Interaction parameters, for mixtures

Figure 8.6 Temperature dependence of interaction parameters for mixtures of deuterated and hydrogenous vinyl butadienes. % =Xab = Xcd.X2 = Xad = Xbc,X = Xac = Xbd Reproduced with...

INTERACTION PARAMETERS FOR LIQUIO-PHASE MIXTURES COMPONENT NAMES... 

The optimum UNIQUAC interaction parameters u, between methylcyclohexane, methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + ethylbenzene using universal values for the UNIQUAC structural parameters. The equilibrium model was optimized using an objective function, which was developed by Sorensen [15],... 

For ternary and higher order mixtures, we have usually assumed that the interaction parameters for the non-water binary pairs in the water rich phase are identical to the vapor (hydrocarbon rich liquid phase) interaction parameters. Some work has been done on changing all water phase interaction parameters we concluded that predicted results were not improved enough to warrant the expenditure of time required to develop the additional parameters. A third interaction parameter for the hydrocarbon rich liquid could also be determined. Again, our work indicated that little improvement resulted from using this third parameter. Additional work is being done on both points. 

Tabk 5.67 Interaction parameters for ternary feldspar mixtures according to Ghiorso (1984). 1 = NaAlSijOg 2 = CaAljSijOg ... 

Flory-Huggins Approach. One explanation of blend behavior lies in the thermodynamics of the preceding section, where instead of a polymer-solvent mixture, we now have a polymer-polymer mixture. In these instances, the heat of mixing for polymer pairs (labeled 1 and 2) tends to be endothermic and can be approximated using the solubility parameter. The interaction parameter for a polymer-polymer mixture, Xi2, can be approximated by... 

To get an idea about the relative volatilities of components we proceed with a simple flash of the outlet reactor mixture at 33 °C and 9 bar. The selection of the thermodynamic method is important since the mixture contains both supercritical and condensable components, some highly polar. From the gas-separation viewpoint an equation of state with capabilities for polar species should be the first choice, as SR-Polar in Aspen Plus [16]. From the liquid-separation viewpoint liquid-activity models are recommended, such as Wilson, NRTL or Uniquac, with the Hayden O Connell option for handling the vapor-phase dimerization of the acetic acid [3]. Note that SR-Polar makes use of interaction parameters for C2H4, C2H6 and C02, but neglects the others, while the liquid-activity models account only for the interactions among vinyl acetate, acetic acid and water. To overcome this problem a mixed manner is selected, in which the condensable components are treated by a liquid-activity model and the gaseous species by the Henry law. 

It is also assumed that, in the case of n-alkane mixtures, the ky-values are independent of the chain length of component j. Dimitrelis and Prausnitz[8] showed that there is a systematic deviation from the Carnahan and Starling[9] repulsive term as the difference in molecular size between two molecules increase. It is thus expected that the value of the interaction parameter ly will be related to the difference in size between the two molecules. It is assumed that the value of ly will approach a constant value when this difference becomes large. The interaction parameters for propane and n-butane were found by fitting this equation of state to the data mentioned above. The parameters are shown in table 2 ... 

When both components of a binary mixture have high molecular weights normal for commercial polymers, the entropy of mixing is negligible in the free energy of mixing expression [48]. The nonequilibrium interaction parameter for binary compatible mixtures in the glassy state is related to the parameter for volume interaction by [49]... 

This method is to be used to predict the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure requires the structure of all components in the mixture, group reference volumes for all groups in the solution as well as the group interaction parameters for all groups. Use of the number average molecular weight of the polymer is recommended. 

For mixtures containing polar substances, more complex predictive equations for yf that involve binary-interaction parameters for each... 

Lichtenthaler et al. (55) determined interaction parameters for 22 solutes in poly(dimethyl siloxane) to test several expressions of the combinatorial entropy of mixing [Eq. (7)]. The magnitude of the interaction parameter is indeed directly dependent on the evaluation of the combinatorial contribution. The combinatorial contribution was computed following both the Flory-Huggins approximation and the multiple-connected-site model recently developed by Lichtenthaler, Abrams and Prausnitz (56). This model, which retains the Flory-Huggins term, also corrects for the bulkiness of the components of the mixture. Interaction parameters were computed through both approximations, showing the sensitivity of the results to the model chosen. 

Teja and Rice [134] have proposed another relationship to calculate the viscosity of mixtures of polar liquids. It is based on a corresponding states treatment for the mixture compressibility factors. This method is more accurate than the previous one for polar-polar mixtures, particularly for aqueous solutions. It uses two reference-solution models for nonspherical molecules and a single interaction parameter. For methanol-water systems, the accuracy was within 9% [5]. 

Note that the spinodal and binodal for any binary mixture meet at the critical point (Fig. 4.8). For interaction parameters x below the critical one (for xhomogeneous mixture is stable at any composition 0 < < 1 For higher values of the interaction parameter (for x > Xc) there is a miscibility gap between the two branches of the binodal in Fig. 4.8. For any composition in a miscibility gap, the equilibrium state corresponds to two phases with compositions

coexistence curve at the same value of x-... 

The effective interaction parameter (hXj/dXj.ej) in Eq. (19) is a function of two unknown parameters, %E/EE and %h/d, so these can be extracted [143] from two experimentally determined values of the overall interaction parameter for each pair of structurally identical mixtures with a swapped isotope labeled component, i.e., for dXj/hXj and hxj/dxj. In order to fit to the specific form AT-1 of the interaction parameter used in the approach described above we re-express all effective interaction parameters as [91] x(hXj/dxi,e1)=xcTc/T, where %c= (N1l/2+Njl/2)2/(2N1Nj) and Tc is given by experiment. It turns out [145] that this is a good approximation for studied random polyolefins (see Fig. 9) as the entro-pic term B of Eq. (17a,b) is small (it contributes less than 6% for most of the blends) and the weak ( -dependence of % may be neglected as it is not directly involved here. 

Table 2 Typical values of the binary interaction parameters for various mixtures.

With this selection the user will be prompted to provide two binary interaction parameters for each pair in the mixture.)... 

The model for the NRTL equation (Renon and Prausnitz, 1968) is similar to the Wilson model but includes a non-randomness constant, a,y (=0,0, that is characteristic of the types of components in each binary. In addition to this constant, the equation, which is generalized to multi-component mixtures, utilizes four interaction parameters for each binary a, Uji, bij, and fey,. The parameters b,j and fey, include a temperature dependency similar to the Wilson coefficients. The parameters and a, may be added to improve the ability to represent the effect of temperature. The equation may thus be used either in its three-parameter form or in its five-parameter form. 

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