer still does not exist (I believe), but one could speculate :
1. Increase in Tg with filler content might signal better chemical bonding and more rigid structure. This would , on the other hand, suggest intuitively, a decrease of the electrical conductivity (better bonding, less various glassy defects leading to "defect conduction").
2. if , on the other hand, the filler introduces some mobile electrical charges through bonding to the matrix (ions, electrons, etc.), one could speculate that even the conductivity might increase with increasing filler content.
In order to answer properly, a careful electrical characterisation is called for here and the method you should use is the Electrical Impedance Spectroscopy. Some d.c. methods are here simply not good enough.
I hope that this will help you on the way.
With best regards
Petr
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