Interaction parameters between binary

Fortunately, it is not necessary to perform all of these thermodynamic assessments. In essence one should ensure that all of die binary systems are completed, but the levels of C and N are so low that it is possible to effectively ignore interaction parameters between these two elements, even if they were possible to determine. The percentage of ternary assessments which is necessary to provide an accurate calculation is, in reality, small, mainly because the ternary IZi 12k solubility product can be small for the minor elements. For... 

The key to obtaining good representation of experimental data is fitting a single binary interaction parameter, ky, to each set of binary data. In most of the modeling described here, our main concern lies with the binary interaction parameters between each of the components and C02, since C02 introduces the most asymmetry (i.e., difference in size and energy parameters) into the system. In a few cases, we include nonzero binary interaction parameters for some of the other components. 

It is important to note, that the interaction parameters between the components (two per binary) were estimated solely from binary phase equilibrium data, including low-pressure VLE data for the binary acetone - water no ternary data were used in the fitting. The values of the interaction parameters obtained are shown in Table III. 

The Krause (37,39) method involves the comparison of the calculated values of Xj9, the interaction parameter between the two polymers and ( X 2)cr interaction parameter at the critical point on a phase diagram mr that particular binary system. Krause (37,39) stated that if Xj2 12 r polymers should be immiscible at... 

The free-volume parameters were estimated from viscosity and temperature data of pure components and the binary interaction parameter between the component and the polymer was determined using the group-contribution lattice-fluid equation of state (GCLF-EOS) (Alvarez, 2005, Alvarez et al, 2008). The innovative application of zero shear viscosity predicted data was proposed in this work for POMS free-volume parameters, as an alternative when experimental polymeric membrane viscosity data are scarce or inexistent. 

It has been shown (3) using Scott s ternary solution treatment (25) of the Flory-Huggins theory, that the overall interaction parameter between the volatile probe (1) and the binary stationary phase (2,3) is given by... 

Here, a and bj are the pure component parameters, defined by Equation 9.26a and b, and is the binary interaction parameter between component i and . 

Where Xij is the binary interaction parameter between gases i and j. For simplicity this model assumes no higher interaction parameters between the gases and polymer, e.g. Xkbc = 0. Again, Equation (11.21) can be simplified by the same assumptions used in the binary and tertiary systems. The solution, assuming gases B and C obey Henry s law, is ... 

Xab Binary thermodynamic interaction parameter between polymers A and B A Thermodynamic distance from the spinodal A = 2((xabN)s- (XabN)... 

In the case of copolymer solutions, the melting temperature also depends on interactions between the different monomeric imits and the solvent. Considering the case in which the crystalline phase is pure (i.e., only monomeric units of a single type crystallize and no solvent is present in the lattice), the decrease in the melting temperature can be derived in a similar manner as for the homopolymer solution case using the Flory-Huggins theory with an appropriate modification [15]. To take into accoimt the interactions between both comonomers and solvent, the net interaction parameter for binary copolymers should be calculated as follows ... 

In order to know the activity coefficients of the binary systems of TEA + 2-ethyl-l-hexanol and NEA+2-ethyl-l-hexanol, the VLE data are also needed. These experimental data are determined using a method based on gas chromatographic technique described previously (Ghannadzadeh, 1993a). The experimental activity coefficients and VLE data can be correlated to several eqtrilibritrm methods such as universal qira-si-chemical (UNIQUAC) and NTRL models. Eqtrilibrium models, such as the UNI-QUAC model (Renon and Prausnitz, 1968) and the non-random two-liquid model (NRTL) (Abrams and Prausnitz, 1975) have been successfully applied for the correlation of several liquid-liquid and vapor-liquid systems. These models depend on optimized interaction parameters between each pair of components in the systems, which can be obtained by experiments. 

A better approach is the copolymer SAFT approach of Radosz and co-workers [81-83], in which the copolymer parameters are estimated on the basis of the molecular weight and structure only. For an AB-type copolymer there are three binary interaction parameters, the interaction parameters between A segments and segments of the solvent molecule, the interaction parameter between B segments... 

At the end of this section, we mention the estimation of interaction parameters between polymer and solvent, or (more generally) between two species A and B in a binary mixture. The simplest possibility is to use the standard Lorentz-Berthelot combining mles [210] ... 

When Zhao and Choi (51] also discussed the solvent-dependence of they found that the problem had essentially originated from an incorrect choice of reference volumes used when calculating the binary interaction parameter between various solvents and the pure polymers, and their blends. Traditionally, in Flory-Hu ins theory the molar volume of the solvent (Vi) is taken as the reference volume (Vo). This problem is valid for ternary systems, and differences in the values of the X parameter originate from the lattice size used. Zhao and Choi [51] have proposed the use of a common reference volume, calculating x zi from the equation ... 

Binary interaction parameter between species (groups) i and L Binary interaction parameter between species (groups) i and L Binary interaction parameter between cations M and anions X Binary interaction parameter between cations M and anions X Binary interaction parameter between repeating units Binary interaction parameter between repeating units and the chloride ion... 

The interaction parameter between the ethylene (E) units and octene (O) units for a binary blend of two random copolymers can be obtained from the copolymer equation ... 

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