Geoffrey C. Maitland

The direct determination of intermolecular potential energy functions from gas viscosity measurements

A new iterative method is proposed for the direct determination of potential energy functions from gas transport properties. Tests of the method on simulated data derived from a known potential function showed that it was capable of reproducing the original function with high accuracy. The method is used to obtain a potential energy function for argon from values of the gas viscosity coefficients in the temperature range 80–2000 K.

Simplified methods for the inversion of thermophysical data

Simplified inversion techniques are described which enable the potential energy functions of molecules to be determined directly from thermophysical data without recourse to additional information. The accuracy of the methods is confirmed by applying them to the data for krypton, a substance for which the potential energy function is well established.

Generalized equation of state for square-well potentials of variable range

An equation of state for square-well fluids of short and long potential range λ is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour–liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to λ ≤ 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation of state to ranges up to λ = 3, and show that, in this case, the phase behaviour of the fluid is essentially that of a fluid of infinite potential range (van der Waals limit). At short ranges (λ < 1.8) the calculated coexistence is virtually identical to that of the previous approach, hence ensuring that its application within a SAFT-VR framework is consistent with previous work. The extension of the approach to longer ranges is of interest in the context of modelling of polar fluids, and in the implementation of cross-over approaches to treat the critical region.

Direct determination of intermolecular potentials from gaseous transport coefficients alone: Part II. Application to unlike monatomic interactions

Intermolecular pair-potential energy functions are given for all the unlike interactions of the monatomic gases. The potentials are obtained by direct inversion of experimental measurements of low density binary mixture viscosity and diffusion coefficients. In those cases where these data extend to sufficiently low temperatures to enable the potential well depth e/k to be determined, the values obtained for this parameter are Kr-Xe 220 ± 5 K, Ar-Xe 170 ± 5 K, Ar-Kr 165 ± 10 K, Ne-Xe 70 ± 5 K, Ne-Kr 60 +10 -5 K, Ne-Ar 60 ± 5 K. For the systems He-Xe, He-Kr, He-Ar and He-Ne only the repulsive branch of the potential energy function is obtained. For all systems the potentials are shown to reproduce well other macroscopic data not used in their construction. The agreement with thermal diffusion data is particularly encouraging. The independent determination of this wide range of potentials provides a direct test of both the hypothesis that they are conformal and the validity of parameter mixing rules. Signifi...

An essentially exact evaluation of transport cross-sections for a model of the helium-nitrogen interaction

Essentially exact calculations of the transport collision integrals for a realistic model of the intermolecular pair potential of helium and nitrogen are reported. The collision dynamics for the interaction of the atom and molecule have been treated within the framework of the Arthurs and Dalgarno closecoupled formalism and the calculations are free from all approximation except inevitable numerical round-off. The direct calculation of collision integrals covers the temperature range 70 K to 300 K. The range has been extended upwards to 500 K with the aid of complementary classical calculations without loss of accuracy. The results serve as the first set of ‘benchmark’ calculations of transport collision integrals for a heavy molecular system with a realistic anisotropic pair potential. They are used to assess the accuracy of various approximate schemes for the evaluation of the same quantities. It is found that classical trajectory methods are in good agreement with the close-coupled calculations above 2...

Direct determination of intermolecular potentials from gaseous transport coefficients alone

Intermolecular pair-potential energy functions are given for all the unlike interactions of the monatomic gases. The potentials are obtained by direct inversion of experimental measurements of low density binary mixture viscosity and diffusion coefficients. In those cases where these data extend to sufficiently low temperatures to enable the potential well depth e/k to be determined, the values obtained for this parameter are Kr-Xe 220 ± 5 K, Ar-Xe 170 ± 5 K, Ar-Kr 165 ± 10 K, Ne-Xe 70 ± 5 K, Ne-Kr 60 +10 -5 K, Ne-Ar 60 ± 5 K. For the systems He-Xe, He-Kr, He-Ar and He-Ne only the repulsive branch of the potential energy function is obtained. For all systems the potentials are shown to reproduce well other macroscopic data not used in their construction. The agreement with thermal diffusion data is particularly encouraging. The independent determination of this wide range of potentials provides a direct test of both the hypothesis that they are conformal and the validity of parameter mixing rules. Signifi...

A justification of methods for the inversion of gas transport coefficients

The iterative procedure for the determination of potential energy functions directly from gas transport coefficients, which has previously been justified by heuristic arguments, is shown to have a sound theoretical basis. The physical basis of the method is given and an iterative inversion scheme shown to emerge naturally from the relevant kinetic theory expressions. Conditions for the inversion to converge on a unique, correct solution are discussed.

Molecular design of responsive fluids: molecular dynamics studies of viscoelastic surfactant solutions

Understanding how macroscopic properties depend on intermolecular interactions for complex fluid systems is an enormous challenge in statistical mechanics. This issue is of particular importance for designing optimal industrial fluid formulations such as responsive oilfield fluids, based on viscoelastic surfactant solutions. We have carried out extensive molecular dynamics simulations, resolving the full chemical details in order to study how the structure of the lamellar phase of viscoelastic surfactant solutions depends on the head group (HG) chemistry of the surfactant. In particular, we consider anionic carboxylate and quaternary ammonium HGs with erucyl tails in aqueous solutions together with their sodium and chloride counterions at room temperature. We find a strong HG dependence of the lamellar structure as characterized by suitable pair correlation functions and density distributions. The depth of penetration of water into the bilayer membrane, the nature of counterion condensation on the HGs and even the order and correlation of the tails in the lamellae depend sensitively on the chemical details of the HG. We also determine the compressibility of the lamellar system as a first step to using atom-resolved molecular dynamics in order to link the molecular and macroscopic scales of length and time. The results give important insight into the links between molecular details and surfactant phase structure which is being exploited to develop more systematic procedures for the molecular design and formulation of industrial systems.

Molecular Dynamics Simulations of CO2 and Brine Interfacial Tension at High Temperatures and Pressures

Molecular dynamics simulations have been performed to study the interfacial tension of CO2 and brine for a range of temperatures between 303 and 393 K and pressures from 2 to 50 MPa. The ions involved in this study are Na(+), Ca(2+), and Cl(-). The results indicate that the interfacial tension decreases with increasing pressure under any temperature condition but increases linearly with the molality of the salt solution. The density profiles calculated from the MD simulation results also indicate a positive excess of CO2 and a negative excess of ions at the interface. The charge of the ions was found to have a larger influence than their size on the interfacial tension, a result that consistent with experimental findings.

The direct determination of pair potential energy functions for mixed interactions: Ar-Kr

Measurements of the viscosity coefficients for argon-krypton gas mixtures over the temperature range 120–1600 K are inverted to give the pair potential energy function for Ar-Kr. The inversion procedure requires an estimate of the well-depth parameter e/k and a method for its determination using second virial coefficient data is described. The resulting Ar-Kr potential function has characteristic parameters e/k=165 K, σ=0·348 nm and r m=0·3902 nm. The conformality of this potential with those for the like-molecule interactions, and the value of parametric combining rules for this system are also investigated.