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Register a new userStructure of polydisperse inverse ferrofluids: Theory and computer simulation
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By using theoretical analysis and molecular dynamics simulations, we investigate the structure of colloidal crystals formed by nonmagnetic microparticles (or magnetic holes) suspended in ferrofluids (called inverse ferrofluids), by taking into account the effect of polydispersity in size of the nonmagnetic microparticles. Such polydispersity often exists in real situations. We obtain an analytical expression for the interaction energy of monodisperse, bidisperse, and polydisperse inverse ferrofluids. Body-centered tetragonal (bct) lattices are shown to possess the lowest energy when compared with other sorts of lattices and thus serve as the ground state of the systems. Also, the effect of microparticle size distributions (namely, polydispersity in size) plays an important role in the formation of various kinds of structural configurations. Thus, it seems possible to fabricate colloidal crystals by choosing appropriate polydispersity in size.
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Taking into account the structural transition and long-range interaction (lattice effect), we resort to the Ewald-Kornfeld formulation and developed Maxwell-Garnett theory for uniaxially anisotropic suspensions to calculate the effective permeability of inverse ferrofluids. And we also consider the effect of volume fraction to the magnetophoretic force on the nonmagnetic spherical particles submerged in ferrofluids in the presence of nonuniform magnetic field. We find that the coupling of ac and dc field case can lead to fundamental and third harmonic response in the effective magnetophoresis and changing the aspect ratio in both prolate and oblate particles can alter the harmonic and nonharmonic response and cause the magnetophoretic force vanish.
Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from simulations. In this paper I put the DEFM on firm theoretical ground by deriving it within the framework of dynamical density functional theory (DDFT), in which the relevant part of correlation-induced free energy is approximated by a function of the instantaneous magnetization. The DEFM is generalized to inhomogeneous finite-size samples for which the macroscopic and mesoscopic scale separation is nontrivial due to the presence of long-range dipole-dipole interactions. The demagnetizing field naturally emerges from microscopic considerations and is consistently accounted for. The resulting particle dynamics on the mesoscopic scale only involves macroscopically local quantities such as local magnetization and Maxwell field. Nevertheless, the local demagnetizing field essentially couples to magnetization at distant macroscopic locations. Thus, a two-scale parallel algorithm, involving information transfer between different macroscopic locations, can be applied to fully resolve particle rotational dynamics in an inhomogeneous sample. I also derive the DEFM for polydisperse ferrofluids, in which the dynamics of particles belonging to different species can be strongly coupled to each other. I discuss the underlying assumptions in obtaining a thermodynamically consistent polydisperse magnetization relaxation equation, which is of the same generic form as that for monodisperse ferrofluids. The theoretical advances presented in this paper are important for both qualitative understanding and quantitative modeling of ferrofluid dynamics.
Ferrofluids belong to an important class of highly functional soft matter, benefiting from their magnetically controllable physical properties. Therefore, it is of central importance to quantitatively predict the dynamic magnetic response of ferrofluids. Traditional dynamic theories, however, are often restricted to the near-equilibrium regime and/or only apply to nearly ideal ferrofluids that are monodisperse, dilute enough, and weakly interacting. In this paper I develop a self-consistent and nonperturbative dynamical mean field theory for typical ferrofluids which are often polydisperse, concentrated, and strongly interacting, possibly driven far from equilibrium. I obtain a general nonperturbative expression for the dynamic magnetic susceptibility, quantitatively agreeing with the spectra obtained from Brownian Dynamics simulations on both mono- and bidisperse samples. Furthermore, I derive a generic magnetization relaxation equation (MRE) for both mono- and polydisperse ferrofluids by employing the projection operator technique in nonequlibrium statistical mechanics. This MRE is in simple closed form and independent of which model is employed to approximate the equilibrium magnetization curve. Existing models can be recovered as low-order approximations of my generic and nonperturbative MRE. My theory can play a key role in studying the dynamics of ferrofluids and other polar fluids. It may also have substantial and immediate consequences to various ferrofluid applications.
The dynamic critical behavior of isotropic Heisenberg ferromagnets with a planar free surface is investigated by means of field-theoretic renormalization group techniques and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed. The relevant boundary terms of the action of the associated dynamic field theory are identified, the implied boundary conditions are derived, and the renormalization of the model in $d<6$ bulk dimensions is clarified. Two distinct renormalization schemes are utilized. The first is a massless one based on minimal subtraction of dimensional poles and the dimensionality expansion about $d=6$. To overcome its problems in going below $d=4$ dimensions, a massive one for fixed dimensions $dle 4$ is constructed. The resulting renormalization group (or Callan Symanzik) equations are exploited to obtain the scaling forms of surface quantities like the dynamic structure factor. In conjunction with boundary operator expansions scaling relations follow that relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar emph{static} bulk and surface exponents. To test the predicted scaling forms and scaling-law expressions for the critical exponents involved, accurate computer-simulation data are presented for the dynamic surface structure factor. These are in conformity with our predictions.
The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbulls empirical rule. Our first estimates for the reduced interfacial free energy, $sigma_{0,bcc}$, between coexisting equilibrium uid and bcc-crystal phases are on the order of a few $k_BT$. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, $sigma_0$ also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.
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