Concentration dependence of the longest relaxation times of dilute and semi-dilute polymer solutions

Abstract

The longest relaxation times of polymer solutions of semi-flexible T4 DNA and flexible 18 M molar mass polyacrylamide (PAAm) in dilute and semi-dilute concentration range are studied by the polymer extension relaxation of stretched single DNA molecules and by the stress relaxation of PAAm solutions measurements. For both polymer solutions, the longest relaxation time normalized by the value at infinite dilution with the same solvent viscosity τ/τ0 increases with increasing concentration. In the dilute regime, the longest relaxation time increases just slightly with increasing concentration as τ/τ0=[1+cA−2(cA)1.5+2(cA)2] as well as the empirical relation of τ/τ0=exp(cA) up to c∼3c∗ with A≈0.5[η], where c∗ is the overlap concentration, in accord with the theory and previous experiments. For the semi-dilute solutions, the scaling of τ/τ0 with concentration shows two different exponents in two concentration regions, corresponding to the unentangled and entangled regimes. The exponents are consistent with those expected by the theory of dynamical scaling for semi-dilute polymer solutions. The crossover concentration from the unentangled to entangled regime ce is found to be ∼9c∗ in a good solvent, in accord with other experiments based on the relaxation of a single molecule, the diffusion coefficient, and the solution viscosity measurements. We also test the universality of the concentration dependence of the longest relaxation time for both flexible and semi-flexible polymers in both good and Θ solvents in the dilute and semi-dilute regimes by analyzing literature data sets.