Thermodynamic Definition
Thermodynamically, the excess chemical potential of mixing between a theta solvent and a polymer is zero. Equivalently, the enthalpy of mixing is zero, making the solution ideal.
You cannot measure the chemical potential by any direct means, but you can correlate it to the solution's osmotic pressure and the solvent's partial specific volume :
You can use a virial expansion to express how osmotic pressure depends on concentration:
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- M is the molecular weight of the polymer
- R is the gas constant
- T is the absolute temperature
- B is the second virial coefficient
This relationship with osmotic pressure is one way to determine the theta condition or theta temperature for a solvent.
The change in the chemical potential when the two are mixed has two terms: ideal and excess:
The second virial coefficient, B, is proportional to the excess chemical potential of mixing:
B reflects the energy of binary interactions between solvent molecules and segments of polymer chain. When B > 0, the solvent is “good,” and when B < 0, the solvent is “poor.” For a theta solvent, the second virial coefficient is zero because the excess chemical potential is zero; otherwise it would fall outside the definition of a theta solvent. A solvent at its theta temperature is, in this way, analogous to a real gas at its Boyle temperature.
Similar relationships exist for other experimental techniques, including light scattering, intrinsic viscosity measurement, sedimentation equilibrium, and cloud point titration.
Read more about this topic: Theta Solvent
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