Dielectric response of shelled toroidal particles carrying localized surface charge distributions. The effect of concentric and confocal shells

• Dielectric spectra of shelled toroidal particles in the Laplace equation framework
• Influence of the choice of coordinate systems on the thickness of cell membranes
• Effect of a non-uniform thickness of the shell on the dielectric parameters of the cells

Dielectric models of biological cells are generally based on spherical or ellipsoidal geometries, where the different adjoining dielectric media are arranged as distinct core and shells, representing the cytosol and the cell membrane. For ellipsoidal particles, this approach implies the assumption of confocal shells that, in turn, means a cell membrane of ill-defined thickness. A quantitative analysis of the influence of a non-uniform thickness of the cell membrane has been not considered so far.In the case of a toroidal particle, this problem can be conveniently addressed by considering the solution of the Laplace equation in two different coordinate systems, i.e., toroidal coordinates (confocal shells and hence non-uniform thickness of the shell membrane) and toroidal polar coordinate, (concentric shells and hence a uniform thickness of the shell membrane).In the present paper, we compare the dielectric spectra of a toroidal particle aqueous suspension obtained from the two above stated solutions of the Laplace equation and we furnish a first quantitative estimate of the differences arising from considering the presence of confocal or concentric shells.This approach offers a complete view of the influence of the membrane thickness on the whole dielectric spectrum of a biological particle suspension, at least as far as toroidal objects are concerned.