Electrostatic depletion forces between planar surfaces

The interaction between two dielectric plates immersed in an electrolyte solution is examined by using a variational perturbation approximation for the grand partition function. This approach differs from previous treatments in that the screening length between the plates is treated as a variational parameter. A key finding is that adjacent to each plate is a layer of ion depletion with thickness given by about one-half of a Bjerrum length. Consequently, for plate-plate separations less than the Bjerrum length, nearly all the electrolyte is excluded from between the plates, and the interaction is given by the sum of a van der Waals interaction and an attractive osmotic depletion force. In contrast to the predictions of previous theories, the interaction between the plates at short range increases with increasing electrolyte concentration and may provide an important contribution to the salt-induced attraction, commonly referred to as salting out. Because the range of the osmotic depletion force is roughly equal to the Bjerrum length, it increases with the square of the valency of the electrolyte. At larger plate-plate separations, the van der Waals interaction is screened as electrolyte enters the space between the plates, leading to an exponential decay of the interactions, as has been previously observed. However, this interaction is slightly stronger than that previously predicted, due to ion depletion from the surface of the interface, also this effect increases with increasing electrolyte concentration

The electric double layer at high surface potentials : the influence of excess ion polarizability

By including the excess ion polarizability into the Poisson-Boltzmann theory, we show that the decrease in differential capacitance with voltage, observed for metal electrodes above a threshold potential, can be understood in terms of thickening of the double layer due to ion-induced polarizability holes in water. We identify a new length which controls the role of excess ion polarizability in the double layer, and show that when this is comparable to the size of the effective Debye layer, ion polarizability can significantly influence the properties of the double layer

Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li$_x$FePO$_4$.Comment: research account, 17 two-column pages, 12 figs, 78 refs - some typos corrected Accounts of Chemical Research (2013

A field theory for ions near charged surfaces valid from weak to strong couplings

A theory is developed to model the behavior of mobile ions around a fixed charged distribution in the presence of dielectric bodies. By treating the short and long-wavelength fluctuations of the electric potential within different approximation schemes, this approach combines the strengths of the mean field approximation and the strong coupling expansion, while retaining the simplicity of the commonly used Poisson-Boltzmann theory. It is capable of accurately describing ion-correlation induced phenomena, such as the attraction between two like charged plates, the repulsion between two oppositely charged plates, and overcharging. The theory is compared with Monte Carlo simulation data for various systems of charged plates with their associated counterions and added electrolyte. Good agreement is found for nearly all conditions examined

The role of image charges in the interactions between colloidal particles

The dielectric interiors of colloidal particles are responsible for dispersion (van der Waals) interactions. However, these dielectric regions also alter the manner in which charges, such as on ions or other colloidal particles, interact with each other, due to the induction of charges at the dielectric interfaces. The impact of these induced charges can be represented in terms of 'image charges'. These image charges result in an ion depletion layer in the vicinity of low dielectric bodies. This depletion layer is responsible for the increase in the surface tension of water upon the addition of electrolytes. In the case of colloidal particles, this depletion layer also leads to an 'electrostatic depletion force' with a range of the order of a Bjerrum length. The relevance of this force to the salting out of proteins is discussed. This electrostatic depletion force is directly analogous to the entropically driven depletion force (due to excluded volume). Although image charge effects have been known, their influence on the behavior of colloidal systems, especially in the presence of mobile ions, has generally not been accounted for (e.g., DLVO theory). We review the previous theoretical and simulation studies of how image charges influence the properties of electrolyte and colloidal systems and discuss the relevance of these effects on experimental system

Translocation of DNA Molecules through Nanopores with Salt Gradients: The Role of Osmotic Flow

Recent experiments of translocation of double-stranded DNA through nanopores [ M. Wanunu et al. Nature Nanotech. 5 160 (2009)] reveal that the DNA capture rate can be significantly influenced by a salt gradient across the pore. We show that osmotic flow combined with electrophoretic effects can quantitatively explain the experimental data on the salt-gradient dependence of the capture rat

The properties of dimers confined between two charged plates

We consider two like-charged planar surfaces immersed in solution of oppositely charged dimer counterions with a bond length l. To analyze this system, we extend and employ a self-consistent field theory that has been shown to be accurate from the weak to the intermediate through to the strong coupling regimes. In the limit of very short dimers, the results converge to the results for pointlike divalent ions. Near the surfaces, the dimers lie parallel to the charged plates. In the intermediate coupling regime, the dimers are aligned perpendicularly to the surface when they are a distance l from a surface. In the weak coupling regime, the interactions are only repulsive. At slightly higher couplings, there is a minimum in the variation of the free energy with distance at approximately the bond length of the dimers, which arises from bridging conformations of the dimers. In the intermediate coupling regime, an additional minimum in the free energy is observed at much smaller distances, which is due to the correlations between the dimers. For large dimer bond lengths, this minimum is metastable with respect to the previous minimum. However, as the bond length decreases, this minimum becomes the stable, while the minimum associated with the dimer bond length becomes metastable and eventually disappears. For shorter dimer bond length the attractive interaction is the result of correlations between counterions and charges on the surfaces. We find that dimers can mediate attractive interaction between like-charged surfaces in the intermediate coupling regime. The analysis of orientations confirms the bridging mechanism for sufficiently long dimers, whereas at high electrostatic couplings charge correlations contribute to the attraction

One-component plasma of point charges and of charged rods

An approximate theory is developed to describe the properties of mobile particles with extended charge distributions in the presence of a neutralizing fixed background charge. Long-wavelength fluctuations of the electric potential are handled within a variational perturbation approximation, and the short-wavelength fluctuations are handled within a cumulant (fugacity) expansion. The distinct treatment of these two contributions to the free energy enables the theory to provide quantitative predictions for the properties of these systems from the weak- to the strong-coupling regimes. With this theory, we study three different variations in the classical one-component plasma model: a plasma of point charges, a plasma of particles consisting of 8 linearly bonded point charges (8-mer), and a plasma of line charges. The theory was found to agree well with the available computer simulation data for the electrostatic interaction energy of these systems for all values of the plasma coupling parameter examined (Gamma=0 to 400). In addition, we find that both the 8-mer rod and the line charge systems form a strongly ordered nematic phase, which is entirely driven by electrostatic interactions. The nematic phase only exists within a finite range of lengths of the charged particles. If the particles are too short or too long, the nematic phase does not appear. Finally, we find that the nematic phase is stable over a broader range of conditions for the line charge system than for the 8-mer rod system; consequently, the phase behavior of the one-component plasma is sensitive to the manner in which the charge is distributed on the particles

A field theory approach for modeling electrostatic interactions in soft matter

Field theoretic approaches have been particularly useful in studying soft matter systems, such as colloidal and biological systems, where long range electrostatic interactions are important. For weakly coupled systems, the eld theoretic methods reduce to the commonly known Poisson-Boltzmann (PB) theory [Chapman (1913); Gouy (1910)], which has been shown to be very accurate for these systems, and has been used with great success to understand and solve numerous problems in soft matter