On the nature of screening in charge-regulated macroion solutions

Author:

Kumari Sunita1ORCID,Podgornik Rudolf2345ORCID

Affiliation:

1. Department of Physics, Indian Institute of Technology 1 , Jodhpur 342037, India

2. School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences 2 , Beijing 100049, China

3. Wenzhou Institute, University of Chinese Academy of Sciences 3 , Wenzhou, Zhejiang 325000, China

4. CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences 4 , Beijing 100190, China

5. Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana 5 , 1000 Ljubljana, Slovenia

Abstract

We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the “uncertainty relation” of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler–Guggenheim–Frumkin model of charge regulation, we then analyze the “screening resonance” and the “overscreening” of the screening properties of the charge-regulated macroion solution.

Funder

National Natural Science Foundation of China

Publisher

AIP Publishing

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy

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