Phase separation

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Entry by Emily Redston, AP 225, Fall 2011

Figure 1 (from Haasen)
Figure 2 (from Haasen)

We typically talk about phase separation in terms of the regular solution model of liquids. The free energy of mixing can be written as,

          <math>G_{mix}= RT (x _{A}\ln x _{A}+x _{B}\ln x _{B})+\epsilon x _{A} x _{B}</math>
            where <math>\epsilon = zN[V_{AB} - {1 \over 2}(V_{BB}+V_{BB})]</math> 

<math>V</math> represents bond energies, <math>z</math> is the number of neighbors, <math>N</math> is the total number of atoms, and <math>x</math> is the mole fraction. The sign of <math>\epsilon</math> is essential in determining the solution's behavior as a function of temperature. If <math>\epsilon</math> < 0 then the change in free energy upon mixing is always negative, so the atoms will always want to be fully mixed. For <math>\epsilon</math> > 0, there is a temperature dependance, and either mixing or phase separation can occur. Phase separation occurs when

                          <math>{G_{mix} \over x_B} = 0</math>





See also:

Phase separation in Phases and Phase Diagrams from Lectures for AP225.


References

The Role of Polymer Polydispersity in Phase Separation and Gelation in Colloid−Polymer Mixtures