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The translational friction of toroids
Author(s) -
Allison Stuart A.,
Easterly Russell A.,
Teller David C.
Publication year - 1980
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.1980.360190805
Subject(s) - toroid , chemistry , expression (computer science) , plane (geometry) , viscosity , mechanics , shell (structure) , ring (chemistry) , settling , limit (mathematics) , tensor (intrinsic definition) , yield (engineering) , thermodynamics , physics , mathematical analysis , materials science , geometry , mathematics , composite material , quantum mechanics , plasma , programming language , organic chemistry , computer science
An approximate analytic expression for the translational friction coefficient of a toroid modeled as a continuous shell of frictional elements is derived using the Kirkwood approximation. The accuracy of this expression was determined by comparing the friction coefficients predicted by it to those predicted by extrapolated shell‐model calculations using the modified Oseen tensor. To show that these calculations do indeed yield the correct friction coefficients, actual translational friction coefficients were determined by observing settling rates of macroscopic model rings or toroids in a high‐viscosity silicone fluid. Our conclusion is that the approximate expression yields friction coefficients that are about 1.5–3% low for finite rings. For thin rings, a comparison is also made with the exact result of Yamakawa and Yamaki [ J. Chem. Phys. 57 , 1572 (1972); 58 , 2049 (1973)] for the translational friction of plane polygonal rings. This comparison shows that the approximate expression yields results which are low by 2–3% unless the rings are extremely thin, in which case the error is larger. In the limit of an infinitely thin ring the approximate expression reduces to the Kirkwood result [ J. Polym. Sci. 12 , 1 (1954)], which is low by 8.3%. We discuss briefly how this work may be useful in determining the structure of DNA compacted by various solvent–electrolyte systems and polyamines.