Onset of Non-Continuum Effects in Microrheology of Entangled Polymer Solutions

Abstract

Microrheology has emerged as a powerful approach for elucidating mechanical properties of soft materials and complex fluids, especially biomaterials. In this technique, embedded microspheres are used to determine viscoelastic properties via generalized Stokes−Einstein relations, which assume the material behaves as a homogeneous continuum on the length scale of the probe. However, this condition can be violated if macromolecular systems form characteristic length scales that are larger than the probe size. Here we report observations of the onset of this effect in DNA solutions. We use microspheres driven with optical tweezers to determine the frequency dependence of the linear elastic and viscous moduli and their dependence on probe radius and DNA length. For well-entangled DNA, we find that the threshold probe radius yielding continuum behavior is ∼3× the reptation tube diameter, consistent with recent theoretical predictions. Notably, this threshold is significantly larger than the mesh size of the polymer network, and larger than typical probe sizes used in microrheology studies.

Optical Tweezers Microrheology Maps the Dynamics of Strain-Induced Local Inhomogeneities in Entangled Polymers

“…This assumption is valid if the DNA molecules in our system do not experience any restriction that forbids their normal relaxation or diffusion dynamics. This criterion is evident in previously reported studies on similar systems [34,38], as well the results we present here, thereby justifying the application of a Fickian diffusion model in our analytical calculations. With these assumptions and simplifications our analytical calculations estimate the homogenization dynamics of the density-inhomogeneity field and establish that this process is indeed the origin of the relaxation times τ1 and τ4.…”

“…Double-stranded 115 kbp (38 μm) DNA was prepared, as previously described [33], by replication of a cloned bacterial artificial chromosome construct in E. coli, followed by extraction, purification, and restriction enzyme treatment to convert supercoiled constructs to linear form. Linear DNA constructs were resuspended in aqueous buffer [10 mM Tris-HCl (pH 8), 1 mM EDTA, 10 mM NaCl] to a concentration of 1.0 mg/ml, corresponding to ~40c* [34] and ~7x the critical entanglement concentration ce [38]. The predicted entanglement tube diameter for this system is dT ≈ 680 nm and the mesh size is ≈ 140 nm [33][34][35][36].…”

Entanglement Density Tunes Microscale Nonlinear Response of Entangled Actin

“…[12][13][14] For example, we previously showed that for flexible polymers, active microrheology reported macroscopic properties for probe sizes > 3x the tube diameter of the network. [15][16][17] Nonetheless, flows induced by microrheology are in fact non-uniform, and can lead to polymer buildup at the leading edge and depletion at the trailing edge of a moving probe leading to unique microscale visoelastic regimes not present at the macroscale, 18,19 leading to unique microscale viscoelastic regimes not present at the macroscale. 19,20 However, it is these discrepancies between the two techniques that can actually shed light on the microscale structures of biopolymer networks and varying lengthscale-dependent mechanical regimes.…”

Crowding Induces Entropically-Driven Changes to DNA Dynamics That Depend on Crowder Structure and Ionic Conditions

“…Unless indicated, NaCl concentration is 10 mM. The viscosity of each crowded solution was measured using optical tweezers microrheology as described previously [40,74].…”