Ribbons of superparamagnetic colloids in magnetic field

Abstract

While the aggregation process of superparamagnetic colloids in strong magnetic field is well known on short time since a few decades, recent theoretical works predicted an equilibrium state reached after a long time. In this talk, we present experimental observations of this equilibrium state with a twodimensional system and we compare our data with the predictions of a pre-existing model. Above a critical aggregation size, a deviation between the model and the experimental data is observed. This deviation is explained by the formation of ribbon-shaped aggregates, due to lateral aggregation of chains. Interestingly, when the magnetic field is removed, particles then freely diffuse from their positions in the agglomerate. It is worthwhile to notice that all the particles initially have the same coordinate on the axis perpendicular to the initial chain. This configuration then enables the observer to study the one dimensional diffusion process, while actually seeing the underlying Brownian motion of the microscopic particles. Moreover, by studying the evolution of the particles distribution, a measurement of the diffusion coefficient is performed. With a calibration using a fluid of known viscosity, this process allows measurement of local viscosities through the Stokes-Einstein relation.

Self-assembly processes of superparamagnetic colloids in a quasi-two-dimensional system

“…It is noticed that in Ref. [12] the approximation β m ≈ is employed, i.e., without considering averages on the magnetic potential, which also will be used in the present work. In the case φ 0 e β m 1, the decrease of the interaction energy ( m → 0) in Eq.…”

“…[12,13] the aggregation process of superparamagnetic colloids under an external magnetic field has been studied, with an interesting finding: in thermodynamic equilibrium the formation of chains leads to stable structures such as ribbons when the magnetic field is increased. Superparamagnetic colloids under a constant magnetic field B = Bŷ in a two-dimensional system building arrays of particles oriented in the direction of the magnetic field have been found experimentally and in numerical simulations [14,15].…”

“…It is noticed that the latter approach depends on a free parameter h (the effective interaction range averaged over the attractive region), and the long time saturated regime is not addressed. Later, the transient and long range equilibrium dynamics are obtained with Langevin dynamics simulations [14,19,20] and in experimental results [12,13,16,17,21]. The evolution of the mean length of the aggregatess(t) scales with t z [15] until the saturation regime, where it converges to a constant value [s(t) →s] in thermodynamic equilibrium after a transient time (t → t sat ).…”

“…Recently [12], in addition to chains, ribbons are found when the magnetic field magnitude is increased in a quasitwo-dimensional chamber. In this regime the experiment is very sensitive to external noise.…”

“…The system is quasi-two-dimensional, the diameter of the cylindrical chamber is 5 mm, with a height of approximately 50 μm, the radius of the particles is 0.6 ± 0.3 μm, then the aspect ratio of the system is about 10 −2 . The present work will be focused on describing recent experimental findings [12], in the range of parameters of stable ribbons in thermodynamic equilibrium. The most important results in this paper are summarized in Sec.…”