Tricritical disorder transition of polymers in a cloudy solvent: Annealed randomness

The effect of annealed randomness caused by impurities diffusing in a polymer solution (i.e., a cloudy solvent) is analyzed exactly within the framework of the continuum Edwards model, in dimension d. It is shown that an infinite series of local P-body interactions of all orders P≥2 is generated in the cloudy solvent, whose coefficients are calculated as functions of the impurity density. The impurities can be repulsive or attractive for the chains. The present state of polymer theory (perturbation expansion, regularization, and renormalization) allows a detailed study of the effect of these interactions to all orders, as a function of dimension d, 2<d≤4. For an impurity density below a special threshold ${\rho }_c$, the polymer solution is not cloudy and is as it would be in a pure solvent. At ${\rho }_c$ the polymer chains undergo a transition toward a standard tricritical FTHETA state, and beyond that density to a dense state with phase separation. For 3<d≤4 the transition is Gaussian. The universal tricritical behavior at the transition in 2<d≤3 is given. The limiting dimension d=2 is singular and subtle and is the cornerstone of a new type of behavior for 0≤d<2.