Regular solution parameter

The regular solution parameters are still assumed to be enthalpic in nature. In other words, the vibrational entropy is, as earlier, considered not to be affected by the mixing. The last term of eq. (9.83), the configurational entropy, is also unaffected by this modification. 

In Fiery s theory of the excluded volume (27), the chains in undiluted polymer systems assume their unperturbed dimensions. The expansion factor in solutions is governed by the parameter (J — x)/v, v being the molar volume of solvent and x the segment-solvent interaction (regular solution) parameter. In undiluted polymers, the solvent for any molecule is simply other polymer molecules. If it is assumed that the excluded volume term in the thermodynamic theory of concentrated systems can be applied directly to the determination of coil dimensions, then x is automatically zero but v is very large, reducing the expansion to zero. 

Often the liquid and solid are not the same metal and sometimes they are mutually insoluble. When the equilibrium value of the molar fraction of solid component A in a liquid B X < 1, by equalling the chemical potentials of A in the solid and liquid phases, X is related to the regular solution parameter X given by equation (4.3) by ... 

Table G. 1 reproduces values calculated by Miedema s model (Niessen et al. 1983) for the partial enthalpy of solution at infinite dilution of a liquid metal solute i in a liquid metal solvent i, AH, (in kJ/mole). For a i-j alloy, the regular solution parameter k can be approximated by [AHj(j( + AHJ(l)]/2.

In this equation, Qm is the molar surface area, m i is a structural parameter defined in Section 1.1 (see Figure 1.3) and A is the regular solution parameter of Ni-Si alloy defined by equation (4.3). From the slope of the osL(XNi) curve for XNi— 0, the adsorption energy is found to be E i,(f ) = —8.2 kJ/mole. Thus, in equations (1.2), all the quantities are known (or can be easily estimated), except W and Wf 1 which represent respectively the work of adhesion and the work of immersion of pure liquid Ni in metastable equilibrium with SiC (i.e., for a supposed non-reactive pure Ni/SiC system). The values deduced from equation (1.2) are Wj4 = 3.17 J/m2 and W = —1.35 J/m2 for pure Ni. They are reported in Figure 7.6 along with the corresponding value of contact angle. 

Chlorobenzene is a somewhat more complicated calculation in that the regular solution parameters are not available. From Perry s "Chemical Engineer s Handbook", the following data is obtained ... 

In the regular solution approximation, this equality is no longer assumed and the heat of mixing is finite. We define the regular solution parameter as... 

The first attempt to calculate phase equilibria in this system on the flrermodynamic basis (Calphad meflrod) was made by [1974Kir] who was able to reproduce the a--y equilibrium data between 750°C and 950°C based on their analysis of the previous evaluations of the Fe-Mn and Cr-Fe systems [1973Kir]. They introduced the regular solution parameters L for a and y phases of tire Cr-Mn system and parameters L for the a and y phases of the Cr-Fe-Mn system, but flrey did not attempt to evaluate tire binary parameters for the Cr-Mn system from any information on fliis binary system. They used aU four parameters to describe their experimental information which was confined to the Fe rich comer of tire ternary system. For reconciling the calculation results with experiment flrey had to introduce the temperature dependence of Are obtained parameters which is so strong that seems to be non-physical. 

Further, the difference in the regular solution parameters can also be found from knowledge of only Tm by... 

Thus, to calculate the composition of the azeotrope point and the difference in the regular solution parameters, only and pure component transition temperatures and enthalpies are required. That so much can be accomplished with only knowledge of T n is very convenient, since the commonly used contact method for determining binary phase diagrams of mesogenic mixtures will only provide temperature information. 

As mentioned above, the experimentally observed Tm will only allow the difference in the regular solution parameters to be calculated but to calculate the phase diagram the individual parameters have to be known. For simple minimum or maximum diagrams where two non-ideal liquid phases appear, for example, a nematic-isotropic equilibrium, two regular solution parameters are necessary. To obtain the individual values once knowing... 

Figure 5 shows the regular solution and ideal solid solution equations that govern surface segregation for two component systems (8]. Here surface tensions of the pure components 1 and 2, and are the atom fractions of the two components at the surface, and X and AT are the atom fractions of the two components in the bulk. is a regular solution parameter that is proportional to the heat of... 

From the calculated activity coefficients a regular solution parameter for pyrope-grossular garnets is derived ... 

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