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.

Compression and self-entanglement of single DNA molecules under uniform electric field

“…We estimate from the optical size that the DNA concentration inside a globule produced under 200 V∕cm is about 7c à (the segment concentration inside a equilibrium DNA coil is c à ). This concentration is very close to the critical concentration (∼9c à ) for the onset of entangled regime in semidilute DNA solutions (34) and thus can possibly lead to selfentangling of the molecule. However, an internal DNA concentration of 7c à alone does not give rise to enough entanglements to fully account for the observed slow expansion as it only corresponds to an equilibrium number of entanglements on order of 1 (35).…”

DNA-based highly tunable particle focuser

“…However, the relaxation times of polymer solutions, which were measured under shear flows, slowly increased until c reaches c* (refs 45,46), which was also observed by single DNA experiments 47 . The relative difference between the relaxation time of the 5 p.p.m.…”

Divergent Shear Thinning and Shear Thickening Behavior of Supramolecular Polymer Networks in Semidilute Entangled Polymer Solutions

“…Only the samples with PVP concentration decidedly in the semidilute entangled regime (~0.23 g/mL and ~0.27 g/mL) exhibit purely shear thinning behavior (Figure 4a). We note here that the critical concentration for entanglement (see Figure S1 and Figure S2 in supporting material) is determined by a semiempirical method, 38,39 and it is possible that the ~0.16 g/mL PVP/DMSO solutions at 25 °C may still be in the semidilute unentangled regime, as the inferred critical concentration for entanglement is 0.155 g/mL. The samples with 1a in ~0.19 g/mL PVP/DMSO solutions at 25 °C, however, exhibit steady shear behavior that is quite different from that of samples in the semidilute unentangled regime (Figure 4a), and so we believe that the ~0.19 g/mL PVP/DMSO solutions at 25 °C are definitely in the semidilute entangled regime.…”