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Berthelot rule

The choice of appropriate potential parameters to use in the study of a certain mixture can be a significant problem. Traditionally the Lorentz Berthelot rules. [Pg.104]

The LJ parameters, elk and a, have been determined from the critical constants, Tc and pc, by adopting the recommendation of Nicolas et al. [11] kTJe = 1.35 andpco3/e = 0.142. However, different values for the potential depth of benzene, 22, have been determined so as to fit the vapor pressure at temperatures from 307.2 K to 553.2 K. The LJ parameters used in this work are summarized in Table 1, where the parameters for graphitic carbon atom are taken from those suggested by Steele [10]. We used the modified Lorentz -Berthelot rule for the cross parameters, that is, the arithmetic mean for o and the geometric mean for e by introducing the binary parameter ktj defined as Eq. (4). [Pg.328]

The energetic inhomogeneity of the surface along the x and y directions is not taken into account, but this is not expected to affect the results significantly at 308 and 333 K [39]. The cross interaction potential parameters between different sites were calculated according to the Lorentz-Berthelot rules Oap = aa + and eafi= ( The potential energy t/ due to the walls inside the slit pore model for each atom of the CO2 molecule is given by the expression C/ = + Uw(H-r where H is the distance between the carbon centers across... [Pg.547]

The water-water intermolecular interaction is described by the TIP4P potential. The ethane molecule consists of two interaction sites, each of which interacts with each other via Lennard-Jones (LJ) potential. The reference of ethane molecule is spherical and is of LJ type interaction with size and energy parameters of 4.18 A and 1.72 kj/mol. The LJ parameters for methyl group of ethane are 3.78 A and 0.866 kj/mol. For the water-guest interaction, the Lorentz-Berthelot rule is assumed. The interaction potentials for all pairs of molecules are truncated smoothly at... [Pg.285]

Finally, /o and Cio corresponding to the 12-6 and m-n LJ parameters were found by fitting to eqn. (2). The Lorentz-Berthelot rules were adopted for the description of the cross-interactions, where epo and Coo have the values corresponding to the SPC/E model, 0.1554 kcal/mol and 3.1655A respectively ... [Pg.445]

Ti2 and 12 were assumed" to be provided by the Lorenz-Berthelot rules... [Pg.67]

In addition to pure component parameters, mixture calculations require the estimation of the unlike-pair interaction parameters. These were obtained in this study using the Lorenz-Berthelot rules ... [Pg.43]

Simulations of ternary systems were performed using the pure component parameters in Table I and the cross parameters for the systems acetone/ CO2 and water/C02 determined previously (fi j - 1 and 0.81 respectively). Because of expected difficulties similar to the ones mentioned for the water/C02 system, no attempt was made to simulate the system acetone/water near room temperature. Thus, we set the acetone/water interaction parameters to the values from the Lorenz-Berthelot rules with fi j-l. Direct simulations of ternary phase equilibria have not been previously reported to the best of our knowledge. [Pg.48]

The interactions between pairs of gas molecules were estimated using the LJ potential =As alr) - Glr), where r is the site-site distance). Two sets of LJ parameters for gas molecules (i.e., and cr) were chosen. One was slkB = 149 K (fe is the Boltzmann constant) and G = 0.378 nm, and the other was dkB 231 K and a = 0.405 nm. The former corresponded to the parameter set for a spherically-approximated CH4 molecule, and the latter for a Xe molecule. The interactions between H2O and gas molecules were also estimated using the LJ potential, and the s and a values for the H20-gas LJ potential were determined using the Lorentz-Berthelot rules. Long-range interactions were smoothly truncated at an intermolecular distance of 1 nm using a switching function. [Pg.436]

They have been employed in the use of the van der Waals equation of state for polymers. They require combining rules for both the cross energy and cross co-volume parameters. Kontogeorgis et al. have employed the typically used geometric mean for the co-volume parameter, but they used the Berthelot rule for the cross-energy parameter ... [Pg.719]

By using this analysis, various combining rules previously proposed in the literature can be deducted from different values for the exponent n of this general equation. For example, the GM rule typically employed in cubic equations of state is obtained for n = 6, while the Berthelot rule is reduced for n = 3. The value n = 6 corresponds to the widely used Lennard-Jones potential function. However, for asymmetric systems, several researchers have suggested that a value closer to n = 3 should be employed " " e.g., Plocker et al. " suggested n = 3.75. [Pg.721]

Another difficulty in developing a molecular theory of liquid mixtures is the relatively poor knowledge of the intermolecular interactions between molecules of different species. While the intermolecular forces between simple spherical particles are well-understood, the intermolecular forces between molecules of different kinds are usually constructed by the so-called combination rules, the most well-known being the Lorentz and the Berthelot rules. [Pg.386]

The parameters in simple potential models for interactions between unlike molecules A and B are often deduced from the corresponding parameters for the A-A and B-B interactions using combination rules . For example, the a and s parameters are often estimated from the Lorentz-Berthelot rules ... [Pg.205]

Equations 13 and 14 follow from the Lorentz-Berthelot rules, an arithmetic mean for unlike-molecule size parameters and a geometric mean for unlike-molecule energy parameters, with deviations allowed for either rule. [Pg.330]

Equations (2) and (3) are directly equivalent to the Lorentz-Berthelot rules in their more familiar form using e and a, the well depth and collision diameter associated with the intermolecular potential (r) ... [Pg.151]

In complete contrast the measurements by Sigmund et al. of the second and third virial coefficients of CF4 + SF showed that the Lorentz-Berthelot rules predict the experimentally determined interaction parameters for the unlike interactions within experimental error. Mixtures of spherically symmetric fluorocarbons thus closely resemble similar hydrocarbon mixtures in this respect. Lange and Stein reported measurements of the second and third virial coefficients for CF3H + CF4 mixtures. A distinct weakness in the unlike interactions was noted although no detailed calculations were made. [Pg.151]

For any kinds of mixtures, in addition to LJ parameters for each component, combining rule (or mixing rule) for unlike interaction should be prepared. Even for simple liquid mixtures, conventional Lorentz-Berthelot rule is not good answer. [Pg.43]

The LJ parameters Sij and r appearing in Eq. (4.14) are obtained by a combination rule using individual atomic parameters. These combination rules include the Lorentz and Berthelot rule and the 6th order combination law given as [5]... [Pg.61]

Some force fields use the geometric mean (Berthelot rule) for both LJ parameters ... [Pg.207]


See other pages where Berthelot rule is mentioned: [Pg.787]    [Pg.205]    [Pg.104]    [Pg.106]    [Pg.713]    [Pg.523]    [Pg.105]    [Pg.383]    [Pg.103]    [Pg.445]    [Pg.575]    [Pg.587]    [Pg.726]    [Pg.89]    [Pg.91]    [Pg.211]    [Pg.306]    [Pg.325]    [Pg.166]    [Pg.141]    [Pg.177]    [Pg.212]    [Pg.342]    [Pg.430]    [Pg.489]    [Pg.1590]    [Pg.312]    [Pg.237]    [Pg.689]   
See also in sourсe #XX -- [ Pg.47 , Pg.92 ]




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Lorentz Berthelot rule

Lorentz-Berthelot combination rules

Lorentz-Berthelot combining rules

Lorentz-Berthelot mixing rules

Lorenz-Berthelot rules

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