Derek Frydel
Universidad Técnica Federico Santa María, Chemistry, Faculty Member
- My research interest is theory of soft-matter.edit
The present work analyzes stationary distributions of active Brownian particles in a harmonic trap. Generally, obtaining stationary distributions for this system is non-trivial, and to date, no exact expressions are available. In this... more
The present work analyzes stationary distributions of active Brownian particles in a harmonic trap. Generally, obtaining stationary distributions for this system is non-trivial, and to date, no exact expressions are available. In this work, we develop and explore a method based on a transformation of the Fokker-Planck equation into a recurrence relation for generating moments of a distribution. The method, therefore, offers an analytically tractable approach, an alternative to numerical simulations, in a situation where more direct analytical approaches fail. Although the current work focuses on the active Brownian particle model, the method is general and valid for any type of active dynamics and any system dimension.
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When it comes to active particles, even an ideal gas model in a harmonic potential poses a mathematical challenge. An exception is a runand-tumble particles (RTP) model in one dimension for which a stationary distribution is known... more
When it comes to active particles, even an ideal gas model in a harmonic potential poses a mathematical challenge. An exception is a runand-tumble particles (RTP) model in one dimension for which a stationary distribution is known exactly. The case of two dimensions is more complex, but the solution is possible. Incidentally, in both dimensions the stationary distributions correspond to a beta function. In three dimensions, a stationary distribution is not known but simulations indicate that it does not have a beta function form. The current work focuses on the three-dimensional RTP model in a harmonic trap. The main result of this study is the derivation of the recurrence relation for generating moments of a stationary distribution. These moments are then used to recover a stationary distribution using the Fourier-Lagrange expansion.
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The present work investigates the effect of inertia on the entropy production rate for all canonical models of active particles for different dimensions and the type of confinement. To calculate , the link between the entropy production... more
The present work investigates the effect of inertia on the entropy production rate for all canonical models of active particles for different dimensions and the type of confinement. To calculate , the link between the entropy production and dissipation of heat rate is explored, resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, is independent of temperature. For the case of a harmonic trap, attains a maximal value for τ = ω −1 , where τ is the persistence time and ω is the natural frequency of an oscillator. For active particles in one-dimensional box, or other nonharmonic potentials, thermal fluctuations are found to reduce .
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We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution... more
We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory, we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.
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In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition j = 0, where j is a flux. Since an... more
In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition j = 0, where j is a flux. Since an analogous equation for passive Brownian particles is first-order, a second-and third-order term are features of active motion. In all cases, the solution has a form of a convolution of two distributions: the Gaussian distribution representing the Boltzmann distribution of passive particles, and the beta distribution representing active motion at zero temperature.
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In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable. Extension of the model to three drifts v... more
In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable. Extension of the model to three drifts v = 0, ±v 0 yields the exact solution but the complexity of the expressions indicates that analytical treatment of higher-state models under the same procedure is impractical. Consequently, we modify our goal and consider a generalized version of the model for an arbitrary distribution of states P(v). To analyze such a system, we reformulate the Fokker–Planck equation as a self-consistent relation. The self-consistent relation is then analyzed by means of Laplace transform techniques.
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In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the... more
In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.
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This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of... more
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the singularity there is no underlying physical cause, therefore, the divergence would have to be a nonlocal phenomenon caused by confining walls at a distance. In this work we examine this claim more carefully. By identifying the correct differential equation for a divergent square-integrable solution and rewriting it in the form of the Schroedinger equation, we infer that the divergent wavefunction would be caused by the potential V(r)=-r delta(r), which is a kind of attractive delta potential. Because of its peculiar form and the fact that it leads to a divergent potential energy = - infinity, the potential V(r) and the divergent wavefunction associated with it are not physically meaningful.
Research Interests: Physics and Singularity
Research Interests: Physics and Lattice Gases
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We study the charge regulation of colloidal particles inside aqueous electrolyte solutions.
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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 constituting ions. One feature of active... more
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 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 chemisorption 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.
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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... more
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 poses a challenging theoretical problem.
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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... more
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.
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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... more
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. Just as the Kirkwood line divides a bulk solution into a fluid with monotonic and oscillatory decaying correlations, it similarly separates charge inversion into two broad domains, with and without oscillating charge density profile. As initially oscillations may appear like a far-field occurrence, eventually they develop into a full fledged layering of a charge density.
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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... more
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.
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We report the results of simulations of the phase diagrams of a quasi-two-dimensional (Q2D) colloid assembly and of a two-dimensional (2D) colloid assembly which have the same colloid-colloid interaction. That interaction is the same as... more
We report the results of simulations of the phase diagrams of a quasi-two-dimensional (Q2D) colloid assembly and of a two-dimensional (2D) colloid assembly which have the same colloid-colloid interaction. That interaction is the same as used in the study reported by Zangi and Rice [Phys. Rev. E 58, 7529 (1998)]. Among the goals of the work reported are elucidation of the influence of small amplitude out-of-plane motion on the phase diagram of a system and determination of the effect of that motion on the role of a hexatic phase in the melting process. Both of the systems we have studied undergo a first-order solid I-solid II and solid II-solid III isostructural transition induced by the attractive and repulsive components of the interaction, respectively. Introduction of the out-of-plane motion shifts the low density portion of the phase boundaries involving the solid II phase. The liquid-solid I coexistence line is nearly the same for the two systems. The solid II-solid III transit...
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We report an experimental determination of the depletion interaction between a pair of large colloid particles present in a binary colloid mixture that has a high density of large particles and is tightly confined between two parallel... more
We report an experimental determination of the depletion interaction between a pair of large colloid particles present in a binary colloid mixture that has a high density of large particles and is tightly confined between two parallel plates, as a function of the small colloid particle density. The bare interaction between the large particles in the one component large colloid suspension, and the effective potential between the large particles in the binary colloid suspension represented as a pseudo-one-component fluid, were obtained by inverting the Ornstein-Zernike equation with the hypernetted chain closure. The depletion interaction is defined by subtracting the bare potential from the effective potential at fixed large colloid density. We find that the depletion potential in the quasi-two-dimensional (Q2D) system is purely attractive and short ranged as described by Asakura-Oosawa model. However, the depth of the depletion potential is found to be almost an order of magnitude larger than the counterpart depletion potential predicted for the same density and diameter ratio in a three-dimensional system. Although it is expected that the confining walls in the Q2D geometry enhance the excluded volume effects that generate entropic attraction, the observed enhancement is much larger than predicted for a Q2D binary mixture of hard spheres. We speculate that this anomalously strong confinement-induced depletion potential is a signature of characteristics of the real confined binary colloid mixture that are not included in any extant theory of the depletion interaction, specifically the omission of the role of the solvent in those theories. One such characteristic could be differential wall or particle wetting that generates a wall induced one-particle effective potential that confines the centers of the small particles to lie closer to the midplane between the walls than expected from the wall separation and the direct particle-wall interaction, thereby enhancing the depletion interaction.
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ABSTRACT We report the results of a study designed to categorize the hydrodynamics of a quasi-two-dimensional system as either a 2D or 3D fluid. The characterization is based on the asymptotic decay of the velocity autocorrelation... more
ABSTRACT We report the results of a study designed to categorize the hydrodynamics of a quasi-two-dimensional system as either a 2D or 3D fluid. The characterization is based on the asymptotic decay of the velocity autocorrelation functions for different modes of motion and different boundary conditions at the enclosing walls. Our results show that for the case of no-slip boundary conditions the long time decay corresponds to neither 2D or 3D behaviour, nor anything in-between. The no-slip walls cause the long time tail of the velocity autocorrelation functions to have an exponential decay, more in agreement with Langevin model predictions. The free-slip boundary conditions create no-friction conditions for the tangential flow, and no-slip conditions for the perpendicular flow. The tangential component of the flow behaves like flow in 2D, but the perpendicular flow is hindered. As a result, the effect of the free-slip walls on the particle motion depends on the particular mode of motion. For perpendicular rotation where there is no flow perpendicular to the walls and for parallel translation where the perpendicular flow component is weak, we retrieve a 2D like decay for the autocorrelation functions. When the greatest part of the flow is in the perpendicular direction, the distinction between the no-slip and free-slip boundary is small, as in perpendicular translation. For the case of parallel rotation, the situation is more complicated as the perpendicular and tangential flows are more or less balanced, thus the no-slip boundary conditions slow down and speed up the autocorrelation decay. In the net result, the slowing down shows up in the increased diffusion coefficient, but the autocorrelation function shows a faster long time decay. As the plate separation decreases, the balance between the two contributions shifts and the diffusion coefficient begins to fall with decreasing separation.
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This work investigates the entropy production rate, , of the run-and-tumble model with a focus on scaling of as a function of the persistence time τ. It is determined that (i) vanishes in the limit τ → ∞, marking it as an equilibrium.... more
This work investigates the entropy production rate, , of the run-and-tumble model with a focus on scaling of as a function of the persistence time τ. It is determined that (i) vanishes in the limit τ → ∞, marking it as an equilibrium. Stationary distributions in this limit are represented by a superposition of Boltzmann functions in analogy to a system with quenched disorder. (ii) Optimal is attained in the limit τ → 0, marking it as a system maximally removed from equilibrium. Paradoxically, the stationary distributions in this limit have the Boltzmann form. The value of in this limit is that of an unconfined run-and-tumble particle and is related to the dissipation energy of a sedimenting particle. In addition to these general conclusions, this work derives an exact expression of for the run-and-tumble particles in a harmonic trap.
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This work considers the four-state run-and-tumble particle model (RTP) at zero temperature. The model is an extension of the RTP model in one-dimension whose drift orientations are limited to two discrete values, v = ±v 0. Hereafter we... more
This work considers the four-state run-and-tumble particle model (RTP) at zero temperature. The model is an extension of the RTP model in one-dimension whose drift orientations are limited to two discrete values, v = ±v 0. Hereafter we refer to this model as the two-state model. The two-state model is exactly solvable and imparts valuable insights. However, at zero temperature, the model yields uniform distributions for all values of parameters and does not provide any information about the structure of stationary distributions. Two states are insufficient for describing the zero temperature case. To arrive at the model that yields inhomogeneous distributions at zero temperature, it is necessary to increase the number of discrete velocities. The four-state model with drifts v = ±v 0 , ±γv 0 (where 0 ≤ γ ≤ 1) is the simplest such an extension. In this paper, the fourstate model at zero temperature is solved exactly and analyzed. Like the distributions of the two-state model for D > 0, the distributions of the four-state model at D = 0 show accumulation of particles near the walls. The physics behind this apparent accumulation is rather different; it is caused by particles recently released from a wall and moving away from it rather than toward it. The faster particles, in fact, are depleted from the walls as they move away faster. The accumulation effect is mostly the contribution of slower particles moving away from the walls.
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We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble... more
We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.
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In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable. Extension of the model to three drifts v... more
In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable. Extension of the model to three drifts v = 0, ±v 0 yields the exact solution but the complexity of the expressions indicates that analytical treatment of higher-state models under the same procedure is impractical. Consequently, we modify our goal and consider a generalized version of the model for an arbitrary distribution of states P (v). To analyze such a system, we reformulate the Fokker-Planck equation as a self-consistent relation. The self-consistent relation is then analyzed by means of Laplace transform techniques.
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This work considers an extension of the Kuramoto model with run-and-tumble dynamics-a type of selfpropelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual... more
This work considers an extension of the Kuramoto model with run-and-tumble dynamics-a type of selfpropelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual particles is no longer fixed but can change sporadically with a new velocity drawn from a distribution g(ω). Because the Kuramoto model undergoes phase transition, it offers a simple case study for investigating phase transition for a system with self-propelled particles.
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This article is the exploration of the viewpoint within which propelled particles in a steady state are regarded as a system with quenched disorder. The analogy is exact when the rate of the drift orientation vanishes and the linear... more
This article is the exploration of the viewpoint within which propelled particles in a steady state are regarded as a system with quenched disorder. The analogy is exact when the rate of the drift orientation vanishes and the linear potential, representing the drift, becomes part of an external potential, resulting in the effective potential $u_{eff}$. The stationary distribution is then calculated as a disorder-averaged quantity by considering all contributing drift orientations. To extend this viewpoint to the case when a drift orientation evolves in time, we reformulate the relevant Fokker-Planck equation as a self-consistent relation. One interesting aspect of this formulation is that is represented in terms of the Boltzmann factor $e^{-\beta u_{eff}}$. In the case of a run-and-tumble model, the formulation reveals an effective interaction between particles.
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In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the... more
In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.
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We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the... more
We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the model itself is intended as a simple representation of penetrable particles encountered in realistic soft-matter systems. Our specific focus is on a binary mixture, where particles of the same species repel and those of the opposite species attract each other. As a consequence of penetrability and the unlimited occupation of each site, the system exhibits thermodynamic collapse, which in simulations is manifested by an emergence of extremely dense clusters scattered throughout the system with energy of a cluster E ∝ −n 2 , where n is the number of particles in a cluster. After transforming a particle system into a spin system, in the large density limit the Hamiltonian recovers a simple harmonic form, resulting in the discrete Gaussian model used in the past to model the roughening transition of interfaces. For finite densities, due to the presence of a nonharmonic term, the system is approximated using a variational Gaussian model.
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To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the... more
To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.
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This work investigates a one-component one-dimensional Coulomb system in sticky wall confinement. Sticky wall is introduced as an alternative and intuitive depiction of charge regulation, the notion that a surface charge is not a fixed... more
This work investigates a one-component one-dimensional Coulomb system in sticky wall confinement. Sticky wall is introduced as an alternative and intuitive depiction of charge regulation, the notion that a surface charge is not a fixed but a fluctuating quantity in dynamic equilibrium with its immediate environment. Emphasis is placed on intuitive derivation and expressions are obtained by observing that the partition function of a charge regulated system can be decomposed into a collection of independent equilibriums with different fixed surface charges. Adsorbed particles behave as ideal-gas particles in a one-dimensional box whose length corresponds to the parameter of stickiness. Among various scenarios considered are a single- and two-wall confinement as well as the case of sticky counterions capable of associating into pairs. Exact solutions provide a view of the role and behavior of surface charge fluctuations, which is an important step in the "beyond-mean-field" analysis. Consequently, the model serves as a simple paradigm of the mechanism that gives rise to the Kirkwood-Shumaker interactions detected in real systems.
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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... more
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.
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The object of the present article is a one-dimensional lattice-gas model of soft particles, wherein particles interact only if they occupy the same or a neighboring site. The model is intended as a simple representation of penetrable... more
The object of the present article is a one-dimensional lattice-gas model of soft particles, wherein particles interact only if they occupy the same or a neighboring site. The model is intended 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. For 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 types of behavior encountered in one-component penetrable particle systems. In addition to confirm the existence of a similar criterion in the one-component lattice-gas model, we find that the same criterion can be used in the two-component system for predicting the occurrence of thermodynamic catastrophe.
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This chapter explores the number of mean field constructions for ions whose structure goes beyond the point charge description, the representation used in the standard Poisson‐Boltzmann (PB) equation. The structural details omitted within... more
This chapter explores the number of mean field constructions for ions whose structure goes beyond the point charge description, the representation used in the standard Poisson‐Boltzmann (PB) equation. The structural details omitted within a point charge picture can be related to electrostatic structure of an ion, giving rise to polarizability, asymmetric interactions, softening of Coulomb interactions if a distribution of an ion charge is extended in space, or can be related to the Pauli exclusion principle, giving rise to the excluded volume effects or other types of repulsive interactions. The efficient theory for hard‐core interactions, the fundamental measure DFT, shows shortcomings even for the weak‐coupling limit conditions. There is an additional motivation for pursuing various mean field constructions. Simple models such as charged hard spheres are easy to simulate, and for these systems one could simply use simulations to cover the entire range of electrostatics, from weak‐ to strong‐coupling regime.
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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 constituting ions. One feature of active... more
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 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 chemisorption 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.
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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... more
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 poses a challenging theoretical problem. Published by AIP Publishing. https://doi.org/10.1063/1.5006947
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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... more
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.
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This work considers an extension of the Kuramoto model with run-and-tumble dynamics-a type of selfpropelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual... more
This work considers an extension of the Kuramoto model with run-and-tumble dynamics-a type of selfpropelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual particles is no longer fixed but can change sporadically with a new velocity drawn from a distribution g(ω). Because the Kuramoto model undergoes phase transition, it offers a simple case study for investigating phase transition for a system with self-propelled particles.