  Theoretical aspects of polymers in mixed solvents are considered using the
Edwards Hamiltonian formalism. Thermodynamic and structural properties are
investigated and some predictions are made when the mixed solvent approaches
criticality. Both the single and the many chain problems are examined. When the
pure mixed solvent is near criticality, addition of a small amount of polymers
shifts the criticality towards either enhanced compatibility or induced phase
separation depending upon the value of the parameter describing the interaction
asymmetry of the solvents with respect to the polymer. The polymer-solvent
effective interaction parameter increases strongly when the solvent mixture
approaches criticality. Accordingly, the apparent excluded volume parameter
decreases and may vanish or even become negative. Consequently, the polymer
undergoes a phase transition from a swollen state to an unperturbed state or
even take a collapsed configuration. The effective potential acting on a test
chain in strong solutions is calculated and the concept of Edwards screening
discussed. Structural properties of ternary mixtures of polymers in mixed
solvents are investigated within the Edwards Hamiltonian model. It is shown
that the effective potential on a test chain in strong solutions could be
written as an infinite series expansion of terms describing interactions via
one chain, two chains etc. This summation can be performed following a similar
scheme as in the Ornstein-Zernike series expansion.
