Nanoscale Lubrication in Biosystems as Rationalized in Terms of Fractons and Spectral-Mechanical Properties of Networked Biopolymers in Ionic Solutions

Abstract

Articular cartilage is a natural tribochemical device just-designed by nature. Yet, a vivid debate goes on toward the mechanisms by which its nanoscopic viscoelastic properties facilitate lubrication in terms of ultralow static and kinetic friction coefficients. In this concisely conducted conceptual discussion, we wish to point out that a nanoscale tribomechanistic description based upon certain "viscoelastic quanta", called fractons, expressing spectral-mechanical properties of viscoelastic nets under the influence of force/pressure factor(s), may contribute substantially to the elucidation of ultralow coefficients of friction in the articular cartilage of predictable relaxational response. Our example unveils a part of a mechanically responsive viscoelastic network, such as a tied piece of hyaluronan molecule, fit in an Edwards type tube, in which upon water--mediated interaction of lipids with the hyaluronan when subjected to loading at the nanoscale, a consecutive stress-field and ion diffusion action is going to occur simultaneously. It results in a natural-logarithmic formula that interrelates a number of hyaluronan's interactive residues, N, with certain molecular-elastic (an exponent γ) and surface-to-volume (nano-colloid type) characteristics of around 2/3 to emerge near thermodynamic equilibrium, that is to say after a frictional loading action performed. It enables to relate uniquely a value of the exponent 0 < γ < 1/2 with a virtual tribomicellization scenario of the nanoscale friction--lubrication event accompanied by inevitable tubular-milieu viscosity alterations when the quasi-static friction scenario shows up, preferably with γ to 1/3 from above for large enough N–s. A periodic vibrational super-biopolymer's mode is exploited, leading to a change in the nanoscale friction-lubrication period from which an opportunity to involve an essential contribution to the (nanoscale) coefficient of friction arises.