The enthalpy of mixing

The enthalpy of mixing is introduced into the Flory-Huggins theory in the spirit of the classical van Laar approach. The mixing can be considered as a quasichemical reaction between solvent contacts and segment contacts l-l+2-2-2(l-2) 

The change in internal energy for the formation of one set of 1 —2 contacts is simply 

In the Flory-Huggins theory, it is assumed that all volume changes that occur on mixing can be ignored so that 

The lattice parameters x and z are eliminated as follows. First, equation (3.11) for V2 shows that x 2Vi= iV2. Second, a dimensionless interaction parameter X introduced such that 

The subscript 1, referring to the solvent, is used here because )j,A ris just the difference in energy of a solvent molecule immersed in pure polymer compared with that in pure solvent. Note that Xi is pivotal parameter in Flory-Huggins theory. With these relationships, the enthalpy of mixing can be expressed as 

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The second term in Equation (15a) gives the enthalpy of mixing of the condensable components. It is difficult to estimate that enthalpy but fortunately it ma)ies only a small contri-... 

Table 1 indicates that the enthalpy of mixing in the liquid phase is not important when calculating enthalpies of vaporization, even though for this system, the enthalpy of mixing is large (Brown, 1964) when compared to other enthalpies of mixing for typical mixtures of nonelectrolytes. 

According to Hildebrand and Scott [5], the enthalpy of mixing per unit volume A/im is related to the volume fraction

solubility parameter 5 of the two components ... 

The enthalpy of mixing is the same as the enthalpy of solution, AH ,, but AHmix is used more commonly for the mixing of two liquids. 

Solubility occurs where the free energy of mixing, AG , is negative. This value is related to the enthalpy of mixing, AH, and the entropy of mixing, AiSjjj, by the Gibbs equation ... 

Entropy of mixing is usually (though not always) positive, hence the sign of AG is generally determined by the size and magnitude of AH. For nonpolar molecules, AH is found to be positive and closely similar to the enthalpy of mixing of small molecules. In such a case, the enthalpy of mixing per unit volume can be approximated to ... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

For example, the enthalpy of mixing of copolymer specimen AH per mole of monomeric units can be expressed... 

This is a deceptively simple question to ask, but one which is quite hard to answer. We have performed titration calorimetry experiments (unpublished) intended to determine the enthalpy of reaction for the reaction of aqueous formaldehyde with polypeptides or proteins, without success. In our experiments, the enthalpy of mixing was much larger than that which could be... 

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

An analysis of a large amount of experimental data by Davies and Navrotsky has also shown that the enthalpy of mixing of ionic solid solutions correlates with the volume mismatch [39], The volume mismatch was in the simplest case assumed to... 

The first term is the ideal entropy of mixing while the second term is the enthalpy of mixing in the regular solution approximation ... 

By simple thermodynamic arguments Brown14 has shown that, consistent with the accuracy of this second-order approximation, one may obtain from the form of Eq. (87) the form of the excess Gibbs free energy of mixing (AG ), the enthalpy of mixing of a molten salt (AHm), and the deviation of the surface tension from linearity ... 

Ordering. New compounds which include the ionic components AX and BX may be formed by ordering of the solid solution ( ). In that case, the entropy of mixing may still be given by Equation 17, whereas the enthalpy of mixing is given by ... 

Freund and Knobel (62) have found that in addition to F-OH-F complexes, F-OH pair interactions are important. Therefore, a mixed type regular and subregular model of the solid solutions should be more appropriate. To a first approximation, the enthalpy of mixing should then have the form ... 

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