Non-linear adsorption modeling of fatty esters and oleic estolide esters via boundary lubrication coefficient of friction measurements

The frictional behaviors of a variety of fatty esters (methyl oleate (MO), methyl palmitate (MP), methyl laurate (ML), and 2-ethylhexyl oleate (EHO)) and oleic estolide esters (methyl oleic estolide ester (ME) and 2-ethylhexyl oleic estolide ester (EHE)) as additives in hexadecane have been examined in a boundary lubrication test regime using steel contacts. Critical additive concentrations were defined and used to perform novel and simple Langmuir analyses that provide an order of adsorption energies: EHE ≥ ME > EHO > MP > MO ≥ ML. Application of Langmuir, Temkin, and Frumkin-Fowler-Guggenheim (FFG) adsorption models via non-linear fitting demonstrates the necessary inclusion of cooperative effects in the applied model. Fits of the steady-state coefficient of friction (COF)-concentration data for EHE, ME, and EHO indicate slight cooperative adsorption. MO, MP, and ML data require larger attractive interaction terms (α ≤ -2.3) to be adequately fit. Primary adsorption energies calculated via a general adsorption model are necessarily decreased while total adsorption energies correlate well with values obtained via critical concentration analyses. To account for multiple surface-site coverage a multiple-site model was defined. The intuitive assumption of multiple-site coverage of more massive components suggests deceptively increased calculated adsorption energies for typically applied models (e.g. FFG, Langmuir).