An efficient method to establish electrostatic screening lengths of restricted primitive model electrolytes.

We present a novel, and computationally cheap, way to estimate electrostatic screening lengths from simulations of restricted primitive model (RPM) electrolytes. We demonstrate that the method is accurate by comparisons with simulated long-ranged parts of the charge density, at various Bjerrum lengths, salt concentrations and ion diameters. We find substantial underscreening in low dielectric solvent, but with an "aqueous" solvent, there is instead overscreening, the degree of which increases with ion size. Our method also offers a possible path to (future) more accurate classical density functional treatments of ionic fluids.

Phase transitions of ionic fluids in nanoporous electrodes.

In this work, we utilise grand canonical Metropolis Monte Carlo simulations, to establish pore-induced freezing of restricted primitive model fluids. A planar pore model is utilised, with walls that are initially neutral, and either non-conducting or perfectly conducting. The phase of the confined electrolyte (solid/fluid) displays an oscillatory dependence on surface separation, in narrow pores. Conditions are chosen so that the bulk is composed of a stable fluid electrolyte. The tendency for the electrolyte to freeze in narrow pores is somewhat stronger in systems with non-conducting walls. We also demonstrate that an applied potential will, above a threshold value, melt a frozen electrolyte. In these cases, the capacitance, as measured by the average surface charge density divided by the applied potential, will be almost vanishing if the applied potential is below this threshold value. We do not see any evidence for a "superionic fluid", which has been hypothesised to generate a strong capacitance in narrow pores, due to an efficient screening of like-charge repulsions by image charges.

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids.

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Interactions between conducting surfaces in salt solutions.

In this work, we simulate interactions between two perfectly conducting surfaces, immersed in a salt solution. We demonstrate that these forces are quantitatively different from those between (equally charged) non-conducting surfaces. There is, for instance, a significant repulsion between net neutral surfaces. On the other hand, there are also qualitative similarities, with behaviours found with non-conducting surfaces. For instance, there is a non-monotonic dependence of the free energy barrier height, on the salt concentration, and the minimum essentially coincides with a flat profile of the apparent surface charge density (i.e. the effective net surface charge density, some distance away from the surface, when accounting for ion neutralization), outside the so-called Stern layer. These conditions can be described as "perfect surface charge neutralization". Despite observed quantitative differences, we demonstrate that it might be possible to mimic a dispersion containing charged colloidal metal particles by a simpler model system with charged non-conducting particles, using modified particle-ion interactions.

Polymer-Like Self-Assembled Structures from Particles with Isotropic Interactions: Dependence upon the Range of the Attraction.

We conduct Metropolis Monte Carlo simulations on models of dilute colloidal dispersions, where the particles interact via isotropic potentials of mean force (PMFs) that display a long-ranged repulsion, combined with a short-ranged and narrow attraction. Such systems are known to form anisotropic clusters. There are two main conclusions from this work. First, we demonstrate that the width of the attractive region has a significant impact on the type of structures that are formed. A narrow attractive well tends to produce clusters in which particles possess fewer neighbors than in systems where the attraction is wider. Second, metastable clusters appear to persist in the absence of specific simulation moves designed to overcome large energy barriers to particle accumulation. The so-called "Aggregation-Volume Bias Monte Carlo" moves were previously developed by Chen and Siepmann, and they facilitate particle exchanges between clusters via unphysical moves that bypass high energy intermediate states. These facilitate the progression of metastable clusters to equilibrium clusters. Metastable clusters are generally large with significant branching of thin filaments of aggregated particles, while stable clusters have thicker backbones and tend to be more compact with significantly fewer particles. This general behavior is observed in both two- and three-dimensional systems. In two dimensions, less anisotropic clusters with backbones possessing lattice structures will occur, particularly for systems where the particles interact with a PMF that has a relatively wide attractive region. We compare our results with PMF calculations established from a more specific model, namely weakly charged polystyrene particles, which carry a thin surface layer of grafted polyethylene oxide polymers in aqueous solution. We hope that our investigations can serve as crude guidelines for experimental research, aiming to construct linear or branched polymers in aqueous solution built up by colloidal monomers that are large enough to be studied by confocal microscopy. We suggest that metastable clusters are more relevant to experimental scenarios where the energetic barriers are too large to be surmounted over typical timescales.

Structural transitions at electrodes, immersed in simple ionic liquid models.

We used a recently developed classical Density Functional Theory (DFT) method to study the structures, phase transitions, and electrochemical behaviours of two coarse-grained ionic fluid models, in the presence of a perfectly conducting model electrode. Common to both is that the charge of the cationic component is able to approach the electrode interface more closely than the anion charge. This means that the cations are specifically attracted to the electrode, due to surface polarization effects. Hence, for a positively charged electrode, there is competition at the surface between cations and anions, where the latter are attracted by the positive electrode charge. This generates demixing, for a range of positive voltages, where the two phases are structurally quite different. The surface charge density is also different between the two phases, even at the same potential. The DFT formulation contains an approximate treatment of ion correlations, and surface polarization, where the latter is modelled via screened image interactions. Using a mean-field DFT, where ion correlations are neglected, causes the phase transition to vanish for both models, but there is still a dramatic drop in the differential capacitance as proximal cations are replaced by anions, for increasing surface potentials. While these findings were obtained for relatively crude coarse-grained models, we argue that the findings can also be relevant in "real" systems, where we note that many ionic liquids are composed of a spherically symmetric anion, and a cation that is asymmetric both from a steric and a charge distribution point of view.

Phase Transitions of Oppositely Charged Colloidal Particles Driven by Alternating Current Electric Field.

We study systems containing oppositely charged colloidal particles under applied alternating current electric fields (AC fields) using overdamped Langevin dynamics simulations in three dimensions. We obtain jammed bands perpendicular to the field direction under intermediate frequencies and lanes parallel with the field under low frequencies. These structures also depend upon the particle charges. The pathway for generating jammed bands follows a stepwise mechanism, and intermediate bands are observed during lane formation in some systems. We investigate the component of the pressure tensors in the direction parallel to the field and observe that the jammed to lane transition occurs at a critical value for this pressure. We also find that the stable steady states appear to satisfy the principle of maximum entropy production. Our results may help to improve the understand of the underlying mechanisms for these types of dynamic phase transitions and the subsequent cooperative assemblies of colloidal particles under such non-equilibrium conditions.

A semi-GCMC simulation study of electrolytic capacitors with adsorbed titrating peptides.

We use semi-grand canonical Monte Carlo simulations to study an electrolytic capacitor with an adsorbed peptide on the electrode surfaces. Only homogeneous peptides are considered, consisting of only a single residue type. We find that the classical double-hump camel-shaped differential capacitance in such systems is augmented by the addition of a third peak, due to the capacitance contribution of the peptide, essentially superimposed on the salt contribution. This mechanistic picture is justified using a simple mean-field analysis. We find that the position of this third peak can be tuned to various surface potential values by adjusting the ambient pH of the electrolyte solution. We investigate the effect of changing the residue type and the concentration of the adsorbed peptide and of the supporting electrolyte. Varying the residue species and pH allows one to modify the capacitance profile as a function of surface potential, facilitating the design of varying discharging patterns for the capacitor.

Interaction of the Large Host Q[10] with Metal Polypyridyl Complexes: Binding Modes and Effects on Luminescence.

Aqueous solution state host-guest systems have been studied, comprising the large host cucurbit[10]uril with luminescent cationic tris(polypyridyl) (PP) metal complexes [Ru(PP)3]2+ and [Ir(PP)3]3+. All complexes bind strongly with the host, with the overall complex charge and size having a minor effect on affinity but influencing the association dynamics and contribution from higher-order (1:2) host-guest species. The 1:2 species contributes more significantly to the binding equilibrium in the case of [Ru(phen)3]2+. The effect of the host upon emission is highly variable and depends on the electronic structure of the guest. The metal-to-ligand charge transfer (MLCT) emission of [Ru(PP)3]2+ is strongly quenched, in contrast to the large enhancements seen previously for MLCT emission of iridium cyclometalated complexes, while the ligand-centered emission of [Ir(PP)3]3+ is little affected. The mechanisms of quenching and enhancement are discussed, together with the implications for the design of larger supramolecular assemblies based on these archetypal emitters.

Non-monotonic phase behaviour of a mixture containing non-adsorbing particles and polymerising rod-like molecules.

HYPOTHESIS: Previous works have shown that many-body interactions induced by dispersants with increasing correlation length will generate a diminishing two-phase region [Soft Matter 14, 6921 (2018)]. We conjecture that the attenuation of the depletion attraction due to many-body interactions is a ubiquitous phenomenon in medium-induced interactions. We propose mixtures of colloidal particles and rod-like polymers as a feasible experimental system for verifying these predictions, since the intra-molecular correlations are not screened in a good solvent for rod-like polymers as they are in flexible polymers. The length of the rods can grow and become the dominant length scale that determines the range of the depletion interactions for the imbedded non-adsorbing particles. Simulations: We study many-body depletion forces induced by polymerizing rod-like polymers on spherical non-adsorbing colloids, using Metropolis Monte Carlo simulations. We also employ a simple mean-field theory to further justify our numerical predictions. FINDINGS: We demonstrate that the phase diagram displays the same qualitative features that have previously been predicted by many-body theory, for mixtures containing flexible polymers under theta solvent conditions. The contraction of the particle two-phase region that we observe, as the correlation length increases beyond some specific value, could be a signature of the weakening of the depletion caused by many-body effects.

Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids.

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom's particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by "diffusion" of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln(L), where L is the pore length.

Tiara[ n]uril: A Glycoluril-Based Macrocyclic Host with Cationic Walls.

The synthesis of new cationic macrocyclic host molecules is described. These macrocycles are comprised of glycoluril oligomers linked to two pyrazolium groups, which form part of a cationic wall facing into their cavities. A number of derivatives have been prepared with an objective to increasing the cavity size, and each new product has been fully characterized. Preliminary investigations of p Kas of Me10Tu[3]2+ and an interaction of L-glutamine indicate a potential for binding anionic molecules that also carry H-bond donor groups.

Many-body effects in a binary nano-particle mixture dispersed in ideal polymer solutions.

A new mean-field theory is developed to treat a binary mixture of nanoparticles imbedded in a polydisperse polymer solution. The theory is based on a many-body polymer-mediated potential of mean force (PMF) between the particles and remains accurate even in the protein regime, where the particles' diameters cannot necessarily be considered large compared to the polymer radius of gyration. As implemented here, the theory is strictly valid for dilute to semi-dilute polymer solutions near the theta temperature (the so-called theta regime) or when the range of the PMF is strongly affected by the polymer size. For non-adsorbing particles, this is the same regime where the celebrated Asakura-Oosawa (AO) model is often used. Unlike the traditional AO model, however, our approach includes polymer flexibility and is accurate in the protein regime. We use the theory to calculate phase diagrams for a binary mixture of unequal-sized particles, both adsorbing and non-adsorbing. To test the theory, we carry out comparisons with simulations and obtained good quantitative agreement, which gives support to its accuracy. On the other hand, the oft-used approach assuming pairwise-additive potentials of mean force produce quantitatively (and sometime qualitatively) different phase diagrams.

A classical density functional theory for the asymmetric restricted primitive model of ionic liquids.

A new three-parameter (valency, ion size, and charge asymmetry) model, the asymmetric restricted primitive model (ARPM) of ionic liquids, has recently been proposed. Given that ionic liquids generally are composed of monovalent species, the ARPM effectively reduces to a two-parameter model. Monte Carlo (MC) simulations have demonstrated that the ARPM is able to reproduce key properties of room temperature ionic liquids (RTILs) in bulk and at charged surfaces. The relatively modest complexity of the model raises the possibility, which is explored here, that a classical density functional theory (DFT) could resolve its properties. This is relevant because it might generate great improvements in terms of both numerical efficiency and understanding in the continued research of RTILs and their applications. In this report, a DFT for rod-like molecules is proposed as an approximate theoretical tool for an ARPM fluid. Borrowing data on the ion pair fraction from a single bulk simulation, the ARPM is modelled as a mixture of dissociated ions and connected ion pairs. We have specifically studied an ARPM where the hard-sphere diameter is 5 Å, with the charge located 1 Å from the hard-sphere centre. We focus on fluid structure and electrochemical behaviour of this ARPM fluid, into which a model electrode is immersed. The latter is modelled as a perfect conductor, and surface polarization is handled by the method of image charges. Approximate methods, which were developed in an earlier study, to take image interactions into account, are also incorporated in the DFT. We make direct numerical comparisons between DFT predictions and corresponding simulation data. The DFT theory is implemented both in the normal mean field form with respect to the electrostatic interactions and in a correlated form based on hole formation by both steric repulsions and ion-ion Coulomb interactions. The results clearly show that ion-ion correlations play a very important role in the screening of the charged surfaces by our ARPM ionic liquid. We have studied electrostatic potentials and ion density profiles as well the differential capacitance. The mean-field DFT fails to reproduce these properties, but the inclusion of ion-ion correlation by a simple approximate treatment yields quite reasonable agreement with the corresponding simulation results. An interesting finding is that there appears to be a surface phase transition at relatively low surface charge which is readily explored by DFT, but seen also in the MC simulations at somewhat higher asymmetry.

Many-body depletion forces of colloids in a polydisperse polymer dispersant in the long-chain limit.

We study a system of spherical non-adsorbing particles immersed in a polydisperse polymer fluid. We derive an analytic expression for the many-body depletion interactions between the colloidal particles in the limit of very long chains. We argue that this expression is essentially exact for long chains and justify this using explicit simulations. In this way we are able to elucidate the profound effect of many-body interactions on the particle thermodynamics. We show that using truncated 2-body depletion interactions leads to strong particle segregation, while the complete many-body description predicts that the total depletion force becomes weak so that the system approximates one which interacts via a so-called Kac potential. This implies that the depletion interactions can be described using mean-field theory. We show that many-body effects cause a significant contraction of the 2-phase region of the particle dispersion. We also investigate the system approaching the (tricritical) θ point, which terminates the line of first-order critical points of the polymer dispersion in a poor solvent and show that many-body effects suppress particle phase transitions.

Many-body interactions between charged particles in a polymer solution: the protein regime.

We study the phase behavior of charged particles in electrolyte solutions wherein non-adsorbing polymers are added to provide an attractive depletion interaction. The polymer has a radius of gyration similar to that of the particle radius, which causes significant many-body effects in the effective polymer mediated interaction between particles. We use a recently developed analytical theory, which gives a closed expression for the full depletion interaction, accounting for all orders of many-body terms in the potential of mean force. We compare with simulations of an explicit polymer model and show that the potential of mean force provides an accurate and computationally efficient description for the charged particle/polymer mixture, over a range of electrolyte concentrations. Furthermore, we demonstrate that the usual pair potential approach is highly inaccurate for these systems. A simple simulation method is used to estimate the limits of stability of the mixture. The pair approximation is shown to predict a much greater region of instability compared with the many-body treatment, due to its overestimation of the polymer depletion effect.

Ionic liquid interface at an electrode: simulations of electrochemical properties using an asymmetric restricted primitive model.

We use Monte Carlo simulations of a coarse-grained model to investigate structure and electrochemical behaviours at an electrode immersed in room temperature ionic liquids (RTILs). The simple RTIL model, which we denote the asymmetric restricted primitive model (ARPM), is composed of monovalent hard-sphere ions, all of the same size, in which the charge is asymmetrically placed. Not only the hard-sphere size (d), but also the charge displacement (b), is identical for all species, i.e. the monovalent RTIL ions are fully described by only two parameters (d, b). In earlier work, it was demonstrated that the ARPM can capture typical static RTIL properties in bulk solutions with remarkable accuracy. Here, we investigate its behaviour at an electrode surface. The electrode is assumed to be a perfect conductor and image charge methods are utilized to handle polarization effects. We find that the ARPM of the ionic liquid reproduces typical (static) electrochemical properties of RTILs. Our model predicts a declining differential capacitance with increasing temperature, which is expected from simple physical arguments. We also compare our ARPM, with the corresponding RPM description, at an elevated temperature (1000 K). We conclude that, even though ion pairing occurs in the ARPM system, reducing the concentration of 'free' ions, it is still better able to screen charge than a corresponding RPM melt. Finally, we evaluate the option to coarse-grain the model even further, by treating the fraction of the ions that form ion pairs implicitly, only through the contribution to the dielectric constant of the corresponding dipolar (ion pair) fluid. We conclude that this primitive representation of ion pairing is not able to reproduce the structures and differential capacitances of the system with explicit ion pairs. The main problem seems to be due to a limited dielectric screening in a layer near the electrode surface, resulting from a combination of orientational restrictions and a depleted dipole density.

Modelling the luminescence of iridium cyclometalated complexes encapsulated in cucurbituril.

Iridium(iii) cyclometalated complexes in aqueous solution often display relatively weak luminescence. It has been shown in previous work that this emission can be significantly enhanced (by up to two orders of magnitude) by encapsulation in cucurbit[10]uril (Q[10]). Luminescence lifetime measurements suggest a dynamic self-quenching mechanism is active, possibly due to displacement of an excited guest complex via collision with an unbound complex. We devise a model for the association of a group of iridium(iii) cyclometalated complexes with Q[10]. The model parameters are then fitted to steady-state emission titration curves. The excellent agreement of experimental data with the model provides valuable mechanistic information relating to the way this class of metal complexes interact and associate with the Q[10] host.

Molecular Simulations of Melittin-Induced Membrane Pores.

Membrane-active peptides (MAPs) are able to induce pores in cell membranes via molecular mechanisms, which are still subject to ongoing research. In this work, we present molecular dynamics simulations that suggest a precursor membrane defect plays an important role in the pore-inducing activity of the prototypical antimicrobial peptide melittin. The simulations reveal that the hydrophobic N-terminus of melittin is able to recognize and insert into the membrane defect in the lipid bilayer and that this leads to a cascading transfer of adsorbed peptides to the membrane defect, leading to peptide aggregation in the pore. We show that this mechanism also acts in the case of a melittin mutant without the flexible central proline hinge, thus indicating the latter is not crucial to the activity of melittin, which is consistent with experiments.

DNA condensation in live E. coli provides evidence for transertion.

Condensation studies of chromosomal DNA in E. coli with a tetranuclear ruthenium complex are carried out and images obtained with wide-field fluorescence microscopy. Remarkably different condensate morphologies resulted, depending upon the treatment protocol. The occurrence of condensed nucleoid spirals in live bacteria provides evidence for the transertion hypothesis.