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

The theory of orientational motion of a Brownian magnetic nanoparticle embedded in a viscoelastic medium and subjected to a time-dependent uniform magnetic field is developed. The rheology of the viscoelastic environment of the particle is modeled by the Jeffreys scheme, which under variation of a minimal number of parameters is able to resemble a wide range of soft materials: from a weakly structured (nearly Newtonian) polymer solution to a gel. It is shown that in the Jeffreys model, the diffusional orientational motion of a particle is a combination of two modes, which could be associated with a fast motion within the polymer mesh cell and a slow displacement that involves deformation of the mesh, respectively. The dependencies of the reference times of both relaxation modes on the Jeffreys viscous and elastic parameters and temperature are found. It turns out that in substantially viscoelastic media, the rate of the slow mode (it dominates in relaxation) quadratically depends on the matrix temperature. This effect does not have analogs in linearly viscous systems. For an ensemble of magnetic nanoparticles in viscoelastic and gel Jeffreys matrices: (1) the dynamic magnetic susceptibility is derived and evaluated both within an exact approach and in a simple approximation; (2) the problem of magnetic relaxometry, i.e., evolution of magnetization after step-wise turning off the field, is solved; (3) the specific power loss caused by viscous dissipation generated by the particles under an ac field is analyzed as a function of the rheological parameters. Results (1) and (2) provide simple models for magnetic nanorheology; consideration (3) advances the physics of magnetic hyperthermia in viscoelastic and gel-like media.