The current technological revolution based on ionic liquids (ILs) is driven by their unique properties. Though ILs have been known to scientists for close to a century (Walden , 1914), they are now the focus of intense activity mainly because of their promise for “environmentally friendly” applications. Some actual and potential uses of ILs include: specific solvents for heterogeneous and homogeneous catalysis; selective solvents for removal of heavy metal contaminants; electrolytes in various electrochemical processes and devices; and as dispersive agents for stabilization of nanoparticles. In all of these applications, the structural properties of ILs and their mixtures in the bulk phase and at interfaces are crucial to their performance (Maier et al. , 2010). In electrowinning processes, such as aluminium refining, metal ion speciation is a crucial consideration in determining the population of electroactive components (Rocher et al. , 2009) and consequently influences the pertinent dynamical processes that lead to oxidation and reduction. These populations are ultimately governed by the free energy of the IL solution, which in turn depends upon the mutual interactions between the IL molecules and the added components. It is now clear that fundamental theoretical studies of structure-property relationships in ILs will provide important new insights, which will assist this kind of research. Not only in the choice and design of ILs for a specific application, but also for scenario based modelling of IL processes. For example, theoretical studies of the structure of ILs at charged surfaces are important for understanding the properties that they impart to electrodeposition processes, including factors such as ionic speciation and mass transport of electroactive species (MacFarlane et al. , 2010). As emphasized by Kornyshev in a recent review article (Kornyshev , 2007), applications of ILs at electrified interfaces to energy-storage systems, electrowetting devices or nanojunction gating media will be strongly promoted by a deeper understanding of the structure and properties of the interfacial double layer. Classical Density Functional Theory of Ionic Liquids

The central idea observes a recursive mapping of $$n$$ -body intramolecular interactions to $$(n+1)$$ -body terms that is consistent with the molecular topology. Iterative application of the line graph transformation is identified as a natural and elegant tool to accomplish the recursion. The procedure readily generalizes to arbitrary $$n$$ -body potentials. In particular, the method yields a complete characterization of $$4$$ -body interactions. The hierarchical structure of atomic index lists for each interaction order $$n$$ is compactly expressed as a directed acyclic graph. A pseudo-code description of the generating algorithm is given. With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of $$n$$ -body interactions can be implemented straightforwardly to handle large bio-molecular systems. Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

Ignoring inertia, a deformable interface separating two fluid films is considered, subject to non-uniform tension driven by the solutal Marangoni effect in the presence of a scalar concentration field. Detailed description of adsorption kinetics is abrogated by a simple ansatz directly relating interfacial tension and bulk solute concentration. Consequently, the formal mathematical treatment and some of the results share features in common with the Rayleigh-Benard-Marangoni thermocapillary problem. Normal mode perturbation analysis in the limit of small interface deformations establishes the existence of an unstable response for low wavenumber excitation. In the classification of Cross & Hohenberg (1993, Pattern formation outside of equilibrium. Rev. Mod. Phys., 65, 851-1112), both type I and type II behaviour are observed. By considering the zero wavenumber situation exactly, it is proved that all eigenvalues are purely imaginary with non-positive imaginary part; hence, a type III instability is not possible. For characteristic timescales of mass diffusion much shorter than the relaxation time of interfacial fluctuations (infinite crispation number): the response growth rate is obtained explicitly; only a single excitation mode is available, and a complete stability diagram is constructed in terms of the relevant control parameters. Otherwise, from a quiescent base state, an infinite discrete spectrum of modes is observed that exhibit avoided crossing and switching phenomena, as well as exceptional points where stationary state pairs coalesce into a single oscillatory standing wave pattern. A base state plane Poiseuille flow, driven by an external pressure gradient, generally exaggerates the response: growth rates of instabilities are enhanced, and stable decay is further suppressed with increasing base flow speed, but the inherent symmetry breaking destroys stationary and standing wave response. Results are obtained in this most general situation by implementing a numerical Chebyshev collocation scheme. The model was motivated by hydrodynamic processes supposed to be involved in gastric digestion of humans.

An experimental method is presented for investigating the effect of the nature of the interface on the relaxation behaviour accompanying hydrodynamic drainage occurring between oil droplets driven together in aqueous solution. This method is based upon force spectroscopy of droplet-droplet interactions. An atomic force microscope is used to drive two droplets together to a pre-defined force and then monitor relaxation of the force between the droplets. It is suggested that the observed relaxation is controlled by the hydrodynamic drainage of the interlamellar fluid separating the droplets. Data is presented for both ionic (sodium dodecyl sulphate) and non-ionic surfactants (Tween-20), uncoated oil droplets and droplets coated with the proteins, beta-casein and beta-lactoglobulin. Uncoated droplets, droplets coated with surfactants and droplets coated with the protein b-casein all exhibited fast relaxation, whereas droplets coated with beta-lactoglobulin exhibited markedly slower relaxation and more complex behaviour.

Recently AFM has been used to measure the interactions in aqueous media between a deformable oil drop attached onto an AFM cantilever and another drop on a substrate. In this study this method has been applied to oil droplets immersed in a solution of a polysaccharide extract having emulsifying properties, sugar beet pectin (SBP). In parallel with the force spectroscopy studies, images of the SBP interfacial films were obtained, in order to probe the effects of interfacial structures on the interactions between the drops. The influence of the SBP concentration in the bulk phase was studied: at a low bulk SBP concentration, where the adsorbed SBP layer is relatively flat, non-adsorbed SBP in the bulk solution gives rise to a depletion interaction between the drops. Upon increasing the SBP concentration, a hysteresis appears in the interactions between the drops. It is hypothesised that this effect is induced by the strong liquid structural correlations occurring within the liquid film separating the droplets. This conjecture is supported by a theoretical description which incorporates depletion interactions into a model for the interactions between deformable droplets. At high SBP concentration a strong repulsive force, attributed to steric repulsion between the thick SBP layers adsorbed onto the drops, is observed. Under different bulk conditions polymer bridges were observed to be formed between the SBP-coated droplets. The results demonstrate how AFM can be used to probe different types of interactions between deformable oil drops in aqueous media at the molecular level. When combined with theoretical models, this approach will advance the understanding of molecular mechanisms that govern the stability of emulsions.

This paper describes an adaptation of Ergon's 2PLS approach (Compression into two-component PLS factorizations. J. Chemom. 2003; 17: 303–312.) to represent a single predictor regression model in terms of a two-factor latent vector model. The purpose of this reduction is to aid model interpretation and diagnostics. Non-orthogonal score vectors are produced from two orthonormal loading vectors: one identical to the first PLS loading vector, and a second built from the regression vector. Using an invertible matrix, the factorization can be alternatively represented by two orthogonal score vectors, one of which is proportional to centred predictions. An auxiliary set of loadings is also calculated, which captures a different model space, but is provided since its associated residuals have useful properties. Identities connecting the two model spaces are provided. The latent vector regression coefficients are not always least-squares estimates but can be represented as the solution to a two-term generalized ridge regression. Consequences of this are addressed. The utility of TinyLVR is demonstrated with example models built using stepwise variate selection and ridge regression.

For non-negative real order, the product of modified Bessel functions of first and second kind is shown to be strictly decreasing for positive real arguments. After recalling some established results, only elementary methods are required to complete the proof.

We report a novel oil-in-water emulsion that is both buoyancy and refractive index matched. The dispersion is created using low-shear cross-flow membrane emulsification technology with a discrete phase comprising a mixture of n-hexane and the perfluorinated oil tetradecafluorohexane, in the form of FC-72. Three-dimensional confocal laser light imaging of a bulk-aggregated emulsion is demonstrated, showing explicit droplet-level detail of the emulsion interior. Magnetic resonance microscopy with a spatial resolution of tens of microns is also described. The proximity of a liquid–liquid binodal in the oil mixture can give rise to a ternary phase separation reminiscent of an O/O/W emulsion.

A new boundary integral formulation is proposed for the solution of electrostatic field problems involving piecewise uniform dielectric continua. Direct Coulomb contributions to the total potential are treated exactly and Green’s theorem is applied only to the residual reaction field generated by surface polarisation charge induced at dielectric boundaries. The implementation shows significantly improved numerical stability over alternative schemes involving the total field or its surface normal derivatives. Although strictly respecting the electrostatic boundary conditions, the partitioned scheme does introduce a jump artefact at the interface. Comparison against analytic results in canonical geometries, however, demonstrates that simple interpolation near the boundary is a cheap and effective way to circumvent this characteristic in typical applications. The new scheme is tested in a naive model to successfully predict the ground state orientation of biomolecular aggregates comprising the soybean storage protein, glycinin.

Noise reduction, restoration, and segmentation methods are developed for the quantitative structural analysis in three dimensions of aggregated oil-in-water emulsion systems imaged by fluorescence confocal laser scanning microscopy. Mindful of typical industrial formulations, the methods are demonstrated for concentrated (30% volume fraction) and polydisperse emulsions. Following a regularized deconvolution step using an analytic optical transfer function and appropriate binary thresholding, novel application of the Euclidean distance map provides effective discrimination of closely clustered emulsion droplets with size variation over at least 1 order of magnitude. The a priori assumption of spherical nonintersecting objects provides crucial information to combat the ill-posed inverse problem presented by locating individual particles. Position coordinates and size estimates are recovered with sufficient precision to permit quantitative study of static geometrical features. In particular, aggregate morphology is characterized by a novel void distribution measure based on the generalized Apollonius problem. This is also compared with conventional Voronoi/Delauney analysis.

The generalized hole corrected Debye-Huckel theory (Penfold et al J. Stat. Mech. (2005) P06009) is implemented. Predictions of thermodynamic functions and simple structural properties compare favourably with results from closure of the Ornstein-Zernike integral equation in the mean spherical approximation, and with Monte Carlo simulation of the charged hard sphere primitive model. A strictly nonelectroneutral system was simulated using a conventional electrolyte program and the properties subsequently corrected for the configuration independent background terms. No convergence difficulties were encountered over the concentration range studied. With the new theory, activity coefficients of good accuracy can be obtained in a simple analytical form that is suitable for use with an approximate free energy density functional describing ion-ion correlations in screening atmospheres.

By eliminating the short range negative divergence of the Debye-Huuckel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model — the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.

Monte Carlo simulations are used to assess the adequacy of the Tanford‐Kirkwood prescription for electrostatic interactions in macromolecules. Within a continuum dielectric framework, the approach accurately describes salt screening of electrostatic interactions for moderately charged systems consistent with common proteins at physiological conditions. The limitations of the Debye‐Hückel theory, which forms the statistical mechanical basis for the Tanford‐Kirkwood result, become apparent for highly charged systems. It is shown, both by an analysis of the Debye‐Hückel theory and by numerical simulations, that the difference in dielectric permittivity between macromolecule and surrounding solvent does not play a significant role for salt effects if the macromolecule is highly charged. By comparison to experimental data, the continuum dielectric model (combined with either an approximate effective Hamiltonian as in the Tanford‐Kirkwood treatment or with exact Monte Carlo simulations) satisfactorily predicts the effects of charge mutation on metal ion binding constants, but only if the macromolecule and solvent are assigned the same or similar permittivities.

An efficient implementation of the generalized van der Waals theory of fluids is presented for the calculation of surface tension in simple fluid mixtures. While detailed correlation analysis is avoided the dominant binding energy contribution and the negative contribution due to the nonlocal entropy are accounted for in the free energy density functional by simple physical approximations of the type originally introduced by van der Waals. Efficient computation is achieved by the use of a single-parameter optimization of a tanh-shaped profile representing the total density as well as the composition variation across the interface. This simple profile nevertheless incorporates the expected adsorption to the interface of the volatile component. Application is made to argon/krypton mixtures represented by Lennard-Jones potentials and Lorentz-Berthelot combining rules. Surface tension predictions compare well with both experimental observations and computer simulation results which also indicated close agreement in particle density profiles, especially if the Berthelot rule is amended with a binary interaction parameter slightly (3%) less than unity. Copyright 2001 Academic Press.

We address the wellknown problems introduced into the theory of fluids by density fluctuations in the form of van der Waals loops and nonclassical critical phenomena. A clean separation of long and short range density fluctuations is achieved by use of cell-constrained models which display well-defined van der Waals loops and classical behaviour around the critical point. For a pure Lennard-Jones fluid with occupancy restricted to 1 or 8 particles per cell, the phase diagram is determined by Monte Carlo simulation. By considering the deviations from the normal simulations without cell constraint, the effects of longer range density fluctuations are exposed. The system size dependence of the van der Waals loops present in all simulations of fluids is analyzed in terms of the GvdW free energy density functional theory, which is formulated on the basis of the cell concept. The loops are found to gradually disappear either with greater cell occupancy or increasing total particle number in the simulation box.

The binding of calcium ions to biomolecules has been investigated by comparing three continuum models, all presupposing the dominance of Coulombic interactions. To reflect disparity in polarization response of protein and solvent, the "refined" model (RM) incorporates an inhomogeneous static dielectric constant but admits only approximate analysis within the mean field ansatz. Conversely, the "primitive" model (PM), with a uniform dielectric response, yields to essentially exact solutions of the statistical mechanical problem by Monte Carlo simulation techniques. The "elementary" model (EM) further assumes linear thermal response and ignores steric constraints altogether to obtain a trivially evaluated, analytic result. Two contrasting biomolecules are considered: the large, positively charged, extracellular serine protease subtilisin exhibiting a low affinity binding site and the smaller, negatively charged, intracellular, nonenzymatic protein buffer calbindin that binds calcium tenaciously. As functions of protein (fixed) charge mutations and solution ionic strength, the EM shows consistently good agreement with observed shifts in equilibrium binding constants (DpK(d)). Predictions from simulation and finite difference solutions of both Poisson-Boltzmann and Debye-Huckel equations in the PM are essentially identical. They also conform closely to experiment, though with systematic deviations at high ionic strength. Evidently both long and short range correlations an suppressed or mitigated in these systems, while nonlinear thermal effects appear to be unimportant even up to 1.0 M monovalent salt. With standard parameters, RM calculations generally overestimate DpK(a)'s, while the differences between RM and PM results are independent of salt concentration. Large electrostatic potentials arising in the RM possibly indicate strained protein conformations, though structural relaxation is not accounted for in any of the models studied. Motivated by exact analysis of salt free cases in planar and spherical geometries, alternative mechanisms explaining the theoretical deviations are discussed, in particular self-image correlation of mobile ions and the location of an effective dielectric interface.

At atmospheric pressure, the bulk density and liquid-liquid coexistence curve for the binary system of methanol and n-hexane have been measured as a function of temperature in the range 293-308 K. Comparison with the most reliable of the sparse literature data shows good agreement. A video image processor designed for automatic digital measurement has been used to determine the interfacial tension by the pendant drop technique. Results into the 0.01 mN m(-1) range have been readily obtained. The coexistence envelope has been analysed in terms of near critical extended scaling theory using non-asymptotic Wegner corrections to indirectly determine the upper critical solution temperature at 309.5 K, in excellent agreement with contemporary work. Of the possible order parameters considered (mole, mass and volume fraction), the volume fraction difference proved the most satisfactory, yielding a critical exponent consistent with 3D Ising universality. Simple scaling relations for the interfacial tension are inadequate for reduced temperatures beyond 10(-2).