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 distribution shape on the melting transition, local ordering,and dynamics in a model size-polydisperse two-dimensional fluid

We study the effect of particle size polydispersity(δ) on the melting transition(T*), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian(G) and uniform(U) distribution functions.For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity,the value of T*initially increases due to improved packing efficiency(φ) followed by a decrease and terminates at δ ≈8%(U-system) and 14%(G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which φ drops suddenly coincides with the peak of the heat capacity(CP) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter(Q_6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T –δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems;however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

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.

Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state. The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effacts on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.

Effects of Shape of Crowders on Dynamics of a Polymer Chain Closure

Using 3D Langevin dynamics simulations, we investigate the effects of the shape of crowders on the dynamics of a polymer chain closure. The chain closure in spherical crowders is dominated by the increased medium viscosity so that it gets slower with the increasing volume fraction of crowders. By contrast, the dynamics of chain closure becomes very complicated with increasing volume fraction of crowders in spherocylindrical crowders. Notably, the mean closure time is found to have a dramatic decrease at a range of volume fraction of crowders 0.36-0.44. We then elucidate that an isotropic to nematic transition of spherocylindrical crowders at this range of volume fraction of crowders is responsible for the unexpected dramatic decrease in the mean closure time.

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.

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.

Effect of the Molecular Structure of Polymer Dispersants on Limestone Suspension Properties in Fine Grinding

Polymer dispersants are widely used as grinding aids to reduce the viscosity of mineral particle suspensions and to improve energy efficiency during fine grinding. The authors studied here the effects of polymer dispersants of different molecular structure on limestone suspension properties in wet stirred media milling. The polymers differed in their molecular weight and PDI （polydispersity index）. Two traditionally fractionated polymer dispersants having a high PDI （over 2） and one made by controlled radical polymerization having a low PDI （1.2） were tested. It was noticed that these dispersants worked as electrosteric stabilizers and prevented the agglomeration of ground limestone particles. Their addition allowed increased solids concentrations to be used in the grinding experiments and at the same time lowered the particle size and specific energy consumption. The particle sizes obtained were about 1 μm regardless of the dispersant or its dose. The dispersant with a low PDI reduced the viscosity more than did the high PDI dispersants. The results indicate that higher solids concentrations can be used at the same dispersant dose when a low PDI dispersant is used, leading to energy savings via increased throughput. Alternatively, a lower dose of low PDI polymer dispersant than of a high PDI polymer dispersant can be used at the same solids concentration.

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.

Mechanochemical degradation of potato starch paste under ultrasonic irradiation

In the paper, changes in the molecular weight, the intrinsic viscosity and the polydispersity (molecular mass distribution) of treated potato starch paste were studied under different ultrasonic conditions which include irradiation time, ultrasonic intensity, potato starch paste concentration, and distance from probe tip on the degradation of potato starch paste. Intrinsic viscosity of potato starch paste was determined following the ASTM (American Society for Testing and Materials) standard practice for dilute solution viscosity of polymers. Molecular mass and polydispersity of potato starch paste were measured on GPC (Gel Permeation Chromatography). The results showed that the average molecular mass and the intrinsic viscosity of starch strongly depended on irradiation time. Degradation increased with prolonged ultrasonic irradiation time, and the increase of ultrasonic intensity could accelerate the degradation, resulting in a faster degradation rate, a lower limiting value and a higher degradation extent. Starch samples were degraded faster in dilute solutions than in concentrated solutions. The molecular mass and the intrinsic viscosity of starch increased with the increase of distance from probe tip. Our results also showed that the polydispersity decreased with ultrasonic irradiation under all ultrasonic conditions. Ultrasonic degradation of potato starch paste occured based on the mechanism of molecular relaxation of starch paste. In the initial stage, ultrasonic degradation of potato starch paste was a random process, and the molecular mass distribution was broad. After that, ultrasonic degradation of potato starch paste changed to a nonrandom process, and the molecular mass distribution became narrower. Finally, molecular mass distribution tended toward a saturation value.

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 for phase-equilibrium calculations for binary solutions with a polydisperse polymer solute. A two-step process is designed to form a real polymer solution containing a solvent and a polydisperse polymer solute occupying a volume at fixed temperature and pressure. In the first step, close-packed pure components including solvent and polymers with different molar masses or different chain lengths are mixed to form a closed-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a volume dependent on temperature and pressure. Revised Freed's model developed previously is adopted for both steps. Besides pure-component parameters, a binary size parameter cr and a binary energy parameter e12 are used. They are all temperature dependent. The discrete-multicomponent approach is adopted to derive expressions for chemical potentials, spinodals and critical points. The continuous distribution function is then used in calculations of moments occurring in those expressions. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations using standard distribution or arbitrary distribution on molar mass or on chain length. Illustrative examples are also presented.

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.

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results： a single granular temperature does not characterize a multi-component mixture and each species attains its own ＂granular temperature＂; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments.

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.

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.

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.