3-4 December 2020
Europe/Warsaw timezone

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

3 Dec 2020, 18:26




A concept of a biopolimer network immersed within an aqueous solution as addressed in terms of flexibility vs. mechanical stability criterion has been proposed. It is based on a transmission of correlated wave of (hydrogen) ions emerging from breaking in a massive way the hydrogen bonds between the biopolymers, such as hyaluronan, and their non-ideal aqueous solution’s surroundings.
Based on the argumentation presented in a paper by Reuveni et al. [1] it has been demonstrated that there exists a clear connection between the ln(N) (a natural logarithm of the biopolymer length N) and an inverse of a difference between two major contributions of this Landau-Peierls instability type paradigm. Providing that the so-called Alexander-Orbach conjecture for the oscillating biopolymeric system applies [2,3] one of the contributions is of mechanical nature, with an exponent g represented by 1/(2-3g) whereas the other appears to be a surface-to-volume characteristic exponent, attaining preferentially a value of ca. 2/3 for a three-dimensional adjacent (articulating) space.
It has been shown in a numerical way that for N of the order of milion(s) biopolymer’s residues, for example for hyaluronan equivalent to its molecular weight of 10^6-6x10^6 Daltons, a measure of the best viscoelastic efficiency for the hyaluronan, there exists an equality ln(N) = b/[1/(2-3g) – 2/3] that, for example, for N=10^6 gives the value of mechanical exponent g close to 1/3, yielding according to [3,4], an excellent passage of the (hydrogen) ions’ wave derived from a breakage of the adjacent hydrogen bonds in the biopolymer-solution system of interest, provided that the constant b, according to [1], can be taken at b=4.5. (In general, for the exponent g > 1/6 holds.) The first results seem to be promising when thoroughly rationalizing nanoscale friction-lubrication properties of biopolymer-solution articulating/confined subspaces exposed to very small nano-Newton loading conditions. For another thermomechanical scenario describing phase-transition and relaxation kinetics of a biopolymeric system, see [5].
[1] S. Reuveni et al. PRL 100, 208101 (2008).
[2] S. Alexander, R. Orbach J. Physique-LETTRES 43, L-625 (1982).
[3] A. Gadomski et al. Tribol. Lett. 30, 83 (2008).
[4] A. Gadomski et al. Mathematical Biosciences 244, 188 (2013) .
[5] A. Gadomski, J. Łuczka, Acta Phys. Pol. B 28, 1827 (1997); A. Gadomski et al. Europ. Phys. J. B 91, 237 (2018).

Email address: agad@utp.edu.pl (to whom the correspondence can be addressed).

Primary authors

Dr. Piotr Bełdowski (Institute of Mathematics and Physics, Faculty of Chemical Technology and Engineering, UTP University of Science and Technology, Bydgoszcz, Poland) ADAM GADOMSKI (UTP UNIVERSITY OF SCIENCE & TECHNOLOGY BYDGOSZCZ, POLAND)

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