Kihara potentials

Ketoglutaifo add, 283,286 Ketones, 275,298 Ketoprofen, 286 Kieselguhr, 117 Kihara potential, 206 Kinetic resistances, 227 Kinetics of adsorption-desorption, 10, 127, 159... 

Robinson begins 30 year hydrate research effort with study of paraffin/olefin hydrates 1963 McKoy and Sinanoglu apply Kihara potential to vdWP theory... 

McKoy and Sinanoglu (1963) and Child (1964) refined the van der Waals and Platteeuw method using different intermolecular potentials such as the Kihara potential. Workers at Rice University, such as Marshall et al. (1964) and Nagata and Kobayashi (1966a,b), first fit simple hydrate parameters to experimental data for methane, nitrogen, and argon. Parrish and Prausnitz (1972) showed in detail how this method could be extended to all natural gases and mixed hydrates. 

The original work by van de Waals and Platteeuw (1959) used the Lennard-Jones 6-12 pair potential. McKoy and Sinanoglu (1963) suggested that the Kihara (1951) core potential was better for both larger and nonspherical molecules. The Kihara potential is the potential currently used, with parameters fitted to experimental hydrate dissociation data. However, it should be noted that the equations presented below are for a spherical core, and while nonspherical core work is possible, it has not been done for hydrates. 

The experimentally fitted hydrate guest Kihara parameters in the cavity potential uj (r) of Equation 5.25 are not the same as those found from second virial coefficients or viscosity data for several reasons, two of which are listed here. First, the Kihara potential itself does not adequately fit pure water virials over a wide range of temperature and pressure, and thus will not be adequate for water-hydrocarbon mixtures. Second, with the spherical Lennard-Jones-Devonshire theory the point-wise potential of water molecules is smeared to yield an averaged spherical shell potential, which causes the water parameters to become indistinct. As a result, the Kihara parameters for the guest within the cavity are fitted to hydrate formation properties for each component. 

Regressed Kihara Potential Parameters ("a" as in Original Reference)... 

In Eq. (1), the Langmuir constant, Cmj, is normally computed from a Kihara potential function. ... 

The most frequently used model potentials are Rigid sphere, point center of repulsion, Sutherland s model, Lennard-Jones potential, modified Buckingham potential, Kihara potential, Morse potential. Their advantages and disadvantages are thoroughly discussed elsewhere [39] [28]. 

Thus, pressure-explicit equations of state for pure substance 1 (for the first integral) and for the gas mixture (the second integral) are required. Five different equations of state have been used in the analysis of this system (1) the five-constant Beattie-Bridgeman equation (2) the eight-constant Benedict-Webb-Rubin equation (3) the twelve-constant modified Martin-Hou equation and (4) and (5), the virial equation using two sets of virial coefficients. The first of these uses pure-substance second and third virial coefficients calculated from the Lennard-Jones 6-12 potential with interaction coefficients determined by the method of Ewald [ ]. The second set differs only in the second virial coefficients and interaction coefficient, these being found using the Kihara potential Solutions of the theoretical equa-... 

Answer by Author Analytical calculations were made with and without quadrupole contributions on the second virial coefficients determined from the Lennard-Jones 6-12 and Kihara potentials. However, the correlation between the experimental and analytical results were superior when the quadrupole contributions were neglected, except for the Kihara potential at 190 K. Therefore, the results presented here do not include these contributions. 

Use of the Hudson and McCoubrey combining rule together with the Kihara potential yields an explicit expression for... 

Although certain of the above-mentioned theories are moderately successful in representing the experimental data of CF4 -t- CH and other fluorocarbon + hydrocarbon mixtures, experimental values of and x are required. At present there is no satisfactory method of obtaining these parameters a priori. Scott, in his 1958 review, considered the various possible factors that could lead to a weakening of the unlike interactions in such mixtures. He concluded that the three most significant were the presence of non-central forces, differences in ionization potential, and differences in size of the two component molecules. The use of the Kihara potential together with the Hudson and McCoubrey rule takes account of all these effects and thus the undoubted success of the Knobler treatment is not surprising. Criticisms could be levelled at his use of a spherically symmetric potential for substances such as n-hexane but the use of a more realistic potential such as the Kihara line-core potential is hardly justified until reliable experimental values for the ionization potentials of the fluorocarbons become available. 

Non-central Potential Functions.—Non-central interactions can also be handled in terms of specific multi-parameter potential functions such as the Stockmayer and Kihara potentials. Although there is an extensive literature on the subject of such potentials, it is only rarely that virial coefficients are sufficiently precise or extensive to warrant their use. For this reason we will deal only briefly with the subject. 

Prausnitz and Myers have used the Kihara potential for the calculation of 5j2 s for mixtures of simple molecules, and Blanks and Prausnitz employed the Stockmayer potential in studies of mixtures involving polar molecules. A variety of specific non-central interactions were included in the potentials that Lichtenthaler and Schafer employed in their analysis of their measurements of virial coefficients of Ar with polar and non-polar molecules. 

APPLICATIONS OF THE KIHARA POTENTIAL TO THERMODYNAMIC AND TRANSPORT PROPERTIES OF GASES. FROM ADVANCES IN THERMOPHYSICAL PROPERTIES AT EXTREME TEMPERATURES AND PRESSURES. 

There are also many variations of the LJ 12-6 potential. One example is the computationally inexpensive tmncated and shifted Lennard-Jones potential (TSLJ), which is commonly used for molecular simulation studies in which large molecular ensembles are regarded, e.g., for investigating condensation processes [15, 16]. Another version of the LJ potential is the Kihara potential [17], which is a non-spherical generalization of the LJ model. 

The Kihara potential function [12] is used as described in McKoy and Sinanoglu [13]. The Kihara potential parameters, a (the radius of the spherical molecular core), a (the collision diameter), and e (the characteristic energy) are taken from Tohidi-Kalorazi [14], The fugacity of water in the empty hydrate lattice, // in Equation , can be calculated by ... 

A more recent measurement for N2 gas at 100 bar[5] is shown in Figure 1 with a fit to the intra-molecular scattering superimposed. Figure 2 shows the inter-molecular cross-section with a fit based on the Kihara potential [6]. Since the N2 molecule has a small anisotropy, very precise measurements are required to discriminate between different potential forms and this situation is similar to that reflected in the liquid studies presented in the previous chapter. A similar treatment of neutron measurements [7] on SFe gas, however, does reveal some interesting facts about the parameterization of the potential and discriminates between dif ferent models. It therefore seems that neutron diffraction studies of the gas phase can yield useful supplementary information about angle-averaged interaction potentials. In this sense B2((1,T) can be seen as an extension of the conventional second virial coefficient B2(T). At present, these two molecules (N2 and SFg) are the only ones that have been studied in detail but the method clearly has scope for wider applications. 

The inter-molecular scattering contribution from Figure 1, compared with a prediction based on the Kihara potential [6]. 

The most important test of our bimolecular potential is its use in statistical thermodynamic models for the prediction of phase equilibria. Monovariant, three-phase pressure-temperature measurements and invariant point determinations of various gas hydrates are available and are typically used to fit parameters in molecular computations. The key component needed for phase equilibrium calculations is a model of the intermolecular potential between guest and host molecules for use in the configurational integral. Lennard-Jones and Kihara potentials are usually selected to fit the experimental dissociation pressure-temperature data using the LJD approximation (2,4,6), Although this approach is able to reproduce the experimental data well, the fitted parameters do not have any physical connection to the properties of the molecules involved. 

T(K) Experimental value Fitted 5-shell integration (Kihara Potential) Ab initio potential ... 

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