Charged cylindrical surfaces: effect of finite ion size

Abstract

A simple statistical mechanical approach is applied to calculate the profile of the density of the number of particles and the profile of the electrostatic potential of an electric double layer formed by a charged cylindrical surface in contact with electrolyte solution. The finite size of particles constituting the electrolyte solution is considered by including the excluded volume effect within the lattice statistics while the electrostatic interactions are considered by means of the mean electrostatic field. It is shown that the excluded volume effect decreases the density of the number of counterions and increases the electrostatic potential near the charged cylindrical surface. The effect is more pronounced for high area densities of charge of the charged surface and for larger counterions. Further, it is shown that the ratio between the density of the number of the counterions near the charged cylindrical surface and the density of the number of counterions far from the charged surface reaches a plateau at large linear charge densities for ions of finite size, while no plateau is reached for dimensionless ions. The effective thickness of the electric double layer in cylindrical geometry is introduced. It is shown that the effective thickness increases with increasing counterion size while its dependence on the area density of charge of the charged surface exhibits a minimum. The theoretical approach presented in this work can be used for description of the electrostatics of the thin cylindrical structures in biological systems such as DNA, protein macromolecules and charged micro and nano tubes. D

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

“…We divide the system into cells [8,35] of volume DV = 2krlDr in cylindrical geometry and DV = 4kr 2 Dr in spherical geometry, where Dr is the dimension of the cell in the r direction. We assume that Dr is small compared to the distance over which macroscopic properties change essentially.…”

“…The free energy is obtained starting from the energy contributions of individual particles which are treated as independent and indistinguishable. The expression for the free energy of the solution in the cell can be obtained from the statistical mechanical relation DF = À kTlnQ cell [8,35,36],…”

“…perform the integration over the extension of the system in r. The electrostatic energy of the whole system is calculated by taking into account that the electrostatic potential at the site of a given ion is created by all other ions and the charged surface. The energy can be expressed using the equations of the classical theory of electromagnetism [8,35]:…”

Electron transfer across a conducting nanowire (nanotube)/electrolyte solution interface

“…Previously the equilibrium structure of diffusive electrical double layer at charged rods was thoroughly investigated in a series of works using the Poisson-Boltzmann theory [49][50][51][52], hypernetted chain/mean spherical approximation (HNC/MSA) [53][54][55][56], molecular dynamics [51,55], and Monte Carlo simulations [56]. Note that the EDL effects on voltammetry at spherical microelectrodes were addressed earlier in works [57][58][59][60].…”

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

“…Bikerman developed the first complete ion-size-effectinduced modified Poisson-Boltzmann model [34]. Since then, Bikerman's modified Poisson-Boltzmann equation (MPB) was reformulated by Eigen and Wicke [35,36], Strating and Wiegel [37,38], Borukhov et al [39], and Bohinc and coresearchers [40,41]. Kilic et al [42] applied the same equation for the analysis of the concentrated electrolytes.…”