Homonuclear Chains Research Articles

Modelling the solid–liquid–vapour phase behaviour of n-alkanes in a TPT-1 framework

We study the global phase behaviour of n-alkanes applying Wertheim's first order thermodynamic perturbation theory (TPT1). The molecules are modelled as homonuclear chains comprised of m freely jointed spherical segments interacting via the Lennard-Jones potential. Vega et al. [J. Chem. Phys. 116, 17 (2002)] have shown that the TPT1 is suitable to treat solid phases as well as fluid phases when model chains are considered, but that the adoption of a fully flexible chain model leads to the under-prediction of triple point temperatures and overestimation of the fluid ranges in comparison to experiment. Here, we propose a model in which a different number of segments are used to treat the fluid and the solid phase. The number of segments used to model the molecules in the fluid phase , and the LJ monomer potential parameters σ and ε are taken from published soft-SAFT values, whereas in the case of the solid phase a reduced temperature-dependent effective chain length is determined through a minimisation between theoretical and experimental liquid-solid phase equilibrium data. We refer to this model as effective-solid TPT1 (es-TPT1). We use the model proposed to calculate the solid–liquid–vapour phase diagrams of several n-alkanes and compare with experimental data. In the approach proposed, the conformation of chains in the solid phase is decoupled from the fluid phase, and an excellent description of the melting properties, as well as accurate predictions of the triple point temperatures for the n-alkanes examined is obtained. This simple solution provides an avenue to model the solid–liquid–vapour phase behaviour of other real substances in a TPT1 framework, and hence within the SAFT family of equations.

Plasmon Excitations in Mixed Metallic Nanoarrays.

Features of the surface plasmon from macroscopic materials emerge in molecular systems, but differentiating collective excitations from single-particle excitations in molecular systems remains elusive. The rich interactions between single-particle electron-hole and collective electron excitations produce phenomena related to the chemical physics aspects within the atomic array. We study the plasmonic properties of atomic arrays of noble (Au, Ag, and Cu) and transition-metal (Pd, Pt) homonuclear chains using time-dependent density functional theory and their Kohn-Sham transition contributions. The response to the electromagnetic radiation is related to both the geometry-dependent confinement of sp-valence electrons and the energy position of d-electrons in the different atomic species and the hybridization between d and sp electrons. It is possible to tune the position of the plasmon resonance, split it into several peaks, and eventually achieve broadband absorption of radiation. Arrays of mixed noble and transition-metal chains may have strongly attenuated plasmonic behavior. The collective nature of the excitations is ascertained using their Kohn-Sham transition contributions. To manipulate the plasmonic response and achieve the desired properties for broad applications, it is vital to understand the origins of these phenomena in atomic chains and their arrays.

SAFT-γ Force Field for the Simulation of Molecular Fluids: 2. Coarse-Grained Models of Greenhouse Gases, Refrigerants, and Long Alkanes

In the first paper of this series [C. Avendaño, T. Lafitte, A. Galindo, C. S. Adjiman, G. Jackson, and E. A. Müller, J. Phys. Chem. B2011, 115, 11154] we introduced the SAFT-γ force field for molecular simulation of fluids. In our approach, a molecular-based equation of state (EoS) is used to obtain coarse-grained (CG) intermolecular potentials that can then be employed in molecular simulation over a wide range of thermodynamic conditions of the fluid. The macroscopic experimental data for the vapor-liquid equilibria (saturated liquid density and vapor pressure) of a given system are represented with the SAFT-VR Mie EoS and used to estimate effective intermolecular parameters that provide a good description of the thermodynamic properties by exploring a wide parameter space for models based on the Mie (generalized Lennard-Jones) potential. This methodology was first used to develop a simple single-segment CG Mie model of carbon dioxide (CO2) which allows for a reliable representation of the fluid-phase equilibria (for which the model was parametrized), as well as an accurate prediction of other properties such as the enthalpy of vaporization, interfacial tension, supercritical density, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule-Thomson coefficient, and speed of sound). In our current paper, the methodology is further applied and extended to develop effective SAFT-γ CG Mie force fields for some important greenhouse gases including carbon tetrafluoride (CF4) and sulfur hexafluoride (SF6), modeled as simple spherical molecules, and for long linear alkanes including n-decane (n-C10H22) and n-eicosane (n-C20H42), modeled as homonuclear chains of spherical Mie segments. We also apply the SAFT-γ methodology to obtain a CG homonuclear two-segment Mie intermolecular potential for the more challenging polar and asymmetric compound 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf), a novel replacement refrigerant with promising properties. The description of the fluid-phase behavior and the prediction of the other thermophysical properties obtained by molecular simulation using our SAFT-γ CG Mie force fields are found to be of comparable quality (and sometimes superior) to that obtained using the more sophisticated all-atom (AA) and united-atom (UA) models commonly employed in the field. We should emphasize that though the focus of our current work is on simple homonuclear models, the SAFT-γ methodology is based on a group contribution methodology which is naturally suited to the development of more sophisticated heteronuclear models.

Transferable SAFT-VR Models for the Calculation of the Fluid Phase Equilibria in Reactive Mixtures of Carbon Dioxide, Water, and n-Alkylamines in the Context of Carbon Capture

The amine functional groups are fundamental building blocks of many molecules that are central to life, such as the amino acids, and to industrial processes, such as the alkanolamines, which are used extensively for gas absorption. The modeling of amines and of mixtures of amines with water (H(2)O) and carbon dioxide (CO(2)) is thus relevant to a number of applications. In this contribution, we use the statistical associating fluid theory for potentials of variable range (SAFT-VR) to describe the fluid phase behavior of ammonia + H(2)O + CO(2) and n-alkyl-1-amine + H(2)O + CO(2) mixtures. Models are developed for ammonia (NH(3)) and n-alkyl-1-amines up to n-hexyl-1-amine (CH(3)NH(2) to C(6)H(13)NH(2)). The amines are modeled as homonuclear chain molecules formed from spherical segments with additional association sites incorporated to mediate the effect of hydrogen-bonding interactions. The SAFT-VR approach provides a representation of the pure component fluid phase equilibria, on average, to within 1.48% of the experimental data in relative terms for the saturated liquid densities and vapor pressures. A simple empirical correlation is derived for the SAFT-VR parameters of the n -alkylamine series as a function of molecular weight. Aqueous mixtures of the amines are modeled using a model of water taken from previous work. The models developed for the mixtures are of high fidelity and can be used to calculate the binary fluid phase equilibrium of these systems to within 2.28% in relative terms for the temperature or pressure and 0.027 in absolute terms for the mole fraction. Regions of both vapor-liquid and liquid-liquid equilibria are considered. We also consider the reactive mixtures of amines and CO(2) in aqueous solution. To model the reaction of CO(2) with the amine, an additional site is included on the otherwise nonassociating CO(2) model. The unlike interaction parameters for the NH(3) + H(2)O + CO(2) ternary mixture are obtained by comparison to the experimental data available for this system. The resulting model is found to correlate and predict the liquid-phase loading (moles of CO(2) per mole of amine) to within 0.091 of experimental data in absolute terms. The parameters describing the NH(3)-CO(2) interaction are then transferred to other n-alkyl-1-amines, and sample predictions of the fluid phase equilibria for the n-propyl-1-amine + H(2)O + CO(2), n-butyl-1-amine + H(2)O + CO(2), and n-hexyl-1-amine + H(2)O + CO(2) mixtures are presented. The latter mixture is found to exhibit regions of liquid-liquid immiscibility.

Multidensity integral-equation theory for short diblock hard-sphere–sticky-hard-sphere chains

The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an m-component equal molar mixture of hard spheres with species 1,2,...,mh and sticky hard spheres with species mh+1,mh+2,...,m. Each spherical particle has two attractive sites A and B except species 1 and m, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density.

Advanced thermodynamic and processing modelling integration for amine scrubbing in post-combustion CO~2~ capture

AbstractThe reduction in CO~2~ emissions from anthropogenic sources has become a topic of widespread interest over the past number of years. As the power generation sector is by far the largest stationary-point-source of CO~2~, being responsible for approximately 35% of total global CO~2~ emissions^1^ this question has special relevance for this industry. As the inclusion of carbon capture facilities incurs a significant energy penalty on the efficiency coal-fired power-stations, there is a strong requirement for the improvement of these systems in terms of the minimisation of operation and maintenance costs, capital costs and the maximisation of efficiency and flexibility. This last issue has relevance for start-up times and ramp-rates. Post-combustion capture methods based on the chemisorption of CO~2~ in aqueous amine solutions are among the most mature and accepted technologies for CO2 capture from power plants^2^. However, amines are complex, associating solvents requiring a sophisticated thermodynamic model, capable of modelling the hydrogen bonding interactions that occur in these systems. One such model is provided by the statistical associating fluid theory (SAFT^3^). This is a molecular approach, specifically suited to hydrogen-bonding, chain-like fluids. In this contribution we use the SAFT approach for potentials of variable range (SAFT-VR^4^) to model the thermodynamics and phase equilibria of a number of amines including ammonia and monoethanolamine. The molecules are modelled as homonuclear chains of tangentially bonded square-well segments of variable range, and a number of short-ranged off-centre attractive square-well sites are used to mediate the anisotropic effects due to association in the fluids. We also determine values of the binary parameters for mixtures and then use these parameters to predict the phase equilibria of amine+water, amine+carbon dioxide as well as water+carbon dioxide mixtures. We then consider the phase equilibria of the ternary mixtures of amine+water+carbon dioxide and finally that of quaternary mixtures of amine+water+carbon dioxide+nitrogen. A good quantitative understanding of the phase behaviour of these quaternary mixtures is essential for accurate modelling of absorption processes for carbon dioxide capture. 1. Steeneveldt, R., Berger, B. & Torp, T.A., ChERD, 84(A9): 739-763, 20062. Rao, A.B.; Rubin, E.S., 2002. A Technical, Economic, and Environmental Assessment of Amine-Based CO2 Capture Technology for Power Plant Greenhouse Gas Control. Environ. Sci. Technol. 36, 4467-44753. Chapman, W.G., Gubbins, K.E., Jackson, G. & Radosz, M., Ind. Eng. Chem. Res., 1990. 29, 1709-17213. Gil-Villegas, A., Galindo, A., Whitehead, P. J., Mills, S. J. & Jackson, G., J. Chem. Phys. 106 (10), 8 March 1997

Developing a predictive group-contribution-based SAFT-VR equation of state

The hetero-segmented version of the statistical associating fluid theory for potentials of variable range (hetero-SAFT-VR) is used to develop a predictive molecular-based group-contribution SAFT-VR equation of state (GC-SAFT-VR). The hetero-SAFT-VR approach models molecules composed of segments of different size and/or energies of interaction enabling an accurate description of real molecules composed of different functional groups. The differences in interactions between functional groups are maintained throughout the theory in contrast to other approaches in which the parameters for functional groups are averaged in order to model a molecule as a homonuclear chain with “group-averaged” parameters. Through the GC-SAFT-VR approach we can study the effect of molecular functionality and topology on the thermodynamic properties of real fluid systems, since parameters are determined for each functional group and chain connectivity is explicitly specified. In this initial study GC-SAFT-VR parameters are developed for key organic functional groups (CH 3, CH 2, CH 2 CH, C O, C 6H 5, OCH 3 and OCH 2) by fitting to experimental vapor pressure and saturated liquid density data for a selected group of compounds that contain these functional groups. The transferability of the parameters obtained is tested by comparing theoretical predictions with experimental data for pure fluids not included in the fitting process and binary mixtures. Using the GC-SAFT-VR approach good agreement is obtained between experimental data and the theoretical predictions for pure substances, including isomers, and their mixtures. The GC-SAFT-VR approach is able to accurately predict the effect of molecular functionality on mixture phase behavior without fitting to any experimental data for the system being studied.

Equations of state for fluids containing alternating heteronuclear chain molecules

Statistical associating fluid theory-dimer (SAFT-D) and monomer–dimer mixture theory equations of state of linear homonuclear chain are extended to fluids containing alternating heteronuclear chain molecules separately. The proposed models account for the appropriate site–site correlation functions at contact. The modified equations of state show a good agreement with generalized Flory dimer theory and MD simulation data for small and medium size ratio of hard sphere diameters.

Solubility of hydrogen in heavy n‐alkanes: Experiments and saft modeling

AbstractNew experimental measurements on the solubility of hydrogen in several normal alkanes, ranging from decane and up to hexatetracontane, are presented. Data cover a temperature range from 280 K to 450 K, and pressures up to 16 MPa were applied. Hydrogen solubilities of up to 30 mol % were measured. These mixtures are described through a molecular‐based equation of state based on the statistical associating fluid theory (SAFT). In the SAFT approach, all the compounds are modeled as homonuclear chains of united‐atom sites interacting through a Lennard‐Jones potential. Optimized values for the chain length, Lennard‐Jones diameter, and dispersive energy characterize the hydrogen molecule. In the case of n‐alkanes, a correlation for these molecular parameters is used. Two additional parameters, independent of the thermodynamic variables, were fitted to the experimental data of a single isopleth for each particular mixture. The agreement between the measured and predicted solubilities is excellent (overall AAD<1.5%) in all the thermodynamic range, and does not significantly worsen as the molecular weight of the compound increases.

Integral equation theories for monodisperse and polydisperse sticky hard sphere chain fluid: Thermodynamic and structural properties in the polymer Percus–Yevick and ideal chain approximations

The thermodynamic and structural properties of a freely jointed homonuclear sticky hard sphere chain fluid are studied using one-component and multi-component multi-density Ornstein–Zernike integral equation theories. In this formalism, a polydisperse chain fluid is modeled as a one-component system of associating sticky hard spheres with finite association strength, while a monodisperse system is modeled as an equal molar m-component mixture of associating sticky hard spheres with infinite association strength in the complete association limit. General analytical solutions to both models are obtained within the polymer Percus–Yevick and ideal chain approximations. Explicit analytical expressions for the contact values of correlation functions are obtained. The coordination number around a sticky hard sphere is calculated and its relationship with the contact value of the correlation function is discussed. Both intermolecular and intramolecular correlation functions beyond the hard core region are calculated numerically. Radial distribution functions of monodisperse dimer and tetramer are compared with those of polydisperse chains (with mean chain lengths of 2 and 4), and it is found that significant discrepancy exists at low density. This disparity, however, diminishes as chain density increases. The Helmholtz energy and pressure of monodisperse homonuclear chains are obtained via the energy route. The critical temperature, critical density, and phase coexistence of the fluid are also obtained.

Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains

An equation of state for square-well chain fluids is developed applying the second-order perturbation theory of Barker and Henderson to a hard-chain reference fluid. The structural information required in the perturbation theory is incorporated using an expression for the radial distribution function of the reference chain fluid proposed by Chiew. The equation of state is simplified by fitting polynomials in density and simple functions of segment number to the original perturbation expressions of first-and second-order. The equation of state is extended to mixtures by applying one-fluid mixing rules and is tested against molecular simulation data of homonuclear chain molecules and mixtures from the literature.

Equations of state of freely jointed hard-sphere chain fluids: Numerical results

We continue our series of studies in which the equations of state (EOS) are derived based on the product-reactant Ornstein–Zernike approach (PROZA) and first-order thermodynamic perturbation theory (TPT1). These include two compressibility EOS, two virial EOS, and one TPT1 EOS (TPT1-D) that uses the structural information of the dimer fluid as input. In this study, we carry out the numerical implementation for these five EOS and compare their numerical results as well as those obtained from Attard’s EOS and GF-D (generalized Flory-dimer) EOS with computer simulation results for the corresponding chain models over a wide range of densities and chain length. The comparison shows that our compressibility EOS, GF-D, and TPT1-D are in quantitative agreement with simulation results, and TPT1-D is the best among various EOS according to its average absolute deviation (AAD). On the basis of a comparison of limited data, our virial EOS appears to be superior to the predictions of Attard’s approximate virial EOS and the approximate virial EOS derived by Schweizer and Curro in the context of the PRISM approach; all of them are only qualitatively accurate. The degree of accuracy predicted by our compressibility EOS is comparable to that of GF-D EOS, and both of them overestimate the compressibility factor at low densities and underestimate it at high densities. The compressibility factor of a polydisperse homonuclear chain system is also investigated in this work via our compressibility EOS; the numerical results are identical to those of a monodisperse system with the same chain length.

Primitive models of chemical association. III. Totally flexible sticky two-point model for multicomponent heteronuclear fixed-chain-length polymerization

A multidensity integral-equation theory for polymerization into freely jointed hard-sphere homonuclear chain fluids proposed earlier [J. Chem. Phys. 106, 1940 (1997)] is extended to the case of multicomponent heteronuclear chain polymerization. The theory is based on the analytical solution of the polymer Percus–Yevick (PPY) approximation for the totally flexible sticky two-point (S2P) model of associating fluids. The model consists of an n-component mixture of hard spheres of different sizes with species 2,…,n−1 bearing two sticky sites A and B, randomly distributed on its surface, and species 1 and n with only one B and A site per particle, respectively. Due to some specific restrictions imposed on the possibility of forming bonds between particles of various species, the present version of the S2P model represents an associating fluid that is able to polymerize into a mixture of heteronuclear chain macromolecules. The structural properties of such a model are studied in the complete-association limit and compared with computer-simulation results for homonuclear hard-sphere chain mixtures, symmetrical diblock copolymers, alternating copolymers, and homonuclear hard-sphere chains in a hard-sphere solvent. Some results for the case of partial association are also presented. The PPY theory represents a quantitatively successful theory for the mixtures of short homonuclear chains and the short copolymer systems studied here. We also expect that the theory will prove to be of the same order of accuracy in investigating the case of partial association.

Excluded volume for a pair of linear chains of tangent hard spheres with an arbitrary relative orientation

Chain molecules formed from m tangent hard-sphere segments are of particular interest in studies of liquid crystalline phases because they represent one of the simplest models which can account for molecular flexibility. In this paper we obtain analytical expressions for the excluded volume for a pair of linear homonuclear chains with an arbitrary relative orientation, and the corresponding expressions for the second virial coefficient. A commonly used molecular theory of anisotropic phases such as the nematic is the approach of Onsager; a simple analytical expression for the orientationally dependent excluded volume for a pair of molecules is required for the efficient minimisation of the Onsager Helmholtz free energy functional at the level of the second virial coefficient. Approximate expressions are examined for the excluded volume, together with a simple analytical function which provides a very accurate description of the exact results. A simple exact relation is obtained for the second virial coefficient of the isotropic system for arbitrary chain lengths using the exact result of Isihara for the dimer, i.e., for m = 2. Recent Monte Carlo numerical integration data for chains of m = 3 to 7 segments are in agreement with exact results. In a future contribution, we hope to compare the results of simulations for the isotropic-nematic phase transition exhibited by linear chains of tangent hard spheres with the Onsager predictions using these expressions for the excluded volume.

Mixing rules for binary Lennard-Jones fluid structures

The mixing rule estimates of the radial distribution functions g αβ ( r), from the van der Waals one-fluid and mean density approximations for Lennard-Jones fluid mixtures, are examined by comparing with Monte Carlo simulations. In addition, these mixing rule estimates of g αβ ( r) are used to calculate the Helmholtz energy for Lennard-Jones homonuclear chain mixtures based on the thermodynamic perturbation theory (TPT). Two simplifying modifications of these mixing rules are proposed for the TPT mixture model. The accuracy of these simplified rules is examined and found to give accurate representation of the theoretically derived Helmholtz energy over a wide range of densities and temperatures.

Equation of state for hard-sphere chain molecules

An equation of state for homonuclear chain molecules is formulated on the basis of thermodynamic perturbation theory of Wertheim. It yields a very accurate prediction of the compressibility factor of different chain molecules including hard spheres and hard dumbbells as well as flexible chains with up to 200 bonds in a molecule. In addition, a large number of molecular simulation results are used to test the thermodynamic first-order perturbation theory (TPT1), the thermodynamic second-order perturbation theory (TPT2), the scaled particle theory (SPT), the Percus-Yevick and Carnahan-Starling (PY-CS) equation, the generalized Flory-Dimer equation (GF-D) and our equation. For short chain molecules ( m ≥ 4), good agreement between the calculated and computer simulation data can be obtained from all of the above equations, but for long chain molecules the equation proposed in this work is better than the other equations.

Modified neglect of diatomic overlap calculations on boron‐nitrogen derivatives of nonbenzenoid aromatics. II. The analysis of the 130 possible nonfully boron‐nitrogen‐alternating isomers of pentaazapentaboraazulene

AbstractModified neglect of diatomic overlap (MNDO) calculations have been used to investigate the ground state properties of the 130 nonfully boron‐nitrogenalternating isomers of pentaazapentaboraazulene (PAPBAZ), N5B5H8. The two most stable of these nonfully boron‐nitrogen‐alternating isomers, 1,2,3a, 5,7‐pentaaza‐3,4,6,8,8a‐pentaboraazulene, (1,2,3a, 5,7‐PAPBAZ) (3), and 1,3,3a,5,7‐PAPBAZ (4) have strongly exothermic heats of formation (−142.5 and −142.4 kcal/mol, respectively), while the two least stable isomers, 1,6,7,8,8a‐PAPBAZ (131) and 1,2,3,3a,8a‐PAPBAZ (132), are calculated to have endothermic heats of formation (+95.43 and +96.31 kcal/mol, respectively). Each isomer optimized as a slightly to extremely nonplanar molecule, but each remained a bicyclic system containing a seven‐membered ring fused to a five‐membered ring. Thus, no ring‐opened structures were observed. An empirical relationship between the heat of formation and the number, position, and type of homonuclear (NN or BB) bonds present in the molecules could be established, but as the heat of formation for the molecules became more positive, the relationship became less strong. A general trend of diminishing energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) was observed as the heat of formation became more positive. In addition to a discussion of the structures of (3), (4), (131), and (132), the structures of 2,3a,4,6,8‐PAPBAZ (9), 2,3a,5,6,8‐PAPBAZ (11), 1,2,4,6,8‐PAPBAZ (15), 2,3a,4,7,8a‐PAPBAZ (19), 1,3a,4,5,8‐PAPBAZ (32), 1,2,3,5,7‐PAPBAZ (47), 1,3a,5,8,8a‐PAPBAZ (67), 1,3a,6,7,8a‐PAPBAZ (87), 3a,4,6,8,8a‐PAPBAZ (106), 1,2,3,5,6‐PAPBAZ (109), 1,2,3a,8,8a‐PAPBAZ (116), and 4,5,6,7,8‐PAPBAZ (130) are discussed in detail. Some of these molecules were chosen because they represent the minima and maxima, respectively, in heats of formation [(3), (4), (130), (131), and (132)], ionization potentials [(9) and (32)], differences in LUMO and HOMO energies [(106) and (32)], and dipole moments [(11) and (87)]. The remaining molecules were chosen because each represent the most stable system containing the following homonuclear chains: B‐B‐B (15), N‐N‐N (19), B‐B‐B‐B (47), N‐N‐N‐N (67), B‐B‐B‐B‐B (109), and N‐N‐N‐N‐N (116).

Percus-Yevick integral-equation theory for athermal hard-sphere chains

A theoretical method for the modelling of athermal freely jointed tangent hard-sphere chain fluids, of fixed length r, is developed based on a ‘particle-particle’ description of the chain system. This approach is based on the Percus-Yevick (PY) theory in the context of the particle-particle Ornstein-Zernike integral equation subject to some imposed connectivity constraints. Analytical expressions for the compressibility equations of state are derived for homonuclear chains, heteronuclear chains, blends or mixtures of homonuclear and heteronuclear chains, and homonuclear chains in a hard-sphere solvent. The PY compressibility equation of state for the athermal hard-sphere chain system is found to consist of (i) a non-bonded hard-sphere PY compressibility pressure contribution, and (ii) a PY bonding contribution due to chain formation. In the case of homonuclear chains the Percus-Yevick solution is found to yield excellent agreement with computer-simulation data reported in the literature. By replacing the PY hard-sphere compressibility pressure contribution with the Carnahan-Starling hard-sphere pressure, the accuracy of the PY bonding term for homonuclear chains is identified. We are, however, unable to determine the accuracy of the PY compressibility pressure of heteronuclear chains, chain mixtures and homonuclear chains in a hard-sphere solvent since computer-simulation data for these systems are not available.

Phase equilibria of associating fluids

As a continuation of our work on spherical associating molecules, we have derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites. The equations are written in terms of a hard-core reference whose pair distribution function is known. In practise, the hard-sphere reference mixture is the easiest to use. A reference system of homonuclear chains is examined in order to account for asymmetries in molecular shape; chains are constructed by bonding equal-sized spheres together. An equation of state for hard-sphere chains is obtained which is in good agreement with recent simulation data. Expressions for mixtures of homonuclear chains of different sizes are also presented. The approach is extended to examine associating chain molecules with multiple bonding sites. The phase equilibria of non-associating chains, and of associating chains with one or two bonding sites are determined. In this study, the separate effects of molecular association and chain size on the coexistence properties are investigated.