Point-like Ions Research Articles

Sedimentation of a Charged Spherical Particle in a Viscoelastic Electrolyte Solution.

When a charged particle translates through an electrolyte solution, the electric double layer around it deforms in response to the fluid motion and creates an electric force opposite the direction of motion, decreasing the settling velocity. This is a multidisciplinary phenomenon that combines fluid mechanics and electrodynamics, differentiating it from the classical problem of an uncharged sedimenting particle. It has many applications varying from mechanical to biomedical, such as in drug delivery in blood through charged microparticles. Related studies so far have focused on Newtonian fluids, but recent studies have proven that many biofluids, such as human blood plasma, have elastic properties. To this end, we perform a computational study of the steady sedimentation of a spherical, charged particle in human blood plasma due to the centrifugal force. We used the Giesekus model to describe the rheological behavior of human blood plasma. Assuming axial symmetry, the governing equations include the momentum and mass balances, Poisson's equation for the electric field, and the species conservation. The finite size of the ions is considered through the local-density approximation approach of Carnahan-Starling. We perform a detailed parametric analysis, varying parameters such as the ζ potential, the size of the ions, and the centrifugal force exerted upon the particle. We observe that as the ζ potential increases, the settling velocity decreases due to a stronger electric force that slows the particle. We also conduct a parametric analysis of the relaxation time of the material to investigate what happens generally in viscoelastic electrolyte solutions and not only in human blood plasma. We conclude that elasticity plays a crucial role and should not be excluded from the study. Finally, we examine under which conditions the assumption of point-like ions gives different predictions from the Carnahan-Starling approach.

Impact of added salt on the characteristics of electric double layer composed of charged nanoparticles

We consider a mixture of large spherical nanoparticles with the charge distributed over the surface and point-like ions embedded in an aqueous solution between two similarly-charged surfaces. The finite size of nanoparticles is included via a lattice gas entropy. The electrostatic energy takes into account exact charge distribution on the nanoparticles surface. For this system the Euler-Lagrange equations are derived and solved numerically. The results show a big impact of nanoparticle's size on the concentration profiles and characteristics of electric double layer. The theoretical model predicts an attractive interaction between like charged surfaces for large enough nanoparticles with large enough charge and the addition of point-like salt ions decreases the range of attraction.

Crystallization in single- and multicomponent neutron star crusts

We use Molecular Dynamics simulations to study the formation and stability of single and multicomponent lattices in the outer crust of Neutron Stars. Including an improved treatment for Gaussian charge distributions of ions we obtain the expressions for the potential and forces arising from electron screened Coulomb interactions using the efficient Ewald sum procedure. %in the plasma. Our findings show that for baryon densities in the outer crust a point-like ion treatment can not fully describe the crystallization behaviour thus the Coulomb parameter, $\Gamma_C$, along with the usual screening parameter, $\kappa$, due to charge neutralizing electron polarizable background, must be complemented with an additional parameter, $\eta$, providing information on the finite size of ions. In our approach we find that including beyond point-like approaches in screened plasmas has a robust impact on calculated lattice energetic stability decreasing crystallization energies per baryon up to $\sim 40\%$ with respect to point-like interaction and, as a consequence, melting point resulting displaced to lower temperatures.

Dipolar Poisson models in a dual view

In this work, we study the continuum theories of dipolar-Poisson models. Both the standard dipolar-Poisson model and the dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential ϕ. Applying the Legendre transform approach introduced by Maggs [Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement D and the polarization field P. We compare the convex functionals in P-space to the non-convex functionals in electric field E-space and apply them to the classic problem of the solvation of point-like ions. Since the dipolar-Poisson model does not properly describe polarization saturation, we argue that only the dipolar-Poisson-Langevin functional can be used to provide a nonlinear generalization of the harmonic polarization functional used in the theory of Marcus for the electron transfer rate to nonlinear regimes. We show that the model can be quantitatively parameterized by molecular dynamics simulations.

Mapping of azimuthal B-fields in Z-pinch plasmas using Z-pinch-driven ion deflectometry

B-field measurements are crucial for the study of high-temperature and high-energy-density plasmas. A successful diagnostic method, ion deflectometry (radiography), is commonly employed to measure MGauss magnetic fields in laser-produced plasmas. It is based on the detection of multi-MeV ions, which are deflected in B-fields and measure their path integral. Until now, protons accelerated via laser–target interactions from a point-like source have been utilized for the study of Z-pinch plasmas. In this paper, we present the results of the first Z-pinch-driven ion deflectometry experiments using MeV deuterium beams accelerated within a hybrid gas-puff Z-pinch plasma on the GIT-12 pulse power generator. In our experimental setup, an inserted fiducial deflectometry grid (D-grid) separates the imploding plasma into two regions of the deuteron source and the studied azimuthal B-fields. The D-grid is backlighted by accelerated ions, and its shadow imprinted into the deuteron beams demonstrates ion deflections. In contrast to the employment of the conventional point-like ion source, in our configuration, the ions are emitted from the extensive and divergent source inside the Z-pinch. Instead of having the point ion source, deflected ions are selected via a point projection by a pinhole camera before their detection. Radial distribution of path-integrated B-fields near the axis (within a 15 mm radius) is obtained by analysis of experimental images (deflectograms). Moreover, we present a 2D topological map of local azimuthal B-fields B(r,z) via numerical retrieval of the experimental deflectogram.

Long-range Rydberg-atom–ion molecules of Rb and Cs

We propose a novel type of Rydberg dimer, consisting of a Rydberg-state atom bound to a distant positive ion. The molecule is formed through long-range electric-multipole interaction between the Rydberg atom and the point-like ion. We present potential energy curves (PECs) that are asymptotically connected with Rydberg $nP$- or $nD$-states of rubidium or cesium. The PECs exhibit deep, long-range wells which support many vibrational states of Rydberg-atom-ion molecules (RAIMs). We consider photo-association of RAIMs in both the weak and the strong optical-coupling regimes between initial and Rydberg states of the neutral atom. Experimental considerations for the realization of RAIMs are discussed.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields.

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model.

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

Transport Properties in Nanochannels: Ionic Size-, Permittivity-, and Viscosity-Related Effects

The transport properties in nanochannels are examined using a modified electrokinetic model (MEM) that takes into account the finite ion size by modeling the hydrated ions as charged dielectric spheres so that the electrolyte solution becomes a nonhomogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. We show that the simultaneous consideration of ionic size, permittivity, and viscosity effects always improve on the predictions of the standard electrokinetic model for point-like ions (SEM), with corrections that are significant in the nanofluidic system’s parameter range. The results reported herein are expected to provide a deeper understanding of the ion transport and fluid flow in nanofluidic devices.

Influence of added salt on the surface induced ordering of nanoparticles with discretely distributed charges

The formation of an electric double layer composed of spherical nanoparticles is analyzed by means of a generalized Poisson-Boltzmann model and Monte Carlo simulations. We study a solution of symmetric and asymmetric mixtures of spherical particles that reside between two planar like-charged surfaces. Each spherical particle carries two elementary charges that are attached at its poles. The electrolyte solution also contains monovalent point-like salt ions. Our theoretical model properly accounts for intra-particle correlations - that is correlations between the spatially separated charges belonging to a single multivalent spherical particle. Correlations between different spherical particles are neglected. It is shown that added salt decreases the number density close to the charged surface and influences the orientation of spherical particles. Increasing salt concentration decreases the order parameter of the spherical particles. Generalized Poisson-Boltzmann results, obtained by solving an integral differential equation, and predictions from Monte Carlo (MC) simulations are in excellent agreement.

Interaction between charged lipid vesicles and point- or rod-like trivalent ions.

This work examines the influence of the charge distribution of trivalent cations on their interaction with soft anionic particles, using a combination of experimental measurements and theoretical modelling. In particular, we perform electrophoresis measurements to determine the zeta-potential of anionic liposomes in the presence of spermidine and lanthanum cations. We work in a range of electrolyte concentration where a reversal in the electrophoretic mobility of the liposomes is expected; however, unlike the case of lanthanum cations, spermidine does not induce mobility reversal of liposomes. As a result, the charge distribution within the counterion appears to be a key factor. This conclusion is supported by a theory that accounts for intra-ionic correlations, which has previously been successfully used to describe the colloidal electric double layer. It allows us to model spermidine as rod-like ions and lanthanum cations as point-like ions in order to test the importance of the ionic geometry in the interactions with soft particles such as lipid vesicles.

Nonlocal statistical field theory of dipolar particles forming chain-like clusters

We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the ’head-to-tail’ mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the point-like test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard–Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson–Boltzmann–Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the ‘Yukawa’-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Rodlike Counterions near Charged Cylinders: Counterion Condensation and Intercylinder Interaction.

We study a system composed of like-charged cylinders and dumbbell-like counterions, with the focus laid on the role of the internal structure of counterions, using MonteCarlo simulations. The dumbbell ions are found to exhibit novel counterion condensation behavior governed by their length. Effective electrostatic interactions mediated between charged parallel cylinders also turn out significantly different from the case of pointlike ions, as a result of the complex interplay between the spatially separated charge distribution in the dumbbell counterions, their orientation, and the curvature of the charged cylinder. We show that at a weak-to-moderate electrostatic coupling strength, where effective like-charge interactions are usually found to be repulsive, the intercylinder interaction can become attractive and display a distinctive sensitivity to the cylinder curvature and dumbbell size, proving the significant effect of ion structure.

Wake-Mediated Propulsion of an Upstream Particle in Two-Dimensional Plasma Crystals.

The wake-mediated propulsion of an "extra" particle in a channel of two neighboring rows of a two-dimensional plasma crystal, observed experimentally by Du etal. [Phys. Rev. E 89, 021101(R) (2014)PRESCM1539-375510.1103/PhysRevE.89.021101], is explained in simulations and theory. We use the simple model of a pointlike ion wake charge to reproduce this intriguing effect in simulations, allowing for a detailed investigation and a deeper understanding of the underlying dynamics. We show that the nonreciprocity of the particle interaction, owing to the wake charges, is responsible for a broken symmetry of the channel that enables a persistent self-propelled motion of the extra particle. We find good agreement of the terminal extra-particle velocity with our theoretical considerations and with experiments.

Vacuum solid-state ion-conducting silver source for application in field emission electric propulsion systems

A point-like silver ion source with thin film of RbAg4I5 solid electrolyte was developed for application in field emission electric propulsion systems. The solid electrolyte produced by mechano-chemical synthesis was deposited on the apex of a silver tip using pulsed laser deposition. The running tests at 195 °C working temperature and 10 kV accelerating potential have demonstrated that the source can continuously produce positive ion current of several hundred pA during a few days with a peak value of 25–50 nA. Using TOF-SIMS analysis it has been shown that the ion current consists of Ag+ with a small contribution of Rb+, lower than 0.5 at.%. We suggest that Ag+ emission occurs mainly by means of field-assisted ion evaporation and/or ion desorption, and the solid electrolyte plays a role of the transport system, in which the emitted Ag+ ions are continually replaced by mobile Ag+ ions delivered from the silver reservoir by direct mass transfer under the influence of an external electric field.

A field theoretic approach to the electric interfacial layer — Mixture of trivalent rod-like and monovalent point-like ions between charged walls

In this paper, we study the interaction between charged macroions (surfaces) immersed in a solution of oppositely charged, rod-like counterions and point-like co-ions. The system is modeled by a field theoretic approach, which was extended to treat mixtures of rod- and point-like ions. The theory is applicable from the weak to the intermediate through to the strong coupling regimes. In the weak coupling limit, the force between the charged surfaces are only repulsive. In the intermediate coupling regime, the rod-like ions can induce attractive force between the charged surfaces. In the strong coupling limit, the inter-ionic charge correlations dominate the attractive forces at short separations between the charged surfaces.

Moderately nonlinear diffuse-charge dynamics under an ac voltage.

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Ion-beam sources based on room-temperature ionic liquids for aerospace applications, nanotechnology, and microprobe analysis (review)

An analytical review of the stages of development and state-of-the-art of ion-beam sources, which are based on room-temperature ionic liquids for aerospace and ion-beam technologies, is presented. The properties of ionic liquids—new ion-conducting materials (“liquid plasma or plasma in a bottle”)—are discussed. The design, operating conditions, and technology of manufacturing pointlike, capillary, matrix, and linear ion sources with ionic liquids are described in detail. The main fields of their application, including electrostatic rocket engines (microthrusters) for CubeSat-format satellites and systems with focused ion beams for technological processing of materials and structures in the nanometer region and for microprobe investigations are analyzed.

Dipolar Poisson-Boltzmann approach to ionic solutions: A mean field and loop expansion analysis

We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a mean-field level, we account for any internal charge distribution of particles. The dipolar degrees of freedom are added to the ionic ones and result in a generalization of the Poisson-Boltzmann (PB) equation called the Dipolar PB (DPB). By looking at the DPB equation around a fixed point-like ion, a closed-form formula for the dielectric constant is obtained. We express the dielectric constant using the "hydration length" that characterizes the hydration shell of dipoles around ions, and thus the strength of the dielectric decrement. The DPB equation is then examined for three additional cases: mixture of solvents, polarizable medium, and ions of finite size. Employing field-theoretical methods, we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. For pure water, the dipolar fluctuations represent an important correction to the mean-field value and good agreement with the water dielectric constant is obtained. For ionic solutions we predict analytically the dielectric decrement that depends on the ionic strength in a nonlinear way. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. A linear dependence of the dielectric constant on the salt concentration is observed at low salinity, and a noticeable deviation from linearity can be seen for ionic strength above 1 M, in agreement with experiments.