Equivalent-circuit model of lubricants

An equivalent-circuit model describing the impedance response of a typical lubricant has to take into account processes divided spatially into bulk lubricant and interfacial electrochemical (adsorption, mass transport, and charge transfer) zones [6]. Separation between these two zones can be achieved following the distributed impedance analysis in Section 6-3. The bulk resistance BULK represents a lossy part of the overall bulk-media relaxation mechanism [3,4], always existing in parallel with a bulk-media capacitance as  

The interfacial zone consists of adsorption, diffusion, and charge-transfer processes of oil additives and contaminants. A linear EIS [6] and NLEIS analysis [7] have led to a refinement of this model, taking into consideration the best fit of kinetic parameters to both nonlinear and fundamental-frequency experimental impedance data. The low-frequency impedance data are modeled as a combination of a CPE representing double-layer charging processes, adsorption (Z pj), diffusion (Zp, ), and charge-transfer resistance (R ) impedance segments. 

Adsorption impedance Z may be represented by a parallel combination of resistance R and CPE p, which represents pseudocapadtance created by charge accumulation at the electrode surface. The adsorbed spedes become involved in complex surface-mediated kinetics, such as temperature-driven complexation of the surface-active oil additives [7]. The experimental and modeled data confirmed the presence of two facile adsorption-driven processes—adsorption of at least two different groups of surface-active oil additives (likely to be detergents and antwear agents), and their mutual complexation. 

In the best-fit model, the low-frequency portion of the impedance was represented by a series of complex adsorption and finite transmission boundary diffusion, placed in parallel with the charge transfer and the double layer CPE, 

Mortier, S. T. Orszulik, Chemistry and technology of lubricants, Blackie Academic Professional, London, 1992. 

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