Calculations on the electric conductivity of a lyotropic mesophase with perforated lamellae

摘要

We calculate the electric conductivity of a system consisting of parallel layers of insulator, embedded into a uniform conductor. Each layer is perforated by holes, which are arranged on a twohyphen;dimensional hexagonal lattice. We investigate various stacking patterns of the layers, in volume fractions of 40percnt; to 50percnt;. The results are used to interpret conductivity measurements on the lamellar lyotropic mesophase. We find that on the basis of conductivity anisotropy, a layered structure of diskhyphen;shaped aggregates, and a structure of perforated layers are not readily distinguishable. The analysis of experimental data indicates that the amphiphile layers in a lamellar phase can be perforated to about 20percnt; of the area. Also, the interpretation of the conductivity data permits evaluation of the periodicity of the layered structure.