Monodisperse Lambda DNA as a Model to Conventional Polymers: A Concentration-Dependent Scaling of the Rheological Properties

Abstract

We have measured the dynamics of completely monodisperse (PDI = 1.0) ultrahigh-molecular-weight linear lambda (λ) DNA solutions as a function of concentration. Due to the very high molecular weight of the DNA, M n = M w > 30 million g/mol, we were able to study the dynamic properties of well-entangled systems even in very dilute (low-concentration) conditions. We report the linear rheology by conducting dynamic oscillatory measurements well into the entanglement regime (11 < C* < 90), where C* is the overlap concentration. The tests are reported in good solvent conditions. Upon comparing our results with previously reported data in the literature by Teixeira et al. [Macromolecules 2007, 40 (7), 2461−2476 and reproducing their data, we can confirm their measurements to have been conducted in the nonlinear regime. This leads to the conclusion that the lambda DNA exhibits extreme strain sensitivity in the observed dynamics, and this induces the earlier onset of nonlinearity as the angular frequency decreases. The time−concentration superposition (TCS) was found to be valid in the terminal zone, which permitted the evaluation of ∼9 decades of dynamics in the mastercurve. The concentration dependence of the time− concentration shift factors (vertical and horizontal) was found to be in good agreement with the plateau moduli and the crossover frequency scaling. A concentration dependence of plateau modulus G N 0 ∼ C 2.29 is obtained from the dynamic tests. The plateau modulus scaling is consistent with the blob model for entangled polymer solutions. The terminal relaxation time shows a change like the unentangled-to-entangled crossover in synthetic polymer solutions from τ d ∼ C 1.1 and τ d ∼ C 3.53 at around 1 mg/mL (24C*). A very high concentration dependence of the zero-shear viscosity, η 0 ∼ C 5.5 , is estimated for the high-concentration samples. We interpret the concentration-dependent scaling to be in an entangled regime observed only in very high molecular weight solutions at sufficiently high concentrations. A Likhtman−McLeish model was used to fit the LVE with the constraint release parameter, c ν , fixed at 1 and 10. The Likhtman−McLeish model does not seem to capture all of the physical processes in the dynamics, and a good fit was not obtained, particularly for the higher-concentration samples though the fit quality improved with the greater constraint release parameter magnitude. Entanglement density predicted by the Likhtman−McLeish model scaled linearly with the entanglement density calculated by the blob model for solutions. The entangled dynamics is possibly nonreptative as reptation or its derivative models do not predict the observed strong nonlinearity and the high susceptibility of the system to strain.

Fluidification of entanglements by a DNA bending protein

“…To further characterise the viscoelastic properties of the system, we use the generalised Stokes-Einstein rela-tion (GSER) to compute the complex stress modulus [30] (see SI). The control sample (pure solution of λDNA at 1.5 mg/ml) displays a pronounced viscoelasticity, with a relaxation time τ 10 seconds and a high-frequency elastic plateau on the order of G p 1 Pa, in agreement with the values previously obtained via microrheology [27,31] and bulk rheology [32] on similar samples (Fig. 2d).…”

Some open challenges in polymer physics*

“…For the 1 mg/ml solution and the 45 kbp molecules, the linear chain entanglement density is approximately , though these estimates may be different depending on the choice of c* and scaling of entanglement density with concentration. [ 156 ] The important point to note from the table [ 153 ] is that for the low molecular weight material at both concentrations and the 45 kbp material at 0.1 mg/ml concentration, the diffusion coefficients are relatively weakly affected by molecular topology. However, for the entangled 45 kbp sample at 1 mg/ml, we see that the “pure” rings and the linear chains in the “pure” ring background both move at a much higher rate than either the linear chains in their own background or the rings in the linear background.…”

“…The results suggest a power law relationship of approximately for the range of parameters investigated. Roovers data [ 122,128 ] are same as from Figure 27A and the DNA data come from Kong et al [ 162 ] and from Banik et al [ 156 ]…”

“…We see in the figure that the linear DNA reaches the low frequency Newtonian regime near to 10 −3 rad/s while both the system with 15% linear chains and that with 50% linear chains remain on a power law‐like response over the entire frequency range tested. The ring mixture with 15% linear material has at least treble the zero shear viscosity of the pure linear [ 156 ] system while the 50% system shows a minimum of a 10‐fold increase. This increase is like the very large diffusion coefficient decrease seen in the same size DNA rings in a linear background concentration of 1 mg/ml.…”

“…The reasons for the larger enhancement in this DNA solution versus the synthetic polymer melts is not currently known, though it can be speculated that the very long linear DNA (contour length is approximately 16 × 10 −6 m) simply threads a very large number of rings, even though the nominal entanglement number is fairly small (). [ 156 ] It is important to further note that for a more concentrated system of = 2 mg/ml the viscosities of the 15% and 50% linear blends were lower than for the 100% linear solution [ 162 ] in the frequency range that could be investigated. Thus, it appears that one aspect of the ring/linear behavior is related to the total concentration of polymer, perhaps reflecting more efficient entanglement development when the concentration is low and the linear chains tend to thread the rings to greater effect.…”