The role of image charges in the interactions between colloidal particles

Surface tension of aqueous electrolyte solutions. A thermomechanical approach

We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous fluid. To obtain the surface tension, we calculate both the normal and tangential pressures using the components of the stress tensor, recently derived by us [Y. A. Budkov and P. E. Brandyshev, J. Chem. Phys. 159, 174103 (2023)] within the framework of Wang's variational field theory. Using this approach, we derive an analytical expression for the surface tension in the linear approximation. At low ionic concentrations, this expression represents the classical Onsager-Samaras limiting law. By utilizing only one fitting parameter, which is related to the affinity of anions to the dielectric boundary, we successfully approximated experimental data on the surface tension of several aqueous electrolyte solutions. This approximation applies to both the solution-air and solution-dodecane interfaces, covering a wide range of electrolyte concentrations.

Scalable trapping of single nanosized extracellular vesicles using plasmonics

Heterogeneous nanoscale extracellular vesicles (EVs) are of significant interest for disease detection, monitoring, and therapeutics. However, trapping these nano-sized EVs using optical tweezers has been challenging due to their small size. Plasmon-enhanced optical trapping offers a solution. Nevertheless, existing plasmonic tweezers have limited throughput and can take tens of minutes for trapping for low particle concentrations. Here, we present an innovative approach called geometry-induced electrohydrodynamic tweezers (GET) that overcomes these limitations. GET generates multiple electrohydrodynamic potentials, allowing parallel transport and trapping of single EVs within seconds. By integrating nanoscale plasmonic cavities at the center of each GET trap, single EVs can be placed near plasmonic cavities, enabling instant plasmon-enhanced optical trapping upon laser illumination without detrimental heating effects. These non-invasive scalable hybrid nanotweezers open new horizons for high-throughput tether-free plasmon-enhanced single EV trapping and spectroscopy. Other potential areas of impact include nanoplastics characterization, and scalable hybrid integration for quantum photonics.

Exosomes trapping, manipulation and size-based separation using opto-thermo-electrohydrodynamic tweezers

Owing to the heterogeneity of exosomes in size and biomolecular composition, there is a need for new approaches for trapping, manipulating, and sorting of single exosomes in solution. Due to their small size ranging from 30 nm to 150 nm and their relatively low refractive index, their stable trapping using optical tweezers has been met with challenges. Trapping exosomes in an optical trap requires nearly 100 mW of input power, which predisposes them to photo-induced damage and membrane rupture at the laser focus. Here, we report a high stability opto-thermo-electrohydrodynamic tweezer for the stable stand-off trapping of single exosomes based on a concentric nanohole array (CNA) using laser illumination and an a.c. field. The CNA system generates two regions of electrohydrodynamic potentials several microns away from the laser focus where single exosomes are trapped. We demonstrate the rapid trapping within seconds, and selective dynamic manipulation of exosomes based on size using only 4.2 mW of input laser power. The proposed platform opens up a promising approach for stabilizing single exosomes in solution and controlling their distribution based on size without the risk of photo-induced damage.

Applicability of the linearized Poisson-Boltzmann theory to contact angle problems and application to the carbon dioxide-brine-solid systems

In colloidal science and bioelectrostatics, the linear Poisson Boltzmann equation (LPBE) has been used extensively for the calculation of potential and surface charge density. Its fundamental assumption rests on the premises of low surface potential. In the geological sequestration of carbon dioxide in saline aquifers, very low pH conditions coupled with adsorption induced reduction of surface charge density result in low pH conditions that fit into the LPB theory. In this work, the Gouy–Chapman model of the electrical double layer has been employed in addition to the LPBE theory to develop a contact angle model that is a second-degree polynomial in pH. Our model contains the point of zero charge pH of solid surface. To render the model applicable to heterogeneous surfaces, we have further developed a model for the effective value of the point of zero charge pH. The point of zero charge pH model when integrated into our model enabled us to determine the point of zero charge pH of sandstone, quartz and mica using literature based experimental data. In this regard, a literature based thermodynamic model was used to calculate carbon dioxide solubility and pH of aqueous solution. Values of point of zero charge pH determined in this paper agree with reported ones. The novelty of our work stems from the fact that we have used the LPB theory in the context of interfacial science completely different from the classical approach, where the focus is on interparticle electrostatics involving colloidal stabilization.

Interactions between conducting surfaces in salt solutions

In this work, we simulate interactions between two perfectly conducting surfaces, immersed in a salt solution. We demonstrate that these forces are quantitatively different from those between (equally charged) non-conducting surfaces. There is, for instance, a significant repulsion between net neutral surfaces. On the other hand, there are also qualitative similarities, with behaviours found with non-conducting surfaces. For instance, there is a non-monotonic dependence of the free energy barrier height, on the salt concentration, and the minimum essentially coincides with a flat profile of the apparent surface charge density (i.e. the effective net surface charge density, some distance away from the surface, when accounting for ion neutralization), outside the so-called Stern layer. These conditions can be described as "perfect surface charge neutralization". Despite observed quantitative differences, we demonstrate that it might be possible to mimic a dispersion containing charged colloidal metal particles by a simpler model system with charged non-conducting particles, using modified particle-ion interactions.

Electrothermoplasmonic Trapping and Dynamic Manipulation of Single Colloidal Nanodiamond

Low-power trapping of nanoscale objects can be achieved by using the enhanced fields near plasmonic nanoantennas. Unfortunately, in this approach the trap site is limited to the position of the plasmonic hotspots and continuous dynamic manipulation is not feasible. Here, we report a low-frequency electrothermoplasmonic tweezer (LFET) that provides low-power, high-stability and continuous dynamic manipulation of a single nanodiamond. LFET harnesses the combined action of the laser illumination of a plasmonic nanopillar antenna array and low-frequency alternating current (ac) electric field to establish an electrohydrodynamic potential capable of the stable trapping and dynamic manipulation of single nanodiamonds. We experimentally demonstrate the fast transport, trapping, and dynamic manipulation of a single nanodiamond using a low-frequency ac field below 5 kHz and low-laser power of 1 mW. This nanotweezer platform for nanodiamond manipulation holds promise for the scalable assembly of single photon sources for quantum information processing and low noise quantum sensors.

Stand-off trapping and manipulation of sub-10 nm objects and biomolecules using opto-thermo-electrohydrodynamic tweezers

Optical tweezers have emerged as a powerful tool for the non-invasive trapping and manipulation of colloidal particles and biological cells^1,2. However, the diffraction limit precludes the low-power trapping of nanometre-scale objects. Substantially increasing the laser power can provide enough trapping potential depth to trap nanoscale objects. Unfortunately, the substantial optical intensity required causes photo-toxicity and thermal stress in the trapped biological specimens³. Low-power near-field nano-optical tweezers comprising plasmonic nanoantennas and photonic crystal cavities have been explored for stable nanoscale object trapping^4-13. However, the demonstrated approaches still require that the object is trapped at the high-light-intensity region. We report a new kind of optically controlled nanotweezers, called opto-thermo-electrohydrodynamic tweezers, that enable the trapping and dynamic manipulation of nanometre-scale objects at locations that are several micrometres away from the high-intensity laser focus. At the trapping locations, the nanoscale objects experience both negligible photothermal heating and light intensity. Opto-thermo-electrohydrodynamic tweezers employ a finite array of plasmonic nanoholes illuminated with light and an applied a.c. electric field to create the spatially varying electrohydrodynamic potential that can rapidly trap sub-10 nm biomolecules at femtomolar concentrations on demand. This non-invasive optical nanotweezing approach is expected to open new opportunities in nanoscience and life science by offering an unprecedented level of control of nano-sized objects, including photo-sensitive biological molecules.

Surface polarization effects in confined polyelectrolyte solutions

Understanding nanoscale interactions at the interface between two media with different dielectric constants is crucial for controlling many environmental and biological processes, and for improving the efficiency of energy storage devices. In this contributed paper, we show that polarization effects due to such dielectric mismatch remarkably influence the double-layer structure of a polyelectrolyte solution confined between two charged surfaces. Surprisingly, the electrostatic potential across the adsorbed polyelectrolyte double layer at the confining surface is found to decrease with increasing surface charge density, indicative of a negative differential capacitance. Furthermore, in the presence of polarization effects, the electrostatic energy stored in the double-layer structure is enhanced with an increase in the charge amplification, which is the absorption of ions on a like-charged surface. We also find that all of the important double-layer properties, such as charge amplification, energy storage, and differential capacitance, strongly depend on the polyelectrolyte backbone flexibility and the solvent quality. These interesting behaviors are attributed to the interplay between the conformational entropy of the confined polyelectrolytes, the Coulombic interaction between the charged species, and the repulsion from the surfaces with lower dielectric constant.

Grand canonical simulations of ions between charged conducting surfaces using exact 3D Ewald summations

We present a useful methodology to simulate ionic fluids confined by two charged and perfectly conducting surfaces. Electrostatic interactions are treated using a modified 3D Ewald sum, which accounts for all image charges across the conductors, as well as the 2D periodicity, parallel to the surfaces. The energy expression is exact, and the method is trivial to implement in existing Ewald codes. We furthermore invoke a grand canonical scheme that utilizes a bias potential, that regulates the surface charge density. The applied bias potential also enables us to calculate individual chemical potentials of the ions. Finally, we argue that our approach leads to a pedagogically appealing description of the Donnan potential, and what it measures in these systems.

An Empirical Research on Influence Factors of Industrial Water Use

The contradiction between increasing demand and current supply has affected the healthy development of industry. Investigating the key influence factors of industrial water use change has important practical significance for water resource management. In this study, the authors propose the vector autoregression model to analyze the dynamic influences of industrial development, technological progress, and environmental protection on industrial water use change, and take Jiangsu Province, China as a case study. Results show that each of the factors had different effects during 2001–2015, in which industrial development was the greatest contributor to the change of industrial water use and showed a positive effect in the forecast period; technological progress played a major role in reducing industrial water use, but the negative effect weakened periodically over time; environmental protection also had a positive influence in the early forecast period, and then showed a marginal effect with time. Results of this study could assist the relevant authorities to formulate appropriate industrial development planning and water saving policies, and to reasonably control the industrial water demand.

A diagrammatic analysis of the variational perturbation method for classical fluids

The statistical mechanics of classical fluids can be approached from the particle perspective, where the focus is on the various positions and interactions of the particles, and from the field perspective, where the focus is on the form of the interaction fields generated by the particles. In this work, we combine these two perspectives by examining the variational perturbation method for classical fluids, which has been widely used to describe nonuniform electrolyte systems. Most of this work has been for low orders of the approximation, it has been limited to cases where the electrostatic interactions are weak. We present an exact diagrammatic representation of the method, which greatly facilitates the enumeration and evaluation of higher order corrections to the free energy functional. This framework is able to encapsulate several different approximate theories. Performing a cumulant expansion, leads to the Debye-Hückel and higher order corrections. Including the contribution of chain diagrams leads to a theory closely related to the splitting theory [Hatlo and Lue, Europhys. Lett., 2010, 89, 25002], which has been shown to be accurate from the weak through to the strong coupling limits. Including all chain and ring diagrams leads to the hypernetted chain approximation; this is a more direct route to the conventional derivation, which also requires a renormalization of the Mayer f-bonds to the total correlation functions. These approximations to the variational perturbation method are applied to the classical one-component plasma in order to assess their relative accuracy and understand their relationship to each other. Strategies for developing improved approximations are discussed.

Ionic liquid interface at an electrode: simulations of electrochemical properties using an asymmetric restricted primitive model

We use Monte Carlo simulations of a coarse-grained model to investigate structure and electrochemical behaviours at an electrode immersed in room temperature ionic liquids (RTILs). The simple RTIL model, which we denote the asymmetric restricted primitive model (ARPM), is composed of monovalent hard-sphere ions, all of the same size, in which the charge is asymmetrically placed. Not only the hard-sphere size (d), but also the charge displacement (b), is identical for all species, i.e. the monovalent RTIL ions are fully described by only two parameters (d, b). In earlier work, it was demonstrated that the ARPM can capture typical static RTIL properties in bulk solutions with remarkable accuracy. Here, we investigate its behaviour at an electrode surface. The electrode is assumed to be a perfect conductor and image charge methods are utilized to handle polarization effects. We find that the ARPM of the ionic liquid reproduces typical (static) electrochemical properties of RTILs. Our model predicts a declining differential capacitance with increasing temperature, which is expected from simple physical arguments. We also compare our ARPM, with the corresponding RPM description, at an elevated temperature (1000 K). We conclude that, even though ion pairing occurs in the ARPM system, reducing the concentration of 'free' ions, it is still better able to screen charge than a corresponding RPM melt. Finally, we evaluate the option to coarse-grain the model even further, by treating the fraction of the ions that form ion pairs implicitly, only through the contribution to the dielectric constant of the corresponding dipolar (ion pair) fluid. We conclude that this primitive representation of ion pairing is not able to reproduce the structures and differential capacitances of the system with explicit ion pairs. The main problem seems to be due to a limited dielectric screening in a layer near the electrode surface, resulting from a combination of orientational restrictions and a depleted dipole density.

Controlling Polyelectrolyte Adsorption onto Carbon Nanotubes by Tuning Ion-Image Interactions

Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamental challenge in nanotechnology. Polyelectrolytes have been shown to stabilize nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. Conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interactions. We develop a simple mean-field model and show that ion-image attraction significantly effects adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes on the basis of their electronic structures, which in turn modify the ion-image attraction.

On the physics of both surface overcharging and charge reversal at heterophase interfaces

A series of Monte Carlo simulations are employed to reveal the physics of both surface overcharging and charge reversal at a negatively charged dielectric interface exposed to a bulk solution containing a +2:−1 electrolyte in the absence and presence of a monovalent salt.

Incorporation of ion and solvent structure into mean-field modeling of the electric double layer

An electric double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the electric double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded volume effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations.

Nanometer-ranged attraction induced by multivalent ions between similar and dissimilar surfaces probed using an atomic force microscope (AFM)

Forces between similar and dissimilar surfaces are quantified and a short-ranged attraction can be identified.

Ion-mediated interactions between net-neutral slabs: Weak and strong disorder effects

We investigate the effective interaction between two randomly charged but otherwise net-neutral, planar dielectric slabs immersed in an asymmetric Coulomb fluid containing a mixture of mobile monovalent and multivalent ions. The presence of charge disorder on the apposed bounding surfaces of the slabs leads to substantial qualitative changes in the way they interact, as compared with the standard picture provided by the van der Waals and image-induced, ion-depletion interactions. While, the latter predict purely attractive interactions between strictly neutral slabs, we show that the combined effects from surface charge disorder, image depletion, Debye (or salt) screening, and also, in particular, their coupling with multivalent ions, give rise to a more diverse behavior for the effective interaction between net-neutral slabs at nano-scale separations. Disorder effects show large variation depending on the properly quantified strength of disorder, leading either to non-monotonic effective interaction with both repulsive and attractive branches when the surface charges are weakly disordered (small disorder variance) or to a dominating attractive interaction that is larger both in its range and magnitude than what is predicted from the van der Waals and image-induced, ion-depletion interactions, when the surfaces are strongly disordered (large disorder variance).

Aggregation of Colloidal Particles in the Presence of Multivalent Co-Ions: The Inverse Schulze-Hardy Rule

Shifts of the critical coagulation concentration (CCC) in particle suspensions in salt solutions containing multivalent co-ions and monovalent counterions are rationalized. One observes that the CCC is inversely proportional to the valence, and this behavior is referred to as the inverse Schulze-Hardy rule. This dependence is established by means of measurements of the stability ratio for positively and negatively charged latex particles with time-resolved light scattering. The same dependence is equally suggested by calculations of the CCC with the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby the full Poisson-Boltzmann equation for the asymmetric electrolytes has to be used. The latter aspect is essential, since in the case of multivalent co-ions the surface charge is principally neutralized by monovalent counterions. This rule complements the classical Schulze-Hardy rule, which applies in the case of multivalent counterions, and states that the CCC is inversely proportional to the sixth power of the valence.

On the stability of aqueous dispersions containing conducting colloidal particles

We use a combination of simulations and a simple theoretical approach to investigate interactions between neutral conducting surfaces, immersed in an electrolyte solution. The study is conducted at the primitive model level, which necessitates the use of multiple image reflections. Our approximate theory is based on a classical density functional formulation of Poisson-Boltzmann theory. The same approach can in principle also be imported to more advanced treatments, where ion correlations are accounted for. An important limiting result that guides our treatment of the image forces, is that the repulsive salt-induced interactions cancel the attractive zero frequency van der Waals attraction at long range. That is, at vanishing frequency, the van der Waals interaction between the conducting surfaces is, at large separations, perfectly screened by the intervening salt solution. The simulations are computationally intensive, due to a strong dependence upon the number of image reflections used, with especially poor convergence when an odd number of images is used. We demonstrate that our approximate density functional approach is remarkably accurate, even in the presence of a 2 : 1 salt, or when the surfaces preferentially adsorb one ion species. The former observation was rather unexpected, given the lack of ion correlations within our mean-field treatment, and is most likely due to a cancellation between two opposing effects, both of which are generated by ion correlations.

Image-charge forces in thin interlayers due to surface charges in electrolyte

The surface forces arising in wetting films of nonpolar liquids or in thin air interlayers between an electrolyte and a nonpolar medium in the case of discrete charging of the dielectric-electrolyte interface are considered. The contributions of polarization effects to the distribution of the electrostatic potential in the three contacting media were calculated. Within the Debye-Hückel approximation, the analytical solutions were derived for the disjoining pressure in thin films, for the case of either dilute or relatively concentrated electrolyte solutions in the aforementioned systems. Analysis of the analytical and numerical results demonstrated that for dilute solutions the contribution of image forces to the disjoining pressure may significantly exceed the van der Waals forces for films from a few to tens of nanometers thick.

Wrapping/unwrapping transition of double-stranded DNA in DNA-nanosphere complexes induced by multivalent anions

Wrapping and unwrapping behaviors of double-stranded DNA around a positively charged nanosphere in solution are studied by using the coarse-grained molecular dynamics (CGMD) simulation method. When monovalent, divalent and trivalent anions are added to the DNA-nanosphere complex solution, double-stranded DNA binds with a nanosphere owing to strong electrostatic attraction. However, when tetravalent anions are added to the DNA-nanosphere complex solution, local charge inversion is observed for a high anion concentration of tetravalent anions and the double-stranded DNA can be unwrapped from the nanosphere because of the local charge inversion near the nanosphere. Moreover, the helical structure of DNA is damaged when double-stranded DNA wraps around the nanosphere and the helical structure can be rebuilt when the double-stranded DNA unwraps from the nanosphere. This study can help us understand how to control the release of DNA in DNA-nanosphere complexes.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Photoresponsive block copolymer: synthesis, characterization, and surface activity control

Amphiphilic block copolymers bearing chromophores are used to achieve photoresponses upon exposure to suitable light, which alter molecular properties, but the photostimulus surface activity control of amphiphilic block copolymers remains to be elucidated. In this work, a series of novel amphiphilic block copolymers consisting of a carboxymethyl betaine monomer (called GLBT) and 4-ethoxy-4'-methacrylamide (EMAAB) with different block ratios have been synthesized using a reversible addition-fragmentation chain-transfer (RAFT) polymerization process. Copolymers were observed to be self-assembled in the aqueous solution above a critical micelle concentration, which was determined by static light scattering measurements and formed vesicles of 120-170 nm in diameter, at different pH values. Copolymers were found to be surface-active at pH 7 but exhibited non-surface activity at acidic and alkaline pH values. After being irradiated with 360 nm UV light, copolymers showed a significant photoresponse both at the surface and in bulk solution as a result of the photoinduced isomerization of azochromophores. The surface property of copolymers was significantly affected by UV irradiation at pH 7, and block copolymers became non-surface-active. The bulk properties changed considerably upon UV exposure where polymer vesicles transformed to micelles as a result of the polarity difference between two azo isomers (cis and trans isomers). All of these transitions were found to be reversible. A new method to control the surface active/nonactive and vesicle/micelle transitions by light and pH has been established by introducing an azobenzene chromophore and GLBT into amphiphlic diblock copolymers.

Repulsion between oppositely charged planar macroions

The repulsive interaction between oppositely charged macroions is investigated using Grand Canonical Monte Carlo simulations of an unrestricted primitive model, including the effect of inhomogeneous surface charge and its density, the depth of surface charge, the cation size, and the dielectric permittivity of solvent and macroions, and their contrast. The origin of the repulsion is a combination of osmotic pressure and ionic screening resulting from excess salt between the macroions. The excess charge over-reduces the electrostatic attraction between macroions and raises the entropic repulsion. The magnitude of the repulsion increases when the dielectric constant of the solvent is lowered (below that of water) and/or the surface charge density is increased, in good agreement with experiment. Smaller size of surface charge and the cation, their discreteness and mobility are other factors that enhance the repulsion and charge inversion phenomenons.

Attraction between neutral dielectrics mediated by multivalent ions in an asymmetric ionic fluid

We study the interaction between two neutral plane-parallel dielectric bodies in the presence of a highly asymmetric ionic fluid, containing multivalent as well as monovalent (salt) ions. Image charge interactions, due to dielectric discontinuities at the boundaries, as well as effects from ion confinement in the slit region between the surfaces are taken fully into account, leading to image-generated depletion attraction, ion correlation attraction, and steric-like repulsive interactions. We investigate these effects by employing a combination of Monte Carlo simulation methods, including explicit-ion simulations (where all electrostatic interactions are simulated explicitly) and implicit-ion simulations (where monovalent ions are replaced by an effective screened electrostatic potential between multivalent ions), as well as an approximate analytical theory. The latter incorporates strong ion-image charge correlations, which develop in the presence of high valency ions in the mixture. We show that the implicit-ion simulations and the proposed analytical theory can describe the explicit simulation results on a qualitative level, while excellent quantitative agreement can be obtained for sufficiently large monovalent salt concentrations. The resultant attractive interaction between the neutral surfaces is shown to be significant, as compared with the usual van der Waals interactions between semi-infinite dielectrics, and can thus play an important role at the nano scale.

Interactions between charged surfaces mediated by molecules with spatially distributed charges

A short review of recent theoretical advances in studies of the interaction between highly charged systems is presented. Such a system could not be described by the mean field theory. More advanced methods have to be used in order to introduce the correlations between highly charged particles. In this work I focus on the system of highly charged surfaces, separated by a solution of molecules with spatially distributed charge. Two different representations of the molecular shape will be considered: rod-like and spherical. The system will be theoretically described by the density functional theory. For sufficiently long molecules and large surface charge densities, an attractive force between like-charged surfaces arises due to the spatially distributed charges within the molecules. The added salt has influence on the condition for the attractive force between like-charged surfaces. The theoretical results will be compared with Monte Carlo (MC) simulations. Recent measurements with multivalent rigid rod-like particles will be discussed.

Polyelectrolyte adsorption onto oppositely charged interfaces: image-charge repulsion and surface curvature

We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results.

Computational evidence of two driving mechanisms for overcharging in an electric double layer near the point of zero charge

We have adopted an ensemble Monte Carlo simulation method to systematically verify two physical driving mechanisms responsible for overcharging which refers to the adsorption of an effective charge onto a like-charged planar surface around the point of zero charge within the primitive model of mixed electrolytes with varying salt concentrations. One is electrostatic in character dominated by dielectric images and the other is purely entropic in origin by ionic size asymmetry effects, of which the former has never been reported both theoretically and experimentally and the latter could be interpreted satisfactorily in terms of available theoretical approaches. The electrostatically driven mechanism is found to critically depend on the ionic sizes while the entropically driven mechanism occurs with almost the same efficiency in a relative wide range of surface charge density. Depending on the delicate interplay between charge and steric correlations, the two distinct driving mechanisms may cooperatively give rise to a more pronounced overcharging process.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.

A fast algorithm for treating dielectric discontinuities in charged spherical colloids

Electrostatic interactions between multiple colloids in ionic fluids are attracting much attention in studies of biological and soft matter systems. The evaluation of the polarization surface charges due to the spherical dielectric discontinuities poses a challenging problem to highly efficient computer simulations. In this paper, we propose a new method for fast calculating the electric field of spaced spheres using the multiple reflection expansion. The method uses a technique of recursive reflections among the spherical interfaces based on a formula of the multiple image representation, resulting in a simple, accurate and close-form expression of the surface polarization charges. Numerical calculations of the electric potential energies of charged spheres demonstrate the method is highly accurate with small number of reflections, and thus attractive for the use in practical simulations of related problems such as colloid suspension and macromolecular interactions.

Simulation of an electrical double layer model with a low dielectric layer between the electrode and the electrolyte

We report Monte Carlo simulation results for double layers of 1:1 and 2:1 electrolytes near an electrode with an inner layer that has a dielectric constant, ε(2), smaller than that of the electrolyte, ε(3). The electrolyte is modeled in the implicit solvent framework (primitive model), while the electrode is a metal electrode in this study (ε(1) → ∞). The charged hard sphere ions are not allowed to enter into the inner layer. We show that the capacitance of the inner layer is C(δ) = ε(0)(ε(2) + ε(3))/2δ, where δ is the thickness of the inner layer. This result is different from that obtained from solutions of the Poisson-Boltzmann equation (ε(0)ε(2)/δ), indicating that interpretation of experimental data with a fitted ε(2) dielectric constant of the inner layer must be done using a different equation. We also show that the properties of the diffuse layer are not independent of the value of ε(2), which is a usual assumption of the Poisson-Boltzmann theory. This is mainly because the repulsive image charges repel both the counterions and the co-ions, while the electrode charge attracts the counterions and repels the co-ions.

A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary

In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ε(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/ε(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example.

Hybrid opto-electric manipulation in microfluidics-opportunities and challenges

Hybrid opto-electric manipulation in microfluidics/nanofluidics refers to a set of methodologies employing optical modulation of electrokinetic schemes to achieve particle or fluid manipulation at the micro- and nano-scale. Over the last decade, a set of methodologies, which differ in their modulation strategy and/or the length scale of operation, have emerged. These techniques offer new opportunities with their dynamic nature, and their ability for parallel operation has created novel applications and devices. Hybrid opto-electric techniques have been utilized to manipulate objects ranging in diversity from millimetre-sized droplets to nano-particles. This review article discusses the underlying principles, applications and future perspectives of various hybrid opto-electric techniques that have emerged over the last decade under a unified umbrella.

Multiple-image treatment of induced charges in Monte Carlo simulations of electrolytes near a spherical dielectric interface

The polarization-induced charges of a dielectric sphere are studied for charged colloidal systems in electrolyte solutions with a primitive model. The method of constructing multiple-image charges is used to approximate the polarization potential of a microion outside the sphere; it is based on a numerical discretization of the potential's analytical integral representation, and can systematically approximate the exact potential with desired accuracy by varyiation of the number of point images. Different aspects of the image effects are then investigated by Monte Carlo simulations for several colloidal systems, in both salt-free and salty environments. Furthermore, we studied the influence of discrete surface charges of different valences, and demonstrate that the polarization charges can significantly strengthen charge reversal for the colloid-microion complex, especially for multivalent interfacial ions.