Theory of structural transformations in ferrofluids: Chains and “gas-liquid” phase transitions

Abstract

We consider a ferrofluid consisting of identical spherical particles with a permanent magnetic moment. Under the assumption that linear flexible chains can appear in the ferrofluid, we estimate the distribution function of the number of particles inside the chain. The analysis is done and simple expressions for the size distribution function are obtained in asymptotics of a strong magnetic interaction between the particles inside one chain. We studied the influence of the linear chains on conditions and scenarios of bulk "gas-liquid" phase transition in the ensemble of the particles under an infinitely strong magnetic field. In order to study the influence of the chains on bulk "gas-liquid" phase transition in the ensemble of the particles, their chemical potential mu is calculated in the model of separate interacting particles as well as in the model with chains, taking into account the interaction between them. When the temperature is low enough, van der Waals loops appear on the plots of mu versus volume concentration phi of the particles in the first model; function mu(phi) increases monotonically in the second model for all examined temperatures. This means that the condensation "gas-liquid" phase transition can take place in the model of individual particles; however, formation of the chains in real ferrofluids prevents the appearance of this transition.

Two-stage kinetics of field-induced aggregation of medium-sized magnetic nanoparticles

“…Appropriate phase diagrams and equilibrium microstructures have been extensively studied theoretically and experimentally [37][38][39][40][41][42][43][44][45][46][47] . Kinetics of phase separation has been studied by light scattering by Socoliuc and Bica 48 for aqueous dispersions of nanoparticles (ferrofluids) and by Laskar et al 49 for nonaqueous ferrofluids.…”

Dynamics of strongly interacting Fermi gases of atoms in a harmonic trap

“…We take into account the quantum pressure by finding the optimal ground state energy [39] E 0 N = max γx,γy,γz…”

Magnetic Soret effect: Application of the ferrofluid dynamics theory

“…This assumption guarantees a nonzero chemical potential for H = 0 and is confirmed by calculations for MF with chains, where the magnetic part contributes additive to the total chemical potential [33]. The nonmagnetic part of the chemical potential is given by µ c = (…”

“…(2.9) allows a direct determination of µ m c if the magnetization M (H, ρ (1) , T ) is known without any assumption about the properties of the MF in contrast to [27,28,33,34]. According to these references the determination of the chemical potential needs the knowledge of quantities like the volume concentration of the nanoparticles [27,33] or the strength of the magnetodipole interaction [33] or the effective field experienced by a single particle in the MF [27,28,34]. Compared with the effort to evaluate these microscopic details, the advantage of the macroscopic approach of the FFD is apparent.…”