Difference between revisions of "Phase separation"

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             where <math>\epsilon = zN[V_{AB} - {1 \over 2}(V_{BB}+V_{BB})]</math>  
 
             where <math>\epsilon = zN[V_{AB} - {1 \over 2}(V_{BB}+V_{BB})]</math>  
V represents bond energies, z is the number of neighbors, N is the total number of atoms, and x is the mole fraction.  
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<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> then the change in free energy upon mixing is always negative, so the atoms will always want to be fully mixed. If <math>/epsilon</math>, then mixing or phase separation can occur depending on the temperature.  
  
  

Revision as of 21:10, 9 December 2011

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>\frac{G_{mix}}{kT}=Nnv _{A}\ln v _{A}+x _{B}\ln v _{B}+\epsilon v _{A} v _{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> then the change in free energy upon mixing is always negative, so the atoms will always want to be fully mixed. If <math>/epsilon</math>, then mixing or phase separation can occur depending on the temperature.





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