Thermodynamics of ferrofluids in applied magnetic fields

Abstract

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B 2 and B 3 ) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B 3 for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ 2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.

Thermodynamics of the Stockmayer fluid in an applied field

“…Choosing a factor of −1 means that the argument of the logarithm should remain positive, and therefore it should not accidentally turn negative at high values of ρ. The LFE theory has been tested against simulation results for DHSs with and without an applied field [44,45]. The LFE theory outperforms the PVE theory for this system.…”

“…A related approach is to recast a PVE of the Helmholtz free energy F in to a logarithmic form [44,45]. The Helmholtz free energy for a system of particles in an applied field can be written…”

“…From the theoretical standpoint, there are many approaches to the general problem of how to describe the thermodynamic and structural properties of dipolar fluids in applied fields, including density functional theory [38,39], integral equations [39][40][41], and thermodynamic perturbation theory [42]. The authors have developed virial expansions (VEs), and improvements thereon, that provide explicit expressions for thermodynamic and structural functions [43,44] which compare very well with computersimulation data. A simple resummation of the VE, based on a logarithmic form for the free energy, gives a convenient and accurate expression for the equation of state [44,45].…”

“…The authors have developed virial expansions (VEs), and improvements thereon, that provide explicit expressions for thermodynamic and structural functions [43,44] which compare very well with computersimulation data. A simple resummation of the VE, based on a logarithmic form for the free energy, gives a convenient and accurate expression for the equation of state [44,45]. Along the way, it has been emphasised that the basic definitions of the virial coefficients contain additional terms related to the field; this was anticipated in earlier work by additional terms related to intramolecular degrees of freedom [46,47].…”

The stress, surface spin and dipolar interaction in the diluted NiFe 2 O 4 nanoparticles by the SiO 2 matrix: Characterization and analyses

“…The ideal superparamagnetism must be no hysteresis and follows the classical Langevin behavior, i.e., the magnetization curves measured at different temperatures must superimpose when plotted against H/T [23]. To test whether it is the case above T B , the initial magnetizing curves were measured at different temperatures with the applied field (H) in the region 0-10,000 Oe for all samples; and M vs H/T curves are plotted in Fig.…”