We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase.

Gyroid phase of fluids with spherically symmetric competing interactions

A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first neighbors and repulsion J_2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J_2/J_1 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J_2/J_1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J_2/J_1. Based on the exact results, for J_2/J_1>1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9<J_2/J_1<1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T=0, local spatial inhomogeneities appear for finite T. Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density \rho that we associate with formation of living clusters, and if the repulsion is strong, another maximum for \rho = 1/2.

/pdf/periodic-ordering-of-clusters-in-a-one-dimensional-lattice-29atau030t.pdf

Periodic ordering of clusters in a one-dimensional lattice model

A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J1 between the first neighbors and repulsion J2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J2/J1 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J2/J1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J2/J1. Based on the exact results, for J2/J1 > 1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9 < J2/J1 < 1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T = 0, local spatial inhomogeneities appear for finite T. Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density ρ that we associate with formation of living clusters, and if the repulsion is strong, another maximum for ρ = 1/2.

/pdf/periodic-ordering-of-clusters-in-a-one-dimensional-lattice-34ywmjxfw3.pdf

Periodic ordering of clusters in a one-dimensional lattice model.

Adsorption at an attractive surface in a system with particles self-assembling into small clusters is studied by molecular dynamics simulation. We assume Lennard-Jones plus repulsive Yukawa tail interactions and focus on small densities. The relative increase in the temperature at the critical cluster concentration near the attractive surface (CCCS) shows a power-law dependence on the strength of the wall-particle attraction. At temperatures below the CCCS, the adsorbed layer consists of undeformed clusters if the wall-particle attraction is not too strong. Above the CCCS or for strong attraction leading to flattening of the adsorbed aggregates, we obtain a monolayer that for strong or very strong attraction consists of flattened clusters or stripes, respectively. The accumulated repulsion from the particles adsorbed at the wall leads to a repulsive barrier that slows down the adsorption process, and the accession time grows rapidly with the strength of the wall-particle attraction. Beyond the adsorbed layer of particles, a depletion region of a thickness comparable with the range of the repulsive tail of interactions occurs, and the density in this region decreases with increasing strength of the wall-particle attraction. At larger separations, the exponentially damped oscillations of density agree with theoretical predictions for self-assembling systems. Structural and thermal properties of the bulk are also determined. In particular, a new structural crossover associated with the maximum of the specific heat and a double-peaked histogram of the cluster size distribution are observed.

Effect of aggregation on adsorption phenomena.

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.

pdf/two-dimensional-pattern-formation-in-ionic-liquids-confined-1akjabi74l.pdf

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

/pdf/mesoscopic-description-of-network-forming-clusters-of-weakly-41cl25ew02.pdf

Mesoscopic description of network-forming clusters of weakly charged colloids

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Mesoscopic description of network-forming clusters of weakly charged colloids