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We theoretically study transient electroosmotic flow of general Maxwell fluids through polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain transient electroosmotic flow from Cauchy momentum equation and Maxwell constitutive equation. For nanochannels grafted with polyelectrolyte layers having different layered distribution of charges, we study the influence of dimensionless relaxation time, dimensionless polyelectrolyte layer thickness and dimensionless drag coefficient on transient electroosmotic flow. We present the results for some particular cases. Firstly, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, total electroosmotic flow is non-zero. In particular, depending on charge distribution within end part of polyelectrolyte layers, the direction of electroosmotic flow can be reversed critically. Secondly, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between layered charge densities of two polyelectrolyte layers. Increasing ks allows electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can control intentionally the direction of the flows as well as strength of electroosmotic flow.

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer. In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

In this paper, we study the electrostatics of pH-responsive polyelectrolyte-grafted spherical particles by using a strong stretching theory that takes into account the excluded volume interaction and the density of chargeable sites on the polyelectrolyte molecules. Based on the free energy formalism, we obtain self-consistent field equations for determining the structure and electrostatics of spherical polyelectrolyte brushes. First, we find that the smaller the radius of the inner core, the longer the height of the polyelectrolyte brush. Then, we also prove that an increase in excluded volume interaction yields an swelling of the polyelectrolyte brush height. In addition, we demonstrate how the effect of pH, bulk ionic concentration, and lateral separation between adjacent polyelectrolyte chains on the electrostatic properties of a spherical polyelectrolyte brush is affected by the radius of inner core, the excluded volume interaction and the chargeable site density.

In this paper, we study the electroosmotic transport in a nanofluidic channel by using a mean-field theory accounting for non-uniform size effect and solvent polarization effect. We witness that in the presence of the given zeta potential, an enhancement of ion size invariably lowers the electroosmotic velocity, thereby increasing the magnitude of electrostatic potential, irrespective of considering solvent polarization. It is also proved that solvent polarization allows both the magnitude of electrostatic potential and the electroosmotic velocities to decrease. In addition, we find that increasing zeta potential augments not only ion size effect but also solvent polarization effect. Furthermore, we demonstrate that decreasing bulk ion number density causes an increase in electroosmotic velocity at the centerline. We compare the properties of aqueous electrolytes with those of the electrolytes where solvent is ethylalcohol. Finally, we study how solvent polarization and ionic size affect streaming potential and electroviscous effect. It is emphasized that the present study can provide a good way to control the nanofluidic transport for a plethora of biological and industrial applications.

We theoretically studied electric double layer by using the mean-field approach including the non-uniform size effect and the orientational ordering of water dipoles in electrolyte solution. Performing the minimization of the free energy, the resulting ion and water distribution functions are determined numerically in the process of solving the Poisson's equation. The effect of non-uniform ionic size and orientational ordering of water dipoles on stratification of counterions of different size in multicomponent electrolyte solution near the charged surface are presented and discussed. Spatial dependence of relative permittivity and differential capacitance of electric double layer are also calculated for binary electrolyte solution and then compared with the predictions of the previous models. Effect of bulk concentration of counterions and ion size effects on surface charge density, excess portion of counterions, relative permittivity and differential capacitance are studied for multicomponent electrolyte solution in detail.

We theoretically study electrostatic properties of electric double layer using a generalized Poisson-Boltzmann approach taking into account the orientational ordering of water dipoles and the excluded volume effect of water molecules as well as those of positive and negative ions with different sizes in electrolyte solution. Our approach enables one to predict that the number densities of water molecules, counterions and coions and the permittivity of electrolyte solution close to a charged surface, asymmetrically vary depending on both of sign and magnitude of the surface charge density and the volume of counterion. We treat several phenomena in more detail. Firstly, an increase in the volume of counterions and an increase in the surface charge density can cause the position of the minimum number density of water molecules to be farther from the charged surface. Secondly, width of the range of voltage in which the properties at the charged surface symmetrically vary decreases with increasing bulk salt concentration. In addition, we show that the excluded volume effect of water molecules and the orientational ordering of water dipoles can lead to early onset and lowering of the maximum of electric capacitance according to surface voltage. Our approach and results can be applied to describing electrostatic properties of biological membranes and electric double layer capacitor for which excluded volume effects of water molecules and ions with different sizes may be important.

In this paper, we study electrostatic properties between two similar or oppositely charged surfaces immersed in an electrolyte solution by using mean-field approach accounting for solvent polarization and non-uniform size effect. Applying a free energy formalism accounting for unequal ion sizes and orientational ordering of water dipoles, we derive coupled and self-consistent equations to calculate electrostatic properties between charged surfaces. Electrostatic properties for similarly charged surfaces depend on counterion size but not coion size. Moreover, electrostatic potential and osmotic pressure between similarly charged surfaces are found to be increased with increasing counterion size. On the other hand, the corresponding ones between oppositely charged surfaces are related to both sizes of positive and negative ions. For oppositely charged surfaces, the electrostatic potential, number density of solvent molecules and relative permittivity of an electrolyte having unequal ion sizes are not symmetric about the centerline between the charged surfaces. For either case, the consideration of solvent polarization results in an decrease in the electrostatic potential and the osmotic pressure compared to the case without the effect.

For binary solvent mixtures composed of ions and two kinds of polar solvents, electric double layer near a charged object is strongly affected by not only the binary solvent composition but also nature of solvents such as volume and dipole moment of a solvent molecule. Accounting for difference in sizes of solvents and orientational ordering of solvent dipoles, we theoretically obtain general expressions for the spatial distribution functions of solvents and ions, in planar geometry and within the mean-field approach. Although focusing on long-range electrostatic interaction, we neglect short-range interactions such as preferential solvation, our approach predicts an asymmetric depletion of the two solvents from the charged surface and a behavior of decreased permittivity of the binary solvent mixture. Furthermore, we suggest that the key factor for the depletion is the ratio of the solvent dipole moment to the solvent volume. The influence of binary solvent composition, volume of solvent and dipole moment of solvent on the number density of solvents, permittivity and differential capacitance are presented and discussed, respectively. We conclude that accounting for difference in the volume and dipole moment between polar solvents is necessary for new approach to represent more realistic situations such as preferential solvation.

The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can predict the phenomena like a heavy decrease in relative permittivity of the suspension and counterion stratification near highly charged colloidal particle. In this work we numerically obtain the electric potential, the counterions concentration and the relative permittivity around a charged particle in a concentrated salt-free suspension corrected by non-uniform size effects and orientational ordering of water dipoles. The results show the worth of such corrections for medium to high particle charges at every particle volume fraction. We conclude that non-uniform size effects and orientational ordering of water dipoles are necessary for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions., Comment: arXiv admin note: text overlap with arXiv:1102.0255 by other authors

We report a theoretical study of ion size effect on various properties in a soft nanochannel with pH-dependent charge density. We develop a free energy based mean-field theory taking into account ion size as well as pH-dependence of charged polyelectrolyte layer grafted on a rigid surface in an electrolyte. The influence of ion size on properties in a soft nanochannel is evaluated by numerically calculating ion number densities and electrostatic potential. We demonstrate that unlike in point-like ions, for finite sizes of ions, a uniform distribution of chargeable sites within the polyelectrolyte layer causes unphysical discontinuities in ion number densities not only for hydrogen ion but also for other kinds of ions. It is shown that the same cubic spatial distribution of chargeable sites as for point-like ions is necessary to ensure continuity of ion number density and zero ion transport at the polyelectrolyte layer - rigid solid interface. We find that considering finite ion size causes an increase in electrostatic potential and electroosmotic velocity and a decrease in ion number densities. More importantly, we demonstrate that in polyelectrolyte layer, pH-dependence of polyelectrolyte charge density makes accumulation of hydrogen ions stronger than for the other positive ion species in the electrolyte and such a tendency is further enhanced by considering finite ion size. In addition, we discuss how consideration of finite ion size affects the role of various parameters on electrostatic and electroosmotic properties.

We study the electric double layer near a charged soft surface by using a mean-field approach including non-uniform size effect and solvent polarization. Based on a free energy model, electrostatic potential and number densities of water and ions are obtained numerically by solving coupled differential equations including the Poisson's equation. We find that the solvent polarization significantly affects electrostatic potential, ion number densities and permittivity in an electrolyte solution near a charged soft surface. We prove that the consideration of the solvent polarization increases the magnitude of Donnan potential. We also demonstrate that within the fixed charge layer the number densities of counterions and coions are slightly smaller than when the solvent polarization is not considered. An increase in the ionic size enhances the influence of solvent polarization on the electrostatic properties within the fixed charged layer of charged soft surface. In the region of high surface-charge-density, the permittivity and the number density of water dipoles considerably decrease due to water polarization.

We theoretically study the size effect of water molecule clusters not only on electrostatic interaction between two charged surfaces in an aqueous electrolyte but also on electroosmotic transport in a nanofluidic channel. Applying a free energy based mean-field approach accounting for different sizes of ions and water molecule clusters, we derive a set of coupled equations to compute electrostatic and electroosmotic properties between charged surfaces. We verify that the smaller the size of a water cluster, the stronger the electroosmotic transport in nanofluidic channels. In addition, we find that an increase in size of a water cluster yields a decrease in electrostatic interaction strength between similar or oppositely charged planar surfaces.

We theoretically investigate electrostatic properties between two charged surfaces with a grafted polyelectrolyte layer in an aqueous electrolyte solution by using the Poisson-Boltzmann approach accounting for ion partitioning. In order to consider the ion partitioning effect, we focus on changes of electrostatic properties due to the difference in dielectric permittivity of the polyelectrolyte layer and the aqueous electrolyte solution. We find that ion partitioning enhances electrostatic potential in the region between two charged soft surfaces and hence increases the electrostatic interaction between two charged soft surfaces. Ion partitioning effect on osmotic pressure is enhanced not only by an increase in the thickness of polyelectrolyte layer and Debye length but also by a decrease in ion radius.

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water molecules, on electric double layer near charged surfaces. Based on the lattice statistical mechanics accounting for finite sizes and dipole moments of ions, Bjerrum pairs and solvent molecules, we consider the formation of Bjerrum pairs and derive the mathematical expressions for Bjerrum pair number density as well as cation/anion number density and water molecule number density. We reveal the several significant phenomena. Firstly, it is shown that our approach naturally yields the equilibrium constant for dissociation-association equilibrium between Bjerrum pairs and ions. Secondly, at low surface charge densities, an increase in the bulk concentration of Bjerrum pairs enhances the permittivity and decreases the differential capacitance. Next, for cases where Bjerrum pairs in an alcohol electrolyte solution have a high value of dipole moment, Bjerrum pair number density increases with decreasing distance from the charged surface, and differential capacitance and permittivity is high compared to ones for the cases with lower values of Bjerrum-pair dipole moments. Finally, we show that the difference in concentration and dipole moment of Bjerrum pairs can lead to some variation in osmotic pressure between two similarly charged surfaces., Comment: 28pages, 13 figures