Guilherme Volpe Bossa

Emergence of a Stern Layer from the Incorporation of Hydration Interactions into the Gouy–Chapman Model of the Electrical Double Layer

In one of the most commonly used phenomenological descriptions of the electrical double layer, a charged solid surface and a diffuse region of mobile ions are separated from each other by a thin charge-depleted Stern layer. The Stern layer acts as a capacitor that improves the classical Gouy-Chapman model by increasing the magnitude of the surface potential and limiting the maximal counterion concentration. We show that very similar Stern-like properties of the diffuse double layer emerge naturally from adding a nonelectrostatic hydration repulsion to the electrostatic Coulomb potential. The interplay of electrostatic attraction and hydration repulsion of the counterions and the surface leads to the formation of a diffuse counterion layer that remains well separated from the surface. In addition, hydration repulsions between the ions limit and control the maximal ion concentration and widen the width of the diffuse double layer. Our mean-field model, which we express in terms of electrostatic and hydration potentials, is physically consistent and conceptually similar to the classical Gouy-Chapman model. It allows the incorporation of ion specificity, accounts for hydration properties of charged surfaces, and predicts Stern layer properties, which we analyze in terms of the effective size of the hydrated counterions.

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.

Dipole Moment of a Charged Particle Trapped at the Air–Water Interface

The interaction between two charged particles (such as nanoparticles or colloids) trapped at the air-water interface becomes dipolar at large separations. The corresponding dipole moment can be modeled by considering a single point charge located exactly at the interface, but this model fails to correctly predict the dipole moments dependence on the salt concentration in the aqueous medium. We extend the single point charge model to two point charges that are separated by a fixed distance and are located at the air-water interface, with one charge being immersed in air and the other in the solvent. The two point charges represent the surface charges at the air-exposed and water-exposed regions of an interface-trapped particle. The two point charges also account for the spatial extension of the particle. On the basis of the Debye-Hückel model, we derive mathematical expressions for the interaction between two pairs of charges and discuss the salt concentration dependence of the dipolar moment at large separations. Our results reveal a residual dipole moment in the limit of large salt content that originates from the charge attached to the air-exposed region of the particle. We discuss nonlinear screening effects and compare the predicted dipolar moments with recent experimental results.

Investigations of the influence of liposome composition on vesicle stability and drug transfer in human plasma: a transfer study

Abstract Liposomal delivery constitutes a promising approach for i.v. administration of temoporfin (mTHPC) because lipid membranes can host these drug molecules. This study investigates the transfer and release of mTHPC to plasma proteins and stability of various liposomal formulations. To this end, we employed traces of radioactive markers and studied the effects of fatty acid chain length and the degree of saturation in the lipophilic tail, addition of cholesterol and PEGylation of the membrane surface and different drug-to-lipid ratios (DLRs). Liposomes were incubated in human plasma for various incubation times. Drawn samples were separated by asymmetrical flow field-flow fractionation (AF4). Drug was recovered in four fractions identified as albumin, high-density lipoprotein (HDL), low-density lipoprotein (LDL) and liposomes. Our results suggest that mTHPC fits best into fluid, unmodified bilayers when the drug-to-lipid ratio is low. Membrane rigidification as well as the presence of cholesterol and PEGyated lipids reduced the ability of the membrane to accommodate the drug but simultaneously improved the vesicle stability in plasma. Both mechanisms jointly affect the total degree of mTHPC release. We analyzed our data using a kinetic model that suggests the drug to be associated with the host membrane in two distinct states of which only one interacts directly with the plasma compartment.

Role of ion hydration for the differential capacitance of an electric double layer

The influence of soft, hydration-mediated ion-ion and ion-surface interactions on the differential capacitance of an electric double layer is investigated using Monte Carlo simulations and compared to various mean-field models. We focus on a planar electrode surface at physiological concentration of monovalent ions in a uniform dielectric background. Hydration-mediated interactions are modeled on the basis of Yukawa potentials that add to the Coulomb and excluded volume interactions between ions. We present a mean-field model that includes hydration-mediated anion-anion, anion-cation, and cation-cation interactions of arbitrary strengths. In addition, finite ion sizes are accounted for through excluded volume interactions, described either on the basis of the Carnahan-Starling equation of state or using a lattice gas model. Both our Monte Carlo simulations and mean-field approaches predict a characteristic double-peak (the so-called camel shape) of the differential capacitance; its decrease reflects the packing of the counterions near the electrode surface. The presence of hydration-mediated ion-surface repulsion causes a thin charge-depleted region close to the surface, which is reminiscent of a Stern layer. We analyze the interplay between excluded volume and hydration-mediated interactions on the differential capacitance and demonstrate that for small surface charge density our mean-field model based on the Carnahan-Starling equation is able to capture the Monte Carlo simulation results. In contrast, for large surface charge density the mean-field approach based on the lattice gas model is preferable.

Poisson-Boltzmann model of electrolytes containing uniformly charged spherical nanoparticles

Like-charged macromolecules typically repel each other in aqueous solutions that contain small mobile ions. The interaction tends to turn attractive if mobile ions with spatially extended charge distributions are added. Such systems can be modeled within the mean-field Poisson-Boltzmann formalism by explicitly accounting for charge-charge correlations within the spatially extended ions. We consider an aqueous solution that contains a mixture of spherical nanoparticles with uniform surface charge density and small mobile salt ions, sandwiched between two like-charged planar surfaces. We perform the minimization of an appropriate free energy functional, which leads to a non-linear integral-differential equation for the electrostatic potential that we solve numerically and compare with predictions from Monte Carlo simulations. Nanoparticles with uniform surface charge density are contrasted with nanoparticles that have all their charges relocated at the center. Our mean-field model predicts that only the former (especially when large and highly charged particles) but not the latter are able to mediate attractive interactions between like-charged planar surfaces. We also demonstrate that at high salt concentration attractive interactions between like-charged planar surfaces turn into repulsion.

Modeling Lipid–Lipid Correlations across a Bilayer Membrane Using the Quasi-chemical Approximation

Mixed fluid-like lipid membranes exhibit interactions not only among the lipids within a given leaflet but also across the bilayer. The ensuing collective interleaflet coupling of entire membrane domains has been modeled previously using various mean-field approaches. Yet, also on the level of individual lipids have correlations across the bilayer been observed experimentally for binary mixtures of charged/uncharged lipids with mismatching combinations of short and long acyl chain lengths. The present study proposes a lattice gas model to quantify these correlations. To this end, we represent a macroscopically homogeneous lipid bilayer by two coupled two-dimensional lattice gases that we study using the quasi-chemical approximation. We demonstrate that the rationalization of previous experimental results is only possible if besides two-body lipid-lipid interactions within and across the bilayer our model also accounts for an additional multibody interaction mechanism, namely the local hydrophobic height mismatch created by pairing short and long chain lipids together. The robustness of the quasi-chemical approximation is verified by comparison with Monte Carlo simulations.

Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations

Abstract.Mean-field electrostatics is used to calculate the differential capacitance of an electric double layer formed at a planar electrode in a symmetric 1:1 electrolyte. Assuming the electrolyte is also ion-size symmetric, we derive analytic expressions for the differential capacitance valid up to fourth order in the surface charge density or surface potential. Our mean-field model accounts exclusively for electrostatic interactions but includes an arbitrary non-ideality in the mixing entropy of the mobile ions. The ensuing criterion for the camel-to-bell shape transition of the differential capacitance is analyzed using commonly used mixing models (one based on a lattice gas and the other based on the Carnahan-Starling equation of state) and compared with Monte Carlo simulations. We observe a reasonable agreement between all our mean-field models and the simulation data for the camel-to-bell shape transition. The absolute value of the differential capacitance for an uncharged (or weakly charged) electrode is, however, not reproduced by our mean-field approaches, not even upon introducing a Stern layer with a thickness equal of the ion radius. We show that, if a Stern layer is introduced, its thickness dependence on the ion size is non-monotonic or, depending on the salt concentration, even inversely proportional.Graphical abstract

Surface tension of a Yukawa fluid according to mean-field theory

Yukawa fluids consist of particles that interact through a repulsive or attractive Yukawa potential. A surface tension arises at the walls of the container that encloses the fluid or at the interface between two coexisting phases. We calculate that surface tension on the level of mean-field theory, thereby either ignoring the particle size (ideal Yukawa fluid) or accounting for a non-vanishing particle size through a nonideal contribution to the free energy, exemplified either on the level of a lattice gas (lattice Yukawa fluid) or based on the Carnahan-Starling equation of state (Carnahan-Starling Yukawa fluid). Our mean-field results, which do not rely on assuming small gradients of the particle concentrations, become exact in the limit of large temperature and large screening length. They are calculated numerically in the general case and analytically in the two limits of small particle concentration and close to the critical point for a phase-separating system. For a sufficiently small particle concentration, our predicted surface tension is accurate whereas for a phase boundary, we expect good agreement with exact calculations in the limit of a large screening length and if the mean-field model employs the Carnahan-Starling equation of state.

Study of pK Values and Effective Dielectric Constants of Ionizable Residues in Pentapeptides and in Staphylococcal Nuclease (SNase) Using a Mean-Field Approach

The determination of pK values of amino acid residues as a function of temperature and ionic concentration is crucial to understanding the dynamics of various biological processes such as adsorption of peptides and their interactions with active sites of enzymes. In this study we developed a mean-field model to calculate the position-dependent dielectric constants of ionizable groups and the mean electrostatic potential on the surface. Such potential, which takes into account the contributions exerted by neighboring groups and ions in solution, is responsible for the fine-tuning of the pK value of each residue. The proposed model was applied to the amino acids Asp, Glu, Lys, His, Tyr, and Cys, and since the results were consistent with experimentally obtained values, the model was extended and applied to computation of pK values of Gly and Ala pentapeptides and of ionizable residues of the enzyme staphylococcal nuclease (SNase). In this latter case, we used an approach similar to a first-neighbors approximation, and the results turned out to be in good agreement with previously reported data when considering only the interactions of charged groups located at distances of maximally 20 Å. These considerations and the little computational cost involved turn the suggested approach into a promising tool for the modeling of force fields in computational simulations.