Douglas Henderson

Intermolecular Forces: Their Origin and Determination

Introduction Theoretical calculation of intermolecular forces Gas imperfections Molecular collisions The kinetic theory of non-uniform dilute gases The transport properties of gases and intermolecular forces Spectroscopic measurements Condensed phases Intermolecular forces: The present position Appendices Substance index Index.

Pair and triplet interactions in argon

Thermodynamic properties of dense gaseous and liquid argon are calculated using perturbation theory based on the hard-sphere potential, together with an accurately determined pair potential function and the triple-dipole dispersion three-body interaction. The first-order contribution of the three-body interaction is calculated both by a Monte Carlo method and by the use of the superposition approximation for the three-body distribution function, with good agreement. Monte Carlo estimates are also found for second-order contributions of the three-body interactions, which prove to be small. Agreement with experiment is excellent at high temperatures and good at low temperatures. Slight discrepancies at low temperatures are probably due partly to the use of the ‘local compressibility’ approximation and perhaps partly to slight uncertainty in the pair potential in the neighbourhood of its zero.

Perturbation theory and liquid mixtures

The perturbation theory of Barker and Henderson which has been successfully applied to single-component fluids and to mixtures of hard spheres is extended to mixtures in which attractive forces are present. Comparison with experimental results and with quasi-experimental machine calculations shows generally good agreement over a wide range of potential parameters.

Density Functional Study of the Electric Double Layer Formed by a High Density Electrolyte

We use a classical density functional theory (DFT) to study the electric double layer formed by charged hard spheres near a planar charged surface. The DFT predictions are found to be in good agreement with recent computer simulation results. We study the capacitance of the charged hard-sphere system at a range of densities and surface charges and find that the capacitance exhibits a local minimum at low ionic densities and small electrode charge. Although this charging behavior is typical for an aqueous electrolyte solution, the local minimum gradually turns into a maximum as the density of the hard spheres increases. Charged hard spheres at high density provide a reasonable first approximation for ionic liquids. In agreement with experiment, the capacitance of this model ionic liquid double layer has a maximum at small electrode charge density.

Virial expansion for the radial distribution function of a fluid using the 6 : 12 potential

The radial distribution function can be expressed in a virial expansion. Using the 6 : 12 potential the second-order density coefficient, g 2(r), is numerically calculated for a wide range of temperatures and intermolecular separations. These results are used to calculate the second-order density coefficient, c 2(r), in the expansion of the direct correlation function and to calculate the fourth virial coefficient, B 4. In addition, approximate results for g 2(r), c 2(r), and B 4 are calculated on the basis of the Percus-Yevick, hypernetted chain, and the self-consistent approximations of Hurst and Rowlinson. These approximate results are compared with the exact results. The Percus-Yevick theory is in good agreement with the exact results at high temperatures but is unsatisfactory at low temperatures. The hyper-netted-chain approximation is in fair agreement with the exact results at high temperatures, is in poor agreement at intermediate temperatures, but is in good agreement at low temperatures. The sel...

Revisiting density functionals for the primitive model of electric double layers

Density functional theory (DFT) calculations are typically based on approximate functionals that link the free energy of a multi-body system of interest with the underlying one-body density distributions. Whereas good performance is often proclaimed for new developments, it is difficult to vindicate the theoretical merits relative to alternative versions without extensive comparison with the numerical results from molecular simulations. Besides, approximate functionals may defy statistical-mechanical sum rules and result in thermodynamic inconsistency. Here we compare systematically several versions of density functionals for ionic distributions near a charged surface using the primitive model of electric double layers. We find that the theoretical performance is sensitive not only to the specific forms of the density functional but also to the range of parameter space and the precise properties under consideration. In general, incorporation of the thermodynamic sum rule into the DFT calculations shows significant improvements for both electrochemical properties and ionic distributions.

Theory of monolayer physical adsorption. II. Fluid phases on a periodic surface

The submonolayer physical adsorption of a simple gas on an exposed single crystal face of an inert solid is treated. A perturbation theory is developed to treat the effect of periodic terms in the gas–solid energy. Monte Carlo computations of the properties of two‐dimensional Lennard‐Jones and hard‐disc fluids are used as a reference system. Isotherms and heats of adsorption are evaluated for a number of values of the gas atom/surface lattice cell size ratio. It is shown that the inclusion of the periodicity has a considerable effect on these properties. In particular, the calculated adsorption isotherms suggest that there is an optimum adsorbate atom size for a given surface symmetry for which the two‐dimensional critical temperature is maximized, in agreement with experimental observations.

Monte Carlo Simulation for the Double Layer Structure of an Ionic Liquid Using a Dimer Model: A Comparison with the Density Functional Theory

Theoretical difficulties in describing the structure and thermodynamics of an ionic liquid double layer are often associated with the nonspherical shapes of ionic particles and extremely strong electrostatic interactions. The recent density functional theory predictions for the electrochemical properties of the double layer formed by a model ionic liquid wherein each cation is represented by two touching hard spheres, one positively charged and the other neutral, and each anion by a negatively charged hard spherical particle, remain untested in this strong coupling regime. We report results from a Monte Carlo simulation of this system. Because for an ionic liquid the Bjerrum length is exceedingly large, it is difficult to perform simulations under conditions of strong electrostatic coupling used in the previous density functional theory study. Results are obtained for a somewhat smaller (but still large) Bjerrum length so that reliable simulation data can be generated for a useful test of the corresponding theoretical predictions. On the whole, the density profiles predicted by the theory are quite good in comparison with the simulation data. The strong oscillations of ionic density profiles and the local electrostatic potential predicted by this theory are confirmed by simulation, although for a small electrode charge and strong electrostatic coupling, the theory predicts the contact ionic densities to be noticeably different from the Monte Carlo results. The theoretical results for the more important electrostatic potential profile at contact are given with good accuracy.

Pair correlation functions for a hard sphere mixture in the colloidal limit

Previously, we have proposed an approximation for the contact values of the radial distribution functions of a hard sphere mixture. For most situations, this approximation is similar to earlier approximations. However, our approximation is quite different in the colloidal limit, where one species is large in size but whose concentration is very dilute. We called this approximation the ad hoc approximation to emphasize that this new approximation was untested. In this paper, we seek to test this ad hoc approximation by computing, by means of a Monte Carlo simulation, the pair correlation functions for a binary hard sphere mixture. We are able to consider mixtures in which the large hard sphere is up to 10 times the size of the small hard sphere and concentrations of the large sphere as small as 1%. While not the colloidal limit, these results are informative. The ad hoc approximation is found to be in good agreement with the simulation results.

Perturbation Theory and the Equation of State of Mixtures of Hard Spheres

The equation of state of a mixture of hard spheres of diameter σ11 and σ22 is evaluated by expanding the free energy of the mixture to second order in powers of the differences σαβ − σ, where σαβ = 12(σαα + σββ) and σ is the diameter of the unperturbed hard spheres. The parameter σ is chosen to make the sum of the first‐order terms zero. The second‐order terms are evaluated using the superposition approximation, and the equation of state is determined by analytic differentiation. The agreement of this perturbation calculation with quasiexperimental Monte Carlo and molecular dynamics results is excellent, even for quite large values of R = σ22 / σ11, but becomes less satisfactory as R becomes very large.