Polydispersity effects on the magnetization of diluted ferrofluids:a lognormal analysis

Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field.

Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

Two-dimensional disordered granular assemblies composed of 2048 polydispersed frictionless disks are simulated using the discrete element method. The height of the first peak of the pair correlation function, gl, the local and global bond orientational parameters ψ6^1 and ψ6^g, and the fluctuations of these parameters decrease with increasing polydispersity s, implying the transition from a polycrystalline state to an amorphous state in the system. As s increases, the peak position of the boson peak aJBp shifts towards a lower frequency and the intensity of the boson peak D（ωBP）/ωBp increases, indicating that the position and the strength of the boson peak are controlled by the polydispersity of the system. Moreover, the inverse of the boson peak intensity ωBP/D（ωBP）, the shear modulus G, and the basin curvature SIS all have a similar dependence on s, implying that the s dependence of the vibrational density of states at low frequencies likely originates from the s dependence of the basin curvature.

Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.

How Polydispersity of Network Polymers Influences Strain-induced Crystal Nucleation in a Rubber

Network polymers in a rubber or a gel often contain non-uniform chain lengths. By means of dynamic Monte Carlo simulations of polymer mixtures with various compositions of two chain lengths, we investigated how the factor of polydispersity influences their strain-induced crystal nucleation. Under a high temperature and a high strain rate, the stretching of both polymers revealed that crystal nucleation is mainly accelerated by the presence of short-chain polymers; nevertheless, both polymers join together in the nucleation process. Further analysis proved that crystal nucleation is initiated from those highly stretched short segments, which are rich on the short-chain polymers.

Effects of polydispersity on the micro–macro behavior of granular assemblies under different deformation paths

The micromechanical and macromechanical behavior of idealized granular assemblies, made by linearly elastic, frictionless, polydisperse spheres, are studied in a periodic, triaxial box geometry, using the dis crete element method. Emphasis is put on the effect of polydispersity under purely isotropic loading and unloading, deviatoric （volume conserving）, and uniaxial compression paths. We show that scaled pressure, coordination number and fraction of rattlers behave in a very similar fashion as functions of volume fraction, irrespective of the deformation path applied. Interestingly, they show a systematic dependence on the deformation mode and polydispersity via the respective jamming volume fraction. This confirms that the concept of a single jamming point has to be rephrased to a range of variable jamming points, dependent on microstructure and history of the sample, making the jamming volume fraction a statevariable. This behavior is confirmed when a simplified constitutive model involving structural anisotropy is calibrated using the purely isotropic and deviatoric simulations. The basic model parameters are found to depend on the polydispersity of the sample through the different jamming volume fractions. The predictive power of the calibrated model is checked by comparison with an independent test, namely uniaxial compression. The important features of the uniaxial experiment are captured and a qualitative prediction for the evolution of stress and fabric is shown involving a ＂softening＂ regime in both stress and fabric stronger for the latter that was not prescribed into the model a priori.

Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems.Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems,respectively.In these processes,particles involved in the avalanche grow slowly in the early stage and explosively in the later stage,which is clearly different from the continuous and steady growth trend in the monodisperse system.By examining the avalanche propagation,the number growth of particles involved in the avalanche and the slope of the number growth,the initial state can be divided into three stages:T1(nucleation stage),T2(propagation stage),T3(overall avalanche stage).We focus on the characteristics of the avalanche in the T2 stage,and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems.We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles.The results support that the polydisperse particle systems are more stable in the T2 stage.

Effect of particle polydispersity on micromechanical properties and energy dissipation in granular mixtures

A series of numerical tests was conducted to study the micromechanical properties and energy dissipation in polydisperse assemblies of spherical particles subjected to uniaxial compression. In general, distributed particle size assemblies with standard deviations ranging from 0% to 80% of the particle mean diameter were examined. The microscale analyses included the trace of the fabric tensor, magnitude and orien- tation of the contact forces, trace of stress, number of contacts and degree of mobilization of friction in contacts between particles. In polydisperse samples, the average coordination numbers were lower than in monodisperse assemblies, and the mobilization of friction was higher than in monodisperse assemblies due to the non-uniform spatial rearrangement of spheres in the samples and the smaller displacements of the particles. The effect of particle size heterogeneity on both the energy density and energy dissipation in systems was also investigated.

Analytical modeling and simulation of porous electrodes: Li-ion distribution and diffusion-induced stress

A new model of porous electrodes based on the Gibbs free energy is developed, in which lithium-ion(Liion) diffusion, diffusion-induced stress(DIS), Butler–Volmer(BV) reaction kinetics, and size polydispersity of electrode particles are considered. The influence of BV reaction kinetics and concentration-dependent exchange current density(ECD) on concentration profile and DIS evolution are numerically investigated. BV reaction kinetics leads to a decrease in Li-ion concentration and DIS. In addition, concentrationdependent ECD results in a decrease in Li-ion concentration and an increase in DIS. Size polydispersity of electrode particles significantly affects the concentration profile and DIS.Optimal macroscopic state of charge(SOC) should consider the influence of the microscopic SOC values and mass fractions of differently sized particles.

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS I.CLOSE-PACKED LATTICE MODEL

using close-packed lattice models,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.An expressionfor the Helmholtz function of mixing is based on the revised Freed model developed previously.Asize parameter c_r and an energy parameter ε are used;the former can be temperature dependent,while the latter can depend on both temperature and chain-length of the polymer.The discretemulticomponent approach is adopted to derive expressions for chemical potentials,spinodals and criti-cal points.The continuous distribution function is then used in calculations of moments occurring inthose expressions.Computation programs are established for cloud-point-curve,shadow-curve,spinodal and critical-point calculations for polymer solutions with standard distribution or arbitrarydistribution of polymer.In the latter case,the derivative method developed previously is applied.lllustrations for phase-equilibrium calculations are

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS Ⅱ.LATTICE-FLUID MODEL

Using lattice-fluid model,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.A two-stepprocess is deslgned to form a real polymer solution containing a solvent and a polydisperse polymersolute occupying a volume at fixed temperature and pressure.In the first step,close-packed purecomponents including solvent and polymers with different molar masses or different chain lengths aremixed to form a closed-packed polymer solution.In the second step,the close-packed mixture,con-sidered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a vol-ume dependent on temperature and pressure.Revised Freed’s model developed previously is adoptedfor both steps.Besides pure-component parameters,a binary size parameter cr and a binary energyparameter ε12 are used.They are all temperature dependent.The discrete-multicomponent approach isadopted to derive expressions for chemical potentials。

Enhancing pharmaceutical potential and oral bioavailability of Allium cepa nanosuspension in male albino rats using response surface methodology

Objective:To enhance the pharmaceutical potential and oral bioavailability of quercetin contents of Allium cepa peel extract by novel nanosuspension technology.Methods:Nanoprecipitation approach was successfully used for the formulation of nanosuspension.To obtain pharmaceutical-grade nanosuspension with minimum particle size and polydispersity index,sodium lauryl sulphate was selected as a stabilizer.Important formulation parameters were statistically optimized by the response surface methodology approach.The optimized nanosuspension was subjected to stability and in vitro dissolution testing and characterized by scanning electron microscopy,atomic force microscopy,Fourier transform infrared spectroscopy,and zeta sizer.To evaluate the preeminence of nanosuspension over coarse suspension,comparative bioavailability studies were carried out in male albino rats.The pharmaceutical potential of developed nanosuspension was evaluated by antioxidant,antimicrobial,and toxicity studies.Results:The optimized nanosuspension showed an average particle size of 275.5 nm with a polydispersity index and zeta potential value of 0.415 and−48.8 mV,respectively.Atomic force microscopy revealed that the average particle size of nanosuspension was below 100 nm.The formulated nanosuspension showed better stability under refrigerated conditions.Nanosuspension showed an improved dissolution rate and a 2.14-fold greater plasma concentration of quercetin than coarse suspension.Moreover,the formulated nanosuspension exhibited enhanced antioxidant and antimicrobial potential and was non-toxic.Conclusions:Optimization of nanosuspension effectively improves the pharmaceutical potential and oral bioavailability of Allium cepa extract.

Molecular dynamics simulation of the response of bi-disperse polyelectrolyte brushes to external electric fields

Langevin dynamics simulations have been performed to investigate the response of bi-disperse and strong polyacid chains grafted on an electrode to electric fields generated by opposite surface charges on the polyelectrolyte （PE）-grafted electrode and a second parallel electrode. Simulation results clearly show that, under a negative external electric field, the longer grafted PE chains are more strongly stretched than the shorter ones in terms of the relative change in their respective brush heights. Whereas under a positive external electric field, the grafted shorter chains collapse more significantly than the longer ones. It was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The effects of smeared and discrete charge distributions of grafted PE chains on the response of PE brushes to external electric fields were also examined.

Studies in Molecular Weight Determination of Cottonseed and Melon Seed Oils Based Biopolymers

Six grades of biopolymers formulated to have oil content of 40% (M1), 50% (M2), and 60% (M3) melon seed oil (MESO) and 40% (C1), 50% (C2), and 60% (C3) cottonseed oil (COSO) respectively, were prepared with phthalic anhydride, and glycerol using alcoholysis-polycondensation process. The extend of polycondensation was monitored by determining the acid value of aliquots of the reaction mixture at various intervals of time. Molecular weight averages and polydispersity index (PDI) of the finished alkyds were determined by Rast method and end-group analysis. Molecular weight averages and PDI vary with differences in oil length of the alkyds, with samples M2 and C2 respectively exhibiting the highest PDI. Molecular weight average obtained from end-group analysis and those determined by Rast method in brackets are 1338.92 (597.00), 982.33 (696.25), 1316.09 (754.03), and 1160.57 (448.13), 765.96 (583.57), 1049.92 (696.25) for samples M1, M2, M3 and C1, C2, C3 respectively. Number molecular weight averages calculated from end-group analysis are larger than those obtained by Rast method for both MESO and COSO alkyds and seem to grossly overestimate their molecular weights. The mode of variation of these properties indicates that the synthesis of MESO and COSO alkyds are complex. Correlation of PDI with the quality of the finished alkyds shows that the higher the PDI value the better the quality of the alkyd. Performance properties such as rate of drying, film hardness and resistance to chemicals were optimum at 50% oil length for both triglyceride oil alkyds.

Determination of Hydrodynamic Parameters of Chitosan Stabilized Bimetallic Nanoparticles

The hydrodynamic characteristics of bimetallic Ag/Cu and Co/Ag nanopar­ticles stabilized by chitosan were determined.The polydispersity index and the diameter of nanoparticles were observed to decrease in contrast to the original polymer during the creation of chitosan stabilized bimetallic nanoparticles,decreasing from 0.342 to 0.12±0.04 and 2.5 micron to 180 nm,respectively.However,the diffusion coefficient of chitosan was in­creased from 0.2 cm^(2)/s to 2.71 cm2/s during the production of stable bime­tallic nanoparticles.The lack of absorption bands at 500 nm and 700 nm-900 nm in the UV spectra of the samples suggests that in the presence of a reducing agent,copper(II)and cobalt(II)ions undergo full reduction.The relationship between the synthesis conditions and the kind of structure of bimetallic nanoparticles“core-shell”has been discovered.Silver atoms have been shown to be both a core and a shell,depending on the synthesis conditions and chemical nature of metal ions.

Modeling of anisotropic polydispersed composites by progressive micromechanical approach

A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly ori- ented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to ob- tain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the ma- trix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.

CFD-DEM simulation of fluorination reaction in fluidized beds with local grid and time refinement method

The gas-solid reaction process with wide particle size distribution is extensively used in the chemical engineering field,especially the particle reacts with the gas gradually,such as fluorination reactions in fluidized beds.When the computational fluid dynamics-discrete element method(CFD-DEM)is used for the coupling simulation of multiphase and polydisperse particle reaction system,the grid size directly affects the accuracy of flow field information and simulation of chemical reaction.Furthermore,particle calculation time step will directly affect the efficiency of coupling calculation.In this work,a local grid and time step refinement method is proposed to simulate multiphase and polydisperse particle fluid-ization reaction system.In this method,the refined DEM grids are automatically generated in the computational domain around the fine particles,and the detailed fluid phase information is obtained with the interpolation algorithm.In the two-phase coupling process,particles are divided into different groups based on physical properties,each group has its own independent time step.The multistage conical-cylindrical spouted bed is proposed for the fluorination reaction process;the operating gas ve-locity range of the polydisperse particle system is extended by the new design while the particle size distribution changes with the gas-solid reaction process.It is demonstrated that the local grid and time step refinement method can improve the accuracy and efficiency of the traditional CFD-DEM method in the reaction process simulation,which describes a polydisperse particle system with wide particle size distribution.Aimed at improving the simulation accuracy and efficiency,this paper will be helpful for simulating the particle reaction process in the gas-solid fluidized bed and beneficial for the development of the CFD-DEM method.

Parameterization of below-cloud scavenging for polydisperse fine mode aerosols as a function of rain intensity

The below-cloud aerosol scavenging process by precipitation is one of the most important mechanisms to remove aerosols from the atmosphere.Due to its complexity and dependence on both aerosol and raindrop sizes,wet scavenging process has been poorly treated,especially during the removal of fine particles.This makes the numerical simulation of below-cloud scavenging in large-scale aerosolmodels unrealistic.To consider the slip effects of submicron particles,a simplified expression for the diffusion scavenging was developed by approximating the Cunningham slip correction factor.The derived analytic solution was parameterized as a simple power function of rain intensity under the assumption of the lognormal size distribution of particles.The resultant approximated expression was compared to the observed data and the results of previous studies including a 3D atmospheric chemical transport model simulation.Compared with the default GEOS-Chem coefficient of 0.00106R0.61 and the observation-based coefficient of 0.0144R0.9268,the coefficient of a and b in∧m=aRb spread in the range of 0.0002-0.1959 for a and 0.3261-0.525 for b over a size distribution of GSD of 1.3–2.5 and a geometric mean diameter of 0.01-2.5μm.Overall,this study showed that the scavenging coefficient varies widely by orders of magnitude according to the size distribution of particles and rain intensity.This study also demonstrated that the obtained simplified expression could consider the theoretical approach of aerosol polydispersity.Our proposed analytic approach showed that results can be effectively applied for reduced computational burden in atmospheric modeling.

Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds,which possesses a significant impact on hydrodynamics of gas-solid flow.Computational fluid dynamics-discrete element method(CFD-DEM)is promising to adequately simulate gas-solid flows with continuous particle size distribution(PSD)while it still suffers from high computational cost.Corresponding coarsening models are thereby desired.This work extends the coarse-grid model to polydisperse systems.Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas-particle drag force in coarse-grid simulations.We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems.Subsequently,the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter.Drag correction models for systems with monodisperse and continuous PSD are developed.A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.

Machine Learning for heat radiation modeling of bi-and polydisperse particle systems including walls

We investigated the ability of four popular Machine Learning methods i.e.,Deep Neural Networks(DNNs),Random Forest-based regressors(RFRs),Extreme Gradient Boosting-based regressors(XGBs),and stacked ensembles of DNNs,to model the radiative heat transfer based on view factors in bi-and polydisperse particle beds including walls.Before training and analyzing the predictive capability of each method,an adjustment of markers used in monodisperse systems,as well as an evaluation of new markers was performed.On the basis of our dataset that considers a wide range of particle radii ratios,system sizes,particle volume fractions,as well as different particle-species volume fractions,we found that(i)the addition of particle size information allows the transition from monodisperse to bi-and polydisperse beds,and(ii)the addition of particle volume fraction information as the fourth marker leads to very accurate predictions.In terms of the overall performance,DNNs and RFRs should be preferred compared to the other two options.For particle-particle view factors,DNN and RFR are on par,while for particle-wall the RFR is superior.We demonstrate that DNNs and RFRs can be built to meet or even exceed the prediction quality standards achieved in a monodisperse system.