Mixing, enthalpy mixtures

Therefore, it is only possible to obtain a homogeneous, single-phase mixture of two polymers when the generally slightly positive mixing enthalpy AH j is sufficiently small or its magnitude is smaller than TAS. However, this is only to be expected for chemically very similar macromolecules. 

Calorimetry constitutes a powerful tool to investigate materials. It is a measurement technique that enables us to obtain values of the thermodynamic quantities of substances. The methods used for the characterization of thermodynamic properties of molten salts include temperature, enthalpy, and heat capacity measurements as mixing enthalpy and phase diagram determinations for their mixtures. 

Mixing of two liquids. The break-off bubble method was developed by Gaune-Escard (1972) and has often been used in the mixing enthalpy measurements of molten salt mixtures. The schematic representation of this method is shown in Figure 4.8a. Inside... 

The solubility parameter approach was first developed by Hildebrand [11] for calculating estimates of the enthalpy of mixing, for mixtures... 

Mixing enthalpy is zero (i.e. no enthalpy changes upon mixing). Indeed, by definition, the specific mixing enthalpy is the difference h — X =i (cf. (4.435), (4.436)) where h is the specific enthalpy of the mixture and h is the specific... 

Recently Loci, Mayhew, and Williamson have examined the extension of the principle of congruence to ternary alkane mixtures. As shown in Figure 10, the enthalpy of mixing of mixtures of alkanes of end-point indices 6 and 16 is very nearly independent of whether or not the end-point index (w = 16) is that of a pure substance (n-hexadecane) or of a mixture (n= 13 + = 19, X = 0.5). 

In this equation Gp and Gq are the Gibbs energies of the two components P and Q and Xp and Xq are the concentrations of the components in the mixture. This equation can be rewritten by expressing the mixing term in the mixing enthalpy (zero in ideal mixtures) and the mixing entropy (G = H - TS is used). For the entropy its expression in terms of the concentration x in an ideal gas mixture is substituted in the equation. For the present purpose this is an acceptable approximation. The atomic concentration Xp is called x and for a binary system the... 

Most correlations used to calculate the activity coefficients are based on the dependence of the free mixing enthalpy on the activity coefficient for each individual component in the mixture. If two pure components are mixed, the entropy in-... 

The free mixing enthalpy Ag, related to one kmol of the mixture, is... 

Thermal separation operations are isobaric apart from pressure drops which occur in the separation apparatus. During mixing the change of the free enthalpy AG of the system, the free mixing enthalpy is equal and opposite to the minimum separation work 1V, required to separate the mixture into its pure components. 

When k components are mixed to obtain 1 mol of a real mixture, as discussed in Chapter 1.4.1, the free mixing enthalpy AgM> is... 

In the Merkel and Ponchon h, w diagram, if the values of the enthalpies / , and h2 of each individual component and the mixing enthalpy Ahj have been found experimentally, the enthalpy of the mixture h can be found from... 

Those criteria are met by a cocrystal screening based on COSMO-RS theory, using the mixing enthalpy (or equivalently the excess enthalpy of a supercooled cocrystal mixture [18]. The main reason for the predictive capability of this theory concerning cocrystal formation is its accurate description of intermolecular interactions. The idea behind a COSMO-RS-based screening can be best understood by having a look at the thermodynamic cycle shown in Scheme 9.1. 

The basic thermodynamic relationship governing mixtures is given by Gibbs free energy AGm. The relationship between AGm and mixing enthalpy and entropy at temperature T is given by ... 

Enthalpies of mixing can be determined, in principle, calorimetrically but for polymer-polymer mixtures the inherent immiscibility of the components and lack of contacts between them means that these parameters cannot normally be determined directly. It is possible to estimate heats of mixing from mixtures of oligomeric analogues, which are often miscible by virtue of their greater entropy of mixing. The interaction energy density B, related to %aB 1 deter-... 

In the case of liquid mixtures which are ideal over the complete range of composition, from =0 to x, = 1, Hi and Vi are therefore the same as hi and t the enthalpy and volume respectively, per mole of the pure component. It follows that the total enthalpy T(=Z%jET ), and the total volume F(=Sn F<), of any such mixture, are the same as those of the components before mixing. Such mixtures can therefore be prepared, at constant temperature and pressure, without heat effect or volume change. 

Enthalpies of mixing for mixtures of anisole + diethylene glycol or + triethylene glycol are given in the original somce. 

The FOVE model can predict negative mixing enthalpy and mixing volume as well as both LCST and UCST. The reorientation of segments arising from specific interaction is, however, ignored. The theory uses an entropy contact parameter, Q12, that counterbalances any effect that specific interaction has on the excess energy of the mixture. 

In many respects these systems show similarities with mixed cation-common anion mixtures of the type (K-Rb)X, (K-Cs)X, and (Rb-Cs)X, which also often have quite small positive enthalpies of mixing. There is reason to believe that these similarities may be due to the fact that in both cases we are considering the mixing of two ions which differ relatively little in size, and are also fairly large and polarizable. As a consequence the small negative Coulomb contribution to the mixing enthalpy (Eq. 8) may be overshadowed by the positive London-van der Waals terms. 

The enthalpy of a vapor mixture is obtained first, from zero-pressure heat capacities of the pure components and second, from corrections for the effects of mixing and pressure. 

For an ideal vapor mixture of m components, there is no enthalpy of mixing. The enthalpy of such a mixture is then... 

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