Prolate Ellipsoidal Particles Research Articles

Shape-Induced Dispersion of Colloids in Anisotropic Fluids

We experimentally study the behavior of micrometer-sized prolate ellipsoidal particles dispersed in a nematic liquid crystal. The latter is an aqueous solution of rodlike micelles. When embedded into such a solvent, ellipsoids with small enough aspect ratios aggregate to form anisotropic structures oriented at an angle with respect to the local background director (as already observed for spheres). This is, however, no longer the case when the aspect ratio reaches a well-defined value: above that value, the ellipsoids remain well dispersed and apparently do no interact with each other, even over very long periods of time (several months). Therefore, there exists a transition from an aggregated to a nonaggregated state as a function of aspect ratio and for a given particle concentration. This behavior has not been predicted so far and we put forward simple calculations to rationalize our observations.

Dynamics of prolate ellipsoidal particles in a turbulent channel flow

The dynamical behavior of tiny elongated particles in a directly simulated turbulent flow field is investigated. The ellipsoidal particles are affected both by inertia and hydrodynamic forces and torques. The time evolution of the particle orientation and translational and rotational motions in a statistically steady channel flow is obtained for six different particle classes. The focus is on the influence of particle aspect ratio λ and the particle response time on the particle dynamics, i.e., distribution, orientation, translation, and rotation. Both ellipsoidal and spherical particles tend to accumulate in the viscous sublayer and preferentially concentrate in regions of low-speed fluid velocity. The translational motion is practically unaffected by the aspect ratio, whereas both mean and fluctuating spin components depend crucially on λ. The ellipsoids tend to align themselves with the mean flow direction and this tendency becomes more pronounced in the wall proximity when the lateral tilting of the elongated particles is suppressed.

On the orientation of ellipsoidal particles in a turbulent shear flow

Direct numerical simulation (DNS) of small prolate ellipsoidal particles suspended in a turbulent channel flow is reported. The coupling between the fluid and the particles is one-way. The particles are subjected to the hydrodynamic drag force and torque valid for creeping flow conditions. Six different particle cases with varying particle aspect ratios and equivalent response times are investigated. Results show that, in the near-wall region, ellipsoidal particles tend to align with the mean flow direction, and the alignment increases with increasing particle aspect ratio. When the particle inertia increases, the particles are less oriented in the spanwise direction and more oriented in the wall-normal direction. In the core region of the channel, the orientation becomes isotropic.

Packing, Flipping, and Buckling Transitions in Compressed Monolayers of Ellipsoidal Latex Particles

The behavior of monolayers of monodisperse prolate ellipsoidal latex particles with the same surface chemistry but varying aspect ratio has been studied experimentally. Particle monolayers at an air-water interface were subjected to compression in a Langmuir trough. When surface pressure measurements and microscopy observations were combined, possible structural transitions were evaluated. Ellipsoids of a sufficiently large aspect ratio display a less abrupt increase in the compression isotherms than spherical particles. Microscopic observations reveal that a sequence of transitions is responsible for this more gradual increase of the surface pressure. When a percolating aggregate network is used as the starting point, locally ordered regions appear progressively. When it reaches a certain surface pressure, the system "jams", and in-plane rearrangements are no longer possible at this point. A highly localized yielding of the particle network is observed. The compressional stress is relieved by flipping the ellipsoids into an upright position and by expelling particles from the monolayer. The latter does not occur for spherical particles with similar dimensions and surface chemistry. In the final stage of compression, buckling of the monolayer as a whole was observed. The effect of aspect ratio on the pressure area isotherms and on the obtained percolation and packing thresholds was quantified.

Influence of demagnetizing field on the permeability of soft magnetic composites

The influence of demagnetizing field on the effective permeability of magnetic composites has been investigated. A theoretical expression of the effective permeability has been obtained and discussed according to four typical composites with spheres, needles, flakes, and aligned prolate ellipsoidal particles. The results indicate that the demagnetizing field within the particles can reduce the effective permeability significantly. In order to increase the effective permeability, it is necessary to decrease the demagnetizing field within the particles. A linear relationship between effective permeability and volume fraction is also observed for composites filled with spherical particles at low volume fraction.

Numerical simulation of porous networks in relation to battery electrodes and separators

Numerical simulation is used to explore the influence of particle shape and overall porosity on the liquid phase conductivity, σ eff , inside porous networks, such as electrodes or separators used for lithium-ion batteries. Such battery components are often modelled by a power law, σ eff = ε α σ 0 , which relates electrolyte bulk conductivity σ 0 and void volume fraction ε via a Bruggeman exponent α . Frequently, a value of 1.5 is assumed for α . In this work, theoretical and experimental evidence is presented to show that a Bruggeman exponent of 1.5 is often not valid for real electrodes or separator materials. It is found that only idealized morphologies, based on spherical or slightly prolate (i.e. rod-type) ellipsoids, are expected to give rise to a Bruggeman law with an exponent of about 1.3. Porous networks based on other particle morphologies such as oblate (i.e. disk-type) ellipsoids or lamellar or flaky materials increase the tortuous path for ionic conductivity and result either in a significant increase of the exponent α , or in a complete deviation from the power law. These models imply that spherical or slightly prolate ellipsoidal particles should be preferred for batteries where high-rate performance is required and that future separators could be designed with higher ionic conductivity.

Overbased detergent particles: Experimental and molecular modelling studies

Overbased detergents (OD) are oil-soluble nanoparticles consisting of a calcium carbonate core and surfactant outer shell. They are important additives in automotive and marine engine oils. Langmuir trough (LT) and molecular dynamics (MD) simulations have been carried out to characterise the interaction between OD particles made from a range of surfactants. We also explore the factors that determine the shape of the particles, in particular by the level of overbasing (amount of calcium carbonate in the core), surfactant type and the presence of stearate co-surfactant. Clint and Taylor (J. H. Clint and S. E. Taylor, Colloids Surf., 1992, 65, 61) derived expressions for the particle size, contact angle and interparticle interaction between spherical particles at the air/water interface in a Langmuir trough surface pressure experiment. We extend this mathematical treatment to encompass the more general case of oblate and prolate ellipsoidal particles. On reinterpreting the experimental data, the derived expressions suggest that the largest deviations from spherical symmetry occur for the phenate and calixarate particles without co-surfactant. This is supported by molecular modelling studies also reported herein. The evidence from the combined LT and MD studies is that the co-surfactant makes the particles more spherical, by disrupting any tendency of the surfactants to self-assemble in an ordered fashion around the surface of the carbonate core.

Monte Carlo simulations on reinforcement of an elastomer by oriented prolate particles

Particulate fillers used to reinforce polymers need not be spherical; some experiments have in fact been carried out on prolate ellipsoidal particles. These experimental results encouraged Monte Carlo simulations on prolate particles in amorphous polyethylene described in the present report. The particles were placed on a cubic lattice, and were oriented in a way consistent with their orientation in the composites experimentally investigated. Rotational isomeric state representations of the chains were then generated for the polymer matrix, with the discarding of spatial configurations that involved chains impinging on any of the particles. The chain end-to-end distributions were found to be non-Gaussian, and their dependences on the excluded volumes of the filler particles were documented. There were found to be particle-induced deformations which corresponded to decreased chain dimensions and radii of gyrations upon insertion of spherical particles amongst the chains, which is consistent with earlier simulations and with recent neutron scattering results. The decreases in dimensions and radii, however, were subsequently followed by increases upon increasing the axial ratios to distort the spherical particles into prolate shapes. The chain dimensions also became anisotropic, with significant differences parallel and perpendicular to the direction of the particle axes. Use of these distributions in the standard three-chain model of rubber-like elasticity gave the corresponding elongation moduli. The stress–strain isotherms thus obtained were found to be dependent on the sizes, numbers and axial ratios of the particles, as expected. In particular, the reinforcement from the prolate particles was found to be greatest in the parallel direction, and the changes were in at least qualitative agreement with the corresponding experimental results.

Experimental and molecular modelling studies of overbased detergent particles

Langmuir trough, Langmuir–Blodgett (LB) film and ellipsometry experiments, and molecular modelling, were carried out to characterise a series of overbased detergent (OD) systems made with several surfactant types, including the first application of these approaches to a new class based on calixarates. Systems were synthesised with low, mid and high levels of basicity, which on the TBN (total base number) scale were 150, 250 and 350, respectively. The diameters determined from the Langmuir trough measurements were 3.4, 3.5 and 3.6 nm, respectively. These are consistently higher than those of phenate particles with the same basicities. The phenate and calixarate particles self-assembled into multilayer LB films on a stearic acid-coated silicon wafer. Film thicknesses were determined by ellipsometry. Differences in the estimated particle diameter for the phenates and calixarates by these two methods suggest that the OD particles are, in general, and to varying extents, non-spherical. In the phenate case the deposited LB film thickness was a strong function of the Langmuir film deposition surface pressure in the region where the monolayer is essentially close-packed, supporting the discoid shape for these particles, which was first predicted by our previous molecular modelling studies. The molecular modelling results suggest that the sulfonate systems are the most spherical, followed probably by the salicylates. Preliminary results on the calix[6]arates suggest that they form prolate ellipsoidal particles, capped at both ends with the surfactant molecule. The experiments and simulations are consistent in indicating that the particle shape and internal atomistic structure inside the inorganic core region of the particle are quite sensitive to the surfactant type.

Dynamical micromagnetics by the finite element method

We developed a new numerical procedure to study dynamical behavior in micromagnetic systems. This procedure solves the damped Gilbert equation for a continuous magnetic medium, including all interactions in standard micromagnetic theory in three-dimensional regions of arbitrary geometry and physical properties. The magnetization is linearly interpolated in each tetrahedral element in a finite element mesh from its value on the nodes, and the Galerkin method is used to discretize the dynamic equation. We compute the demagnetizing field by solution of Poisson's equation and treat the external region by means of an asymptotic boundary condition. The procedure is implemented in the general purpose dynamical micromagnetic code (GDM). GDM uses a backward differential formula to solve the stiff ordinary differential equations system and the generalized minimum residual method with an incomplete Cholesky conjugate gradient preconditioner to solve the linear equations. GDM is fully parallelized using MPI and runs on massively parallel processor supercomputers, clusters of workstations, and single processor computers. We have successfully applied GDM to studies of the switching processes in isolated prolate ellipsoidal particles and in a system of multiple particles.

Determination of mean particle volume, a monte carlo simulation

Either length measurements or area measurements may be made on a sample of profiles for the purpose of estimating the mean volume of a population of convex particles. Diameters of spheres, caliper diameters of ellipsoids and intercept lengths are available length measurements. Profile areas can be evaluated by planimetry or point counting. Either all the available profiles in random sections or point sampled profiles can be utilized. We have applied a Monte Carlo simulation to compare several of the stereologic methods for the estimation of the mean volumes of spheres and ellipsoids. Populations of spherical, prolate ellipsoidal and oblate ellipsoidal particles were subjected to random sectioning and measurement. Diameter, point sampled intercept length, area and point sampled area were measured in the case of the spherical particles. With the ellipsoids, the same measurement excepting diameters were performed. The measurements were converted to volumes by the appropriate equations, and the means, the standard deviations of the means and the 95% confidence intervals were determined for increasing sample sizes. All the methods provide estimates that converge on their theoretical mean volumes. The area measurements and particularly the point sampled area measurement show some advantage over the length measurements, but differences among the methods are small, not entirely consistent over the different cases and unlikely to be significant in most real applications.

Anisotropic Phase Separation in Amorphous Fe-Ge Alloys

ABSTRACTMagnetron sputtered amorphous FexGe100-x films have been examined with anomalous small-angle x-ray scattering (ASAXS) in an attempt to characterize composition fluctuations which have been previously reported in this system. Films grown under various deposition conditions have been studied, with the scattering vector both in and oblique to the plane of the films, to search for anisotropy. By manipulating the deposited power flux and rates of growth, films which have the same composition can be grown to different states of phase separation. The total correlation functions have been calculated from the oblique scattering experiments. The anisotropy can be successfully modeled as a close-packing of oriented prolate ellipsoidal particles, with the elongated axis along the direction of film growth. A method for using these measurements to determine the compositions of the phase-separating species has been developed and utilized. The results indicate phase separation into a-Ge and a-FeGe2 for the a-FexGe100-x (x<33) alloy.

Numerical micromagnetics by the finite element method

We developed a new numerical procedure to study dynamical behavior in micromagnetic systems. This procedure solves the damped Gilbert equation for a continuous magnetic medium, including all interactions in standard micromagnetic theory in three-dimensional regions of arbitrary geometry and physical properties. The magnetization is linearly interpolated in each tetrahedral element in a finite element mesh from its value on the nodes, and the Galerkin method is used to discretize the dynamic equation. We compute the demagnetizing field by solution of Poisson's equation and treat the external region by means of an asymptotic boundary condition. The procedure is implemented in the general purpose dynamical micromagnetic code (GDM). GDM uses a backward differential formula to solve the stiff ordinary differential equations system and the generalized minimum residual method with an incomplete Cholesky conjugate gradient preconditioner to solve the linear equations. GDM is fully parallelized using MPI and runs on massively parallel processor supercomputers, clusters of workstations, and single processor computers. We have successfully applied GDM to studies of the switching processes in isolated prolate ellipsoidal particles and in a system of multiple particles.

On the orderly nature of the motion of nonspherical aerosol particles. II. Inertial collision between a spherical large droplet and an axially symmetrical elongated particle

The efficiency of inertial collision between prolate ellipsoidal particles and a spherical large droplet was calculated. The calculation was performed by simultaneously solving both the equation of translation and the equation of rotation of the spheroids for various initial orientations of the latter. The field of flow around the large droplet was acquired from a previous numerical solution of the Navier-Stokes equation, and the expression for the fluid dynamic torque was taken from Jeffery [ Proc. Roy. Soc. 102A, 161–179 (1923)]. The results show a pronounced sensitivity to the initial conditions of orientation. If compared to the collisional efficiencies of a volumetrically equivalent sphere, the efficiencies of the ellipsoidal elongated particles in the investigated cases are up to about 3.5 times greater than the former. The calculational method is applicable to the inertial impaction of any aerosol particle of a general ellipsoid shape which may simulate straight fibers, needles, or oblate (atmospheric) particles of mineral origin.