Estimation of composites conductivity using a general mixing rule

It is proposed to use a mixing rule for the estimation of conductivity, σ, in ‘conductor–insulator’ composites (M–A) and composite solid electrolytes (MX–A). The mixing rule in its classical form σα=(1−f)·σMα+f·σAα (where f is the volume fraction of A; σM,A are conductivity of the phases M and A; −1<α<1) is applicable only for some specific morphology of the composite. This equation may be generalized by introducing the dependence α(f)=α1·(1−f)+α2·f in order to take variation of the morphology with f into account. For MX–A systems the general mixing rule has the form σα(f)=(1−f−fS)·σMXα(f)+fS·σSα(f)+f·σAα(f), where fS is the volume fraction of high-conducting interface regions estimated in terms of the brick-wall model; σS is the conductivity via the interface. The general mixing rules are rather simple, convenient, agree with effective medium models, qualitatively describe percolation effects and satisfactorily represent the experimental data in many composites.