Two-Parameter Scaling for Polymers in 9 Solvents

We revive an old conjecture that a fixed number of binary contacts between chains collectively make up the topological constraint commonly referred to as an entanglement. This leads us to a general scaling theory for semidilute polymer solutions which involves two length scales, the screening length and the tube diameter a. In good solvents these two lengths have the same concentration dependence and we recover the de Gennes results. In 9 solvents the two length scales depend on concentration differently. Combining the concentration dependences of these two length scales with concepts from theories of rubber elasticity and reptation leads to new predictions for the plateau modulus G ~ feT/(a2{) ~ c7/3 and viscosity y ~ Af2/3(c/c*)14/3 in 9 solvents, where M is the polymer molecular weight and c* is the overlap concentration. These predictions are found to compare favorably with available experimental data.