42

Ha Noi Metroplolitan University

THE PHENOMENA OF CHARGE INVERSION

AND EFFECTIVE ATTRACTION BETWEEN

THE SPHERICAL MACROMOLECULES IN ELECTROLYTE SOLVENT

Nguyen Vu Nhan1, Nguyen Viet Duc2, Toan T. Nguyen2

1

Hanoi Metropolitan University

2

Key Laboratory for Multiscale Simulation of Complex Systems,

VNU University of Science, Vietnam National University

Abstract: The phenomena of charge inversion and effective attraction between the like charged spherical macromolecules in electrolyte solvent has been studied by using

Poisson - Boltzmann mean-field theory, alongside the assumption that counterions

condense on the surface of macromolecules to form a strongly correlation liquid. This

oversimplified model is able to capture many important features of these phenomena,

provide essential understanding of electrostatics in strong interaction regime in

biological and soft matter systems.

Keywords: Charge inversion, like-charged attraction, polyelectrolyte solution, Poisson Boltzmann equation, biological macromolecule.

Email: nvnhan@hnmu.edu.vn

Received 16 October 2019

Accepted for publication 15 November 2019

1. INTRODUCTION

In recent years, the there are many researches on physical properties of biological and

soft maters macro-molecules, such as colloidal particles, vesicles, micelles, proteins,

DNA… Insightly knowledge about structure and also interaction of biological molecules is

essential to understand biological processes [1]. Most of these systems function in aqueous

solution in the presence of many electrolytes such as NaCl, MgCl2… Standard theoretical

and computational approaches to understand the electrostatics of these system has been

mostly based on the Poisson-Boltzmann self-consistence mean field theory [2]. Since this

is a mean field theory, its validity is limited to electrolyte solution with weak electrostatic

interaction. When the counterion concentration in the solution is too large, or the solution

contain highly valent ions, there are effects that the mean field theory cannot explain, such

43

Scientific Journal No35/2019

as the effect of the inversion of charges, the like - charge attraction between

macromolecules... [3]. Strongly correlated liquid theory and similar theories have been

employed to investigate electrostatics in these systems [3,4]. In many cases, one can

understand the essential physics by separating the mobile ions into two populations, a

condensed counterion population on the surface of macroions which can be treated in the

strong interaction limit, and a diffuse counterion population further away into the aqueous

solution which can be treated using conventional weak interaction electrostatic theories [3].

In this paper, we gave a brief overview of these approaches and applying it to calculate the

attraction among spherical macroions in electrolyte solution. Our results can contribute to

understand electrostatics in microemulsion systems, protein solutions, or other soft matter

and biological systems with charged macromolecules.

2. BRIEF REVIEW ON POISSON-BOLTZMANN MEAN FIELD THEORY

Consider the Poisson equation of electrostatics:

(1)

in which,

is the electric charge density, and

is electric field,

and

are dielectric

constant of air and relative dielectric constant of medium (water in our case) equivalently.

The latter is related to the electrostatic potential by the formula:

(2)

In electrolyte solution containing ions with valence Z+ and Z-, the electric charge

density can be written in the following form:

Ha Noi Metroplolitan University

THE PHENOMENA OF CHARGE INVERSION

AND EFFECTIVE ATTRACTION BETWEEN

THE SPHERICAL MACROMOLECULES IN ELECTROLYTE SOLVENT

Nguyen Vu Nhan1, Nguyen Viet Duc2, Toan T. Nguyen2

1

Hanoi Metropolitan University

2

Key Laboratory for Multiscale Simulation of Complex Systems,

VNU University of Science, Vietnam National University

Abstract: The phenomena of charge inversion and effective attraction between the like charged spherical macromolecules in electrolyte solvent has been studied by using

Poisson - Boltzmann mean-field theory, alongside the assumption that counterions

condense on the surface of macromolecules to form a strongly correlation liquid. This

oversimplified model is able to capture many important features of these phenomena,

provide essential understanding of electrostatics in strong interaction regime in

biological and soft matter systems.

Keywords: Charge inversion, like-charged attraction, polyelectrolyte solution, Poisson Boltzmann equation, biological macromolecule.

Email: nvnhan@hnmu.edu.vn

Received 16 October 2019

Accepted for publication 15 November 2019

1. INTRODUCTION

In recent years, the there are many researches on physical properties of biological and

soft maters macro-molecules, such as colloidal particles, vesicles, micelles, proteins,

DNA… Insightly knowledge about structure and also interaction of biological molecules is

essential to understand biological processes [1]. Most of these systems function in aqueous

solution in the presence of many electrolytes such as NaCl, MgCl2… Standard theoretical

and computational approaches to understand the electrostatics of these system has been

mostly based on the Poisson-Boltzmann self-consistence mean field theory [2]. Since this

is a mean field theory, its validity is limited to electrolyte solution with weak electrostatic

interaction. When the counterion concentration in the solution is too large, or the solution

contain highly valent ions, there are effects that the mean field theory cannot explain, such

43

Scientific Journal No35/2019

as the effect of the inversion of charges, the like - charge attraction between

macromolecules... [3]. Strongly correlated liquid theory and similar theories have been

employed to investigate electrostatics in these systems [3,4]. In many cases, one can

understand the essential physics by separating the mobile ions into two populations, a

condensed counterion population on the surface of macroions which can be treated in the

strong interaction limit, and a diffuse counterion population further away into the aqueous

solution which can be treated using conventional weak interaction electrostatic theories [3].

In this paper, we gave a brief overview of these approaches and applying it to calculate the

attraction among spherical macroions in electrolyte solution. Our results can contribute to

understand electrostatics in microemulsion systems, protein solutions, or other soft matter

and biological systems with charged macromolecules.

2. BRIEF REVIEW ON POISSON-BOLTZMANN MEAN FIELD THEORY

Consider the Poisson equation of electrostatics:

(1)

in which,

is the electric charge density, and

is electric field,

and

are dielectric

constant of air and relative dielectric constant of medium (water in our case) equivalently.

The latter is related to the electrostatic potential by the formula:

(2)

In electrolyte solution containing ions with valence Z+ and Z-, the electric charge

density can be written in the following form:

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