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.

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.

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.

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.

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.

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.

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.

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.

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.

Non-monotonic temperature response of polymer mediated interactions.

In a recent publication, Feng et al. [Feng et al., Nat. Mater., 2015, 14, 61] reported a very interesting re-entrant solidification behaviour of colloidal particles in an aqueous solution containing polyethylene oxide (PEO). In this system, a crystalline colloidal phase, which is present at low temperatures, melts to a homogeneous fluid upon increasing the temperature. Further raising the temperature, however, eventually gives rise to a flocculated colloidal phase. Feng et al. proposed that the low-temperature crystalline phase is caused by polymer depletion while, at higher temperature, an increased attraction between polymers and particles leads to bridging attractions, and colloidal flocculation. The intermediate temperature regime sees the colloidal interactions dominated by charge repulsion, giving rise to a fluid phase. In the model by Feng et al., polymers are treated as hard spheres, which interact with the colloids via a phenomenological, temperature dependent potential. In this work, we develop a more detailed polymer density functional treatment, based on a model for aqueous PEO solutions that was originally developed by Karlström [Karlström, J. Phys. Chem., 1985, 89, 4962] for bulk solutions. In this model, monomers are assumed to be in either of two classes of states, labelled A and B, where B is more solvophobic than A. On the other hand, the degeneracy of the B states exceed that of A, causing the population of solvophobic monomers to increase with temperature. If the colloidal particles are also solvophobic, then this model displays the same qualitative temperature response as was observed by Feng et al. That is, at low temperatures, A type monomers predominate and one observes depletion interactions, whereas polymer bridging dominates at higher temperatures, due to the attraction between B-type monomers and the colloidal surface. Interestingly, the intermediate temperature regime is characterized by a polymer mediated interaction between colloids which is repulsive. That is, according to our model the homogeneous fluid phase would form even in the absence of repulsive electrostatic interactions. We emphasize that our model does not rely upon any temperature-dependent interactions. Furthermore, all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. Finally, we show that interactions between colloids, mediated by neutral non-grafted polymers, generally follow the trend: attraction ⇒ repulsion (or vanishing interaction) ⇒ attraction as the surface affinity toward monomers proceeds from repulsive to attractive.

Iridium Cyclometalated Complexes in Host-Guest Chemistry: A Strategy for Maximizing Quantum Yield in Aqueous Media.

The weaker emission typically seen for iridium(III) cyclometalated complexes in aqueous medium can be reversed via encapsulation in cucurbit[10]uril (Q[10]). The Q[10] cavity is shown to effectively maximize quantum yields for the complexes, compared to any other medium. This may provide significant advantages for a number of sensor applications. NMR studies show that the complexes are accommodated similarly within the host molecule, even with cationic substituents attached to the ppy ligands, indicating that the hydrophobic effect is the dominant driving force for binding. Cavity-encapsulated 1:1 host-guest species dominate the emission, but 1:2 species are also indicated, which also give some enhancement of intensity. Results demonstrate that the enhancement is due primarily to much lower rates of nonradiative decay but also suggest that the encapsulation can cause a change in character of the emitting state.

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers.

We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson-Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreements between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of equilibrium clusters at high polymer concentrations, but low particle volume fractions and salt levels.

Fused coarse-grained model of aromatic ionic liquids and their behaviour at electrodes.

A fused coarse-grained model of aromatic ionic liquids 1-alkyl-3-methylimidazoliums tetrafluoroborate ([CnMIM(+)][BF4(-)]) has been constructed. Structural and dynamical properties calculated from our model are compared with experimental data as well as with corresponding results from simulations of other suggested models. Specifically, we adopt a fused-sphere coarse-grained model for cations and anions. This model is utilized to study structure and differential capacitance in models of flat and porous carbon electrodes. We find that the capacitance varies with pore size, in a manner that is related to the packing of ions inside the pore. For very narrow pores, diffusion is slow and the establishment of thermodynamic equilibrium may exceed the practical limits for our molecular dynamics simulations.

Ion pairing and phase behaviour of an asymmetric restricted primitive model of ionic liquids.

An asymmetric restricted primitive model (ARPM) of electrolytes is proposed as a simple three parameter (charge q, diameter d, and charge displacement b) model of ionic liquids and solutions. Charge displacement allows electrostatic and steric interactions to operate between different centres, so that orientational correlations arise in ion-ion interactions. In this way the ionic system may have partly the character of a simple ionic fluid/solid and of a polar fluid formed from ion pairs. The present exploration of the system focuses on the ion pair formation mechanism, the relative concentration of paired and free ions and the consequences for the cohesive energy, and the tendency to form fluid or solid phase. In contrast to studies of similar (though not identical) models in the past, we focus on behaviours at room temperature. By MC and MD simulations of such systems composed of monovalent ions of hard-sphere (or essentially hard-sphere) diameter equal to 5 Å and a charge displacement ranging from 0 to 2 Å from the hard-sphere origin, we find that ion pairing dominates for b larger than 1 Å. When b exceeds about 1.5 Å, the system is essentially a liquid of dipolar ion pairs with a small presence of free ions. We also investigate dielectric behaviours of corresponding liquids, composed of purely dipolar species. Many basic features of ionic liquids appear to be remarkably consistent with those of our ARPM at ambient conditions, when b is around 1 Å. However, the rate of self-diffusion and, to a lesser extent, conductivity is overestimated, presumably due to the simple spherical shape of our ions in the ARPM. The relative simplicity of our ARPM in relation to the rich variety of new mechanisms and properties it introduces, and to the numerical simplicity of its exploration by theory or simulation, makes it an essential step on the way towards representation of the full complexity of ionic liquids.

A many-body Hamiltonian for nanoparticles immersed in a polymer solution.

We developed an analytical theory for the many-body potential of mean force (POMF) between N spheres immersed in a continuum chain fluid. The theory is almost exact for a Θ polymer solution in the protein limit (small particles, long polymers), where N-body effects are important. Polydispersity in polymer length according to a Schulz-Flory distribution emerges naturally from our analysis, as does the transition to the monodisperse limit. The analytical expression for the POMF allows for computer simulations employing the complete N-body potential (i.e., without n-body truncation; n < N). These are compared with simulations of an explicit particle/polymer mixture. We show that the theory produces fluid structure in excellent agreement with the explicit model simulations even when the system is strongly fluctuating, e.g., at or near the spinodal region. We also demonstrate that other commonly used theoretical approaches, such as truncation of the POMF at the pair level or the Asakura Oosawa model, are extremely inaccurate for these systems.

Multistep Molecular Dynamics Simulations Identify the Highly Cooperative Activity of Melittin in Recognizing and Stabilizing Membrane Pores.

The prototypical antimicrobial peptide, melittin, is well-known for its ability to induce pores in zwitterionic model lipid membranes. However, the mechanism by which melittin accomplishes this is not fully understood. We have conducted all-atom and coarse-grained molecular dynamics simulations which suggest that melittin employs a highly cooperative mechanism for the induction of both small and large membrane pores. The process by which this peptide induces membrane pores appears to be driven by its affinity to membrane defects via its N-terminus region. In our simulations, a membrane defect was deliberately created through either lipid flip-flop or the reorientation of one adsorbed melittin peptide. In a cooperative response, other melittin molecules also inserted their N-termini into the created defect, thus lowering the overall free energy. The insertion of these peptide molecules ultimately allowed the defect to develop into a small transmembrane pore, with an estimated diameter of ∼1.5 nm and a lifetime of the order of tens of milliseconds. In the presence of a finite membrane tension, we show that this small pore can act as a nucleation site for the stochastic rupture of the lipid bilayer, so as to create a much larger pore. We found that a threshold membrane tension of 25 mN/m was needed to create a ruptured pore. Furthermore, by actively accumulating at its edge, adsorbed peptides are able to cooperatively stabilize this larger pore. The defect-mediated pore formation mechanism revealed in this work may also apply to other amphipathic membrane-active peptides.