Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

Electric polarizability of DNA in aqueous salt solution

Monte Carlo simulations are performed to determine the anisotropy of the electric polarizability of a model DNA fragment in aqueous salt solution. By taking into consideration the participation of coions in the electroneutrality condition, at every simulation step, we obtain a list of counterions constituting the net charge arranged in increasing order of their distance from the DNA and calculate the contribution to the dipole moment from the first n counterions in the list. We define a partial polarizability tensor due to these n counterions to understand the origin of the polarizability in close relation to the solution structure. The ionic distributions are described by the counterion condensation theory. Characteristic features of the electric properties of polyelectrolytes are reproduced. The anisotropy of the electric polarizability Deltaalpha of DNA decreases with the addition of salt, yielding values comparable to experiment. The effect of electrophoretic motion of the polyion is examined by estimating its upper limit.     

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 coion's 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 counterion's 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.     

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Computer simulation of the ionic atmosphere around Z-DNA

We describe a coarse-grained model for Z-DNA that mimics the DNA shape with a relatively small number of repulsive interaction sites. In addition, negative charges are placed at the phosphate positions. The ionic atmosphere around this grooved Z-DNA model is then investigated with Monte Carlo simulation. Cylindrically averaged concentration profiles as well as the spatial distribution of ions have been calculated. The results are compared to those for other DNA models differing in the repulsive core. This allows the examination of the effect of the DNA shape in the ionic distribution. It is seen that the penetrability of the ions to the DNA groove plays an important role in the ionic distribution. The results are also compared with those reported for B-DNA. In both conformers the ions are structured in alternating layers of positive and negative charge. In Z-DNA the layers are more or less concentric to the molecular axis. Besides, no coions enter into the single groove of this conformer. On the contrary, the alternating layers of B-DNA are also structured along the axial coordinate with some coions penetrating into the major groove. In both cases we have found five preferred locations of the counterions and two for the coions. The concentration of counterions reaches its absolute maximum at the narrow Z-DNA groove and at the minor groove of B-DNA, the value of the maximum being higher in the Z conformer.     

Distribution of counterions in the double layer around a cylindrical polyion

The modified Poisson-Boltzmann (MPB) equation, and the Monte Carlo (MC) method, were applied to the cell model of a polyelectrolyte solution in order to calculate the distribution of counterions around a cylindrical polyion. Both methods suggest stronger binding of counterions to the polyion than predicted by the ordinary Poisson-Boltzmann (PB) equation. The inclusion of counterion-counterion correlation being neglected in the PB equation, leads to a better agreement of the calculated osmotic coefficients with those measured.     

Equation of state of charged colloidal suspensions and its dependence on the thermodynamic route

The thermodynamic properties of highly charged colloidal suspensions in contact with a salt reservoir are investigated in the framework of the renormalized Jellium model (RJM). It is found that the equation of state is very sensitive to the particular thermodynamic route used to obtain it. Specifically, the osmotic pressure calculated within the RJM using the contact value theorem can be very different from the pressure calculated using the Kirkwood-Buff fluctuation relations. On the other hand, Monte Carlo simulations show that both the effective pair potentials and the correlation functions are accurately predicted by the RJM. It is suggested that the lack of self-consistency in the thermodynamics of the RJM is a result of neglected electrostatic correlations between the counterions and coions.     

Density-functional theory and Monte Carlo simulation study on the electric double layer around DNA in mixed-size counterion systems

A density-functional approach and canonical Monte Carlo simulations are presented for describing the ionic microscopic structure around the DNA molecule immersed in mixed-size counterion solutions. In the density-functional approach, the hard-sphere contribution to the Helmholtz energy functional is obtained from the modified fundamental measure theory [Y.-X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)], and the electrostatic contribution is evaluated through a quadratic functional Taylor expansion. The new theory is suitable to the systems containing ions of arbitrary sizes and valences. In the established canonical Monte Carlo simulation, an iterative self-consistent method is used to evaluate the long-range energy, and another iterative algorithm is adopted to obtain desired bulk ionic concentrations. The ion distributions from the density-functional theory (DFT) are in good agreement with those from the corresponding Monte Carlo (MC) simulations. It is found that the ratio of the bulk concentrations of two species of counterions (cations) makes significant contribution to the ion distributions in the vicinity of DNA. Comparisons with the electrostatic potential profiles from the MC simulations show that the accuracy of the DFT becomes low when a small divalent cation exists. Both the DFT and MC simulation results illustrate that the electrostatic potential at the surface of DNA increases as the anion diameter or the total cation concentration is increased and decreases as the diameter of one cation species is increased. The calculation of electrostatic potential using real ion diameters shows that the accuracy of DFT predictions for divalent ions is also acceptable.     

Preferential interaction between DNA and small ions in mixed-size counterion systems: Monte Carlo simulation and density functional study

Competitive binding between counterions around DNA molecule is characterized using the preferential interaction coefficient of individual ion in single and mixed electrolyte solutions. The canonical Monte Carlo (MC) simulation, nonlinear Poisson-Boltzmann (PB) equation, and density functional theory (DFT) proposed in our previous work [Wang, Yu, Gao, and Luo, J. Chem. Phys. 123, 234904 (2005)] are utilized to calculate the preferential interaction coefficients. The MC simulations and theoretical results show that for single electrolyte around DNA, the preferential interaction coefficient of electrolyte decreases as the cation size is increased, indicating that the larger cation has less accumulation ability in the vicinity of DNA. For the mixed electrolyte solution, it is found that cation diameter has a significant effect on the competitive ability while anion diameter has a negligible effect. It proves that the preferential interaction coefficients of all ions decrease as the total ionic concentration is increased. The DFT generally has better performance than the PB equation does when compared to the MC simulation data. The DFT behaves quite well for the real ionic solutions such as the KCl-NaCl-H2O, NaCl-CaCl2-H2O, and CaCl2-MgCl2-H2O systems.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

The orientation parameter for energy transfer in restricted geometries including block copolymer interfaces: a Monte Carlo study

We describe Monte Carlo simulations of resonance energy transfer (RET) experiments for immobile donor (D) and acceptor (A) dyes confined to planar, cylindrical, and spherical restricted geometries. We compare values of the quantum efficiency (PhiET) evaluated through consideration of individual donor-acceptor pairs, with values calculated assuming a pre-averaged value of the orientation parameter /kappa/2 = 0.476 appropriate for infinite three dimensional (3D) space. For dyes confined to restricted geometries where the length scale of the confining dimension is less than or equal to the F?rster radius R0, the coupling of the orientation parameter and the donor-acceptor distance becomes noticeable. Values of Phi(ET) obtained by proper consideration of the orientation parameter are smaller than those calculated using /kappa/2 = 0.476. We use this Monte Carlo method to reanalyze the fluoresce decay measured from dye-labeled poly(isoprene-b-methyl methacrylate) diblock copolymer with lamellar structure,(1) from which the interface thickness for PI-PMMA lamella can be retrieved. We found the retrieved interface thickness is sensitive to the choice of dipole orientation. If all dipoles in the confined polymer interface have a random orientation, the value of interface thickness was found to be 0.9 +/- 0.2 nm through consideration of individual dipole orientations. Assumption of /kappa/2 = 0.476 in the FRET calculations leads to a larger value of interface thickness (1.3 +/- 0.2 nm) due to the neglect of the coupling between dipole orientation and D-A distance for the dyes confined to lamellar interfaces.     

Counterion-counterion correlation in the double layer around cylindrical polyions: counterion size and valency effects

Monte Carlo simulation and Poisson-Boltzmann results on some aspects of structure and thermodynamics of aqueous polyelectrolyte solutions are presented. The polyelectrolyte solution is described by an infinitely long cylindrical polyion surrounded by counterions modeled as rigid ions moving in a continuum dielectric. Ion-ion correlations in the form of volume average of the counterion-counterion distribution function in the double layer surrounding the polyion are reported for mono- and divalent counterions and for a range of polyion concentrations and charge density parameters in each case. These results confirm again strong influence of the charge density parameter of polyions on properties of polyelectrolyte solutions. The structural information is supplemented by the calculated thermodynamic properties such as osmotic coefficients and heats of dilutions; the latter quantity has not been examined yet in detail by computer simulations. The results are discussed in view of the existing experimental data from the literature for these properties.     

The interaction between charged aggregates in electrolyte solution. A Monte Carlo simulation study

The Monte Carlo simulation technique has been used to calculate the electrostatic force acting upon a charged aggregate outside a similarly charged wall. Contrary to intuition and existing electrostatic theories, the force is found to be attractive for some realistic values of the parameters determining the system. High surface charge density, low temperature, low relative permitivity and polyvalent neutralizing counterions are all factors that favour a net attraction between the wall and the aggregate. In some cases the resulting electrostatic attractive force is found to be an order of magnitude larger than the ordinary van der Waals attraction applied in the DLVO theory of colloidal stability. The attractive interaction is interpreted as being due to currelations between the counterions in the electric double layers.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.     

Influence of atomistic physics on electro-osmotic flow: an analysis based on density functional theory

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.     

Gamma distribution model to provide a direct assessment of the overall quality of quantum Monte Carlo-generated electron distributions

Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.