Issue
J. Phys. II France
Volume 7, Number 6, June 1997
Page(s) 887 - 902
DOI https://doi.org/10.1051/jp2:1997160
DOI: 10.1051/jp2:1997160
J. Phys. II France 7 (1997) 887-902

Persistence Length of Intrinsically Stiff Polyampholyte Chains

B.-Y. Ha and D. Thirumalai

Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA

(Received 16 October 1996, revised 3 February 1997, accepted 28 February 1997)

Abstract
We calculate the contribution, $l_{\rm PA}$, to the persistence length arising from charge fluctuations of an intrinsically stiff polyampholyte (PA) chain. The interaction between charges along the PA backbone is taken to be given by the Debye-Hückel potential. When the charges along the chain are uncorrelated the contribution to $l_{\rm PA}$ comes from two sources. One of them is due to the overall charge on the PA chain for which the contribution to $l_{\rm PA} \varpropto \kappa^{-2}$ where $\kappa^{-1}$ is the Debye screening length. Surprisingly the contribution to $l_{\rm PA}$ from charge fluctuations $(\delta \sigma)^2$, namely due to the polyampholyte effect, is proportional to $-(\delta \sigma)^4 \kappa^{-1}$ so that there is a reduction in the total persistence length when PA chain is overall neutral. We also show that the shape of a PA chain is cylindrical with length $l_{\rm p} = l_{\rm0} + l_{\rm PA}$ with $l_{\rm0}$ being the bare persistence length. The diameter of an overall neutral chain can become of the order of a monomer size which is considerably smaller than that of the corresponding polyelectrolyte. As a consequence, we argue that the interaction between two neutral stiff polyampholyte chains is attractive. The implication of the effective attractive interaction is that a dilute dispersion of neutral polyampholyte PA chains would phase separate into dense (with possible nematic order) and a rare phase. When correlations between the charges are included one gets a polyelectrolyte like behavior with $l_{\rm PA} \varpropto \kappa^{-2}$ even when the chain is neutral. If the range of correlation, $\lambda$, is large compared to the screening length (usually difficult to obtain in experiments) there is a large negative contribution to $l_{\rm PA}$ which scales as $l_{\rm PA}\varpropto -(\delta \sigma)^4\lambda/\kappa^2$ where $l_{\rm B}$ is the Bjerrum length.



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