Free of mixing

We may also define a free energy of mixing [240]. The alternative (and equally acceptable) definition of G given in Eq. 111-87 is... 

Fig. IV-22. Excess free energy of mixing of condensed films of octadecanol-docosyl sulfate at 25°C, at various film pressures. Top curve t = 5 dyn/cm bottom curve ir = 50 dyn/cm intermediate curves at 5-dyn/cm intervals. The curves are uncorrected for the mixing term at low film pressure. (From Ref. 246.)...

The broken bond approach has been extended by Nason and co-workers (see Ref. 85) to calculate as a function of surface composition for alloys. The surface free energy follows on adding an entropy of mixing term, and the free energy is then minimized. 

The molar Helmholtz free energy of mixing (appropriate at constant volume) for such a synnnetrical system of molecules of equal size, usually called a simple mixture , is written as a fiinction of the mole fraction v of the component B... 

Figure A2.5.15. The molar Gibbs free energy of mixing versus mole fraetionxfor a simple mixture at several temperatures. Beeause of the synuuetry of equation (A2.5.15) the tangent lines indieating two-phase equilibrium are horizontal. The dashed and dotted eiirves have the same signifieanee as in previous figures.

The entropy of a solution is itself a composite quantity comprising (i) a part depending only on tire amount of solvent and solute species, and independent from what tliey are, and (ii) a part characteristic of tire actual species (A, B,. ..) involved (equal to zero for ideal solutions). These two parts have been denoted respectively cratic and unitary by Gurney [55]. At extreme dilution, (ii) becomes more or less negligible, and only tire cratic tenn remains, whose contribution to tire free energy of mixing is... 

To produce glass bottles, the mixture is prepared ia unit batches. Mixing is critical because complete homogeneity of the batch is necessary to produce quaUty glass. Gullet is added to the batch, usuady at discharge from the mixer. The cudet must be of the same color and basic composition, and be free of contamination such as metal bottie caps and tramp metal scraps. 

Solubility Parameter. CompatibiHty between hydrocarbon resins and other components in an appHcation can be estimated by the Hildebrand solubiHty parameter (2). In order for materials to be mutually soluble, the free energy of mixing must be negative (3). The solubiHty of a hydrocarbon resin with other polymers or components in a system can be approximated by the similarities in the solubiHty parameters of the resin and the other materials. Tme solubiHty parameters are only available for simple compounds and solvents. However, parameters for more complex materials can be approximated by relative solubiHty comparisons with substances of known solubiHty parameter. 

Alkali Treatment. Caustic washing is the treatment of materials, usually products from petroleum refining, with solutions of caustic soda. The process consists of mixing a water solution of lye (sodium hydroxide or caustic soda) with a petroleum fraction. The treatment is carried out as soon as possible after the petroleum fraction is distilled, since contact with air forms free sulfur, which is corrosive and difficult to remove. The lye reacts either with any hydrogen sulfide present to form sodium sulfide, which is soluble in water, or with mercaptans, foUowed by oxidation, to form the less nocuous disulfides. 

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... 

One proposed approach (75) to modeling the phase behavior for hydrogen bonding pairs uses the following expression for the free energy of mixing (eq. 7). 

Practical Solubility Concepts. Solution theory can provide a convenient, effective framework for solvent selection and blend formulation (3). When a solute dissolves in a solvent, a change in free energy occurs as a result of solvent—solute interactions. The change in free energy of mixing must be negative for dissolution to occur. In equation 1,... 

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