Pure component intermolecular potential

The pure component intermolecular potential parameters used in this study are shown in Table I. They were obtained as follows for carbon dioxide, we fitted the experimental critical temperature and pressure (12) using data from ( ) for the critical constants of the Lennard-Jones (U) system (T - 1.31, - 0.13). For acetone, a... 

Table I. Pure component intermolecular potential parameters...

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

Although accurate values of mixed coefficients are slightly more difficult to obtain than pure-gas values, they are attractive theoretically for two reasons. Firstly, by careful choice of components the interaction terms in PI2 and Up can be simplified, and secondly, mixed ririals provide a stiff test of the intermolecular potential parameters determined from pure-gas virials. 

Repulsive Interactions (Harmonic Oscillator in a Box). In most stable solutions and in pure liquids where the components are at or near relatively deep intermolecular potential minima, attractive interactions dominate the intermo-lecular repulsive terms. Unstable solutions of large solute molecules dissolved in a solution of small solvent molecules can be prepared in the solid phase by trapping experiments. Certain trapped free radicals may therefore show the effects of solvent-solute repulsive interactions, which would be evidenced by blue shifts in the infrared spectrum of these cramped solutes. Diatomic carbon (C2) trapped in solid xenon shows this effect strongly (30, 31, 32) in both the upper and lower... 

Tbe basic scheme for modeling the phase behavior of binary mixtures is first to input the pure component characteristic parameters Tc, Pc, and to, and then determine the binary mixture parameters, kj. and iij., by fitting data such as pressure-composition isotherms. Normally k.. and tIj. are expected to be lie between 0.200. If the two species are close in chemical ize and intermolecular potential, the binary mixture parameters will have values very close to zero. In certain cases a small value of either of these two parameters can have a large influence on the calculated results. 

We will now discuss the problem of determining effective or optimal diameters for use with the HSE theory for real fluids when both the form of the intermolecular potential and its parameters are unknown but accurate equations of state which represent the PVT behavior over an extensive range are available for the pure components. 

Estimating Pure-Component Lennard-Jones Parameters for the 6-12 Intermolecular Potential... 

Three second virial coefficients are therefore needed to describe the binary interactions in a two-component mixture B and 22 the virial coefficients of the pure components, and Bi2, the interaction virial coefficient, which depends on the intermolecular potential between molecules 1 and 2. The third virial coefficient of the mixture is composed of four terms Cm, C222, Cm, and C122. 

Combination Rules.—The relation between simple empirical potential functions and the more fundamental and more detailed descriptions of intermolecular interactions is tenuous. Most simple potentials provide a convenient means by which the gross details of the interactions can be specified. As a result, one should not expect that the combination rules that provide the best representation for the dispersion or repulsive interactions will prove the most satisfactory for a given potential. A variety of empirical rules for combining pure-component potential parameters has been proposed the most widely used have been... 

Focused models are used to study local properties in pure liquids, solutions, and interfaces. The largest use is to study solvation effects and reactions in solutions. In these cases M is composed of a solute supplemented by a solvation cluster (also a single solute molecule may be used). In these models the more detailed description of M is ensured by using the BO approximation, followed by a MO-based description of the electronic structure (there are also methods that replace the QM description of the electronic structure with some simpler semiclassical model). The S components are generally described with the aid of the intermolecular potentials we shall examine in the following sections. The description of the coupling takes into account the nature of the description chosen for both M and S. 

In the area of applications, an important goal for research in coming years will be to develop a set of pure component group-based potentials and combining rules that can be used for general predictions of both pure component and mixture phase behavior. Early results for realistic mixtures [117] suggest that relatively simple intermolecular potential models can be used to predict the phase behavior of broad classes of binary systems. For mixtures with large differences in polar character of the components. 

The same intermolecular potential-energy functions may be applied to correlate interaction virial coefficients. In the case where there are no, or insufficient, experimental data, but adequate data exist for the pure components, it may be possible to estimate with useful accuracy the unlike interaction parameters from combining rules such as ... 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

If no experimental data are available for the implementation of this approach in its entirety then the use of a model intermolecular pair potential with scaling parameters derived from some other property or by estimation is to be preferred above any other means of evaluation for the dilute-gas state. In the dense fluid state it is at present necessary to make use of a procedure based upon an approximate theory. The Enskog theory in one of its forms is usually the best procedure of this kind. However, its application requires the availability of some experimental data for the property of interest at least for pure components so that again its application is limited. 

The thermal conductivity of a multicomponent mixture of monatomic species therefore requires a knowledge of the diermal conductivity of the pure components and of three quantities characteristic of the unlike interaction. The final three quantities may be obtained by direct calculation from intermolecular potentials, whereas the interaction thermal conductivity, Xgg, can also be obtained by means of an analysis of viscosity and/or diffusion measurements through equations (4.112) and (4.125) or by the application of equation (4.122) to an analysis of the thermal conductivity data for all possible binary mixtures, or by a combination of both. If experimental data are used in the prediction it may be necessary to estimate both and This is readily done using a realistic model potential or the correlations of the extended law of corresponding states (Maitland et al. 1987). Generally, either of these procedures can be expected to yield thermal conductivity predictions with an accuracy of a few percent for monatomic systems. Naturally, all of the methods of evaluating the properties of the pure components and the quantities characteristic of binary interactions that were discussed in the case of viscosity are available for use here too. 

The representations of the viscosity of the pure components carbon dioxide and ethane include explicit contributions for the viscosity in the zero-density limit (Vesovic et al. 1990 Hendl et al. 1994). The representation of the viscosity of binary mixtures in the same limit requires values of just the interaction viscosity, i2, of equations (4.115) and (4.116) and the quantity A 2 of equation (4.117) in order to evaluate, and thus represent, the viscosity of an arbitrary binary mixture. Since the intermolecular pair potential of the carbon dioxide-ethane interaction is not known, it is not possible to evaluate either of these quantities theoretically. 

In many solutions strong interactions may occur between like molecules to form polymeric species, or between unlike molecules to form new compounds or complexes. Such new species are formed in solution or are present in the pure substance and usually cannot be separated from the solution. Basically, thermodynamics is not concerned with detailed knowledge of the species present in a system indeed, it is sufficient as well as necessary to define the state of a system in terms of the mole numbers of the components and the two other required variables. We can make use of the expressions for the chemical potentials in terms of the components. In so doing all deviations from ideal behavior, whether the deviations are caused by the formation of new species or by the intermolecular forces operating between the molecules, are included in the excess chemical potentials. However, additional information concerning the formation of new species and the equilibrium constants involved may be obtained on the basis of certain assumptions when the experimental data are treated in terms of species. The fact that the data may be explained thermodynamically in terms of species is no proof of their existence. Extra-thermodynamic studies are required for the proof. 

At the interface in a two-phase system the difference in chemical potential of each component is due to different intermolecular interactions in the two phases. If one of the phases (n = 1, say) is a pure substance, In Ai = 0,... 

The remaining critical component in the simulations is the potential functions that describe the intra- and intermolecular energetics for the system. The intermolecular part is usually represented in a Coulomb plus Lennard-Jones form with the interactions occurring between sites located on the nuclei. Simple potential functions are now available that give excellent thermodynamic and structural results for many pure liquids including water,... 

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