Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions.

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Pattern Formation in Two-Component Monolayers of Particles with Competing Interactions.

Competing interactions between charged inclusions in membranes of living organisms or charged nanoparticles in near-critical mixtures can lead to self-assembly into various patterns. Motivated by these systems, we developed a simple triangular lattice model for binary mixtures of oppositely charged particles with additional short-range attraction or repulsion between like or different particles, respectively. We determined the ground state for the system in contact with a reservoir of the particles for the whole chemical potentials plane, and the structure of self-assembled conglomerates for fixed numbers of particles. Stability of the low-temperature ordered patterns was verified by Monte Carlo simulations. In addition, we performed molecular dynamics simulations for a continuous model with interactions having similar features, but a larger range and lower strength than in the lattice model. Interactions with and without symmetry between different components were assumed. We investigated both the conglomerate formed in the center of a thin slit with repulsive walls, and the structure of a monolayer adsorbed at an attractive substrate. Both models give the same patterns for large chemical potentials or densities. For low densities, more patterns occur in the lattice model. Different phases coexist with dilute gas on the lattice and in the continuum, leading to different patterns in self-assembled conglomerates ('rafts').

Mesoscopic Inhomogeneities in Concentrated Electrolytes.

A mesoscopic theory for water-in-salt electrolytes combining density functional and field-theoretic methods is developed in order to explain the unexpectedly large period of the oscillatory decay of the disjoining pressure observed in recent experiments for the lithium bis(trifluoromethylsulfonyl)-imide (LiTFSI) salt [T. S. Groves et al., J. Phys. Chem. Lett. 2021, 12, 1702]. We assumed spherical ions with different diameters and implicit solvent, inducing strong, short-range attraction between ions of the same sign. For this highly simplified model, we calculated correlation functions. Our results indicate that mesoscopic inhomogeneities can occur when the sum of the Coulomb and the water-mediated interactions between like ions is attractive at short and repulsive at large distances. We adjusted the attractive part of the potential to the water-in-LiTFSI electrolyte and obtained both the period and the decay rate of the correlations, in semiquantitative agreement with the experiment. In particular, the decay length of the correlations increases nearly linearly with the volume fraction of ions.

Adsorption in Mixtures with Competing Interactions.

A binary mixture of oppositely charged particles with additional short-range attraction between like particles and short-range repulsion between different ones in the neighborhood of a substrate preferentially adsorbing the first component is studied by molecular dynamics simulations. The studied thermodynamic states correspond to an approach to the gas-crystal coexistence. Dependence of the near-surface structure, adsorption and selective adsorption on the strength of the wall-particle interactions and the gas density is determined. We find that alternating layers or bilayers of particles of the two components are formed, but the number of the adsorbed layers, their orientation and the ordered patterns formed inside these layers could be quite different for different substrates and gas density. Different structures are associated with different numbers of adsorbed layers, and for strong attraction the thickness of the adsorbed film can be as large as seven particle diameters. In all cases, similar amount of particles of the two components is adsorbed, because of the long-range attraction between different particles.

Capillary Ionization and Jumps of Capacitive Energy Stored in Mesopores.

We study ionic liquid-solvent mixtures in slit-shaped nanopores wider than a few ion diameters. Using a continuum theory and generic thermodynamic reasoning, we reveal that such systems can undergo a capillary ionization transition. At this transition, the pores spontaneously ionize or deionize upon infinitesimal changes of temperature, slit width, or voltage. Our calculations show that a voltage applied to a pore may induce a capillary ionization, which-counterintuitively-is followed by a re-entrant deionization as the voltage increases. We find that such ionization transitions produce sharp jumps in the accumulated charge and stored energy, which may find useful applications in energy storage and heat-to-energy conversion.

Phase Transitions and Electrochemical Properties of Ionic Liquids and Ionic Liquid-Solvent Mixtures.

Recent advances in studies of ionic liquids (IL) and ionic liquid-solvent mixtures are reviewed. Selected experimental, simulation, and theoretical results for electrochemical, thermodynamical, and structural properties of IL and IL-solvent mixtures are described. Special attention is paid to phenomena that are not predicted by the classical theories of the electrical double layer or disagree strongly with these theories. We focus on structural properties, especially on distribution of ions near electrodes, on electrical double layer capacitance, on effects of confinement, including decay length of a dissjoining pressure between confinig plates, and on demixing phase transition. In particular, effects of the demixing phase transition on electrochemical properties of ionic liquid-solvent mixtures for different degrees of confinement are presented.

Self-assembly in mixtures with competing interactions.

A binary mixture of particles interacting with spherically-symmetrical potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume fractions. Motivated by the mixture of oppositely charged particles with different adsorption preferences immersed in a near-critical binary solvent, we assume short-range attraction long-range repulsion for the interaction between like particles, and short-range repulsion long-range attraction for the interaction between different ones. In order to predict structural and thermodynamic properties of such complex mixtures, we develop a theory combining the density functional and field-theoretical methods. We show that concentration fluctuations in mesoscopic regions lead to a qualitative change of the phase diagram compared to mean-field predictions. Both theory and MD simulations show coexistence of a low-density disordered phase with a high-density phase with alternating layers rich in the first and second components. In these layers, crystalline structure is present in the solid, and absent in the liquid crystals. The density and the degree of order of the ordered phase decrease with increasing temperature, up to a temperature where the theory predicts a narrow two-phase region with increasing density of both phases for increasing temperature. MD simulations show that monocrystals of the solid and liquid crystals have a prolate shape with the axis parallel to the direction of concentration oscillations, and the deviation from the spherical shape increases with increasing periodic order.

Structural and Thermodynamic Peculiarities of Core-Shell Particles at Fluid Interfaces from Triangular Lattice Models.

A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential-one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns-for example clusters or stripes-occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature.

3D structure of the electric double layer of ionic liquid-alcohol mixtures at the electrochemical interface.

Mixtures of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate with amphiphilic cosolvents, such as methanol and ethanol, nanoconfined between graphene walls are studied by means of molecular dynamics simulations and the results are compared with those of the pure ionic liquid and its mixtures with water confined in the same conditions. We investigate the adsorption of cosolvent molecules at the graphene walls as well as their distribution across the system. The results show that, due to a higher affinity of the polar groups to be close to the anions in combination with the electrostatic and excluded volume interactions, there exists a high tendency of the OH groups to lie close to the anode, inducing small changes in the first cation layer. The orientation of cosolvent molecules is found to be closely related to the alignment of the molecular dipole moment. We also investigate the lateral ionic distribution in the layers close to the electrodes, which shows a structural transition from liquid-like lamellar ordering to solid-like hexagonal patterns as the size of the cosolvent molecules increases leading to smaller position fluctuations of the ions. The dependence of the specific patterns on the nature of the electrodes is also studied. This study strongly suggests that the ionic patterns formed in the first ionic layers next to the charged interfaces are universal since their existence does not crucially depend on the atomic composition of the interfacial material, but only on the net charge density of the considered ionic layer, which significantly changes the ionic mobility in this region.

Two-dimensional pattern formation in ionic liquids confined between graphene walls.

We perform molecular dynamics simulations of ionic liquids confined between graphene walls under a large variety of conditions (pure ionic liquids, mixtures with water and alcohols, mixtures with lithium salts and defective graphene walls). Our results show that the formation of striped and hexagonal patterns in the Stern layer can be considered as a general feature of ionic liquids at electrochemical interfaces, the transition between patterns being controlled by the net balance of charge in the innermost layer of adsorbed molecules. This explains previously reported experimental and computational results and, for the first time, why these pattern changes are triggered by any perturbation of the charge density at the innermost layer of the electric double layer (voltage and composition changes, and vacancies at the electrode walls, among others), which may help tuning electrode-ionic liquid interfaces. Using Monte Carlo simulations we show that such structures can be reproduced by a simple two-dimensional lattice model with only nearest-neighbour interactions, governed by highly screened ionic interactions and short-range and excluded volume interactions. We also show that the results of our simulations are consistent with those inferred from the Landau-Brazovskii theory of pattern formation in self-assembling systems. The presence of these patterns at the ionic liquid graphene-electrode interfaces may have a strong impact on the process of ionic transfer from the bulk mixtures to the electrodes, on the differential capacitance of the electrode-electrolyte double layer or on the rates of redox reactions at the electrodes, among other physicochemical properties, and is therefore an effect of great technological interest.

The effect of antagonistic salt on a confined near-critical mixture.

We consider a near-critical binary mixture with addition of antagonistic salt (hydrophilic cations and hydrophobic anions) confined between weakly charged and selective surfaces. A mesoscopic functional for this system is developed from a microscopic description by a systematic coarse-graining procedure. The functional reduces to the Landau-Brazovskii functional for amphiphilic systems for a sufficiently large ratio between the correlation length in the critical binary mixture and the screening length. Our theoretical result agrees with the experimental observation [Sadakane et al., J. Chem. Phys., 2013, 139, 234905] that the antagonistic salt and the surfactant both lead to a similar mesoscopic structure. For very low salt concentration ρion the Casimir potential is the same as in the presence of inorganic salt. For larger ρion the Casimir potential takes a minimum followed by a maximum for separations of order of tens of nanometers, and exhibits an oscillatory decay very close to the critical point. For separations of tens of nanometers the potential between surfaces with a linear size of hundreds of nanometers can be of order of kBT. We have verified that in the experimentally studied samples [Sadakane et al., J. Chem. Phys., 2013, 139, 234905, Leys et al., Soft Matter, 2013, 9, 9326] the decay length is too small compared to the period of oscillations of the Casimir potential, but the oscillatory force could be observed closer to the critical point.

How ions in solution can change the sign of the critical Casimir potential.

We show that hydrophilic ions present in a confined, near-critical aqueous mixture can lead to an attraction between like charge surfaces with opposing preferential adsorption of the two species of the mixture, even though the corresponding Casimir potential in uncharged systems is repulsive. This prediction agrees with a recent experiment [Nellen et al., Soft Matter, 2011, 7, 5360]. We also show that oppositely charged hydrophobic surfaces can repel each other, although the Casimir potential between uncharged surfaces with like preferential adsorption (selectivity) is attractive. This behavior is expected when the electrostatic screening length is larger than the correlation length, and one of the confining surfaces is strongly selective and weakly charged, whereas the other confining surface is weakly selective and strongly charged. The Casimir potential can change sign because the hydrophilic ions near the weakly hydrophobic surface can overcompensate the effect of hydrophobicity, and this surface can act as a hydrophilic one. We also predict a more attractive interaction between charged, hydrophilic surfaces and a more repulsive interaction between charged, hydrophobic surfaces than given by the sum of the Casimir and Debye-Hückel potentials. Our theory is derived systematically from a microscopic approach, and combines the Landau-type and Debye-Hückel theories with an additional contribution of an entropic origin.

The origin of the attraction between like charged hydrophobic and hydrophilic walls confining a near-critical binary aqueous mixture with ions.

The effect of ionic solute on a near-critical binary aqueous mixture confined between charged walls with different adsorption preferences is considered within a simple density functional theory. For the near-critical system containing small amounts of ions, a Landau-type functional is derived on the basis of the assumption that the correlation, ξ, and the Debye screening length, κ(-1), are both much larger than the molecular size. The corresponding approximate Euler-Lagrange equations are solved analytically for ions insoluble in the organic solvent. A nontrivial concentration profile of the solvent is found near the charged hydrophobic wall as a result of the competition between the short-range attraction of the organic solvent and the electrostatic attraction of the hydrated ions. An excess of water may be present near the hydrophobic surface for some range of the surface charge and ξκ. As a result, the effective potential between the hydrophilic and the hydrophobic surface can be repulsive far from the critical point, then attractive and again repulsive when the critical temperature is approached, in agreement with a recent experiment (Nellen et al 2011 Soft Matter 7 5360).

Optimization of coarse-grained interaction potential: inside inherent limitations of coarse-graining methods.

We studied the inherent limitations of coarse-grained (CG) potentials within the recently developed approach (Kowalczyk et al. J. Phys. Chem. B2009, 113, 12988-12998). For all studied fluids, the spherically symmetric CG potential constructed according to our scheme modified in this work balances the reproduction of various equilibrium properties (i.e., structural and thermodynamic) measured in CG simulations. The inherent loss of atomistic information at the CG level correlates with the contribution from short-range directional interactions. The highest loss of atomistic information at 298 K and 1 bar is reported for protic liquids (i.e., methanol and acetamide), while the best description at the CG level was obtained for molecular hydrogen and carbon dioxide. The investigated aprotic liquids (i.e., benzene, toluene, and acetone) can be CG into spherically symmetric interaction potentials with some loss of atomistic details. Interestingly, we show that the proposed optimal CG potential reproduces also the interfacial properties of vapor-liquid coexistence for aprotic benzene at 298 K. For all studied fluids, we find that one can easily reproduce structural properties without preserving their cohesive properties or vice versa. However, a general conclusion from our study is the following: an increase in the protic character of a fluid leads to an increase of inherent loss of atomistic details at the CG level.

Distribution of ions near a charged selective surface in critical binary solvents.

Near-critical binary mixtures containing ionic solutes near a charged wall preferentially adsorbing one component of the solvent are studied. Within the Landau-Ginzburg approach extended to include electrostatic interactions and the chemical preference of ions for one component of the solvent, we obtain a simple form for the leading-order correction to the Debye-Hückel theory result for the charge density profile. Our result shows that critical adsorption influences significantly distribution of ions near the wall. This effect may have important implications for the screening of electrostatic interactions between charged surfaces immersed in binary near-critical solvents.

Role of short-range directional interactions in coarse-graining of protic/aprotic liquids.

We study the role of short-range directional interactions in coarse-graining (CG) of protic (i.e., acetamide, methanol, ethanol, and water) and aprotic (i.e., acetone, benzene, and toluene) liquids at normal conditions. For this purpose, we introduce a new CG method in which the average interactions between atomistic molecules and CG beads measured in an N,P,T ensemble are preserved. We show that the spherically symmetric effective CG potential constructed according to our scheme is able to reproduce structural/thermodynamic properties of aprotic liquids; the heat of vaporization and total bonding energy profile for monomer are reproduced with good accuracy, while the density and radial distribution function are reproduced with fair accuracy within the proposed method. In contrast, the isobaric heat capacity is underestimated in the CG simulation because some of the fluctuations have been washed out from atomistic aprotic liquids. For protic liquids, spherically symmetric effective CG potential produces more structure, enhanced packing of beads, and underestimated isobaric heat capacity of CG liquids. This fundamental difference between protic and aprotic liquids can be explained by the presence of short-range directional interactions in the former liquids. We conclude that some information during the CG into spherically symmetric interaction potentials of protic liquids has to be lost. However, understanding how short-range directional interactions influence the structural and thermodynamic properties of the CG liquids seems to be the key for improving the CG methods.

A simple lattice model for the microstructure of neat alcohols: application to liquid methanol.

Simple lattice model for self-associating molecules such as methanol or tert-butanol is proposed and studied in mean-field (MF) approximation in the case of methanol. In addition to the isotropic van der Waals interaction, the hydrogen bonding is present in this model when the neighboring alcohol molecules are in appropriate orientations. The orientation of the polar molecule is given by the unit vector n parallel to the vector connecting the center of the tail group with the center of the head group of the molecule. Stability region of the uniform fluid phase against gas-liquid separation and order-disorder transition is obtained for neat methanol in MF approximation. In order to describe the self-association patterns in the liquid, we consider the grand-canonical ensemble average of the scalar product of the orientations of the molecules as a function of the vector Delta x describing the separation between the centers of the molecules. For methanol we find in MF oscillatory decay of for Delta x perpendicular n(x) and for Delta x parallel n(x); the wavelength is somewhat less than two molecular diameters in both cases, and the decay length is larger in the perpendicular direction. This indicates that on average alternating antiparallel and parallel orientations of the second molecule are found for increasing separation from the first molecule in both directions. Such local orientational ordering of the molecules is consistent with association into zigzag chainlike clusters found in recent spectroscopic measurements and computer simulations. In Fourier representation the above structure function assumes maximum for the wave number that coincides with the prepeak position for site-site correlations found in simulations. We argue that can provide a useful tool for discriminating between different local arrangements of any polar molecules.

Simple three-state lattice model for liquid water.

A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered (O) and disordered (D) forms of water are treated as two components, and we assume that the density of the D component is larger. The density of the sample is determined by the fraction of cells occupied by the O and D forms of water. Due to the larger density of the D state, the strength of the van der Waals (vdW) interactions increases in the direction O-O