arXiv subjects

Rudolf Podgornik

Publications and source records attributed to Rudolf Podgornik.

At least 19 recordsLinked to original sources

arXiv2026

The effects of ionic valency and size asymmetry on counterion adsorption

We study the effect of asymmetry in solvent and ionic size on the equilibrium properties of multivalent ionic solutions near a charged surface. For a single ionic species in solution, we derive a generalized Grahame equation at the charged surface. For general size ratio between the ions and the solvent, we obtain analytical results for the concentration profiles as a function of the distance from the surface. For weak surface charge and small ion-to-solvent size ratio, the profile follows the classical Poisson-Boltzmann equation in dilute solution conditions. However, for high surface charge and large ionic size, the concentration profile saturates near the surface, leading to distinctive dependencies of the solution properties on the surface charge density and size asymmetry. Furthermore, the crossover between dilute and saturated regimes depends on the surface charge and ionic size asymmetry. We suggest that a solution containing multiple ionic species of different valencies and sizes stratifies close to the surface in the saturation regime. This leads to the formation of layers that are ordered according to the ions' valency-to-size ratio.

cond-mat.soft↗

arXiv2025

Charge Regulation Effect on Nanoparticles Interaction Mediated by Polyelectrolyte

The ability to precisely control surface charge using charged polymers is fundamental to many nanotechnology applications, enabling the design and fabrication of materials with tailored properties and functionalities. Here, we study the effect of charge regulation (CR) on the interaction between two nanoparticles (NPs) mediated by an oppositely charged polyelectrolyte (PE) in an electrolyte solution. To this end, we employ a hybrid CR Monte Carlo / molecular dynamics simulation framework to systematically explore the effects of pH, salt concentration, and polymer chain length on NP surface charge behavior. For comparison, we also conduct molecular simulations under constant charge (CC) conditions. Our results reveal that CR enhances PE adsorption onto NP surfaces compared to the CC case, where polymer bridging dominates across a wide range of NP intersurface separations. This enhanced adsorption under CR leads to a weak net repulsion driven by osmotic forces. In contrast, the CC model yields a stronger net attraction due to the bridging force. Furthermore, we find that the CR effects are more pronounced at low salt concentration, whereas at high salt concentration, counterion screening dominates in both CR and CC cases, diminishing the CR effect. These findings highlight the importance of incorporating charge regulation in characterizing nanoparticle interactions within a complex biochemical environment, particularly in low salt concentrations.

cond-mat.soft↗

arXiv2025

Anomalous proteinaceous shells with octagonal local order

Proteinaceous shells useful for various biomedical applications exhibit a wide range of anomalous structures that are fundamentally different from icosahedral viral capsids described by the Caspar-Klug paradigmatic model. Exploring the Protein Data Bank, we have identified nine different types of anomalous shells structurally close to flat octagonal quasicrystals. As we show, these numerous shells have cubic nets cut from short-period approximants of an octagonal tiling composed of square and rhombic tiles. The approximants and parent tiling are easily obtained within the Landau density wave approach, while the nonequilibrium assembly of them can be simulated using the pair potentials derived from critical density waves. Gluing a polyhedron net and mapping it onto a spherical surface induces tile distortions, and to reduce them, we introduce and minimize the effective elastic energy of the system. Thus, we return quasi-equivalence to previously equivalent tiles. Possible cubic faceting of the octagonal spherical tilings is discussed in terms of the topological charge distribution over the tiling vertices. The proposed structural models describe numerous proteinaceous shells including about half of the known symmetrical enzymes. Our results constitute a fundamental basis for further applications of identified octagonal assemblies and can help to discover and study similar systems in the future.

cond-mat.soft↗

arXiv2025

Moment analysis of two-dimensional active Brownian run-and-tumble particles

We study an active Brownian run-and-tumble particle (ABRTP) model, that consists of an active Brownian run state during which the active velocity of the particle diffuses on the unit circle, and a tumble state during which the active velocity is zero, both with exponentially distributed time. Additionally we add a harmonic trap as an external potential. In the appropriate limits the ABRTP model reduces either to the active Brownian particle model, or the run-and-tumble particle model. Using the method of direct integration the equation of motion, pioneered by Kac, we obtain exact moments for the Laplace transform of the time dependent ABRTP, in the presence or absence of a harmonic trap. In addition we estimate the distribution moments with the help of the Chebyshev polynomials. Our results are in excellent agreement with the experiments.

cond-mat.stat-mech↗

arXiv2025

Effect of charge regulation on the screening properties of zwitterionic macroion solutions

Precisely controlling the surface charge of zwitterionic macromolecules is crucial for tailoring their properties and optimizing them for specific applications. Here, we present a generalized calculation scheme for determining the screening length in solutions containing zwitterionic macroions, where the charge of the macroion is controlled by the electrolyte solution. This scheme bypasses the need to solve the Poisson Boltzmann equation by expressing the inverse screening parameter in terms of the derivative of pressure with respect to chemical potential. The scheme reveals that the screening length has two components: one related to the Debye length with effective charges, and another stemming from the macroion surface dissociation equilibrium, which exhibits a screening resonance behavior. Furthermore, we find that the nonuniform surface charge distribution induced by pH responsive charge regulation strongly affects the screening behavior. The charge regulation properties of macroions, even in dilute solutions, are a key factor in the screening of electrostatic interactions, offering insights into complex biological and nanomaterial systems.

cond-mat.soft↗

arXiv2025

Exact moments for a run and tumble particle in a harmonic trap with a finite tumble time

We study the problem of a run and tumble particle in a harmonic trap, with a finite run and tumble time, by a direct integration of the equation of motion. An exact 1D steady state distribution, diagram laws and a programmable Volterra difference equation are derived to calculate any order of moments in any other dimension, both for steady state as well as the Laplace transform in time for the intermediate states. We also use the moments to infer the distribution by considering a Gaussian quadrature for the corresponding measure, and from the scaling law of high order moments.

cond-mat.stat-mech↗

arXiv2025

Continuum theory of electrostatic-elastic coupling interactions in colloidal crystals

A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling, which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields. We derive linearized, Debye-Hückel-like mean-field equations that can be analytically solved, incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields. By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length. This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.

cond-mat.soft↗

arXiv2025

Correlation decoupling of Casimir interaction in an electrolyte driven by external electric fields

It has been established for a long time that the long range van der Waals or thermal Casimir interaction between two semi-infinite dielectrics separated by a distance $H$ is screened by an intervening electrolyte. Here we show how this interaction is modified when an electric field of strength $E$ is applied parallel to the dielectric boundaries, leading to a non-equilibrium steady state with a current. The presence of the field induces a long range thermal repulsive interaction, scaling just like the thermal Casimir interaction between dielectrics without the intervening electrolyte, {\em i.e.} as $1/H^3$. At small $E$ the effect is of order $E^2$ while at large fields it saturates to an $E$ independent value. We explain the results in terms of a decoupling mechanism between the charge density fluctuations of cations and anions at large applied fields.

cond-mat.stat-mech↗

arXiv2025

Repulsive thermal van der Waals interaction in multi-species asymmetric electrolytes driven by external electric fields

It is well established that the long-range component of the thermal van der Waals interaction between two semi-infinite dielectrics becomes short-range when an electrolyte is present between them, this is the well known phenomenon of screening. In Phys. Rev. Lett, 133, 238002 (2024) it was shown that for a binary symmetric electrolyte, an electric field parallel to the dielectric boundaries disrupts screening and a long-range thermal repulsive interaction appears. At large applied fields this long-range repulsive interaction can be explained by the fact that the cations and anions have differing average drifts moving in opposite directions, leading to the correlation of charge density fluctuations between the two species to decouple. Here we extend these results to binary electrolytes which are asymmetric as well as electrolytes with more than two ionic species.

cond-mat.soft↗

arXiv2024

Diffusive dynamics of charge regulated macro-ion solutions

Onsager's variational principle is generalized to address the diffusive dynamics of an electrolyte solution composed of charge-regulated macro-ions and counterions. The free energy entering the Rayleighian corresponds to the Poisson-Boltzmann theory augmented by the charge-regulation mechanism. The dynamical equations obtained by minimizing the Rayleighian include the classical Poisson-Nernst-Planck equations, the Debye-Falkenhagen equation, and their modifications in the presence of charge regulation. By analyzing the steady state, we show that the charge regulation has an important impact on the non-equilibrium macro-ion spatial distribution and their effective charge, deviating significantly from their equilibrium values. Our model, based on Onsager's variational principle offers a unified approach to the diffusive dynamics of electrolytes containing components that undergo various charge association/dissociation processes.

cond-mat.soft↗

arXiv2024

Spool-nematic ordering of dsDNA and dsRNA under confinement

The ability of double-stranded DNA or RNA to locally melt and form kinks leads to strong non-linear elasticity effects that qualitatively affect their packing in confined spaces. Using analytical theory and numerical simulation we show that kink formation entails a mixed spool-nematic ordering of double-stranded DNA or RNA in spherical capsids, consisting of an outer spool domain and an inner, twisted nematic domain. These findings explain the experimentally observed nematic domains in viral capsids and imply that non-linear elasticity must be considered to predict the configurations and dynamics of double-stranded genomes in viruses, bacterial nucleoids or gene-delivery vehicles. The non-linear elastic theory suggests that spool-nematic ordering is a general feature of strongly confined kinkable polymers.

cond-mat.soft↗

arXiv2024

Spontaneous Domain Formation in Spherically-Confined Elastic Filaments

Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity-driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously-ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.

cond-mat.soft↗

arXiv2024

Fabry-Pérot nanocavities controlled by Casimir forces in electrolyte solutions

We propose a design for tuning the resonant spectra of Fabry-Pérot nanocavities mediated by the Casimir force. The system involves a suspended gold nanoplate approaching to a dielectric-coated gold substrate in a univalent electrolyte solution. The gold nanoplate can be stably suspended due to the delicate balance between repulsive and attractive components of the Casimir forces. In an electrolyte solution, the presence of ionic-charge fluctuations can partially or totally screen the thermal $n$=0 Matsubara term, resulting in strongly modified interactions. As a result, the separation between the gold nanoplate and the substrate experiences a significant modulation in response to variations in salt concentration. Under proper conditions, we find that the modulation of the Casimir force would strongly shift the resonances of Fabry-Pérot nanocavities at the optical frequencies, when the Debye length of the electrolyte decreases from 1000 nm to 10 nm. Finally, the temperature dependence of the thermal Casimir force would provide an additional modulation of Fabry-Pérot nanocavity resonances for their eventual fine tuning. These results open up a promising venue for general tuning of the optical resonances with potential applications in re-configurable microfluidic nanophotonics.

quant-ph↗

arXiv2023

Electrostatic interactions between charge regulated spherical macroions

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte -- thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

cond-mat.soft↗

arXiv2023

On the nature of screening in charge regulated macroion solutions

We present a derivation of the screening length for a solution containing a charge regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the ``uncertainty relation" of the Legendre transform which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler-Guggenheim-Frumkin model of charge regulation we then analyze the ``screening resonance" and the ``overscreening" of the screening properties of the charge-regulated macroion solution.

physics.bio-ph↗

arXiv2023

Stability of Taylor-Couette Flow with Odd Viscosity

Odd viscosity can emerge in 3D hydrodynamics when the time reversal symmetry is broken and anisotropy is introduced. Its ramifications on the stability of the prototypical Taylor-Couette flow in curved geometries have remained unexplored. Here, we investigate the effects of odd viscosity on the stability of Taylor-Couette flow under axisymmetric perturbations both analytically and numerically, deriving analytically the critical Taylor number for different odd viscosities in the narrow gap case as well as fully numerically implementing the wide gap case. We find that the odd viscosity modifies the vortex pattern by creating secondary vortices, and exerts an intriguing ``lever'' effect in the stability diagram, completely suppressing the instability of Taylor-Couette flow under axisymmetric perturbations when the odd viscosity is large, irrespective of its sign. Our findings highlight the role of odd viscosity for the rich flow patterns of the Taylor-Couette geometry and provide guidance for viscometer experiments when odd viscosity is present.

physics.flu-dyn↗

arXiv2023

Interplay between finite thickness and chirality effects on the Casimir-Lifshitz torque with nematic cholesteric liquid crystals

We theoretically investigate the combined effects of the chirality and the finite total thickness of nematic cholesteric liquid crystals on the Casimir-Lifshitz torque. We find that, the larger the thickness, the more sinusoidal the angular dependence of the torque becomes. We use a Fourier decomposition to quantify this result. The general direction of the torque depends on whether the configuration of two cholesterics is heterochiral or homochiral.

quant-ph↗

arXiv2023

Curvature effects in interfacial acidity of amphiphilic vesicles

We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge regulated moieties. Basing our approach on the linear Debye-Hückel as well as the non-linear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-Guggenheim adsorption isotherm model of the charge regulation process, we analyse and review the dependence of the local pH on the position, as well as bulk electrolyte concentration, bulk pH and curvature of the amphiphilic single membrane vesicle. With appropriately chosen adsorption parameters of the charge regulation model, we find a good agreement with available experimental data.

cond-mat.soft↗