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Inhalation OctOber 2021 25 liquid mixture miscibility and solid phase solubil- ity can be estimated using the same framework, potentially with modified versions of UNIFAC and UNIQUAC models described in reference 17. Sample formulation property results Next, sample results are presented that demonstrate the property framework approach for SVP, surface tension and viscosity, to show the quality of repre- sentation of the data and, in the case of viscosity, the predictive power of the approach. Experimental data from references 14, 15 and 16 was used, and the UNIFAC and UNIQUAC model parameters were selected to optimally fit these models to these data in a least squares sense. To demonstrate the need for an expression for SVP that incorporates the non-ideal behavior, Figure 2 compares the result of an HFA134a/ethanol mix- ture SVP from Raoult's law (Equation 1)—the dotted straight line—with that from the modi- fied Raoult's law (Equation 2) using the UNIFAC model for activity coefficients—the solid line. e UNIFAC predetermined interaction param- eters for the molecules HFA134a and ethanol are presented in full in reference 18, having been calculated from both SVP and surface tension experimental data. ese can now be used for SVP prediction at alternate temperatures or with addi- tional formulation constituents present, without further experimental data. Activity coefficients provide a thermodynamic basis for molecular interactions that cause deviation in mixture behavior and properties in liquid systems, and vapor/liquid, liquid/liquid and solid/liquid sys- tems. ey are related to the excess Gibbs free energy G E generated when a solution is created, due to any molecular interactions, over and above that of an ideal, non-interacting mixture: RT ln γ i = ∂G E ∂n i (3) where R is the universal gas constant, T the mixture temperature, and n i the number of moles of species in the mixture. erefore, activity coefficient values greater than 1 indicate that the presence of mole- cules of species i causes repulsive interaction in the mixture, whereas a value less than 1 indicates these molecules tend to attract the other molecules in the mixture (leading to G E < 0). Various models exist to describe activity coefficients as well as to fit SVP or vapor/liquid equilibrium experimental data. In this article, UNIQUAC (Uni- versal Quasi-chemical Activity Coefficients) and UNIFAC (UNIQUAC Functional-group Activity Coefficients) are used, which are described in more detail in reference 18. Both models use properties of the functional groups present in mixture compo- nents. UNIQUAC only requires two parameters per pair of components in the mixture and can accu- rately represent activity coefficients and SVP data, even for highly non-ideal mixtures (compared to the 6 coefficients required for the fit in Figure 1). UNIFAC is a predictive model that uses pure com- ponent properties only and a set of predetermined functional group interaction parameters, which are available for some HFA/ethanol mixtures [18]. Other thermophysical properties Since molecular interactions also control other liquid mixture and solution properties, activity coefficients can be successfully used to represent or predict those properties. For example, the same numerical UNIQUAC parameters can be used in a modi- fied model, suitable for liquid viscosity prediction, known as UNIMOD (Modified UNIQUAC) [19]. Calculated activity coefficients (from any model) can be used to determine mixture surface tension, with the Sprow and Prausnitz method [20], and liquid mass diffusion coefficients, using methods discussed in detail in reference 21. Simultaneous representation or estimation of all these properties is possible, either by using the activ- ity coefficients estimated from SVP experimental data, or by incorporating all the data and physical property models into an overall thermodynamic framework—as shown in recent papers presented at RDD2021 [18] and DDL2020 [22]. In addition, Figure 2 Saturated vapor pressure (SVP) measurement [16] and UNIFAC prediction for HFA134a/ ethanol mixtures, at 20.0°C. 6 5 4 3 2 1 0 Vapour Pressure (bar) 0 0.2 0.4 0.6 0.8 1 Ethanol Mole Fraction