Dear CHE 530 students,

I'm writing with two additional comments about Flory-Huggins theory.

(1) In the definition that I wrote for free energy of mixing, the units for \Delta G_{mix} are

energy per mole of lattice sites

The meaning of the "per mole" that comes from R (in G/RT) is important, since it isn't the usual "moles of solvent", "moles of polymer", or "moles of molecules in the mixture".

(2) My instinct in class about solvent activity was correct. The solvent activity is defined as

ln a_s = (\mu_s - \mu_s^0) / RT

and the right side can then be calculated using Flory-Huggins theory.

In chemical engineering, we're more used to working with fugacity, which is defined as

ln (f_s / f_s^0) = (\mu_s - \mu_s^0) / RT

where f_s is the fugacity of the solvent in the mixture, and f_s^0 is the fugacity of the solvent in its standard state at this temperature.

Usually the standard state is defined as

f_s^0 = y_s P

which at low pressure in an ideal solution equals P_s^{sat}, i.e. the vapor pressure of pure solvent. The variable y_s equals the vapor phase mole fraction of solvent in a vapor above the pure solvent, and P is the total pressure (probably 1 atm).

The activity can be calculated from what we use as an activity coefficient by multiplying the activity coefficient by a concentration. In other words,

a_s = \gamma_s x_s = \Gamma_s \phi_s

where a_s is activity x_s is mole fraction solvent \phi_s is volume fraction of solvent \gamma_s is activity coefficient based on mole fraction (the usual case in chem eng thermo) \Gamma_s is activity coefficient based on volume fraction

Please feel free to contact me if you have any questions.

Prof. Greenfield

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