Description of non-regular membrane structures: a novel phenomenological approach

A new phenomenological approach to the analysis of complex membrane structures and surfaces and the processing of corresponding experimental data obtained, for example, from the roughness study is presented. The methodology is based on a postulate about the crucial information contained in non-regularities of measured spatial dynamic variables, as well as on the acceptance of a new scaling equation. Accordingly, power spectra and structural functions of different orders are determined by non-regularities of different types resulting from dynamical spikes and jumps of the measured variables. It is also shown that equations for power spectra as well as for structural functions are the same at every spatial–temporal level of the system under consideration. It is demonstrated that multi-parametric invariant relationships characterize a new kind of self-similarity. Appropriate phenomenological parameters are introduced. It is shown that these parameters characterize self-similarity in the rate of loss of correlation links between non-regularities of one type as well as self-similarity in the dynamics of memory loss in the dynamic variable, as the spatial distance from any fixed point increases, for non-regularities of a second type. An algorithm is developed which makes it possible to obtain as many parameters as it is necessary for the characterization of the dynamic state of a system and changes of its state during evolution. Application of this approach to the analysis of surface roughness of a perfluorinated cation-exchange membrane coated with platinum layer is demonstrated.