Rheology and orientational distributions of rodlike particles with magnetic moment normal to the particle axis for semi-dense dispersions (analysis by means of mean field approximation)

We have considered a semi-dense dispersion composed of ferromagnetic rodlike particles with a magnetic moment normal to the particle axis to investigate the rheological properties and particle orientational distribution in a simple shear flow as well as an external magnetic field. We have adopted the mean field approximation to take into account magnetic particle-particle interactions. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the magnetic moment of the rodlike particle is strongly restricted in the field direction, so that the particle points to directions normal to the flow direction (and also to the magnetic field direction). This characteristic of the particle orientational distribution is also valid for the case of a strong particle-particle interaction, as in the strong magnetic field case. To the contrary, for a weak interaction among particles, the particle orientational distribution is governed by a shear flow as well as an applied magnetic field. When the magnetic particle-particle interaction is strong under circumstances of an applied magnetic field, the magnetic moment has a tendency to incline to the magnetic field direction more strongly. This leads to the characteristic that the viscosity decreases with decreasing the distance between particles, and this tendency becomes more significant for a stronger particle-particle interaction. These characteristics concerning the viscosity are quite different from those for a semi-dense dispersion composed of rodlike particles with a magnetic moment along the particle direction.     

Transport coefficients and orientational distributions of spheroidal particles with magnetic moment normal to the particle axis (Analysis for an applied magnetic field normal to the shear plane)

We have investigated the influence of the magnetic field strength, shear rate, and rotational Brownian motion on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. The rodlike particle is modeled as a magnetic spheroidal particle which has a magnetic moment normal to the particle axis; such a particle may typically be a hematite particle. In the present study, an external magnetic field is applied in the direction normal to the shear plane of a simple shear flow. The basic equation of the orientational distribution function has been derived from the balance of torques and solved numerically. The results obtained here are summarized as follows. Although the orientational distribution function shows a sharp peak in the shear flow direction for a very strong magnetic field, such a peak is not restricted to the field direction alone, but continues in every direction of the shear plane. This is due to the characteristic particle motion that the particle can rotate around the axis of the magnetic moment in the shear plane, although the magnetic moment nearly points to the magnetic field direction. This particle motion in the shear plane causes negative values of the viscosity due to the magnetic field. The viscosity decreases, attains a minimum value, and then converges to zero as the field strength increases. Additionally, the diffusion coefficient is significantly influenced by such characteristic particle motion in the shear plane for a strong magnetic field.     

Transport coefficients and orientational distributions of rodlike particles with magnetic moment normal to the particle axis under circumstances of a simple shear flow

We have investigated the influences of the magnetic field strength, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of rodlike particles of a dilute colloidal dispersion. This dispersion is composed of ferromagnetic spheroidal particles with a magnetic moment normal to the particle axis. In the present analysis, these spheroidal particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved numerically. The results obtained here are summarized as follows. For a very strong magnetic field, the rodlike particle is significantly restricted in the field direction, so that the particle points to a direction normal to the flow direction (and also to the magnetic field direction). However, the present particle does not exhibit a strong directional characteristic, which is one of the typical properties for the previous particle with a magnetic moment parallel to the particle axis. That is, the particle can rotate around the axis of the magnetic moment, although the magnetic moment nearly points to the field direction. The viscosity significantly increases with the field strength, as in the previous particle model. The particle of a larger aspect ratio leads to the larger increase in the viscosity, since such elongated particles induce larger resistance in a flow field. The diffusion coefficient under circumstances of an applied magnetic field is in reasonable agreement between theoretical and experimental results.     

Orientational Brownian motion in a viscoelastic medium

A model has been proposed for the complete (2D) orientational Brownian motion of axially symmetric particles in a Kelvin viscoelastic medium. It has been shown that the elastic response of the carrier medium can be correctly determined by introducing an additional variable, the moment elastic forces, which, together with the particle-orientation vector, composes the complete set of phase variables of a system. A set of stochastic equations (Langevin equations) has been derived for these values. This set has been employed to construct, under the effective field approximation, a simple set of moment equations describing the magnetization dynamics of a ferrogel, i.e., a dispersion of single-domain nanoparticles in a gel matrix. The theoretical results qualitatively agree with the data of magnetic microrheology of gelatin-based ferrogels.     

Rheological properties and particle behaviors of a non-dilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow (analysis by means of mean-field approximation)

We have investigated the rheological properties and the orientational distributions of particles of a non-dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The mean-field approximation is applied to take into account the interactions between spherocylinder particles. The basic equation of the orientational distribution function has been derived from the balance of the torques (including the term due to the mean field approximation) acting on the particle in an applied magnetic field; this is an integrodifferential equation. Then, the governing equation has been solved by means of the method of successive approximation and Galerkin's method. The results obtained here are summarized as follows. For the case of strong magnetic interactions between particles, the particle exhibits a sharp peak of the orientational distribution even for a weak applied magnetic field. In this case, the mean magnetic moment of the particle becomes large, which leads to strong interactions between the applied magnetic field and the particle. Thus, the particle tends to point to the magnetic filed direction under these situations. Also, in this case, a large increase in viscosity is obtained due to such a restriction concerning the particle orientation.     

On the behavior of an oblate spheroidal hematite particle in a simple shear flow under a uniform magnetic field applied in the flow direction

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. A hematite particle with oblate spheroidal shape has an important characteristic; that is, it is magnetized in a direction normal to the particle axis. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the various factors. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.     

Molecular dynamics simulation of the nematic liquid crystal phase in the presence of an intense magnetic field

The influence of an intense external field on the dynamics of the nematic liquid crystal phase is investigated using a molecular dynamics simulation for the Gay-Berne nematogen under isobaric-isothermal conditions. The molecular dynamics as a function of the second-rank orientational order parameter P<2> for a system consisting of a nematic liquid crystal in the presence of an intense magnetic field is compared with that of a similar system without the field. The translational motion of molecules is determined as a function of the translational diffusion coefficient tensor and the anisotropy and compared with the values predicted theoretically. The rotational dynamics of molecules is analyzed using the first- and the second-rank orientational time correlation functions. The translational diffusion coefficient parallel with respect to the director is constrained by the intense field, although the perpendicular one is decreased as the P<2> is increased, just as it is in the system without the field. However, no essential effect of the strong magnetic field is observed in the rotational molecular dynamics. Further, the rotational diffusion coefficient parallel with respect to the director obtained from the first-rank orientational time correlation function in the simulation is qualitatively in agreement with that in the real nematic liquid crystalline molecules. The P<2> dependence of the rotational diffusion coefficient for the system with the intense magnetic field shows a tendency similar to that for the system without the field.     

3D Monte Carlo simulations of a magnetic disk-like particle dispersion

We have investigated the aggregate structures of a colloidal dispersion composed of ferromagnetic disk-like particles with a magnetic moment normal to the particle axis at the particle center, by means of 3D Monte Carlo simulations. Such disk-like particles have been modeled as a circular disk-like particle with the side section shape of spherocylinder. We have attempted to clarify the influences of the magnetic field strength, magnetic interactions between particles and volumetric fraction of particles. In order to discuss quantitatively the aggregate structures of clusters, we have focused on the radial distribution and orientational pair correlation functions, etc. For no applied magnetic field cases, long column-like clusters come to be formed with increasing magnetic particle–particle interactions. The internal structures of these clusters clearly show that the particles incline in a certain direction and their magnetic moments alternate in direction between the neighboring particles in the clusters. For applied magnetic field cases, the magnetic moment of each particle inclines in the magnetic field direction and therefore the column-like clusters are not formed straightforwardly. If the magnetic field is much stronger than magnetic particle–particle interactions, the particles do not have a tendency to form the clusters. As the influence of magnetic particle–particle interactions is significantly strong, thick chain-like clusters or column-like clusters or brick-wall-like clusters come to be formed along the magnetic field direction.     

Influence of magnetic interactions between clusters on particle orientational characteristics and viscosity of a colloidal dispersion composed of ferromagnetic spherocylinder particles: analysis by means of mean field approximation for a simple shear flow

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.     

Rheological properties and orientational distributions of dilute ferromagnetic spherocylinder particle dispersions. Part II. Analysis for the two typical magnetic field directions

We have investigated the orientational distributions and rheological properties of dilute colloidal dispersions, which consist of ferromagnetic spherocylinder particles. First, the governing equation of the orientational distribution function has been derived for the typical two cases of magnetic field directions: the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The equation has been solved approximately by Galerkin's method. With these numerical solutions we have obtained the results of the orientational distribution and viscosity. The results obtained for the magnetic field in the shear flow direction are summarized as follows. In the case of a weak magnetic field, the particle tends to orient nearly toward the shear flow direction and its opposite direction. As the magnetic field increases, the orientation of the particle is restricted and the viscosity increases significantly. As the influence of the magnetic field becomes dominant, an overshoot in the viscosity curve appears. This is due to the fact that there is a maximum deviation of the averaged particle direction from the magnetic field direction. When the strength of the magnetic field increases significantly, the particle inclines close to the magnetic field direction and the viscosity converges to a constant value. Particles with a larger aspect ratio give rise to a larger increment in the viscosity since such elongated particles induce larger resistance in a flow field. We also have obtained results for the case of the magnetic field in the direction parallel to the angular velocity vector of the shear flow. When the flow field is dominant over both the rotational Brownian motion and the magnetic interaction, the particle rotates in the plane nearly perpendicular to the magnetic field direction. As the magnetic field increases, the particle inclines toward the magnetic direction. For this direction of field, the viscosity is independent of the magnetic field and is always zero.     

Rheological Properties and Orientational Distributions of Dilute Ferromagnetic Spherocylinder Particle Dispersions

We have investigated the rheological properties and the orientational distributions of particles of a dilute colloidal dispersion, which is composed of ferromagnetic spherocylinder particles, subject to a simple shear flow. The governing equation of an orientational distribution function has been derived from the balance of the torques acting on a particle in an applied magnetic field. After a spherical harmonic expansion, an approximate solution to the governing equation has been found by Galerkin's method. The results obtained are summarized as follows. The orientational distribution function has a sharper peak for a stronger magnetic field, and the position of the peak changes from the flow direction to the magnetic field direction as the magnetic field comes to govern the shear flow. Since the orientation of the particle is highly restricted in the field direction as the magnetic field becomes strong, the viscosity increases significantly. The particles with a larger aspect ratio lead to the larger increment in the viscosity, since they induce a larger resistance in a flow field. Copyright 2001 Academic Press.     

Orientational motions of vibrational chromophores in molecules at the air/water interface with time-resolved sum frequency generation

The first time-resolved experiments in which interfacial molecules are pumped to excited electronic states and probed by vibrational sum frequency generation (SFG) are reported. This method was used to measure the out-of-plane rotation dynamics, i.e. time dependent changes in the polar angle, of a vibrational chromophore of an interfacial molecule. The chromophore is the carbonyl group, the rotation observed is that of the -C=O bond axis, with respect to the interfacial normal, and the interfacial molecule is coumarin 314 (C314) at the air/water interface. The orientational relaxation time was found to be 220+/-20 ps, which is much faster than the orientational relaxation time of the permanent dipole moment axis of C314 at the same interface, as obtained from pump-second harmonic probe experiments. Possible effects on the rotation of the -C=O bond axis due to the carbonyl group hydrogen bonding with interfacial water are discussed. From the measured equilibrium orientation of the permanent dipole moment axis and the carbonyl axis, and knowledge of their relative orientation in the molecule, the absolute orientation of C314 at the air/water interface is obtained.     

Flow-through immunomagnetic separation system for waterborne pathogen isolation and detection: Application to Giardia and Cryptosporidium cell isolation

Simultaneous sample washing and concentration of two waterborne pathogen samples were demonstrated using a rotational magnetic system under continuous flow conditions. The rotation of periodically arranged small permanent magnets close to a fluidic channel carrying magnetic particle suspension allows the trapping and release of particles along the fluidic channel in a periodic manner. Each trapping and release event resembles one washing cycle.The performance of the magnetic separation system (MSS) was evaluated in order to test its functionality to isolate magnetic-labelled protozoan cells from filtered, concentrated tap water, secondary effluent water, and purified water. Experimental protocols described in US Environmental Protection Agency method 1623 which rely on the use of a magnetic particle concentrator, were applied to test and compare our continuous flow cell separation system to the standard magnetic bead-based isolation instruments. The recovery efficiencies for Giardia cysts using the magnetic tube holder and our magnetic separation system were 90.5% and 90.1%, respectively, from a tap water matrix and about 31% and 18.5%, respectively, from a spiked secondary effluent matrix. The recovery efficiencies for Cryptosporidium cells using the magnetic tube holder and our magnetic separation system were 90% and 83.3%, respectively, from a tap water matrix and about 38% and 36%, respectively, from a spiked secondary effluent matrix. Recoveries from all matrices with the continuous flow system were typically higher in glass tubing conduits than in molded plastic conduits.     

Computational probes of molecular motion in the Lewis-Wahnstrom model for ortho-terphenyl

We use molecular dynamics simulations to investigate translational and rotational diffusion in a rigid three-site model of the fragile glass former ortho-terphenyl, at 260 K< or =T< or =346 K and ambient pressure. An Einstein formulation of rotational motion is presented, which supplements the commonly used Debye model. The latter is shown to break down at supercooled temperatures as the mechanism of molecular reorientation changes from small random steps to large infrequent orientational jumps. We find that the model system exhibits non-Gaussian behavior in translational and rotational motion, which strengthens upon supercooling. Examination of particle mobility reveals spatially heterogeneous dynamics in translation and rotation, with a strong spatial correlation between translationally and rotationally mobile particles. Application of the Einstein formalism to the analysis of translation-rotation decoupling results in a trend opposite to that seen in conventional approaches based on the Debye formalism, namely, an enhancement in the effective rate of rotational motion relative to translation upon supercooling.     

Solute rotational dynamics at the water liquid/vapor interface

The rotational dynamics of a number of diatomic molecules adsorbed at different locations at the interface between water and its own vapors are studied using classical molecular dynamics computer simulations. Both equilibrium orientational and energy correlations and nonequilibrium orientational and energy relaxation correlations are calculated. By varying the dipole moment of the molecule and its location, and by comparing the results with those in bulk water, the effects of dielectric and mechanical frictions on reorientation dynamics and on rotational energy relaxation can be studied. It is shown that for nonpolar and weekly polar solutes, the equilibrium orientational relaxation is much slower in the bulk than at the interface. As the solute becomes more polar, the rotation slows down and the surface and bulk dynamics become similar. The energy relaxation (both equilibrium and nonequilibrium) has the opposite trend with the solute dipole (larger dipoles relax faster), but here again the bulk and surface results converge as the solute dipole is increased. It is shown that these behaviors correlate with the peak value of the solvent-solute radial distribution function, which demonstrates the importance of the first hydration shell structure in determining the rotational dynamics and dependence of these dynamics on the solute dipole and location.     

Inertial and bias effects in the rotational brownian motion of rodlike molecules in a uniaxial potential

Inertial effects in the rotational brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h, both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.     

Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.     

Collective molecular precession induced by rotating illumination in photosensitive langmuir monolayers

Langmuir monolayers of an amphiphilic azobenzene derivative exhibit easily perturbable mesophases with long-range orientational order that couples strongly to linearly polarized light, resulting in symmetric photoaligned textures. Controlled rotation of the polarization plane induces continuous collective precession of the molecular field, which reveals the shear-thinning nature of the surface rotational viscosity. The dynamics is controlled by a balance between the strength of the optical coupling and viscous dissipation so that an increase in the rotational velocity results in a dampening of the synchronous anharmonic oscillations of the orientational field, as revealed by a space-time analysis of the Brewster angle microscopy images.     

Relaxation equations for the magnetic moment of a system of coupled spins

Redfield's equation [4] for the spin-density matrix is used to derive the macroscopic relaxation equations for the magnetic moment of a system of three nuclear spins coupled by dipole-dipole interaction. The relaxation is due to the Brownian rotation of the molecule in which the spin nuclei are randomly placed. The relaxation problem is solved for a system of spins at the vertices of an isosceles triangle; four exponentials are involved. A formula is derived for the number of relaxation equations governing the magnetic moment in the case of an arbitrary number of interacting spins.     

Coherent Disperse Structures in Magnetic Suspensions

Results of computer and physical simulation of cooperative behavior of a system of interacting ferroparticles in a liquid matrix under the action of rotating magnetic field are reported. It is shown that, under far from equilibrium (with respect to orientational variables) conditions, the phenomenon of dissipative self-organization arises resulting in the formation of coherent disperse structures.