Nonextensivity in magnetic nanoparticle ensembles

Abstract

A superconducting quantum interference device and Faraday rotation technique are used to study dipolar interacting nanoparticles embedded in a polystyrene matrix. Magnetization isotherms are measured for three cylindrically shaped samples of constant diameter but various heights. Detailed analysis of the isotherms supports Tsallis' conjecture of a magnetic equation of state that involves temperature and magnetic field variables scaled by the logarithm of the number of magnetic nanoparticles. This unusual scaling of thermodynamic variables, which are conventionally considered to be intensive, originates from the nonextensivity of the Gibbs free energy in three-dimensional dipolar interacting particle ensembles. Our experimental evidence for nonextensivity is based on the data collapse of various isotherms that require scaling of the field variable in accordance with Tsallis' equation of state.

Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics

“…Indeed, the correctness of the scaling appearing in Eq. (9) for nonstandard systems, i.e., for those with θ = 0, has been profusely verified for several systems in the literature [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]; one of them is going to be discussed in Section 4 below. Furthermore, it has been shown that such scalings preserve important thermodynamical relations such as the Euler and Gibbs-Duhem [21].…”

Magnetic nanoparticles: recent advances in synthesis, self-assembly and applications

“…The samples creating the m vs. T data shown in Fig. 18 142 From measurements like these ZFC/FH and FC m vs. T curves together with magnetic isothermal m vs. H measurements and the investigation of thermoremanent magnetization one can determine information such as the nanoparticle number, the moment per particle, and some qualitative estimates of the anisotropy energy which determines the blocking temperature of the nanoparticle ensemble.…”

“…18 shows a prototypical magnetometric investigation of nearly interaction free g-Fe 2 O 3 nanoparticles which have been randomly dispersed in a polystyrene matrix. 142 The particles were produced by a synthetic strategy, more specifically, via thermal decomposition of metal carbonyls in the presence of appropriate surfactants. 82,145,146 The procedure is known to result in highly uniform nanoparticles.…”

Coordination Polymers Based on Amphiphilic Oligomeric Silsesquioxanes and Transition Metal Ions (Co2 +, Ni2+): Structure and Stimuli‐Responsive Properties

“…The curves in Figure 8 show a significant increase in the magnetic properties with an increase in the concentration of Ni or Co and a behavior similar to superparamagnetic behavior, typical of metal nanoparticles. [ 66 ]…”