Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology.

In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length Lh between 200 nm and 650 nm, and cobalt ferrite spheres with diameter dh between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration Rg or the correlation length ξ of the polymer solution.

Size effects on rotational particle diffusion in complex fluids as probed by Magnetic Particle Nanorheology.

Rheological approaches based on micro- or nanoscopic probe objects are of interest due to the low volume requirement, the option of spatially resolved probing, and the minimal-invasive nature often connected to such probes. For the study of microstructured systems or biological environments, such methods show potential for investigating the local, size-dependent diffusivity and particle-matrix interactions. For the latter, the relative length scale of the used probes compared to the size of the structural units of the matrix becomes relevant. In this study, a rotational-dynamic approach based on Magnetic Particle Nanorheology (MPN) is used to extract size- and frequency-dependent nanorheological properties by using an otherwise well-established polymer model system. We use magnetically blocked CoFe2O4 nanoparticles as tracers and systematically vary their hydrodynamic size by coating them with a silica shell. On the polymer side, we employ aqueous solutions of poly(ethylene glycol) (PEG) by varying molar mass M and volume fraction φ. The complex Brownian relaxation behavior of the tracer particles in solutions of systematically varied composition is investigated by means of AC susceptometry (ACS), and the results provide access to frequency dependent rheological properties. The size-dependent particle diffusivity is evaluated based on theoretical descriptions and macroscopic measurements. The results allow the classification of the investigated compositions into three regimes, taking into account the probe particle size and the length scales of the polymer solution. While a fuzzy cross-over is indicated between the well-known macroscopic behavior and structurally dominated spectra, where the hydrodynamic radius is equal to the radius of gyration of the polymer (rh ∼ Rg), the frequency-related scaling behavior is dominated by the correlation length ξ respectively by the tube diameter a in entangled solutions for rh < Rg.

Local dynamics in supramolecular polymer networks probed by magnetic particle nanorheology.

Transient supramolecular polymer networks are promising candidates as soft self-healing or stimuli-sensitive materials. In this paper, we employ a novel nanorheological approach, magnetic particle nanorheology (MPN), in order to better understand the local dynamic properties of model supramolecular networks from a molecular point of view. Hence, the bond strength between four-arm star-shaped polyethylene glycol (PEG) functionalized at the four extremities with terpyridine ligands is tuned by implementing different metal ions with variable complexation affinities for the ligand. We show that MNP allows for the evaluation of the strength and connectivity of the polymer networks by the estimation of relaxation times, mesh size, and also the viscoelastic properties of these materials. These results are compared and complemented to former outcomes on these systems that were obtained by macroscopic analytical methods. A clear dependence between the strength of the metal-ligand complex and the local dynamics of the polymeric network is observed by the nanorheological approach, which is in good agreement with previous predictions related to the complex formation constants.