Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

<div><p>We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales—from diffusion of molecular probes to macroscopic viscous flow—we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.</p></div

Comparison with the theoretical model.

<p>Bulk viscosity data for all the investigated solutions of a) PMAANa and b) PSSNa plotted according to Dobrynin’s theoretical model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref047" target="_blank">47</a>] based on de Gennes’ concept of scaling of electrostatic blobs [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref060" target="_blank">60</a>]—<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e007" target="_blank">Eq 5</a>. Panel b) includes also data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref061" target="_blank">61</a>]. Despite some deviations, the model seems to describe the data acceptably well.</p

Hydrodynamic radii of the probes used throughout the FCS experiments (<i>r</i>_p), along with the probe charges at the pH of phosphate buffer (7.4).

<p>Hydrodynamic radii of the probes used throughout the FCS experiments (<i>r</i>_p), along with the probe charges at the pH of phosphate buffer (7.4).</p

Macroviscosity measurements.

<p>Results of measurements of macroscopic viscosity (rotational rheometry) of aqueous solutions of a) PMAANa and b) PSSNa at ionic strength of 0.154 M and pH of 7.4. Good conformity with the model originally developed for neutral polymer solutions (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e003" target="_blank">Eq 3</a>, solid line) is observed in both cases. In panel b) literature data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.ref061" target="_blank">61</a>] are included (empty symbols). These data correspond to viscosity measurements on a 1200 kDa PSSNa sample at 0.01 M NaCl. This still falls within the high salt regime and the results follow the model proposed hereby.</p

Nanoviscosity measurements.

<p>Results of fluorescence correlation spectroscopy (FCS) measurements of probe diffusion rates in solutions of PMAANa of different molecular masses. The probes used were rhodamine dyes, apoferritin and TAMRA-labelled dextrans. Ionic strength was kept at 0.154 M. Diffusion coefficients were translated to effective viscosities experienced by the probes via <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e008" target="_blank">Eq 6</a>. The data are plotted according to the model from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161409#pone.0161409.e003" target="_blank">Eq 3</a>. All the probes are of neutral or negative electric charge (no electrostatic attraction to the polyelectrolyte chains).</p