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

A new phenomenological approach to the analysis of complex membrane structu res and surfaces and the processing of corresponding experimental data obta ined, for example, from the roughness study is presented. The methodology i s based on a postulate about the crucial information contained in non-regul arities of measured spatial dynamic variables, as well as on the acceptance of a new scaling equation. Accordingly, power spectra and structural funct ions of different orders are determined by non-regularities of different ty pes resulting from dynamical spikes and jumps of the measured variables. It is also shown that equations for power spectra as well as for structural f unctions are the same at every spatial-temporal level of the system under c onsideration. It is demonstrated that multi-parametric invariant relationsh ips characterize a new kind of self-similarity. Appropriate phenomenologica l parameters are introduced. It is shown that these parameters characterize self-similarity in the rate of loss of correlation links between non-regul arities of one type as well as self-similarity in the dynamics of memory lo ss in the dynamic variable, as the spatial distance from any fixed point in creases, for non-regularities of a second type. An algorithm is developed w hich 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 st ate during evolution. Application of this approach to the analysis of surfa ce roughness of a perfluorinated cation-exchange membrane coated with plati num layer is demonstrated. (C) 2000 Elsevier Science B.V. All rights reserv ed.