Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions

Abstract

We present a soft-potential-enhanced Poisson–Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl−, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.

Interaction between two polyelectrolytes in monovalent aqueous salt solutions

“…In a recent work [50], the prediction of ion number concentration from PB theory was enhanced with a cylindrical soft-potential correction (SPB) of the form…”

“…In the original work of Vahid et al [50] where the SPB theory was introduced it was applied to model monovalent ion distributions around single polystyrene sulphonate (PSS) molecules. The corresponding ion densities were accurately reproduced for a wide range of system parameters, including salt and ion sizes.…”

“…Recently, we have developed a soft-potential-enhanced PB (SPB) theory to efficiently and accurately compute ion density distributions in the weak-coupling regime [50]. The soft potential in the SPB theory contains only one (physical) parameter, which can be fixed to give a good description for monovalent ion densities and electrostatic potentials around single rodlike PE for a wide range of salt and ion sizes.…”

“…The soft potential in the SPB theory contains only one (physical) parameter, which can be fixed to give a good description for monovalent ion densities and electrostatic potentials around single rodlike PE for a wide range of salt and ion sizes. The SPB approach was shown to work well for monovalent salt concentrations up to 1 M and ion sizes ranging from those corresponding to small, hard monovalent ions, such as Na + and Cl − , to almost an order of magnitude larger ions with diameter comparable to the PE diameter [50].…”

Interaction between two polyelectrolytes in monovalent aqueous salt solutions

“…12,52 Recently, we have developed a soft-potential-enhanced PB (SPB) theory to efficiently and accurately compute ion density distributions in the weak-coupling regime. 53 The soft potential in the SPB theory contains only one (physical) parameter, which can be fixed to give a good description for monovalent ion densities and electrostatic potentials around single rodlike PE for a wide range of salt and ion sizes. The SPB approach was shown to work well for monovalent salt concentrations up to 1 M and ion sizes ranging from those corresponding to small, hard monovalent ions, such as Na + and Cl À , to almost an order of magnitude larger ions with diameter comparable to the PE diameter.…”