arXiv subjects

Derek Frydel

Publications and source records attributed to Derek Frydel.

35 records · Page 2Linked to original sources

arXiv2019

General theory of charge regulation within the Poisson-Boltzmann framework: study of a sticky-charged wall model

This work introduces a sticky-charge wall model as a simple and intuitive representation of charge regulation. Implemented within the mean-field level of description, the model modifies the boundary conditions without affecting the underlying Poisson-Boltzmann (PB) equation of an electrolyte. Employing various modified PB equations, we are able to assess how various structural details of an electrolyte influence charge regulation.

cond-mat.soft↗

arXiv2018

Soft-particle lattice-gas in 1d: one- and two-component cases

The object of the present article is a 1d lattice-gas system comprised of soft-particles, wherein particles interact only if they occupy the same or a neighboring site, as a simple representation of penetrable particles of soft condensed matter. To represent different scenarios, two different realizations of the lattice model are considered, a one-component and a two-component system, where in the two-component case particles of the same species repel and those of opposite species attract each other. The systems are analyzed entirely within the transfer matrix framework. Special attention is paid to the criterion devised in Ref. [Phys. Rev. E 63, 031206 (2001)], which serves to separate two classes of behavior encountered in a one-component penetrable particle systems. In addition to confirm the existence of a similar criterion for the one-component lattice-gas model, we find that the same criterion can be applied to the two-component system to provide conditions for thermodynamic catastrophe.

cond-mat.soft↗

arXiv2018

Mean-field theory of active electrolytes: dynamic adsorption and overscreening

We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active dynamics is that particles adhere to hard-surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemipsorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.

cond-mat.soft↗

arXiv2018

Two-component Gaussian core model: strong-coupling limit, Bjerrum pairs, and gas-liquid phase transition

In the present work we investigate a gas-liquid transition in a two-component Gaussian core model, where particles of the same species repel and those of different species attract. Unlike a similar transition in a one-component system with particles having attractive interactions at long separations, and repulsive interactions at short separations, a transition in the two-component system is not driven solely by interactions, but by a specific feature of the interactions, the correlations. This leads to extremely low critical temperature, as correlations are dominant in the strong-coupling limit. By carrying out various approximations based on standard liquid-state methods, we show that a gas-liquid transition of the two-component system posses a challenging theoretical problem.

cond-mat.soft↗

arXiv2017

Inhomogeneous fluid of penetrable-spheres: application of the random phase approximation

The focus of the present work is the application of the random phase approximation (RPA), derived for inhomogeneous fluids [Frydel and Ma, Phys. Rev. E 93, 062112 (2016)], to penetrable-spheres. As penetrable-spheres transform into hard-spheres with increasing interactions, they provide an interesting case for exploring the RPA, its shortcomings, and limitations, the weak- versus the strong-coupling limit. Two scenarios taken up by the present study are a one-component and a two-component fluid with symmetric interactions. In the latter case, the mean-field contributions cancel out and any contributions from particle interactions are accounted for by correlations. The accuracy of the RPA for this case is the result of a somewhat lucky cancellation of errors.

cond-mat.stat-mech↗

arXiv2016

The double-layer structure of overscreened surfaces by smeared-out ions

Charge inversion occurring for smeared-out ions is accompanied by an oscillatory charge density profile, indicating a layering of an alternating charge. The layering effect, however, is not coextensive with charge inversion, and charge inversion accompanied by a monotonically decaying profile is possible. The present work focuses on the structure of a double-layer of overscreened charged surfaces by smeared-out charges and probes the link between the structure of a double-layer and the bulk properties of an electrolyte, with special view to the role of the Kirkwood crossover.

cond-mat.soft↗

arXiv2016

Density functional formulation of the Random Phase Approximation for inhomogeneous fluids: application to the Gaussian core and Coulomb particles

Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_λ({\bf r},{\bf r}')$, where $λ$ determines the interaction strength. To obtain $h_λ({\bf r},{\bf r}')$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine that this approximation is identical to the variational Gaussian approximation derived within the framework of the field-theory. We then apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.

cond-mat.stat-mech↗

arXiv2015

Introduction to statistical field-theory: from a toy model to a one-component plasma

Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich transformation). We then consider Gaussian type of approximations, wherein correlational contributions enter as harmonic fluctuations around the saddle-point solution. The work focuses on how to construct a self-consistent, non-perturbative approximation without recourse to a variational construction based on the Gibbs-Bogolyubov-Feynman inequality that is inapplicable to a complex action. To address this problem, we propose a construction based on a selective satisfaction of a set of exact relations generated by considering a dual representation of a partition function, in its original and transformed form.

cond-mat.stat-mech↗

arXiv2014

Mean-field electrostatics beyond the point-charge description

This review explores the number of mean-field constructions for ions whose structure goes beyond the point-charge description, a representation used in the standard Poisson-Boltzmann equation. The exploration is motivated by a body of experimental work which indicates that ion-specific effects play a significant role, where ions of the same valence charge but different size, polarizability, or shape yield quite different, and sometimes surprising results. Furthermore, there are many large ions encountered in soft-matter and biophysics that do not fit into a point-charge description, and their extension in space and shape must be taken into account of any reasonable representation.

cond-mat.soft↗

arXiv2013

The double-layer of penetrable ions: an alternative route to charge reversal

We investigate a double-layer of penetrable ions near a charged wall. We find a new mechanism for charge reversal that occurs in the weak-coupling regime and, accordingly, the system is suitable for the mean-field analysis. The penetrability is achieved by smearing-out the ionic charge inside a sphere, so there is no need to introduce non-electrostatic forces and the system in the low coupling limit can be described by a modified version of the Poisson-Boltzmann equation. The predictions of the theory are compared with the Monte Carlo simulations.

cond-mat.soft↗

arXiv2012

Extended Poisson-Boltzmann descriptions of the electrostatic double layer: implications for charged particles at interfaces

The work reviews on a general level various modified Poisson-Boltzmann equations and demonstrates their use on the specific system of charged particles at an interface. This system is special, first, because it exhibits the long-range interactions on account of an air-water interface, and two, because the strength of these interactions depends on the structure of a double-layer. Thus, this system is particularly sensitive to the type of the modified Poisson-Boltzmann equation used.

cond-mat.soft↗

arXiv2012

A close look into the excluded volume effects within a double layer

We explore the effect of steric interaction on the ionic density distribution near a charged hard wall. For weakly charged walls, small particles, and monovalent ions the mean-field Poisson-Boltzmann equation provides an excellent description of the density profiles. For large ions and large surface charges, however, deviations appear. To explore these, we use the density functional theory. We find that local density functionals are not able to account for steric interactions near a wall. Based on the weighted density approximation we derive a simple analytical expression for the contact electrostatic potential which allows us to analytically calculate the differential capacitance of the double layer.

cond-mat.soft↗

arXiv2012

Sound-mediated dynamic correlations between colloidal particles in a quasi-one-dimensional channel

We study the hydrodynamic interactions between colloids suspended in a compressible fluid inside a rigid channel. Using lattice-Boltzmann simulations and a simplified hydrodynamic theory, we find that the diffusive dynamics of density perturbations (sound) in the confined fluid give rise to particle correlations of exceptionally long spatial range and algebraic temporal decay. We examine the effect of these sound-mediated correlations on two-particle dynamics and on the collective dynamics of a quasi-one-dimensional suspension.

cond-mat.soft↗

arXiv2011

Hydrodynamic Pair Attractions Between Driven Colloidal Particles

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian Dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.

cond-mat.soft↗

arXiv2010

Long-range dynamic correlations in confined suspensions

Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice-Boltzmann simulations, we show that the hydrodynamic screening is qualitatively modified when the time-dependent response and finite compressibility of the host liquid are taken into account. Diffusive compression modes in the confined liquid cause the particles to have velocity correlations of unbounded range, whose amplitude decays with time only as $t^{-3/2}$.

cond-mat.soft↗

arXiv1999

Total energy density as an interpretative tool

We present an unambiguous formulation for the total energy density within density-functional theory. We propose that it be used as a tool for the interpretation of computed energy and electronic structure changes during structural transformations and chemical reactions, augmenting the present use of electron density changes and changes in the Kohn-Sham local density of states and Kohn-Sham energy density.

cond-mat.mtrl-sci↗

arXiv1999

Adiabatic connection from accurate wavefunction calculations

An extremely easy method for accurately calculating the adiabatic connection of density functional theory is presented, and its accuracy tested on both Hooke's atom and the He atom. The method is easy because calculations are needed only for different values of parameters in the external potential, which can be achieved with almost any electronic structure code.

cond-mat.mtrl-sci↗