Influence Of Polydispersity Research Articles

Stability of the circular Couette flow of a ferrofluid in an axial magnetic field: Influence of polydispersity

The gap between two concentric rotating cylinders is filled with a ferrofluid. A homogeneous magnetic field is applied parallel to the cylinder axis. The stability of the circular Couette flow is analyzed with different models that take into account the polydispersity of the ferrofluid to a varying degree. Their results are compared and their merits are discussed.

Influence of polydispersity on the phase behavior of colloidal goethite

The effect of fractionation on the phase behavior of colloidal goethite dispersions with different polydispersities (17%, 35%, and 55% in length) has been studied by small angle x-ray scattering and transmission electron microscopy. All systems show at least nematic and smectic phases. The occurrence of the latter phase at such a high polydispersity is remarkable. It is shown that in the highly polydisperse systems strong fractionation occurs, which is able to reduce the local length polydispersity up to a factor of 2. A columnar phase was only found in the 35% and 55% polydisperse systems. It seems that the columnar phase accommodates the particles that do not fit into the smectic layers and, thus, reduces the length polydispersity within the smectic phase even further. The fact that a columnar phase was not found in the system of lowest polydispersity indicates that the smectic phase is the most stable phase at higher concentrations.

A Simplified Model to Estimate the Size Distribution Change of Polydispersed Aerosol for Cyclone Separator

A simplified solution for the removal efficiency of a polydispersed aerosol by a cyclone collector is studied theoretically. The radial back mix approach based on Leith and Licht (1972) was modified and the moment method, which assumes the particle size distribution as a lognormal distribution, was used for numerical calculation. Consequently, the influence of polydispersity on overall collection efficiency was evaluated in a cyclone collector. The obtained simple and straightforward results give information on change of the particle size distribution such as total particle number concentration, geometric mean particle diameter, and geometric standard deviation through the cyclone collector. This obtained model also shows how the particles are collected throughout the cyclone as a function of time.

Magnetization of two-dimensional magnetic fluids

The influence of polydispersity on the magnetization of two-dimensional dipolar discs withshort-range repulsive interaction is studied by means of Monte Carlo simulations and ahigh field approximation perturbation theory. Within the framework of perturbation theoryan analytical expression is derived for the magnetization of monodisperse and polydispersesystems. The theoretical predictions are in good agreement with the corresponding MonteCarlo simulation data.

Acoustic waves in granular materials

The numerous sound propagation mechanisms in granular materials are rather complex and strongly depend on the material micro-scale parameters, such as inter-particle friction or damping. The use of DEM (Discrete Element Simulations) allows us to tune these parameters and hence to understand their influence. In both regular (crystal-like) and polydisperse (sand-like) systems of spheres, a small perturbation is created on one side of the simulation box and examined during its propagation and on arrival at the opposite side. Starting from a regular packing, a tiny size variation comparable to the typical contact deformation already changes sound propagation considerably [1]. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, mainly due to scattering effects. Furthermore, the wave propagation and transmission properties are studied on fully polydisperse, frictional and cohesive packings under increasing load until breakage of the material [2]. [1] O. Mouraille and S. Luding, Sound wave propagation in weakly polydisperse granular materials, Ultrasonics, submitted. [2] O. Mouraille, O. Herbst and S. Luding, Testing cohesive and frictional granular materials with the discrete element model, in preparation.

Influence of Polydispersity on the Micellization of Triblock Copolymers Investigated by Pulsed Field Gradient Nuclear Magnetic Resonance

The molecular motion in water of the poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer with the nominal composition EO97PO68EO97 (F127) was investigated with the aid of pulsed field gradient nuclear magnetic resonance (PFG NMR). The signal decays in the PFG experiments have been recorded for 1 wt % F127 in the temperature range from 288 to 313 K and in the concentration range 0.1−35 wt % at 298 K. Below the critical micellization temperature (cmt) or the critical micellization concentration (cmc), the PFG signal decays approximately linearly when the intensities are plotted on a logarithmic scale versus the experimentally relevant parameter. At the cmt or cmc, the signal decays are curved. The NMR data were processed using inverse Laplace transformation to obtain the distribution of self-diffusion coefficients, P(D). At 288 K for a 1 wt % solution, a narrow distribution was observed, while at 302 K a bimodal distribution was observed. This observation can be explained by the polydispersity of the polymer. It implies that, at a given temperature, only the more hydrophobic compound of F127 takes part in the aggregation process, while the more hydrophilic components diffuse as free nonassociated polymer. Increasing the temperature to 313 K resulted in a monomodal distribution, suggesting that all the polymers are aggregated. It is suggested that an ideal mixing model for the Pluronic micelles can explain the self-diffusion data. The NMR self-diffusion raw data were also analyzed with the COmponent REsolved (CORE; Stilbs, P.; Paulsen, K. Rev. Sci. Instrum. 1996, 67, 4380−4386) algorithm, resulting in spectra for free block copolymer and micellized block copolymer. With an increase in temperature, the intensity of the peaks for free block copolymer is reduced, whereas the intensity of the peaks for aggregated block copolymer increases. The ratios between the size of the PEO and PPO blocks (mEO/nPO) show a marked increase in free polymer compared to the ratio observed in micellized polymer when the temperature is increased. The effect of added salts to a 1 wt % F127 solution at 303 K was investigated to determine how the populations of free and micellized surfactant were changed on account of the ions present. Finally, the diffusion behavior of Pluronic F68 (EO76PO29EO76) at 35 wt % has been investigated from 298 to 313 K. Both the diffusion time and the time of the gradient have been varied. The data show that the diffusion is Gaussian in the temperature range.

Influence of Polydispersity on the Absorbance Spectra of ZnO Nanoparticles

Influence of polydispersity on UV absorption spectra of ZnO nanoparticles, which were prepared from zinc bromide and sodium hydroxide as well as zinc acetate and sodium hydroxide in 2-propanol, had been studied. The particle size was measured with UV absorption spectrometry in-situ and high resolution transmission electron microscope (HRTEM). The growth kinetics of ZnO nanoparticles was in agreement with LSW(Lifshitz-Slyozov-Wagner) model for coarsening where the particle volume was proportional to aging time. However, the particle size distribution was found to be inconsistent with the LSW model, which has been reported previously for other systems. Computer numerical calculation was used to determine the effect of the distribution function on the UV absorption spectra of ZnO suspension. It was found that absorption spectra bent near the UV absorption edge and shifted with the increase of standard deviation (SD) of normal distribution function, which can lead to an over-estimation of the particle size from UV spectra. For monodispersed ZnO suspensions (SD/■- 5%), the over-estimation of particle size is only about 2%. If SD/■- of the particle is 15%, the over-estimation can be as high as 15.1%.

Magnetization of rotating ferrofluids: the effect of polydispersity

The influence of polydispersity on the magnetization is analysed in a non-equilibriumsituation where a cylindrical ferrofluid column is forced to rotate with constant frequency,like a rigid body in a homogeneous magnetic field that is applied perpendicular to thecylinder axis. Then, the magnetization and the internal magnetic field are no longer parallelto each other and their directions differ from that of the applied magnetic field.Experimental results on the transverse magnetization component perpendicular to theapplied field are compared and analysed as functions of rotation frequency and fieldstrength with different polydisperse Debye models that take into account the polydispersityin different ways and to a varying degree.

Effects of Polydispersity on Phase Behavior of Diblock Copolymers

The influence of polydispersity on the phase behavior of diblock copolymer melts is studied using a self-consistent field theoretic model. A perturbation theory is developed for the polydisperse sy...

Limit of validity of the stress-optical rule for polystyrene melts: Influence of polydispersity

Simultaneous measurements of stress and birefringence have been performed during uniaxial extension at constant strain rate of a polydisperse polystyrene melt. In contrast to melts with narrow molecular weight distribution, the relationship between stress and birefringence is found to depend on the temperature and the strain rate in the non-linear region. Failure of the stress-optical rule initiates for lower stress levels, the actual critical stress increasing with the reduced extension rate towards the value measured for quasi-monodisperse systems. In agreement with predictions by van Meerveld [J. van Meerveld, Validity of the linear stress optical rule in mono-, bi- and polydisperse systems of linear entangled chains, J. Non-Newtonian Fluid Mech. 123 (2004) 259–267], this premature failure of SOR occurs within the strain rate regime where only a fraction of the chains of the melt is expected to stretch significantly.

Magnetic properties in monolayers of a model polydisperse ferrofluid

The influence of polydispersity on the equilibrium properties of monolayers of three-dimensional dipolar spheres with short-range repulsive interactions is studied by means of Monte Carlo simulations and a high field approximation perturbation theory. The particle distribution in the simulations is realized in the semigrand ensemble by tuning appropriately the underlying particle distribution density. The magnetization curves are calculated as functions of density and temperature, and the obtained results are compared with the data determined in a monodisperse equivalent of the system. In-plane and out-of-plane initial magnetic susceptibilities are determined using external fields applied parallel or normal to the monolayer plane. Susceptibility data for the true two- and three-dimensional counterparts of the system are also calculated for comparison. Our findings for the magnetic properties can partly be explained by the structural characteristics obtained from the simulations.

Influence of Polydispersity on the Self-Assembly of Diblock Copolymers

The domain sizes and morphological boundaries in diblock copolymers have been predicted to be influenced by changes in the molecular weight distribution of one or both of the blocks. To systematically explore these effects, we prepared several sets of poly(ethylene-alt-propylene)-b-poly(dl-lactide) diblock copolymers with controlled molecular weights, compositions, and polydispersity indices. The polydispersity of the polylactide block was controlled by taking advantage of the equilibrium nature of the ring-opening polymerization of lactide. Small-angle X-ray scattering was used to evaluate the influence of block copolymer polydispersity on the equilibrium domain spacing and resultant ordered state morphology. We found that the domain spacing increased with increasing polydispersity and demonstrated that an increase in polydispersity at constant polylactide composition can result in a change in morphology for compositionally asymmetric diblock copolymers. More specifically, when the polylactide block is the minority component, a polydispersity increase in that block results in a change of morphology to one with larger mean interfacial curvature. Conversely, an increase in the polydispersity of the polylactide segment in a block copolymer with a majority of polylactide drives transitions to structures with smaller mean interfacial curvature. The experimental results were corroborated by self-consistent mean-field theory.

Influence of polydispersity on the effective interaction in a quasi-two-dimensional pseudo-one-component colloid fluid

We report the results of simulations of one-component and binary quasi-two-dimensional polydisperse hard sphere colloid fluids. When the polydisperse one-component system is regarded as an effective monodisperse one-component system, our results show that polydispersity gives rise to effective pair attraction and soft repulsion. These effective interactions depend on both the degree of polydispersity and the system density. At low density only the effective soft repulsion survives and the effective attraction becomes negligible. For the binary system, the depletion interaction develops extra features due to polydispersity, specifically a repulsive interaction with range twice the average particle diameter. At low density this extra feature vanishes. To carry out our study we have devised a method for continuous sampling of the polydisperse mixture according to a prescribed particle diameter distribution.

Heat capacity in a model polydisperse ferrofluid with narrow particle size distribution

The influence of polydispersity on the phase equilibrium properties and the heat capacity of a dipolar system with additional short-range (repulsive + attractive) interactions (modeled by a shifted Lennard-Jones pair potential) is studied by means of a Monte Carlo scheme. The particle distribution of the investigated system is realized in the semigrand ensemble by tuning appropriately the underlying particle distribution density. The phase coexistence and heat capacity data are calculated with and without an applied magnetic field, and the obtained results are compared with the data determined in a monodisperse equivalent of the system.

Impact of polydispersity on light propagation in colloidal photonic crystals

The influence of polydispersity, or variations in the size of particles, on the transmittance of slabs of colloidal photonic crystals is analyzed. A model based on simulated annealing simulates the assembly of particles with a given size distribution into a dense array. The model reveals the existence of a transition between ordered and random packing at a polydispersity between 3% and 4%; this transition is associated with large changes in optical properties, in the form of greatly increased scattering and reduced contrast associated with the transmittance in and out of the stop band. The predictions of the model correspond closely to experimental measurements.

To the theory of rheological properties of ferrofluids: influence of drop-like aggregates

Many experiments show that drop-like aggregates, consisting of tremendous number of magnetic particles, can appear in ferrofluids under suitable conditions. Our work deals with theoretical study of influence of these drops on macroscopical rheological properties of the systems. The estimates show that appearance of the drops leads to significant (more than order of magnitude) increase of viscosity of ferrofluid under magnetic field parallel to gradient of flow. This conclusion is in agreement with known experimental results. Our analysis is performed for a model monodisperse system of magnetic particles suspended in a Newtonian fluid. The influence of polydispersity, the general and inevitable property of ferrofluids, on the magnetoviscous effects in these systems is discussed.

Modeling of the Phase Separation Behavior of Polydisperse Semi‐Flexible Diblock Copolymers

AbstractSummary: A modified random phase approximation method with a cumulant expansion for the semi‐flexible structure factor of diblock copolymers was exercised to describe the phase separation behavior of semi‐flexible and polydisperse diblock copolymers. Scattering curves and spinodal diagrams were calculated applying monomer specific input parameters. The influence of polydispersity was included applying basic concepts of mathematical statistics utilizing several probability density distributions in the case of the two single blocks. In contrast to semi‐flexibility, the main effect of polydispersity was found to shift the spinodal up, thus to enlarge the range of existence of the homogeneous phase.Twofold Schultz‐Zimm distribution of diblock copolymers.magnified imageTwofold Schultz‐Zimm distribution of diblock copolymers.

To the theory of rheological properties of ferrofluids: influence of drop-like aggregates

Many experiments show that drop-like aggregates, consisting of tremendous number of magnetic particles, can appear in ferrofluids under suitable conditions. Our work deals with theoretical study of influence of these drops on macroscopical rheological properties of the systems. The estimates show that appearance of the drops leads to significant (more than order of magnitude) increase of viscosity of ferrofluid under magnetic field parallel to gradient of flow. This conclusion is in agreement with known experimental results. Our analysis is performed for a model monodisperse system of magnetic particles suspended in a Newtonian fluid. The influence of polydispersity, the general and inevitable property of ferrofluids, on the magnetoviscous effects in these systems is discussed.

Phase separation in model polydisperse ferrofluids.

The influence of polydispersity on the phase equilibrium properties of a dipolar system with additional short-range (repulsive+attractive) interactions (modeled by a shifted Lennard-Jones pair potential) is studied by means of Gibbs ensemble Monte Carlo simulations. The critical temperature and density as well as the magnetization at the critical point are calculated as a function of the applied magnetic field, and the obtained results are compared with the data determined in a monodisperse equivalent of the system.

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.