Temperature dependent interaction parameters

It was speculated that additional temperature - dependent interaction parameters would be required to bring the predicted values and the experimental results into quantitative agreement nevertheless, no attempt was made at that time to try to accomplish this. 

The second modification concerns the correlation of the composition of the aqueous liquid phase. In order to accomplish this, a temperature - dependent interaction parameter was used for the aqueous liquid phase and the previous temperature -independent parameter was used for the non-aqueous liquid phase and the vapor phase. Thus for the aqueous - liquid phase Eqn. 

The introduction of this parameter for each aqueous binary pair means that the interaction between the water molecule and the gas molecule in the aqueous liquid phase is much different from that in the nonaqueous phases. For all the aqueous binaries which have been examined in this study, the temperature -dependent interaction parameters take on negative values at ambient temperature and monotonically increase as temperature increases. This indicates that the attraction energy between the water molecular and the other molecules decreases as the temperature increases. 

Malinin (7), Todheide and Franck (8) and Takenouchi and Kennedy (9) reported equilibrium data for this system at temperatures up to 350°C and pressures to 3500 bars. However, the vapor phase data of these authors do not always agree with each other. The aqueous phase data have been used to extend the temperature - dependent interaction parameter to 300°C. 

The temperature - dependent interaction parameters were determined from 77°F to 680°F using the data of Culberson and McKetta (20) and of Sultanov et al. (18). This parameter increases with temperature and appears to converge to the value of the constant parameter used for the vapor phase as the critical temperature of water is approached. 

A constant interaction parameter was capable of representing the mole fraction of water in the vapor phase within experimental uncertainty over the temperature range from 100°F to 460°F. As with the methane - water system, the temperature - dependent interaction parameter is also a monotonically increasing function of temperature. However, at each specified temperature, the interaction parameter for this system is numerically greater than that for the methane - water system. Although it is possible for this binary to form a three-phase equilibrium locus, no experimental data on this effect have been reported. 

Propane - Water System. The interaction parameters for the propane - water system were obtained over a temperature range from 42°F to 310°F using exclusively the data of Kobayashi and Katz (24). This is because among the available literature on the phase behavior of this binary system, their data appear to give the most extensive information. A constant interaction parameter was obtained for the propane-rich phases at all temperatures. The magnitude of the temperature - dependent interaction parameter for this binary was less than that for the ethane - water binary at the same temperature. Azarnoosh and McKetta (25) also presented experimental data for the solubility of propane in water over about the same temperature range as that of Kobayashi and Katz but at pressures up to 500 psia only. However, a different set of temperature - dependent parameters... 

The data of Rebert and Hayworth (32j were used to extend the temperature - dependent interaction parameters to temperatures above the critical point of n-hexane. 

Temperature-dependent interaction parameters for selected paraffin-water binary systems... 

Figure 10. Temperature-dependent interaction parameters for nitrogen, carbon dioxide, and hydrogen sulfide with water...

X0 is a positive, inverse temperature-dependent interaction parameter per solvent molecule (Allcock and Lampe, 1981). 

The original UNIFAC model(Fredenslund et al., 1975) was used in this work, as it is a widely applicable model with the most available parameters which are updated and extended regularly. For gas/n-alkane systems, temperature dependent interaction parameters were used, and the UNIFAC expression ... 

The GC concept has received great attention for the prediction of activity coefficients during the last 30 years. It has been applied to many different types of properties of pure compounds, as shown in Section 16.2, but also for phase equilibrium calculations for mixtures. Especially well known is the UNIEAC equation for the activity coefficient. The UNIFAC model is available in several modified forms, e.g., by Larsen et al. and Gmehling and Weidlich. ° These modified UNIFAC models contain, unlike the original UNIFAC, temperature-dependent interaction parameters. 

Correlate the LCST of binary polymer-solvents using a linearly temperature-dependent interaction parameter... 

Differentiation of equation (12.88) shows that the temperature dependent interaction parameter x(F) has a minimum value at the temperature given by... 

Collections of useful Pitzer parameters can be taken from Rosenblatt [11], Zemaitis et al. [12], and Pitzer [13]. Temperature-dependent interaction parameters should be used if a wide temperature range must be covered, as it is common practice for nonelectrolyte systems as well. It is important especially for strong acids and bases. The Pitzer equation is usually valid up to molalities of 6 mol/kg. 

In the entropic-free volume model, the activity coefficient of the solvent is given by Eqs. (44)-(48) with p = 1 [52]. The residual contribution is represented by the residual contribution of the UNIFAC model with temperature-dependent interaction parameters [53]. The liquid molar volumes needed for the calculation of the free volume of a component can be taken from experiment or calculated from the Tait equation [4] or by the group contribution method of Elbro et al. [56]. This model is relatively easy to use. 

Valderrama, J.O. Ibrahim, A.A Cisternas, L.A. (1990). Temperature-dependent interaction parameters in cubic equations of state for nitrogen-containing mixtures. Fluid Phase Equilib, Vol.59, pp. 195-205... 

Solutions in which the data can be fitted well enough to a constant value of the interaction parameter are classified as strictly regular . A better fit can be obtained by a temperature-dependent interaction parameter of the form... 

We have employed the temperature-dependent interaction parameter determined by CP measurements to calculate the spinodal miscibility boundary of PMMA-NP/PS composites as a function of nanoparticle radius at constant blend composition (see Figure 1). Complete miscibility across the 275-675 K temperature range was predicted for PMMA-nanoparticles with radius less than 6.8 nm in spite of the well-known immiscibility between PMMA and PS homopolymers. Conversely, for PMMA-nanoparticles with radius higher than 7.2 nm, complete immiscibility (phase separation) is expected. For PMMA-NP of radius in between 6.8 and 7.2 nm, partial miscibility was predicted as a function of temperature (the blends displaying upper critical solution temperature (UCST)-type behavior). No significant changes was observed when % values from SANS experiments [11, 12] were employed in the calculations. 

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