Comment on "Algebraic perturbation theory for polar fluids: A model for the dielectric constant"

Ferrofluids and bio-ferrofluids: looking back and stepping forward

Ferrofluids investigated along for about five decades are ultrastable colloidal suspensions of magnetic nanoparticles, which manifest simultaneously fluid and magnetic properties. Their magnetically controllable and tunable feature proved to be from the beginning an extremely fertile ground for a wide range of engineering applications. More recently, biocompatible ferrofluids attracted huge interest and produced a considerable increase of the applicative potential in nanomedicine, biotechnology and environmental protection. This paper offers a brief overview of the most relevant early results and a comprehensive description of recent achievements in ferrofluid synthesis, advanced characterization, as well as the governing equations of ferrohydrodynamics, the most important interfacial phenomena and the flow properties. Finally, it provides an overview of recent advances in tunable and adaptive multifunctional materials derived from ferrofluids and a detailed presentation of the recent progress of applications in the field of sensors and actuators, ferrofluid-driven assembly and manipulation, droplet technology, including droplet generation and control, mechanical actuation, liquid computing and robotics.

Linear and nonlinear magnetic properties of ferrofluids

Within a high-magnetic-field approximation, employing Ruelle's algebraic perturbation theory, a field-dependent free-energy expression is proposed which allows one to determine the magnetic properties of ferrofluids modeled as dipolar hard-sphere systems. We compare the ensuing magnetization curves, following from this free energy, with those obtained by Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] as well as with new corresponding Monte Carlo simulation data. Based on the power-series expansion of the magnetization, a closed expression for the magnetization is also proposed, which is a high-density extension of the corresponding equation of Ivanov and Kuznetsova. From both magnetization equations the zero-field susceptibility expression due to Tani et al. [Mol. Phys. 48, 863 (1983)] can be obtained, which is in good agreement with our MC simulation results. From the closed expression for the magnetization the second-order nonlinear magnetic susceptibility is also derived, which shows fair agreement with the corresponding MC simulation data.

The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.

Relative Permittivity of Polar Liquids. Comparison of Theory, Experiment, and Simulation

A molecular-based second-order perturbation theory is applied to calculate the relative permittivity of polar liquids. Our basic model is the dipolar hard sphere fluid. The main purpose of this work is to propose various approaches to take into account the molecular polarizability. In the continuum approach, we apply the Kirkwood-Fröhlich equation and use the high-frequency relative permittivity. The Kirkwood g-factor representing molecular correlations is calculated by a perturbation theory. In the molecular approach, the molecular polarizability is built into the model on the molecular level (the polarizable dipolar hard sphere fluid). To calculate the relative permittivity of this system, an equation obtained from a renormalization procedure is used. In both approaches, we apply a series expansion for the relative permittivity and show that these series expansions give results in better agreement with simulation data than the original equations. After testing our theoretical equations against our own Monte Carlo simulation results, we compare the results obtained from our theoretical equations and simulations to experimental data for amines, ethers, and halogenated, sulfur, and hydroxy compounds. We propose a procedure to calculate potential parameters (hard sphere diameter, reduced polarizability, and reduced dipole moment) from experimental data such as the permanent dipole moment, refractive index, density, and temperature. We show that for compounds of low relative permittivity the polarizable dipolar hard sphere (PDHS) model and the continuum approach give reasonable results. For nonassociative liquids of higher relative permittivity, the PDHS model overestimates experimental data due to unsatisfactory representation of the shape of the molecules. In the case of associative liquids, the PDHS model works well, and in some cases it underestimates the experimental values due to the unsatisfactory treatment of electrostatic interactions.

Magnetic properties and structure of polydisperse ferrofluid models

The influence of polydispersity on the equilibrium properties of dipolar systems with short range repulsive interactions (modeled by a shifted and truncated Lennard-Jones pair potential) is studied by means of canonical Monte Carlo simulation and a high field approximation perturbation theory. The particle concentrations and the average magnetic moments of the investigated systems are typical of real ferrofluids. The magnetization curves are calculated and the microstructures are analyzed as a function of density, and the obtained results are compared with the data determined in the monodisperse equivalents of the systems. At weak and moderate magnetic fields the magnetization is found to be generally higher in the polydisperse system than in the corresponding monodisperse one. Our findings for the magnetic properties can partly be explained by the structural characteristics obtained from the simulations.

Reply to "Comment on 'Algebraic perturbation theory for polar fluids: A model for the dielectric constant' "

In their Comment [Phys. Rev. E 62, 8842 (2000)] Szalai et al. use the "Fourier-transform-convolution method" to correct the two three-body integrals entering our algebraic perturbation theory for polar fluids [Phys. Rev. E 59, 5085 (1999)]. We present an alternative analytical calculation of these integrals that is more transparent than that of Szalai et al. Compared with the original expression for the dielectric constant [Phys. Rev. E 59, 5085 (1999)] the corrected one demonstrates a better agreement with the simulation data for low and moderate values of the coupling constant.