# Difference between revisions of "Phase separation"

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

− | + | <font size="+2"><math>G_{mix}= RT (x _{A}\ln x _{A}+x _{B}\ln x _{B})+\epsilon x _{A} x _{B}</math></font> | |

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> | ||

− | <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, either mixing or phase separation | + | <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> | ||

## Revision as of 21:29, 9 December 2011

Entry by Emily Redston, AP 225, Fall 2011

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