Evidence that self-similar microrheology of highly entangled polymeric solutions scales robustly with, and is tunable by, polymer concentration

• Published in: arXiv.org
• Main Authors: Seim, Ian, Cribb, Jeremy A, Newby, Jay M, Vasquez, Paula, Lysy, Martin, est, M Gregory, Hill, David B
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.10.2018
• Subjects: Beads; Human behavior; Hyaluronic acid; Hydrogels; Mucus; Nanoparticles; Polyethylenes; Polymers; Power law; Rheological properties; Rheology; Scaling; Self-similarity; Stiffness
• ISSN: 2331-8422

We report observations of a remarkable scaling behavior with respect to concentration in the passive microbead rheology of two highly entangled polymeric solutions, polyethylene oxide (PEO) and hyaluronic acid (HA). This behavior was reported previously [Hill et al., PLOS ONE (2014)] for human lung mucus, a complex biological hydrogel, motivating the current study for synthetic polymeric solutions PEO and HA. The strategy is to identify, and focus within, a wide range of lag times \({\tau}\) for which passive micron diameter beads exhibit self-similar (fractional, power law) mean-squared-displacement (MSD) statistics. For lung mucus, PEO at three different molecular weights (Mw), and HA at one Mw, we find ensemble-averaged MSDs of the form \({\langle}{\Delta}r^{2}({\tau}){\rangle} = 4D_{\alpha}{\tau}^{\alpha}\), all within a common band, [1/60 sec, 3 sec], of lag times \({\tau}\). We employ the MSD power law parameters \((D_{\alpha},{\alpha})\) to classify each polymeric solution over a range of highly entangled concentrations. By the generalized Stokes-Einstein relation, power law MSD implies power law elastic \(G'({\omega})\) and viscous \(G''({\omega})\) moduli for frequencies \(1/{\tau}\), [0.33 sec\(^{-1}\), 60 sec\(^{-1}\)]. A natural question surrounds the polymeric properties that dictate \(D_{\alpha}\) and \({\alpha}\), e.g. polymer concentration c, Mw, and stiffness (persistence length). In [Hill et al., PLOS ONE (2014)], we showed the MSD exponent \({\alpha}\) varies linearly, while the pre-factor \(D_{\alpha}\) varies exponentially, with concentration, i.e. the semi-log plot, \((log(D_{\alpha}),{\alpha})(c)\) of the classifier data is collinear. Here we show the same result for three distinct Mw PEO and HA at a single Mw. Future studies are required to explore the generality of these results for polymeric solutions, and to understand this scaling behavior with polymer concentration.