Abstract :
The effect of uniaxial and multiaxial mechanical
strain on the electrical conductivity of particle filled
polymer composites is investigated in the framework of
concentration-driven percolation. For composites consisting
of low aspect ratio, rigid conductive particles in a
compliant polymer matrix, a simple argument leads to the
conclusion that the effective volume fraction of conductive
particles (the ratio of total particle volume to the total
volume of the deformed composite) plays a dominant role,
with conductivity remaining isotropic despite the directional
bias of the strain state. As such, conductivity is
expected to exhibit classical power, law-dependence on
concentration, which in this case takes the form of a straindependent
effective volume fraction. Consideration of
deformation effects on particle agglomerates suggest,
however, that particle-to-particle network connections are
likely to be affected most significantly along directions
experiencing the most severe strains, introducing a directional
bias in network connectivity at a higher length scale.
To assess the importance of this possible directional bias,
random resistor network models are used to study the
conductivity of uniaxially strained composites. For conservative
assumptions on the severity of the bias in bond
probabilities, network conductivities exhibit approximately
isotropic, concentration-driven behavior for moderate
strains, supporting the predictive utility of the simple percolation
conduction-effective volume fraction approach.
Further corroboration is provided by experiments in the
literature on silicone-graphite composites subjected to
uniaxial compressive strain, where good agreement is
obtained through moderate strains for the theoretically
correct value of the conduction exponent in concentrationdriven
percolation
