Effective interactions between electric double layers

Azimuthal frustration and bundling in columnar DNA aggregates

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the interaxial separation of two DNA molecules, but also on their azimuthal orientation. The optimal mutual azimuthal angle is a function of the DNA-DNA interaxial separation, which leads to azimuthal frustrations in an aggregate. On the basis of the pair potential, the positional and orientational order in columnar B-DNA assemblies in solution is investigated. Phase diagrams are calculated using lattice sums supplemented with the entropic contributions of the counterions in solution. A variety of positionally and azimuthally ordered phases and bundling transitions is predicted, which strongly depend on the counterion adsorption patterns.

Nonmonotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient B2 of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the "primitive model." The salt and counterions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that B2 first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that linear and nonlinear Poisson Boltzmann theories fail for large ionic strength. The observed nonmonotonicity of B2 is compared with experiments. Implications for protein crystallization are discussed.

Time evolution of the formation of different size cationic liposome-polyelectrolyte complexes

We report on the time evolution of the aggregation behaviour of cationic liposome-polyelectrolyte complexes studied by means of dynamic light scattering technique. Pure dioleoyltrimethilammoniumpropane (DOTAP) and mixed DOTAP-dipalmitoylphosphatidylcholine (DPPC) liposomes in polyacrylate sodium salt aqueous solutions in a wide concentration range have been investigated and the size and size distributions of the resulting aggregates evaluated from the intensity autocorrelation function of the scattered light. Under appropriate conditions, we found two discrete aggregation regimes, resulting in two different structural arrangements, whose time evolution depends on the charge ratio and the polyelectrolyte molecular weight. A first small component of average size in the 100-500 range nm coexists with a larger component, whose typical size increases with time, up to some micrometers. The cluster growth from a single liposome, 70 nm in diameter, to the formation of polymer-coated liposome aggregates has been briefly discussed in the light of steric stabilization of colloids. Moreover, it has been found that the kinetics of aggregation of the larger, time-dependent, component follows a dynamical scaling within the diffusion-limited cluster aggregation (DLCA) regime. The understanding of structures resulting from interactions between polyelectrolytes with oppositely charged liposomes may help towards formulation of "lipoplexes" (cationic lipid-DNA complexes) to use as non-viral gene carriers.

Overcharging in colloids: beyond the Poisson-Boltzmann approach

A broad range of manufactured products and biological fluids are colliods. The ability to understand and control the processes (of scientific, technological and industrial interest) in which such colloids are involved relies upon a precise knowledge of the electrical double layer. The traditional approach to describing this ion cloud around colloidal particles has been the Gouy-Chapman model developed on the basis of the Poisson-Boltzmann equation. Since the early 1980s, however, more sophisticated theoretical treatments have revealed both quantitative and qualitative deficiencies in the Poisson-Boltzmann theory, particularly at high ionic strengths and/or high surface charge densities. This review deals with these novel approaches, which are mostly computer simulations and approximate integral equation theories based on the so-called primitive model. Special attention is paid to phenomena that cannot be accounted for by the classic theory as a result of neglecting ion size correlations, such as overcharging, namely, the counterion concentration in the immediate neighborhood of the surface is so large that the particle surface is overcompensated. Other illustrative examples are the nonmonotonic behavior of the electrostatic potential and attractive interactions between equally charged surfaces. These predictions are certainly remarkable and, on paper, they can have an effect on experimentally measurable quantities (for instance, electrophoretic mobility). Even so, these new approaches have scarcely been applied in practice. Thus a critical survey on the relevance of ion size correlation in real systems is also included. Overcharging of macroions can also be brought about by adsorption of oppositely charged polyelectrolytes. Noteworthy examples and theoretical approaches for them are also briefly reviewed.

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modeling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.

Simple approach for charge renormalization in highly charged macroions

We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.

Generalizations for the Potential of Mean Force between Two Isolated Colloidal Particles from Monte Carlo Simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin-Landau-Verwey-Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Gamma=z(2)l(B)/a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l(B)=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Gamma approximately 0.5 and, second, that onset of attraction occurs at Gamma approximately 1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.

Osmotic pressure of charged colloidal suspensions: a unified approach to linearized Poisson-Boltzmann theory

We study theoretically the equation of state of a fluid suspension of charged objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed against an electrolyte solution using the cell model and linear Poisson-Boltzmann (PB) theory. From the volume derivative of the grand potential functional of linear theory we obtain two expressions for the osmotic pressure in terms of the potential or ion profiles, neither of which coincides with the expression known from nonlinear PB theory, namely, the density of microions at the cell boundary. We show that the range of validity of linearization depends strongly on the linearization point and prove that expansion about the self-consistently determined average potential is optimal in several respects. For instance, screening inside the suspension is automatically described by the actual ionic strength, resulting in the correct asymptotics at high colloid concentration. Together with the analytical solution of the linear PB equation for cell models of arbitrary dimension and electrolyte composition, explicit and very general formulas for the osmotic pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis also shows that whether or not linear theory predicts a phase separation depends crucially on the precise definition of the pressure, showing that depending on the choice, an artificial phase separation in systems as important as DNA in physiological salt solution may result.

Three-body forces between charged colloidal particles

Within nonlinear Poisson-Boltzmann theory we calculate the pair and triplet interactions between charged colloidal spheres, specifically in the nonlinear regime of low salt concentrations and high charges. We find repulsive pair interactions and attractive triplet interactions. Within a van der Waals-like mean-field theory we estimate in which parameter regime a gas-liquid coexistence is to be expected.

Thermodynamics of ionic microgels

We present a theory of dilute aqueous suspensions of microgel particles. It is found that as the number of charged monomers in the polymer network composing mesoscopic gel increases, the particles undergo a swelling transition. Depending on the hydrophobicity of the polymer, this transition can be either continuous or discontinuous. Furthermore, similar to charge stabilized colloidal particles, we find that the electrophoretic mobility of the microgel is controlled by an effective charge. Unlike the colloids, however, for which the effective charge grows asymptotically with the logarithm of the bare charge, the effective charge of an ionic microgel scales as Z(eff) approximately Z0.5. The findings are in good agreement with the experimental measurements.

Conformations and interactions of star-branched polyelectrolytes

Combining monomer-resolved molecular dynamics simulations with a theory based on a variational free energy, we calculate the conformational properties and the effective interactions of star-branched polyelectrolytes for a large variety of arm numbers, degrees of polymerization, and charge fractions, with and without added salt. We find quantitative agreement between theory and simulation and put forward analytical expressions that allow the calculation of the interaction between such macromolecules.

Poisson-Boltzmann theory for membranes with mobile charged lipids and the pH-dependent interaction of a DNA molecule with a membrane

We consider a planar stiff model membrane consisting of mobile surface groups whose state of charge depends on the pH and the ionic composition of the adjacent electrolyte solution. To calculate the mean-field interaction potential between a charged object and such a model membrane, one needs to solve a Poisson-Boltzmann boundary value problem. We here derive and discuss the boundary condition at the membrane surface, a condition that is generally appropriate for biological membranes where two charge-regulating mechanisms are present at the same time: the pH-dependent chemical charge regulation and a regulation through the in-plane mobility of the surface groups. As an application of this general formalism, we consider the specific example of a single DNA molecule, approximated by a cylinder with smeared-out surface charges, interacting with such a model membrane. We study the effect that the two competing charge-regulating mechanisms have on the DNA/membrane interaction and the distribution of surface ions in the plane of the membrane. We find that, at short DNA-membrane distances, membrane fluidity can have a considerable impact on the DNA adsorption behavior and can lead to such counterintuitive phenomena as the adsorption of a negatively charged DNA onto a (on average) negatively charged membrane.

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

We calculate the two-, three-, four-, and five-body (state-independent) effective potentials between the centers of mass (c.m.'s) of self-avoiding walk polymers by Monte Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)(n), and decrease in absolute magnitude with increasing n. We find semiquantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective density dependent two-body potentials that exactly reproduce the pair-correlations between the c.m. of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the density independent three-body potential. Triplet correlations between the c.m. of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair potential cannot simultaneously reproduce the two- and three-body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of three-body potentials.

Accurate calculation of three-body depletion interactions

We compute three-body depletion interactions in a hard-sphere mixture within the framework of density-functional theory and by considering the infinite dilution limit of the functional. The results look very accurate and show three-body interactions much smaller than the pair depletion ones, revealing that these are strongly influenced by correlations and have a decay length similar to the two-body depletion potential. The results are compared with the predictions of the Asakura-Oosawa model for the triplet interactions.

Influence of solvent granularity on the effective interaction between charged colloidal suspensions

We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard-sphere solvent. Apart from molecular oscillating forces for nearly touching colloids that arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerably reduced as compared to the prediction based on the primitive model. When these forces are repulsive, the long-distance behavior can be described by an effective Yukawa pair potential with a solvent-renormalized charge. As a function of colloidal volume fraction and added salt concentration, this solvent-renormalized charge behaves qualitatively similar to that obtained via the Poisson-Boltzmann cell model, but there are quantitative differences. For divalent counterions and nanosized colloids, on the other hand, the hydration may lead to overscreened colloids with mutual attraction while the primitive model yields repulsive forces. All these new effects can be accounted for through a solvent-averaged primitive model (SPM) which is obtained from the full model by integrating out the solvent degrees of freedom. The SPM was used to access larger colloidal particles without simulating the solvent explicitly.

Effective macroion-macroion potentials in asymmetric electrolytes

Effective macroion-macroion potentials in solutions of macroions carrying 60 elementary charges and either monovalent or divalent counterions have been calculated at different concentrations by means of Monte Carlo simulations with a consequent inversion of radial distribution functions according to Lyubartsev and Laaksonen [Phys. Rev. E 52, 3730 (1995)]. With monovalent counterions, the effective potentials are essentially of a Yukawa type, whereas with divalent ones, an attractive region appears at short separation. A charge renormalization scheme invoking the cell model and the assumption of a Yukawa-type potential works favorably only in the case of monovalent counterions.

Effective interaction between helical biomolecules

The effective interaction between two parallel strands of helical biomolecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than 6 A it can be both attractive and repulsive. Furthermore, we report a nonmonotonic behavior of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the biomolecules is suitably renormalized.