Adsorption of charged particles on an oppositely charged surface: oscillating inversion of charge

Programmable ion-sensitive transistor interfaces. I. Electrochemical gating

Electrochemical gating is the process by which an electric field normal to the insulator electrolyte interface shifts the surface chemical equilibrium and further affects the charge in solution [Jiang and Stein, Langmuir 26, 8161 (2010)]. The surface chemical reactivity and double-layer charging at the interface of electrolyte-oxide-semiconductor (EOS) capacitors is investigated. We find a strong pH-dependent hysteresis upon dc potential cycling. Varying salinity at a constant pH does not change the hysteretic window, implying that field-induced surface pH regulation is the dominant cause of hysteresis. We propose and investigate this mechanism in foundry-made floating-gate ion-sensitive field-effect transistors, which can serve as both an ionic sensor and an actuator. Termed the chemoreceptive neuron metal-oxide-semiconductor (CνMOS) transistor, it features independently driven control gates (CGs) and sensing gates (SGs) that are capacitively coupled to an extended floating gate (FG). The SG is exposed to fluid, the CG is independently driven, and the FG is capable of storing charge Q(FG) of either polarity. Asymmetric capacitive coupling between the CG and SG to FG results in intrinsic amplification of the measured surface potential shifts and influences the FG charge injection mechanism. This modified SG surface condition was monitored through transient recordings of the output current, performed under alternate positive and negative CG pulses. Transient recordings revealed a hysteresis where the current was enhanced under negative pulsing and reduced after positive pulsing. This hysteresis effect is similar to that observed with EOS capacitors, suggesting a field-dependent surface charge regulation mechanism at play. At high CG biases, nonvolatile charge Q(FG) tunneling into the FG occurs, which creates a larger field and tunes the pH response and the point of zero charge. This mechanism gives rise to surface programmability. In this paper we describe the operational principles, tunneling mechanism, and role of electrolyte composition under field modulation. The experimental findings are then modeled by a Poisson-Boltzmann formulation with surface pH regulation. We find that surface ionization constants play a dominant role in determining the pH tuning effect. In the following paper [K. Jayant et al., Phys. Rev. E 88, 012802 (2013)] we extend the dual-gate operation to molecular sensing and demonstrate the use of Q(FG) to achieve manipulation of surface-adsorbed DNA.

Dressed counterions: polyvalent and monovalent ions at charged dielectric interfaces

We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion" approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte Carlo simulations. We then apply the dressed counterion approach within the framework of the generalized strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as dielectric inhomogeneities in the limit of strong Coulomb interactions. Limitations and applicability of this theory are examined by comparing the results with simulations.

Insights from Monte Carlo simulations on charge inversion of planar electric double layers in mixtures of asymmetric electrolytes

Monte Carlo simulations of a planar negatively charged dielectric interface in contact with a mixture of 1:1 and 3:1 electrolytes are carried out using the unrestricted primitive model under more realistic hydrated ion sizes. Two typical surface charge densities are chosen to represent the systems from the weak to strong coupling regimes. Our goal is to determine the dependence of the degree of charge inversion on increasing concentration of both mono- and trivalent salts and to provide a systematic study on this peculiar effect between short-range and electrostatic correlations. The numerical results show that addition of monovalent salt diminishes the condensation of trivalent counterions due to either the favorable solvation energy or the available space constraints. As the concentration of trivalent salt increases, on the other hand, the inclusion of the ionic size and size asymmetry results in a damped oscillatory charge inversion at low enough surface charge and another counterintuitive surface charge amplification. It is proposed that both of the anomalous events in the weak coupling regime are thought to be entropic in origin which is completely different from the electrostatic driven charge inversion in the strong coupling regime. In addition, the electrostatic images arising from the dielectric mismatch lead to a decaying depletion effect on the structure of double layer with growing salt concentration in the case of low charged interface but have no effect at high surface charge values. The microscopic information obtained here points to the need for a more quantitative theoretical treatment in describing the charge inversion phenomenon of real colloidal systems.

Non-mean-field theory of anomalously large double layer capacitance

Mean-field theories claim that the capacitance of the double layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double layer capacitor is substantially smaller. We propose an alternate non-mean-field theory of the ionic double layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our "one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudocapacitance.

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

The role of multipoles in counterion-mediated interactions between charged surfaces: strong and weak coupling

We present general arguments for the importance, or lack thereof, of structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.

Polyelectrolyte-induced aggregation of liposomes: a new cluster phase with interesting applications

Different charged colloidal particles have been shown to be able to self-assemble, when mixed in an aqueous solvent with oppositely charged linear polyelectrolytes, forming long-lived finite-size mesoscopic aggregates. On increasing the polyelectrolyte content, with the progressive reduction of the net charge of the primary polyelectrolyte-decorated particles, larger and larger clusters are observed. Close to the isoelectric point, where the charge of the adsorbed polyelectrolytes neutralizes the original charge of the particles' surface, the aggregates reach their maximum size, while beyond this point any further increase of the polyelectrolyte-particle charge ratio causes the formation of aggregates whose size is progressively reduced. This re-entrant condensation behavior is accompanied by a significant overcharging. Overcharging, or charge inversion, occurs when more polyelectrolyte chains adsorb on a particle than are needed to neutralize its original charge so that, eventually, the sign of the net charge of the polymer-decorated particle is inverted. The stability of the finite-size long-lived clusters that this aggregation process yields results from a fine balance between long-range repulsive and short-range attractive interactions, both of electrostatic nature. For the latter, besides the ubiquitous dispersion forces, whose supply becomes relevant only at high ionic strength, the main contribution appears due to the non-uniform correlated distribution of the charge on the surface of the polyelectrolyte-decorated particles ('charge-patch' attraction). The interesting phenomenology shown by these system has a high potential for biotechnological applications, particularly when the primary colloidal particles are bio-compatible lipid vesicles. Possible applications of these systems as multi-compartment vectors for the simultaneous intra-cellular delivery of different pharmacologically active substances will be briefly discussed.

Strong-coupling electrostatics in the presence of dielectric inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.

Electrostatic image effects for counterions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semi-infinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak-coupling level the image charge effects are generally small, making their mark only in the second-order fluctuation term. However, in the strong-coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long-range image potentials.

Effects of dielectric discontinuities on two charged plates

Counterions in a biological system are charged in water and interact with charged macroions, which are generally made up of hydrocarbons. The dielectric difference between water and the hydrocarbon substrates occurs naturally, and may greatly affect the electrostatic properties of biological systems. Particularly for a slab geometry, bulk counterions that are dissolved in water are driven to the midplane of the slab because of their repulsive interaction with their image charges. The pressure between two charged plates becomes less repulsive since the low dielectric constant of the hydrocarbon substrate creates stronger association between counterions and surface charges as compared to the case of no dielectric discontinuity.

Anionic polyelectrolyte adsorption on mica mediated by multivalent cations: a solution to DNA imaging by atomic force microscopy under high ionic strengths

Adsorption of DNA molecules on mica, a highly negatively charged surface, mediated by divalent or trivalent cations is considered. By analyzing atomic force microscope (AFM) images of DNA molecules adsorbed on mica, phase diagrams of DNA molecules interacting with a mica surface are established in terms of concentrations of monovalent salt (NaCl) and divalent (MgCl2) or multivalent (spermidine, cobalt hexamine) salts. These diagrams show two transitions between nonadsorption and adsorption. The first one arises when the concentration of multivalent counterions is larger than a limit value, which is not sensitive to the monovalent salt concentration. The second transition is due to the binding competition between monovalent and multivalent counterions. In addition, we develop a model of polyelectrolyte adsorption on like-charged surfaces with multivalent counterions. This model shows that the correlations of the multivalent counterions at the interface between DNA and mica play a critical role. Furthermore, it appears that DNA adsorption takes place when the energy gain in counterion correlations overcomes an energy barrier. This barrier is induced by the entropy loss in confining DNA in a thin adsorbed layer, the entropy loss in the interpenetration of the clouds of mica and DNA counterions, and the electrostatic repulsion between DNA and mica. The analysis of the experimental results provides an estimation of this energy barrier. We then discuss some important issues, including DNA adsorption under physiological conditions.

Condensation of DNA-actin polyelectrolyte mixtures driven by ions of different valences

Multivalent ions can induce condensation of like-charged polyelectrolytes into compact states, a process that requires different ion valences for different polyelectrolyte species. In this work we examine the condensation behavior in binary anionic polyelectrolyte mixtures consisting of DNA coils and F-actin rods in the presence of monovalent, divalent, and trivalent ions. As expected, monovalent ions do not condense either component and divalent ions selectively condense F-actin rods out of the polyelectrolyte mixture. For trivalent ions, however, we observe a microphase separation between the two polyelectrolytes into coexisting finite-sized F-actin bundles and DNA toroids. Further, by increasing the DNA volume fraction in the mixture, condensed F-actin bundles can be completely destabilized, leading to only DNA condensation within the mixture. We examine a number of possible causes and propose a model based on polyelectrolyte competition for ions.

Direct observation of counterion organization in F-actin polyelectrolyte bundles

Attractions between like-charged polyelectrolytes have been observed in a variety of systems (W.M. Gelbart, R.F. Bruinsma, P.A. Pincus, V.A. Parsegian, Phys. Today 53, September issue, 38 (2000)). Recent biological examples include DNA, filamentous viruses, and F-actin. Theoretical investigations on idealized systems indicate that counterion correlations play a central role, but no experiments that specifically probe such correlations have been performed. Using synchrotron X-ray diffraction, we have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well-defined biological polyelectrolyte) and found an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actin's helical symmetry; rather, the counterions organize into "frozen" ripples parallel to the actin filaments and form structures reminiscent of charge density waves. Moreover, these 1D counterion charge density waves form a coupled mode with twist deformations of the oppositely charged actin filaments. This counterion organization is not sensitive to thermal fluctuations in temperature range accessible to protein-based polyelectrolyte systems. Moreover, the counterion density waves are "pinned" to the spatial periodicity of charges on the actin filament even if the global filament charge density is varied, indicating the importance of charge periodicity on the polyelectrolyte substrate.

Density-functional theory of spherical electric double layers and ζ potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.

Metal ion-induced lateral aggregation of filamentous viruses fd and M13

We report a detailed comparison between calculations of inter-filament interactions based on Monte-Carlo simulations and experimental features of lateral aggregation of bacteriophages fd and M13 induced by a number of divalent metal ions. The general findings are consistent with the polyelectrolyte nature of the virus filaments and confirm that the solution electrostatics account for most of the experimental features observed. One particularly interesting discovery is resolubilization for bundles of either fd or M13 viruses when the concentration of the bundle-inducing metal ion Mg(2+) or Ca(2+) is increased to large (>100 mM) values. In the range of Mg(2+) or Ca(2+) concentrations where large bundles of the virus filaments are formed, the optimal attractive interaction energy between the virus filaments is estimated to be on the order of 0.01 kT per net charge on the virus surface when a recent analytical prediction to the experimentally defined conditions of resolubilization is applied. We also observed qualitatively distinct behavior between the alkali-earth metal ions and the divalent transition metal ions in their action on the charged viruses. The understanding of metal ions-induced reversible aggregation based on solution electrostatics may lead to potential applications in molecular biology and medicine.