M. S. Wertheim

Bio: M. S. Wertheim is an academic researcher from Rutgers University. The author has contributed to research in topics: Integral equation & Helmholtz free energy. The author has an hindex of 20, co-authored 31 publications receiving 9709 citations. Previous affiliations of M. S. Wertheim include Yale University & Michigan Technological University.

Fluids with highly directional attractive forces. I. Statistical thermodynamics

Abstract: A new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers-mers due to highly directional attraction. A breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs. The bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables: singlet densityρ and monomer densityρ 0. Results for the thermodynamic functions as functionals ofρ andρ 0 are given in the form of graph sums. Pair correlations are analyzed in terms of a new matrix analog of the direct correlation function. It is shown that the low-density limit is treated exactly, while major difficulties arise when the Mayer expansion, which employs onlyp, is used. The intricate resummations required for the Mayer expansion are illustrated for the case where dimers are the only association products.

Exact solution of the percus-yevick integral equation for hard spheres

Abstract: ABS>The equation of state and the pair distribution for the Percus- Yevick integral equation for the radiai distribution function of a classical fluid are obtained in closed form for the prototype of interacting hard spheres. (D.C.W.)

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

Abstract: The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.

Fluids with highly directional attractive forces. III. Multiple attraction sites

Abstract: We derive a reformulation of statistical thermodynamics for fluids of molecules which interact by highly directional attraction. The molecular model consists of a repulsive core and several sites of very short-ranged attraction. We explore the relationship between graph cancelation in the fugacity expansion and three types of steric incompatibility between repulsive and attractive interactions involving several molecules. The steric effects are used to best advantage in a limited regrouping of bonds. This controls the density parameters which appear when articulation points are eliminated in the graphical representation. Each density parameter is a singlet density for a species consisting of molecules with a specified set of sites bonded. The densities satisfy subsidiary conditions of internal consistency. These conditions are equivalent to a minimization of the Helmholtz free energyA. Graphical expressions forA and for the pressurep are derived. Analogs of thes-particle direct correlation functions and of the Ornstein-Zernike equation are found.

Fluids with highly directional attractive forces. IV. Equilibrium polymerization

Abstract: We investigate approximation methods for systems of molecules interacting by core repulsion and highly directional attraction due to several attraction sites. The force model chosen imitates a chemical bond by providing for bond saturation when binding occurs. The dense fluid is an equilibrium mixture ofs-mers with mutual repulsion. We use a previously derived reformulation of statistical thermodynamics, in which the particle species are monomeric units with a specified set of attraction sites bonded. Thermodynamic perturbation theory (TPT) and integral equations of two types are derived. The use of TPT is illustrated by explicit calculation for a molecular model with two attraction sites, capable of forming chain and ring polymers. Successes and defects of TPT are discussed. The integral equations for pair correlations between particles of specified bonding include calculation of self-consistent densities of species. Methods of calculating thermodynamic properties from the solutions of integral equations are given.

Equation of State for Nonattracting Rigid Spheres

Abstract: A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid‐sphere behavior.

Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules

Abstract: A modified SAFT equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain reference fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixtures of small spherical molecules such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassociating molecules were identified for 78 substances by correlating vapor pressures and liquid volumes. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor−liquid equilibria of mixtures, the equation of state shows substantial predictive capabilities and good precision for correlating mixtures. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng−Robinson model is also given for vapor−liquid equilibria of binary systems, confirming the good performance of the suggested equation of state. ...

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

Abstract: Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current inte...

Carbon capture and storage (CCS): the way forward

Abstract: Carbon capture and storage (CCS) is broadly recognised as having the potential to play a key role in meeting climate change targets, delivering low carbon heat and power, decarbonising industry and, more recently, its ability to facilitate the net removal of CO2 from the atmosphere. However, despite this broad consensus and its technical maturity, CCS has not yet been deployed on a scale commensurate with the ambitions articulated a decade ago. Thus, in this paper we review the current state-of-the-art of CO2 capture, transport, utilisation and storage from a multi-scale perspective, moving from the global to molecular scales. In light of the COP21 commitments to limit warming to less than 2 °C, we extend the remit of this study to include the key negative emissions technologies (NETs) of bioenergy with CCS (BECCS), and direct air capture (DAC). Cognisant of the non-technical barriers to deploying CCS, we reflect on recent experience from the UK's CCS commercialisation programme and consider the commercial and political barriers to the large-scale deployment of CCS. In all areas, we focus on identifying and clearly articulating the key research challenges that could usefully be addressed in the coming decade.