Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains

Details Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains Bending rigidity of stiff polyelectrolyte chains: Single chain and a bundle of multichains

2002-08-23

arxiv.org/abs/cond-mat/0208466v2

Macromolecules Vol. 36, p9658 (2003)

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 2 figures

Scientific paper

10.1021/ma021226k

We study the bending rigidity of highly charged stiff polyelectrolytes, for both a single chain and many chains forming a bundle. A theory is developed to account for the interplay between competitive binding of counterions and charge correlations in softening the polyelectrolyte (PE) chains. The presence of even a small concentration of multivalent counterions leads to a dramatic reduction in the bending rigidity of the chains that are nominally stiffened by the repulsion between their backbone charges. The variation of the bending rigidity as a function of $f_{0}$, the fraction of charged monomers on the chain, does not exhibits simple scaling behavior; it grows with increasing $f_{0}$ below a critical value of $f_{0}$. Beyond the critical value, however, the chain becomes softer as $f_{0}$ increases. The bending rigidity also exhibits intriguing dependence on the concentration of multivalent counterion $n_{2}$; for highly charged PEs, the bending rigidity decreases as $n_2$ increases from zero, while it increases with increasing $n_{2}$ beyond a certain value of $n_{2}$. When polyelectrolyte chains form a $N$-loop condensate (e.g., a toroidal bundle formed by $N$ turns (winds) of the chain), the inter-loop coupling further softens the condensate, resulting in the bending free energy of the condensate that scales as $N$ for large $N$.

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