Magnetic response of a viscoelastic ferrodispersion: From a nearly Newtonian ferrofluid to a Jeffreys ferrogel

Rotational dynamics of magnetic nanoparticles in different matrix systems

Dynamic magnetic measurements on magnetic nanoparticle (MNP) samples have been widely used for the determination of structural MNP parameters as well as for the realization of bioassays. On the other hand, proposed that the MNPs are thermally blocked, i.e., that the dynamics are dominated by the Brownian rotation, and knowing the distribution of their hydrodynamic size, information on the matrix properties can be obtained. In contrast to conventional rheology, the local environment of the MNPs is sensed on the nanoscale so that important information on the embedding of MNPs in the matrix and thus the particle-matrix interaction is obtained. Depending on the characteristic length scales of the matrix and the size of the MNPs, rheological parameters, such as viscosity and shear modulus, derived from nanorheological measurements can differ from the values obtained from conventional rheology. To measure the MNP dynamics, different experimental techniques can be applied. In this contribution, the focus lies on ac susceptometry and fluxgate magnetorelaxometry. The analysis of the complex ACS spectra is generally carried out within a modified Debye model. Different approaches for the estimation of rheological parameters from the complex ACS spectra will be presented. Two model systems will exemplarily be discussed in detail. As a Newtonian matrix system, water-glycerol mixtures were studied. It is demonstrated that the dynamic viscosity can accurately be estimated from ACS measurements on well thermally blocked single-core as well as on multicore MNP systems, which include Brownian and Néel dynamics. As a viscoelastic matrix system, aqueous gelatin solutions were studied. Gelatin is known to be a Voigt-Kelvin model system, in which elastic and viscous forces are parallel. In particular, we studied the gelation dynamics by repetitive measurements of the complex ACS spectrum. Different approaches to derive viscosity and shear modulus are applied and compared. In order to identify magnetoviscous effects in dynamic magnetic measurements, the magnetic field dependence of the Brownian relaxation time has to be eliminated. ACS measurements on various sufficiently strongly diluted aqueous MNP suspensions were performed in dependence of ac field amplitude and superimposed dc field strength and compared to theory. Excellent agreement was found.

Magnetic torque-driven deformation of Ni-nanorod/hydrogel nanocomposites

Nickel (Ni) nanorods were prepared by the anodized aluminum oxide (AAO) template method and dispersed in poly(acrylamide) (PAM) hydrogels. The deformation of the magnetoresponsive composites was studied with particular attention to the consequences of finite magnetic shape anisotropy as compared to rigid dipoles on the field-dependent torque. For comparison with experiments, the composite was described as an elastic continuum with a local magnetic torque density, applied by discrete particles and determined by the local orientation of their magnetic anisotropy axis with respect to the magnetic field. The mean magnetic moment of the single domain particles m and their volume density in the composite φ vol were derived from the static field-dependent optical transmission (SFOT) of linear polarized light. The mechanical coupling between the particles and their viscoelastic environment was retrieved from the rotational dynamics of the nanorods using oscillating field-dependent optical transmission (OFOT) measurements. Field- and orientation-dependent magnetization measurements were analyzed using the Stoner–Wohlfarth (SW) model and a valid parameter range was identified by introducing an effective anisotropy constant K A as a new empirical model parameter. This adapted SW-model for quantitative description of the field- and orientation dependence of the magnetic torque was validated by measuring the local rotation of nanorods in a soft elastic hydrogel. Finally, torsional and bending deformation of thin magnetically textured composite filaments were computed and compared with experiments.

Free and confined Brownian motion in viscoelastic Stokes-Oldroyd B fluids

We linearize the Stokes-Oldroyd B model for small perturbations and instantaneous hydrodynamic friction to simulate the environment for a free and confined Brownian particle. We use the standard Green's function approach to determine the viscoelasticity, and show that the expression obtained for the frequency dependent viscosity is similar to that given by the Jeffrey's model, though the latter describes viscoelasticity by the bulk storage and loss moduli that is represented by a complex elastic modulus [Formula: see text] of the fluid concerned. In contrast, we consider the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually, and determine an expression for frequency-dependent viscosity that would be useful for microrheology performed from Brownian trajectories measured in experiments. Finally, we evaluate the trajectory of a free Brownian particle in a viscoelastic environment using our formalism, and calculate various important parameters quantifying Brownian dynamics, which we then extend to the particle confined in a harmonic potential as provided by optical tweezers.

Magnetorelaxometry in the Presence of a DC Bias Field of Ferromagnetic Nanoparticles Bearing a Viscoelastic Corona

With allowance for orientational Brownian motion, the magnetorelaxometry (MRX) signal, i.e., the decay of magnetization generated by an ensemble of ferromagnet nanoparticles, each of which bears a macromolecular corona (a loose layer of polymer gel) is studied. The rheology of corona is modelled by the Jeffreys scheme. The latter, although comprising only three phenomenological parameters, enables one to describe a wide spectrum of viscoelastic media: from linearly viscous liquids to weakly-fluent gels. The "transverse" configuration of MRX is considered where the system is subjected to a DC (constant bias) field, whereas the probing field is applied perpendicularly to the bias one. The analysis shows that the rate of magnetization decay strongly depends on the state of corona and slows down with enhancement of the corona elasticity. In addition, for the case of "transverse" MRX, we consider the integral time, i.e., the characteristic that is applicable to relaxation processes with an arbitrary number of decay modes. Expressions for the dependence of the integral time on the corona elasticity parameter and temperature are derived.

Magnetic susceptibility, nanorheology, and magnetoviscosity of magnetic nanoparticles in viscoelastic environments

While magnetic nanoparticles suspended in Newtonian solvents (ferrofluids) have been intensively studied in recent years, the effects of viscoelasticity of the surrounding medium on the nanoparticle dynamics are much less understood. Here we investigate a mesoscopic model for the orientational dynamics of isolated magnetic nanoparticles subject to external fields, viscous and viscoelastic friction, as well as the corresponding random torques. We solve the model analytically in the overdamped limit for weak viscoelasticity. By comparison to Brownian dynamics simulations we establish the limits of validity of the analytical solution. We find that viscoelasticity not only slows down the magnetization relaxation, shifts the peak of the imaginary magnetic susceptibility χ^{″} to lower frequencies, and increases the magnetoviscosity but also leads to nonexponential relaxation and a broadening of χ^{″}. The model we study also allows us to test a recent proposal for using magnetic susceptibility measurements as a nanorheological tool using a variant of the Germant-DiMarzio-Bishop relation. We find for the present model and certain parameter ranges that the relation of the magnetic susceptibility to the shear modulus is satisfied to a good approximation.