Robert Penfold

A simple analysis of ion-ion correlation in polyelectrolyte solutions

In the Poisson–Boltzmann theory of macroion screening in electrolyte solutions the chief simplifying assumption is the neglect of correlations within the ionic atmosphere. Using a generalized van der Waals density functional analysis incorporating ion–ion correlation in a local approximation we obtain a simple correlation corrected Poisson–Boltzmann theory. For point charges in the salt free case, this local correlation approximation leads to asymptotic instability (a ‘‘structuring catastrophe’’) though the correction is well behaved to low orders in perturbation theory. Results in zeroth order and in a zeroth order field approximation are compared with an extended series of Monte Carlo simulations within a cell model (and a planar electrode model). An excellent agreement is found over a wide range of coupling strengths.

Molecular basis for the emulsifying properties of sugar beet pectin studied by atomic force microscopy and force spectroscopy

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.

A critical investigation of the Tanford-Kirkwood shceme by means of Monte Carlo simulations

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.

A simple analysis of the classical hard sphere one component plasma. I. Hole corrected Debye–Hückel theory

The principal simplifying assumptions in the description of Coulomb fluids are the neglect of correlations within the ionic atmosphere and the disregard of ion size effects. In order to account for short range repulsions, a straightforward heuristic approach is considered where a Debye–Huckel charge density is augmented with a central hard sphere and the possibility of an electrostatic exclusion zone is included to prevent an unphysical negative contact density. This approach leads to an analysis describing the relative competition between hard sphere and electrostatic mechanisms, which undergoes a well‐defined interchange in the (γ,η) parameter space. While the structural information is, by construction, limited, thermodynamic properties agree remarkably well with both the rescaled mean spherical approximation and Monte Carlo simulations, up to moderate densities.

Monotonicity of some modified Bessel function products

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.

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids II. Binary mixtures of n-alkanes and miscible gas

Abstract A representation of alkanes and alkane/gas mixtures is proposed in terms of simple fluids interacting through pairwise square well potentials parameterised by the range of attractive forces. Using the model, vapour–liquid equilibria and interfacial tension (IFT) are studied both for pure alkane fluids (C4, C5, C6, C8, C10 and C14) and their high pressure binary mixtures formed with methane, nitrogen or carbon dioxide. Potential parameters for the isolated components are first determined from the critical parameters, Pitzer’s acentric factor and one surface tension datum at a chosen temperature. Cross-term interactions between species are obtained from modified Lorentz–Berthelot rules which provide good fits to the vapour–liquid coexistence densities as functions of mixture composition. At a general state point, the interfacial tension is predicted using generalised van der Waals (gvdW) theory, which is a mean field free energy density functional theory. This semiempirical procedure typically produces very satisfactory agreement with experimental interfacial tension data.

The liquid–liquid coexistence curve and the interfacial tension of the methanol–n-hexane system

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 .

Probing the role of interfacial rheology in the relaxation behaviour between deformable oil droplets using force spectroscopy

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, β-casein and β-lactoglobulin. Uncoated droplets, droplets coated with surfactants and droplets coated with the protein β-casein all exhibited fast relaxation, whereas droplets coated with β-lactoglobulin exhibited markedly slower relaxation and more complex behaviour.

Ion–ion correlations in polyelectrolyte solutions: Hard sphere counterions

The intimately related mechanisms of macroion screening and ion–ion correlations in electrolyte solutions are investigated with the aim to explore the simplest theoretical estimations of the latter on the former. The Poisson–Boltzmann theory of macroion screening in electrolyte solutions was developed under two important assumptions. Specifically, the correlated motion of the mobile ions is ignored by identifying the mean field electrostatic potential with the potential of average force and, moreover, only point charges are considered so that finite size effects are not accounted for. Utilizing the generalized van der Waals free energy density functional formulation for inhomogeneous fluids, we obtain simple corrections to the Poisson–Boltzmann result where both these mechanisms are treated in local and nonlocal approximations. By incorporating a somewhat more realistic short range repulsive interaction, the asymptotic instability encountered in the point particle case is avoided and self‐consistent densi...

A rapid boundary integral equation technique for protein electrostatics

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 Greens 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.