molecules and is the number of polymer molecules, each of which has segments. For a random walk on a lattice we can calculate the entropy change (the increase in spatial uncertainty) as a result of mixing solute and solvent. where is Boltzmann's constant. Define the lattice volume fractions and These are also the probabilities that a given lattice site, chosen at random, is occupied by a solvent molecule or a polymer segment, respectively. Thus For a small solute whose molecules occupy just one lattice site, equals one, the volume fractions reduce to molecular or mole fractions, and we recover the usual entropy of mixing. In addition to the entropic effect, we can expect an enthalpy change. There are three molecular interactions to consider: solvent-solvent , monomer-monomer (not the covalent bonding, but between different chain sections), and monomer-solvent . Each of the last occurs at the expense of the average of the other two, so the energy increment per monomer-solvent contact is The total number of such contacts is where is the coordination number, the number of nearest neighbors for a lattice site, each one occupied either by one chain segment or a solvent molecule. That is, is the total number of polymer segments (monomers) in the solution, so is the number of nearest-neighbor sites to all the polymer segments. Multiplying by the probability that any such site is occupied by a solvent molecule, we obtain the total number of polymer-solvent molecular interactions. An approximation following mean field theory is made by following this procedure, thereby reducing the complex problem of many interactions to a simpler problem of one interaction. The enthalpy change is equal to the energy change per polymer monomer-solvent interaction multiplied by the number of such interactions The polymer-solvent interaction parameter chi is defined as It depends on the nature of both the solvent and the solute, and is the only material-specific parameter in the model. The enthalpy change becomes Assembling terms, the total free energy change is where we have converted the expression from molecules and to moles and by transferring the Avogadro constant to the gas constant . The value of the interaction parameter can be estimated from the Hildebrand solubility parameters and where is the actual volume of a polymer segment. In the most general case the interaction and the ensuing mixing parameter, , is a free energy parameter, thus including an entropic component. This