Guillermo Iván Guerrero-García

A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics

We report a GPU implementation in HOOMD Blue of long-range electrostatic interactions based on the orientation-averaged Ewald sum scheme, introduced by Yakub and Ronchi (J. Chem. Phys. 2003, 119, 11556). The performance of the method is compared to an optimized CPU version of the traditional Ewald sum available in LAMMPS, in the molecular dynamics of electrolytes. Our GPU implementation is significantly faster than the CPU implementation of the Ewald method for small to a sizable number of particles (∼10(5)). Thermodynamic and structural properties of monovalent and divalent hydrated salts in the bulk are calculated for a wide range of ionic concentrations. An excellent agreement between the two methods was found at the level of electrostatic energy, heat capacity, radial distribution functions, and integrated charge of the electrolytes.

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.

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coions size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterions size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.

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.

Inversion of the Electric Field at the Electrified Liquid–Liquid Interface

The thermodynamics of the general system of two immiscible electrolytes in the presence of an electric field depends strongly on the distribution of ions near the liquid interface. Here, we calculate the corresponding electrostatic potential difference, excess surface tension, and differential capacity via Monte Carlo simulations, which include ion correlations and polarization effects, and via a modified nonlinear Poisson-Boltzmann theory. Macroscopically, we find good agreement between our results and experimental data without needing any fitting parameter. At higher salt concentrations, charge overcompensation in the lower-permittivity region is observed, which results in a local inversion of the electric field accompanied by charge inversion near the interface. We find that these interesting phenomena are mainly driven by the excluded-volume effects associated with large organic ions in the oil phase, although polarization effects and between-layer ion correlations have a significant impact in the adsorption of ions close to the liquid interface. In addition, our Monte Carlo simulations predict that the differential capacity is maximal at the point of zero charge, in contrast with the classical Poisson-Boltzmann theory results.

Effective charges and virial pressure of concentrated macroion solutions

Significance Colloids constitute the basic components of many everyday products and are integrated into the fabric of modern society. Understanding their assembly is key for nanotechnological and biotechnological advances. At the single-particle level, colloids commonly possess electric charge. Consequently, the structure to which they conform is strongly influenced by electrostatic interactions. In solution, these interactions are modified by the presence of ions. We have developed a model for computing the corresponding effective electrostatic interactions as well as the osmotic pressure. Our model extends the applicability of Derjaguin−Landau−Verwey−Overbeek theory to dense systems in which many-body effects are crucial. This will allow previously impossible, mesoscale studies of colloidal assembly to be performed analytically or by simulation with implicit ions models. The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin−Landau−Verwey−Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion−macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.

Charged hydrophobic colloids at an oil–aqueous phase interface

Hydrophobic poly(methyl methacrylate) (PMMA) colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image-charge effects lead to strong binding of colloidal particles to the interface, even though the particles are wetted very little by the aqueous phase. We study both the behavior of individual colloidal particles as they approach the interface and the interactions between particles that are already interfacially bound. We demonstrate that using particles which are minimally wetted by the aqueous phase allows us to isolate and study those interactions which are due solely to charging of the particle surface in oil. Finally, we show that these interactions can be understood by a simple image-charge model in which the particle charge q is the sole fitting parameter.

Excluded volume and ion-ion correlation effects on the ionic atmosphere around B-DNA: theory, simulations, and experiments.

The ionic atmosphere around a nucleic acid regulates its stability in aqueous salt solutions. One major source of complexity in biological activities involving nucleic acids arises from the strong influence of the surrounding ions and water molecules on their structural and thermodynamic properties. Here, we implement a classical density functional theory for cylindrical polyelectrolytes embedded in aqueous electrolytes containing explicit (neutral hard sphere) water molecules at experimental solvent concentrations. Our approach allows us to include ion correlations as well as solvent and ion excluded volume effects for studying the structural and thermodynamic properties of highly charged cylindrical polyelectrolytes. Several models of size and charge asymmetric mixtures of aqueous electrolytes at physiological concentrations are studied. Our results are in good agreement with Monte Carlo simulations. Our numerical calculations display significant differences in the ion density profiles for the different aqueous electrolyte models studied. However, similar results regarding the excess number of ions adsorbed to the B-DNA molecule are predicted by our theoretical approach for different aqueous electrolyte models. These findings suggest that ion counting experimental data should not be used alone to validate the performance of aqueous DNA-electrolyte models.

Electrolyte-Mediated Assembly of Charged Nanoparticles

Solutions at high salt concentrations are used to crystallize or segregate charged colloids, including proteins and polyelectrolytes via a complex mechanism referred to as “salting-out”. Here, we combine small-angle X-ray scattering (SAXS), molecular dynamics (MD) simulations, and liquid-state theory to show that salting-out is a long-range interaction, which is controlled by electrolyte concentration and colloid charge density. As a model system, we analyze Au nanoparticles coated with noncomplementary DNA designed to prevent interparticle assembly via Watson–Crick hybridization. SAXS shows that these highly charged nanoparticles undergo “gas” to face-centered cubic (FCC) to “glass-like” transitions with increasing NaCl or CaCl2 concentration. MD simulations reveal that the crystallization is concomitant with interparticle interactions changing from purely repulsive to a “long-range potential well” condition. Liquid-state theory explains this attraction as a sum of cohesive and depletion forces that originate from the interelectrolyte ion and electrolyte–ion–nanoparticle positional correlations. Our work provides fundamental insights into the effect of ionic correlations in the salting-out mechanism and suggests new routes for the crystallization of colloids and proteins using concentrated salts.