Lattice models of ionic systems

Interface structures in ionic liquid crystals

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which additionally carry charges. This combination gives rise to a complex interplay of the underlying (anisotropic) contributions to the pair interactions. It promises interesting and distinctive structural and orientational properties to arise in systems of ILCs, combining properties of liquid crystals and ionic liquids. While previous theoretical studies have focused on the phase behavior of ILCs and the structure of the respective bulk phases, in the present study we provide new results, obtained within density functional theory, concerning (planar) free interfaces between an isotropic liquid L and two types of smectic-A phases (SA or SAW). We discuss the structural and orientational properties of these interfaces in terms of the packing fraction profile η(r) and the orientational order parameter profile S2(r) concerning the tilt angle α between the (bulk) smectic layer normal and the interface normal. The asymptotic decay of η(r) and of S2(r) towards their values in the isotropic bulk is discussed, too.

Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice

Magnetic monopoles, proposed as elementary particles that act as isolated magnetic south and north poles, have long attracted research interest as magnetic analogs to electric charge. In solid-state physics, a classical analog to these elusive particles has emerged as topological excitations within pyrochlore spin ice systems. We present the first real-time imaging of emergent magnetic monopole motion in a macroscopically degenerate artificial spin ice system consisting of thermally activated Ising-type nanomagnets lithographically arranged onto a pre-etched silicon substrate. A real-space characterization of emergent magnetic monopoles within the framework of Debye-Hückel theory is performed, providing visual evidence that these topological defects act like a plasma of Coulomb-type magnetic charges. In contrast to vertex defects in a purely two-dimensional artificial square ice, magnetic monopoles are free to evolve within a divergence-free vacuum, a magnetic Coulomb phase, for which features in the form of pinch-point singularities in magnetic structure factors are observed.

Simulations of ionic liquids confined by metal electrodes using periodic Green functions

We present an efficient method for simulating Coulomb systems confined by metal electrodes. The approach relies on Green function techniques to obtain the electrostatic potential for an infinite periodically replicated system. This avoids the use of image charges or an explicit calculation of the induced surface charge, both of which dramatically slows down the simulations. To demonstrate the utility of the new method, we use it to obtain the ionic density profiles and the differential capacitances, which are of great practical and theoretical interest, for a lattice model of an ionic liquid.

Lattice Model of an Ionic Liquid at an Electrified Interface

We study ionic liquids interacting with electrified interfaces. The ionic fluid is modeled as a Coulomb lattice gas. We compare the ionic density profiles calculated using a popular modified Poisson-Boltzmann equation with the explicit Monte Carlo simulations. The modified Poisson-Boltzmann theory fails to capture the structural features of the double layer and is also unable to correctly predict the ionic density at the electrified interface. The lattice Monte Carlo simulations qualitatively capture the coarse-grained structure of the double layer in the continuum. We propose a convolution relation that semiquantitatively relates the ionic density profiles of a continuum ionic liquid and its lattice counterpart near an electrified interface.

Magnetic-charge ordering and phase transitions in monopole-conserved square spin ice

Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics. In this work, we investigate a series of magnetic-charge (monopole) phase transitions in artificial square spin ice model using the conserved monopole density algorithm. It is revealed that the dynamics of low monopole density lattices is controlled by the effective Coulomb interaction and the Dirac string tension, leading to the monopole dimerization which is quite different from the dynamics of three-dimensional pyrochlore spin ice. The condensation of the monopole dimers into monopole crystals with staggered magnetic-charge order can be predicted clearly. For the high monopole density cases, the lattice undergoes two consecutive phase transitions from high-temperature paramagnetic/charge-disordered phase into staggered charge-ordered phase before eventually toward the long-range magnetically-ordered phase as the ground state which is of staggered charge order too. A phase diagram over the whole temperature-monopole density space, which exhibits a series of emergent spin and monopole ordered states, is presented.

ac Wien Effect in Spin Ice, Manifest in Nonlinear, Nonequilibrium Susceptibility

The Wien effect is a model process for field-induced charge creation. Here it is derived for a nonelectrical system: the spin ice "magnetolyte"-a unique system showing perfect charge symmetry. An entropic reaction field, analogous to the Jaccard field in ice, opposes direct current, but a frequency window exists in which the Wien effect for magnetolyte and electrolyte are indistinguishable. The universal enhancement of monopole density speeds up the magnetization dynamics, which manifests in the nonlinear, nonequilibrium ac susceptibility. This is a rare instance where such effects may be calculated, providing new insights for electrolytes. Experimental predictions are made for Dy2Ti2O7 spin ice.

Thermal and structural properties of ionic fluids

The electrostatic interaction in ionic fluids is well known to give rise to a characteristic phase behavior and structure. Sometimes its long range is proposed to single out the electrostatic potential over other interactions with shorter ranges. Here the importance of the range for the phase behavior and the structure of ionic fluids is investigated by means of grandcanonical Monte Carlo simulations of the lattice restricted primitive model (LRPM). The long-ranged electrostatic interaction is compared to various types of short-ranged potentials obtained by sharp and/or smooth cutoff schemes. Sharply cutoff electrostatic potentials are found to lead to a strong dependence of the phase behavior and the structure on the cutoff radius. However, when combined with a suitable additional smooth cutoff, the short-ranged LRPM is found to exhibit quantitatively the same phase behavior and structure as the conventional long-ranged LRPM. Moreover, the Stillinger-Lovett perfect screening property, which is well known to be generated by the long-ranged electrostatic potential, is also fulfilled by short-ranged LRPMs with smooth cutoffs. By showing that the characteristic phase behavior and structure of ionic fluids can also be found in systems with short-ranged potentials, one can conclude that the decisive property of the electrostatic potential in ionic fluids is not the long range but rather the valency dependence.

The one-dimensional Coulomb lattice fluid capacitor

The one-dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one-dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three-dimensional ionic liquid based capacitors. Notably, we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean-field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.

High pressure route to generate magnetic monopole dimers in spin ice

The gas of magnetic monopoles in spin ice is governed by one key parameter: the monopole chemical potential. A significant variation of this parameter could access hitherto undiscovered magnetic phenomena arising from monopole correlations, as observed in the analogous electrical Coulomb gas, like monopole dimerization, critical phase separation, or charge ordering. However, all known spin ices have values of chemical potential imposed by their structure and chemistry that place them deeply within the weakly correlated regime, where none of these interesting phenomena occur. Here we use high-pressure synthesis to create a new monopole host, Dy(2)Ge(2)O(7), with a radically altered chemical potential that stabilizes a large fraction of monopole dimers. The system is found to be ideally described by the classic Debye-Huckel-Bjerrum theory of charge correlations. We thus show how to tune the monopole chemical potential in spin ice and how to access the diverse collective properties of magnetic monopoles.

Magnetic monopoles in spin ice

Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles-that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

Nonasymptotic Critical Behavior of a Ternary Ionic System

Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.

Simulation of symmetric tricritical behavior in electrolytes

Despite extensive experimental, theoretical, and simulation efforts, a unified description of ionic phase transitions and criticality has not yet emerged. In this work, we investigate the phase behavior of the restricted primitive model of electrolyte solutions on the simple cubic lattice using grand canonical Monte Carlo simulations and finite-size scaling techniques. The phase diagram of the system is distinctly different from its continuum-space analog. We find order-disorder transitions for reduced temperatures T* < or approximately 0.51, where the ordered structures resemble those of the NaCl crystal. The order-disorder transition is continuous for 0.15 < or approximately T* < or approximately 0.51 and becomes first order at lower temperatures. The line of first-order transitions is a line of three-phase coexistence between a disordered and two ordered phases. The line of continuous, second-order transitions meets this line of triple points at a tricritical point at T* approximately equal to 0.1475. We locate the line of continuous transitions, and the line of triple points using finite-size scaling techniques. The tricritical temperature is estimated by extrapolation of the size-dependent tricritical temperatures obtained from a sixth-order Landau expansion of the free energy. Our calculated phase diagram is in qualitative agreement with mean-field theories.

Phase diagrams in the lattice restricted primitive model: from order-disorder to gas-liquid phase transition

The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (NN) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich phase behavior as the NN strength is varied. In particular, the phase diagram is very similar to that of the continuum RPM for high NN strength. Specifically, we have found both gas-liquid phase separation, with associated Ising critical point, and a first-order liquid-solid transition. We discuss how the line of continuous order-disorder transitions present for the low NN strength changes into continuum-space behavior as one increases the NN strength and compare our findings with recent theoretical results by Ciach and Stell [Phys. Rev. Lett. 91, 060601 (2003)].

Effect of charge-density fluctuations on the order-disorder transition in the lattice restricted primitive models of electrolytes

Lattice restricted primitive models, where equally charged ions of a diameter sigma are located at sites of a simple cubic lattice with a lattice constant a , are studied within the field-theoretic approach. We focus on the transition between charge-disordered and charge-ordered phases for sigma/a=1 and sigma/a=2 . By using renormalization-group methods we show that at high concentrations of ions the transition is continuous for sigma/a=1 , while for sigma/a=2 it is only first order, as found previously in simulations. For sigma/a=1 the effect of charge-density fluctuations on the positions of the continuous transition and the tricritical point (TCP) is determined within a formalism developed in this work. The temperature and the concentration of ions at the TCP agree very well with simulation results.

Criticality, tricriticality, and crystallization in discretized models of electrolytes

The Restricted Primitive Model of ionic systems is studied within a field-theoretic approach in order to provide a theoretic basis for the qualitative difference in the phase diagrams obtained in simulations for sigma/a=1,sigma/a=2, and sigma/a>/=3 ( a is the lattice constant and sigma is the ion diameter). The evolution of the phase diagrams from the case sigma/a=1 to the case sigma/a=square root[2] [nearest-neighbor ( NN ) occupancy excluded] is studied in the model with NN repulsion, 0</=J</= infinity, supplementing Coulomb forces. The boundary of stability of the charge-disordered phase with respect to short-wavelength charge fluctuations and the tricritical point are found in a mean-field ( MF ) approximation. Next, the effect of fluctuations is studied and we find that for J exceeding a particular value J0 a fluctuation-induced first-order phase transition should be expected instead of the continuous transition found in MF. At J= J0 the line of continuous transitions splits into two lines enclosing the two-phase region, whose thickness increases from zero when J>/= J0 increases. We argue that this transition corresponds to formation of a bcc ionic crystal. For high densities the ions form an fcc crystal, for which we find a fluctuation-induced first-order charge-ordered-charge-disordered transition, in agreement with recent simulation studies. Our results also shed light on the simulation results obtained for an off-lattice ionic system, for which a schematic phase diagram is constructed.

Thermodynamics of electrolytes on anisotropic lattices

The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space 1/r electrostatic interactions have been investigated. At all degrees of anisotropy, only coexistence between a disordered low-density phase and an ordered high-density phase with the structure similar to ionic crystal was found, in contrast to recent theoretical predictions. Tricritical parameters were determined to be increasing functions of anisotropy parameters which is consistent with theoretical calculations based on the Debye-Hückel approach. At large anisotropies a two-dimensional-like behavior is observed, from which we estimated the dimensionless tricritical temperature and density for the two-dimensional square lattice electrolyte to be T*(tri)=0.14 and rho*(tri)=0.70.

Effect of space discretization on phase diagrams in ionic systems: a field-theoretic approach

Using Landau-Ginzburg-Wilson field-theoretic methods we determine for what kind of space discretization the transition between charge-disordered and charge-ordered phases in the restricted primitive model is fluctuation-induced first order. We identify this transition with ionic-crystal formation. We predict four types of generic phase diagrams in ionic systems for various kinds of space discretization for low and intermediate densities of ions. Our results also shed light on the simulation results obtained for an off-lattice ionic system over a wide range of densities, including the fcc crystal.

Monte carlo study of coulombic criticality in polyelectrolytes

The role of charges in determining the water solubility of polyelectrolytes, a question of considerable relevance to biology, is currently unresolved. We use computer simulations to study the purely Coulombic phase separation of flexible polyelectrolytes with monovalent counterions in an athermal solvent. In agreement with recent theories we find that the critical temperature for this transition increases with chain length, but that the critical density remains unchanged. We therefore stress that the phase behavior of polyelectrolytes is qualitatively different from uncharged polymers, where the critical density decreases towards zero for long chains.