4.1 Azeotrope-breaking criteria

Applying the cubic model of the equation of state, only the critical properties and acentric factor of the individual components in mixtures are sufficient to define the phase behavior in the interested sector of the parameters.

The degenerated critical azeotrope point is a boundary state separating azeotrope and non-azeotrope and produces the limit of the critical azeotrope at xi ! 0 or at xi ! 1. The solution of the thermodynamic equation system for a degenerated critical azeotrope [5–7, 9]

$$
\left(\frac{\partial \hat{p}}{\partial V}\right)\_{T,x} = \left(\frac{\partial^2 \hat{p}}{\partial V^2}\right)\_{T,\hat{x}} = \left(\frac{\partial \hat{p}}{\partial x}\right)\_{T,\hat{x}} = 0,\tag{15}
$$

gives the following relationship for dimensionless parameters Zi:

$$Z\_2 = \mp Z\_1 - (\mathbf{1} \pm Z\_1) \left(\frac{\mathbf{1} - Z\_4}{\mathbf{1} \pm Z\_3} - \mathbf{1}\right) \Lambda,\tag{16}$$

where the upper signs + or � correspond to x2 = 0 and the lower signs - to x2 = 1, respectively.

To define the azeotropic states, the parameters Zi can be expressed via critical (pseudocritical) temperatures Tci and pressures Pci of pure components and empirical binary interaction parameters k12 and l12 (17). The unlike pair interaction parameters Z2 and Z4 (i.e., a12 and b12) can be estimated solving simultaneously the system of Eqs. (17) for the given Z1 and Z3 (or the set of pure component constants a11, b11, a22, b22) that are determined from the critical parameters of the components:

$$\mathbf{Z}\_{1} = \frac{\mathbf{T}\_{c2}^{2}/\mathbf{P}\_{c2} - \mathbf{T}\_{c1}^{2}/\mathbf{P}\_{c1}}{\mathbf{T}\_{c2}^{2}/\mathbf{P}\_{c2} + \mathbf{T}\_{c1}^{2}/\mathbf{P}\_{c1}}, \mathbf{Z}\_{2} = \frac{\mathbf{T}\_{c2}^{2}/\mathbf{P}\_{c2} - 2(\mathbf{1} - \mathbf{k}\_{12})\frac{\mathbf{T}\_{c1}\mathbf{T}\_{c2}}{\sqrt{\mathbf{P}\_{c1}\mathbf{T}\_{c2}}} + \mathbf{T}\_{c1}^{2}/\mathbf{P}\_{c1}}{\mathbf{T}\_{c2}^{2}/\mathbf{P}\_{c2} + \mathbf{T}\_{c1}^{2}/\mathbf{P}\_{c1}},$$

$$\mathbf{Z}\_{3} = \frac{\mathbf{T}\_{c2}/\mathbf{P}\_{c2} - \mathbf{T}\_{c1}/\mathbf{P}\_{c1}}{\mathbf{T}\_{c2}/\mathbf{P}\_{c2} + \mathbf{T}\_{c1}/\mathbf{P}\_{c1}},\tag{17}$$

$$\mathbf{Z}\_{4} = \frac{\mathbf{T}\_{c1}/\mathbf{P}\_{c1} - (\mathbf{1} - \mathbf{l}\_{12})(\mathbf{T}\_{c1}/\mathbf{P}\_{c1} + \mathbf{T}\_{c2}/\mathbf{P}\_{c2}) + \mathbf{T}\_{c2}/\mathbf{P}\_{c2}}{\mathbf{T}\_{c2}/\mathbf{P}\_{c2} + \mathbf{T}\_{c1}/\mathbf{P}\_{c1}}.$$

The boundary between azeotrope and zeotrope states in Z1–Z2 plane at fixed values of Z3 and Z4 is a straight line. The definition of azeotropic and zeotropic states for refrigerants is depicted in Figure 7.
