(I discuss the Flory-Huggins parameter as chi from here onward). So I had learned in class that when discussing polymers the Flory-Huggins Theory helps us figure out whether mixing is thermodynamically favorable. We had also discussed UCST and LCST behavior. Now from what I understood (and where there might be a misconception), with a chi value less than 0 the solution always mixes, chi value equal to 0 the solution is ideal (with no preferable interactions) and a chi value greater than 0 the solution may or may not mix depending on the entropy related terms in the Flory-Huggins equation.
Looking at the case where the chi values is greater than 0 the reaction (solvation reaction) is endothermic based on the equation in terms of internal energies ((z/2kbT)(2*uAB-(uAA+uBB)) where u represents the energy of interaction between molecules A and B). However, we also know that if I model chi as A+B/T then, as temperature is increased, the chi value can change giving rise to either UCST or LCST behavior. Which means a reaction (of solvation) that is endothermic (chi greater than 0) could either increase or decrease in terms of Gibbs (or Helmoltz's) free energy with rising temperature. However, this cannot be reconciled then with Le Chatelier's Principle which would tell me that for an endothermic reaction of solvation, rising temperature would always push the reaction to be more thermodynamically favorable to the products. Could someone please point out my error in logic?
In advance, thank you!