P. González-Mozuelos

Ion condensation in salt‐free dilute polyelectrolyte solutions

We study ion condensation in salt‐free dilute solutions of polyelectrolyte chains of different fractal geometries, from random walks to rigid rods. In finite size chains with a discrete charge distribution, ion condensation is only observed in multiple chain systems. A thermodynamic analysis of ion condensation with linearized interactions among the condensed counterions and the monomers leads to rigid rod lowest free energy conformations, regardless of the values of the valency of the monomers (zm), the negative value of the ratio of the valency of the counterions to the valency of the monomers (Pz), and the ratio of the Bjerrum length (lB) to the distance between charges along the polyion (b). As z2mPzlB/b increases, however, the fraction of condensed counterions increases and the polyion concentration at which ion condensation appears decreases. Above this critical polyion concentration, ion condensation is observed even when lB/b<1/z2mPz. When correlations are included, representing the tendency of th...

Effective pair potentials for charged colloidal particles

A general formalism for ionic fluids is presented. We report general and exact expressions for the distribution functions which directly satisfy the Stillinger–Lovett moment conditions. General and exact expressions are also provided for the effective pair potentials among charged colloidal particles. These general expressions are a direct consequence of the multicomponent Ornstein–Zernike (OZ) equations and the asymptotic behavior of the direct correlation functions in charged systems. The effective pair potentials show two distinct parts: short-ranged and electrostatic. For the primitive model (PM) with pointlike small ions the electrostatic component is reduced, for sufficiently large distances, to a screened Coulomb potential with renormalized charges. The general expression of the effective electrostatic interaction gives a clear insight of the specific conditions of validity of the Derjaguin–Landau–Verwey–Overbeek (DLVO) model and of the possible directions in which this model may be improved. We al...

Potential of mean force between identical charged nanoparticles immersed in a size-asymmetric monovalent electrolyte

In a previous theoretical and simulation study [G. I. Guerrero-García, E. González-Tovar, and M. Olvera de la Cruz, Soft Matter 6, 2056 (2010)], it has been shown that an asymmetric charge neutralization and electrostatic screening depending on the charge polarity of a single nanoparticle occurs in the presence of a size-asymmetric monovalent electrolyte. This effect should also impact the effective potential between two macroions suspended in such a solution. Thus, in this work we study the mean force and the potential of mean force between two identical charged nanoparticles immersed in a size-asymmetric monovalent electrolyte, showing that these results go beyond the standard description provided by the well-known Derjaguin-Landau-Verwey-Overbeek theory. To include consistently the ion-size effects, molecular dynamics (MD) simulations and liquid theory calculations are performed at the McMillan-Mayer level of description in which the solvent is taken into account implicitly as a background continuum with the suitable dielectric constant. Long-range electrostatic interactions are handled properly in the simulations via the well established Ewald sums method and the pre-averaged Ewald sums approach, originally proposed for homogeneous ionic fluids. An asymmetric behavior with respect to the colloidal charge polarity is found for the effective interactions between two identical nanoparticles. In particular, short-range attractions are observed between two equally charged nanoparticles, even though our model does not include specific interactions; these attractions are greatly enhanced for anionic nanoparticles immersed in standard electrolytes where cations are smaller than anions. Practical implications of some of the presented results are also briefly discussed. A good accord between the standard Ewald method and the pre-averaged Ewald approach is attained, despite the fact that the ionic system studied here is certainly inhomogeneous. In general, good agreement between the liquid theory approach and MD simulations is also found.

Effective attractions between like-charged colloidal particles

We apply the Ornstein–Zernike equations together with the extended Zerah–Hansen approach, described in a previous paper [J. Chem. Phys. 109, 11074 (1998)], to determine the microstructure of a colloidal suspension at finite concentrations. Using these results as an input, the effective pair potential between two colloidal particles is also calculated following the general approach described in that paper. It is found that, for sufficiently large concentrations, this effective potential develops an attractive well with a minimum located at a distance of almost four macroparticle diameters. It is also shown that this attraction is generated by the inversion of the sign of the effective charged distribution surrounding each macroparticle involved in the electrostatic component of the effective pair potential.

Electrostatic trapping of a colloidal monolayer near a charged wall

The structure of a model colloidal suspension in the vicinity of a charged wall is studied in the framework of the Derjaguin–Landau–Verwey–Overbeek interaction potential and the hypernetted‐chain approximation. Here we consider the case of dilute suspension of highly charged macroparticles interacting with weakly repulsive, neutral, and attractive walls. As the wall–particle electrostatic interactions become successively less repulsive, the formation of a monolayer of colloidal particles, strongly adsorbed onto the surface, is predicted by our results. This monolayer of electrostatically confined particles mimic the effect of an effective surface charge distribution adjacent to the wall which, together with the bare wall surface charge, induces on the other, nonconfined, colloidal particles the same local‐concentration profile as that in front of a highly charged and repulsive wall.

Association in electrolyte solutions: Rodlike polyelectrolytes in multivalent salts

We describe a new approach to determine the degree of association between ionic components in complex electrolyte solutions. We use the electrostatic contribution to the free energy that arises from the exact separation into long and short ranged parts of the correlation functions in a dilute electrolyte solution to determine the effective charge of the various ionic components. We describe the short-ranged direct correlations between different ionic components with delta functions whose strength give the direct association between them. The association is determined self-consistently by minimizing the resulting free energy, which contains long and short range correlations contributions. Association between like charges is mediated by direct association between opposite charges. We analyze rodlike polyelectrolyes in monovalent and/or multivalent salts. We find a broad minimum in the absolute value of effective rod charge at long distances as a function of monovalent salt concentration. This minimum is due to the association of the salt ions among themselves. We also determine the number of multivalent and monovalent ions associated to the rods. The degree of association is a function of the smallest length scale, which determines the electrostatic potential between ionic species at contact.

Random phase approximation for complex charged systems: Application to copolyelectrolytes (polyampholytes)

We study binary polyelectrolytes in the melt state and in concentrated solutions using the random phase approximation (RPA). We compute the thermodynamics and electrostatics of chemically linked polyelectrolytes chains into block copolymer molecules (copolyelectrolytes). Polyelectrolytes blends and copolyelectrolytes in the presence of free ions have Debye–Huckel‐type effective monomer–monomer interactions, even when the polymer chains are not charged. Copolyelectrolyte of chemically linked chains of opposite charge in the absence of counterions, have ion–ion effective interactions characteristic of a dielectric medium, contrary to the case of polyelectrolyte blends where these effective interactions are Debye–Huckel type, even on the absence of free ions. The dielectric constant in such a diblock copolymer melt is proportional to the square of the degree of polymerization Np. In the reference state (without interactions) RPA assumes random walk statistics, which are nearly unperturbed in the dielectric; ...

Structure of a colloidal suspension confined in a planar slit

In this paper we present a simple theoretical scheme to calculate the inhomogeneous structure of an aqueous monodisperse suspension of highly charged spherical particles confined between two parallel charged walls. The theoretical model is based on the Derjaguin–Landau–Verwey–Overbeek level of description for the particle–particle and wall–particle interactions. The main features of the theoretically predicted local‐concentration profile are found to be in good agreement with our Monte Carlo simulations for the same model. In particular, in the limiting case of large wall‐to‐wall separation, the predictions of previous work, concerning the structure of a suspension in the neighborhood of a highly repulsive wall, are found to agree with our simulation results.

An exact method to obtain effective electrostatic interactions from computer simulations: The case of effective charge amplification

We discuss here an exact method to determine the parameters regulating the screened Coulomb interactions among spherical macroions immersed in a simple electrolyte. This approach provides rigorous definitions for the corresponding screening length, effective permittivity, and renormalized charges, and can be employed for precise and reliable calculations of these parameters within any scheme. In particular, we introduce a simple procedure for extracting this information from computer simulations. The viability of this approach is demonstrated by applying it to a three-component model system which includes anionic nanoparticles and monovalent cations and anions. The mean forces between nanoparticles are determined directly from simulations with two macroions, plus small ions, inside a single cell with periodic boundary conditions. The values of the parameters of interest, on the other hand, are gathered from two separate sets of computer simulations: one set provides information about the short-range correlations among the small ions, which in turn determine the screening length and effective permittivity; the second set supplies the short-range components of the ionic distribution around one isolated macroion, which also determine its renormalized charge. The method presented here thus avoids the uncertain fitting of these parameters from the asymptotic tail of the mean force and allows us to investigate in detail this connection between the renormalized charge of the macroion and the short-range (virtual) part of the ionic cloud surrounding it. Using the standard prescription to extract an effective charge from the corresponding renormalized value, we then proceed to clarify the mechanisms behind the possibility of effective charge amplification (i.e., an effective charge larger than the bare macroion charge). Complementarily, we report results for the corresponding bridge functions too.

Large counterions boost the solubility and renormalized charge of suspended nanoparticles

Colloidal particles are ubiquitous in biology and in everyday products such as milk, cosmetics, lubricants, paints, or drugs. The stability and aggregation of colloidal suspensions are of paramount importance in nature and in diverse nanotechnological applications, including the fabrication of photonic materials and scaffolds for biological assemblies, gene therapy, diagnostics, targeted drug delivery, and molecular labeling. Electrolyte solutions have been extensively used to stabilize and direct the assembly of colloidal particles. In electrolytes, the effective electrostatic interactions among the suspended colloids can be changed over various length scales by tuning the ionic concentration. However, a major limitation is gelation or flocculation at high salt concentrations. This is explained by classical theories, which show that the electrostatic repulsion among charged colloids is significantly reduced at high electrolyte concentrations. As a result, these screened colloidal particles are expected to aggregate due to short-range attractive interactions or dispersion forces as the salt concentration increases. We discuss here a robust, tunable mechanism for colloidal stability by which large counterions prevent highly charged nanoparticles from aggregating in salt solutions with concentrations up to 1 M. Large counterions are shown to generate a thicker ionic cloud in the proximity of each charged colloid, which strengthens short-range repulsions among colloidal particles and also increases the corresponding renormalized colloidal charge perceived at larger separation distances. These effects thus provide a reliable stabilization mechanism in a broad range of biological and synthetic colloidal suspensions.