Mixing rule deviation parameters

The method can be extended to include nonpherical, nonpolar species (such as the lower molecular weight alkanes) by introduction of a third parameter in the equation of state, namely the Prigogine factor for chain-type molecules (9). This modified hard-sphere equation of state accurately describes VE(T, x) for liquefied natural gas mixtures at low pressures. Ternary and higher mixture VE values are accurately predicted using only binary mixing rule deviation parameters. 

There are two mixing rule deviation parameters (fey and /y) which must be evaluated for each pair of species in a mixture. In the present investigation, only binary mixture VE data were used in the evaluation of these parameters. 

Next, the VLE was calculated using these parameters and the results together with the experimental data are shown in Figure 14.4. The erroneous phase behavior has been suppressed. However, the deviations between the experimental data and the EoS-based calculated phase behavior are excessively large. In this case, the overall fit is judged to be unacceptable and one should proceed and search for more suitable mixing rules. Schwartzentruber et al. (1987) also modeled this system and encountered the same problem. 

It was shown by Englezos et al. (1998) that use of the entire database can be a stringent test of the correlational ability of the EoS and/or the mixing rules. An additional benefit of using all types of phase equilibrium data in the parameter estimation database is the fact that the statistical properties of the estimated parameter values are usually improved in terms of their standard deviation. 

Polymer gel Polymer cohesive energy density P (cal cm ) Deviation from geometric mean mixing rule parameter z Non-Gaussian elasticity parameter, N Curve fit crosslink density (10s mol cm-3) Experimental crosslink density (10s mol cm-3)... 

The good agreement between experimental and calculated values is pointed out by the average absolute deviation, AAD. The results demonstrate the possibility to compute the solubility as well as the partition coefficients with the Peng-Robinson-equation of state and a mixing rule with two interaction parameters. 

Excess volume predictions are extremely sensitive to the value used for the unlike-molecule size parameter. Small deviations must be allowed from the commonly used arithmetic mean mixing rule for size parameters if quantitative results are to be obtained for VE simultaneously with other measurable excess thermodynamic functions (GE and HE). It should be noted that similar conclusions have been drawn for mixtures of globular molecules (8). 

Using Equation 17 instead of Equation 16 in the mixing rules for the GIB model did not greatly change the ability of the equation to fit the VE data. There were only slight changes in deviation parameters and standard deviations for the N2 -f CH4 and Ar -f C2H6 systems. 

This leaves us wilh a single parameter / with which we describe deviations from the Berthelot mixing rule ... 

Mixing rules with a binary interaction parameter and with an excess function were not studied by Centeno etal. (2011). To examine their capability for prediction of blend viscosity, datareported in the literature were taken as example (Table 1.7). The method developed by Ratcliff and Khan indicates that it is necessary to include an excess function to account for deviation from ideality by means of the following equation ... 

Hydrocarbon-Hydrocarbon Interaction. Figure 5c shows the general characteristics of mixed monolayers in which hydrocarbon-hydrocarbon interaction occurs—e.g., trimyristin-myristic acid monolayers (16). The average area per molecule shows a deviation, whereas the surface potential per molecule follows the additivity rule. Hydrocarbon-hydrocarbon interaction also increases the cohesive force in the lipid layer and therefore reduces the fluidity of the mixed monolayer. It is evident from Figures 3a and 3c that surface fluidity is the only parameter which distinguishes an intermolecular cavity effect from hydrocarbon-hydrocarbon interaction. 

Vegard [84,85] established that in ionic salts there is a linear relation between the lattice parameters of a mixed crystal and the concentrations of the components. This rule applies also to mixed crystals of organic compounds. Thus, low-temperature phases of compounds CBr4 nCln (n = 0 — 4) are isostructural and form continuous series of mixed crystals [86]. It has been, moreover, identified that the fractional occupancy of the halogen atoms fully controls the lattice dimensions. Lattice parameters as a function of the fractional occupancy of chlorine atom slightly deviate fl om the Vegard s law (Fig. 6.6). 

Kasaya et al. (1983) investigated the mixed valency behaviour of Tm in the concentrational section Ybj. Tm Bg by means of susceptibility measurements and Ln, absorption spectroscopy. Due to the thermodynamic instability of TmB a rather limited solid solubility is observed for 0 < x < 0.5. Lattice parameters show a negative deviation from Vegard s rule. Samples were prepared by borothermal reduction of the mixed oxides in vacuum and exact values of x were derived from X-ray fluorescence analysis. 

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