Counterion-Mediated Weak and Strong Coupling Electrostatic Interaction between Like-Charged Cylindrical Dielectrics

We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). The results are compared with extensive Monte-Carlo simulations exhibiting good agreement with the limiting weak and strong coupling results in their respective regime of validity.Comment: 19 pages, 10 figure

Overscreening in 1D lattice Coulomb gas model of ionic liquids

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble one dimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean field level of approximation, without any additional interactions.Comment: 4 pages 5 .eps figure

Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals

In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary value problems, using a collocation method within the Isogeometric Analysis paradigm. In such setting the regular part of the integrand can be defined as the product of a tensor product B-spline and a general function. The rules are derived by using first the spline quasi-interpolation approach to approximate such function and then the extension of a well known algorithm for spline product to the bivariate setting. In this way efficiency is ensured, since the locality of any spline quasi-interpolation scheme is combined with the capability of an ad--hoc treatment of the B-spline factor. The numerical integration is performed on the whole support of the B-spline factor by exploiting inter-element continuity of the integrand

Electrostatic image effects for counter-ions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak coupling level the image charge effects are generally small, making their mark only in the second order fluctuation term. However, in the strong coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long range image potentials.Comment: 21 pages, 8 figure

Role of Multipoles in Counterion-Mediated Interactions between Charged Surfaces: Strong and Weak Coupling

We present general arguments for the importance, or lack thereof, of the structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean-field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.Comment: 12 pages, 3 figure

Strong Coupling Electrostatics in the Presence of Dielectric Inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the inter-surface space upon increasing the solvent/membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.Comment: 4 pages, 3 figure

Field theoretic description of charge regulation interaction

In order to find the exact form of the electrostatic interaction between two proteins with dissociable charge groups in aqueous solution, we have studied a model system composed of two macroscopic surfaces with charge dissociation sites immersed in a counterion-only ionic solution. Field-theoretic representation of the grand canonical partition function is derived and evaluated within the mean-field approximation, giving the Poisson-Boltzmann theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations around the mean-field are then analyzed in the lowest order correction that we calculate analytically and exactly, using the path integral representation for the partition function of a harmonic oscillator with time-dependent frequency. The first order (one loop) free energy correction gives the interaction free energy that reduces to the zero-frequency van der Waals form in the appropriate limit but in general gives rise to a mono-polar fluctuation term due to charge fluctuation at the dissociation sites. Our formulation opens up the possibility to investigate the Kirkwood-Shumaker interaction in more general contexts where their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ

Counterion-mediated Electrostatic Interactions between Helical Molecules

We study the interaction of two cylinders with helical charge distribution mediated by neutralizing counterions, by analyzing the separation as well as the azimuthal angle dependence of the interaction force in the weak and strong coupling limit. While the azimuthal dependence of the interaction in the weak coupling limit is overall small and mostly negligible, the strong coupling limit leads to qualitatively new features of the interaction, among others also to an orientationally dependent optimal configuration that is driven by angular dependence of the correlation attraction. We investigate the properties of this azimuthal ordering in detail and compare it to existing results.Comment: 11 pages, 12 figure

Investigating the process of ethical approval in citizen science research. The case of public health

Undertaking citizen science research in Public Health involving human subjects poses significant challenges concerning the traditional process of ethical approval. It requires an extension of the ethics of protection of research subjects in order to include the empowerment of citizens as citizen scientists. This paper investigates these challenges and illustrates the ethical framework and the strategies developed within the CitieS-Health project. It also proposes first recommendations generated from the experiences of five citizen science pilot studies in environmental epidemiology within this project

Diffusion and interaction effects on molecular release from collapsed microgels

The transport of biomolecules, drugs, or reactants in stimuli-responsive polymer networks in aqueous media is fundamental for many material and environmental science applications, including drug delivery, biosensing, catalysis, nanofiltration, water purification, and desalination. The transport is particularly complex in dense polymer media, such as collapsed hydrogels, where the molecules strongly interact with the polymer network and diffuse via the hopping mechanism. In this study, we employ the Dynamical Density Functional Theory (DDFT) to investigate the non-equilibrium release kinetics of non-ionic subnanometer-sized molecules from collapsed microgel particles. The theory is consistent with previous molecular dynamics simulations of collapsed poly($N$-isopropylacrylamide) (PNIPAM) polymer matrices, accommodating molecules of varying shapes and sizes. We found that, despite the intricate physico-chemical properties involved in the released process, the kinetics is predominantly dictated by two material parameters: the diffusion coefficient of the molecules inside the microgel ($D^*$) and the interaction free energy of the molecules with the microgel ($\Delta G$). Our results reveal two distinct limiting regimes. For large, slowly diffusing molecules weakly attracted to the polymer network, the release is primarily driven by diffusion, with a release time scaling as $\tau_{1/2} \sim 1/D^*$. Conversely, for small molecules strongly attracted to the polymer network, the release time is dominated by the interaction, scaling as $\tau_{1/2} \sim \exp(-\Delta G/k_{\textrm{B}} T)$. Our DDFT calculations are directly compared with an analytical equation for the half-release time, demonstrating excellent quantitative agreement. This equation represents a valuable tool for predicting release kinetics from collapsed microgels of non-ionic molecules.Comment: 15 pages, 6 figure