Monte Carlo simulations on the effects of nanoparticles on chain deformations and reinforcement in amorphous polyethylene networks

Reinforcing effects in an amorphous polyethylene matrix were estimated for spherical filler particles arranged either on a cubic lattice or randomly in space. Attention was first focused on the effects of the type of arrangement of the particles on the microscopic properties of the polymer chains. Specifically, Monte Carlo rotational isomeric state (MC-RIS) simulations were carried out to predict the effects of the volumes excluded by the filler particles on the configurational distribution functions of the chains, and from these distributions the elastomeric properties of the composites. The calculations were carried out for a range of particle sizes and particle volume fractions. As expected, filler inclusions are found to increase the non-Gaussian behavior of the chains. The results were compared with those from small-angle neutron scattering (SANS) experiments. In the case of arrangement on a cubic lattice, chains dimensions were always found to decrease. In the randomly-dispersed filler arrangements, there were significant increases in chain dimensions relative to the unfilled system in some instances, and the changes were in excellent agreement with the SANS results. The present simulations thus give further encouragement to interpretations of chain deformations in filled systems in terms of volume exclusion effects from the nanoparticle inclusions, including their dispersions and arrangements within polymer matrices.     

Monte Carlo simulations on filler-induced network chain deformations and elastomer reinforcement from oriented oblate particles

Although the filler particles typically used to reinforce elastomers are at least approximately spherical, prolate (needle-shaped) or oblate (disc-shaped) particles have been used in some cases. The fact that anisotropic structures and properties can be obtained in these cases has encouraged a number of experimental and theoretical investigations. The present study extends some earlier Monte Carlo simulations on prolate particles in an amorphous polyethylene matrix, but now focuses on oblate particles. The particles were placed on a cubic lattice, and were oriented in a way consistent with their orientation in composites that were the subject of an experimental investigation by one of the authors. Rotational isomeric state representations of the chains were then generated to model the elastomeric network in the presence of the filler particles. The chain end-to-end distributions were found to be non-Gaussian, and to depend significantly on the excluded volumes of the particles. The particle-induced deformations of the network chains were consistent with results of some other relevant simulations and with recent neutron scattering results. Specifically, the chain dimensions were found to decrease with increase in the axial ratios characterizing the oblate shapes. As anticipated, the chain dimensions became anisotropic, with significant differences parallel and perpendicular to the direction of the particle axes. In general, the network chains tended to adopt more compressed configurations relative to those of prolate particles having equivalent sizes and aspect ratios. Use of these distributions in a standard molecular model for rubberlike elasticity gave values of the elongation moduli, and these were found to depend on the sizes, number, and axial ratios of the particles, as expected. In particular, the reinforcement from the oblate particles was found to be greatest in the plane of the particles, and the changes were in at least qualitative agreement with the corresponding experimental results.     

Modeling the elastomeric properties of stereoregular polypropylenes in nanocomposites with spherical fillers

The elastomeric properties of networks of stereoregular polypropylenes (PP) filled with spherical nanoparticles have been modeled in an attempt to obtain better insights into elastomer reinforcement. The polymers were either isotactic or syndiotactic PP in the amorphous state, and the simulations were based on rotational isomeric state (RIS) theory combined with the largest eigenvalue method for deriving conditional bond probabilities. Monte Carlo simulations gave distributions of the end-to-end distance of these chains in the presence of the particles, and these were used in the Mark-Curro theoretical approach to calculate values of the normalized stress, and the reduced stress (shear modulus) under uniaxial stretching. The simulations were calculated for PP chains having 100-200 skeletal bonds, for several temperatures from 481 to 650 K, and for varying filler particle sizes (up to 100 Å). The presence of the filler nanoparticles was found to influence chain conformations, frequently leading to significant chain extensions, which significantly affect the elastomeric properties of the nanocomposites.     

Collapsed chains as models for filler particles in a polymer melt

Simulations of dense melts of coarse-grained chains have been modified so that they contain filler particles. Since the filler particles and matrix chains are constructed from the same repeat unit, all of the intermolecular energetic interactions in the system (filler-filler, filler-matrix, matrix-matrix) are identical. The collapse of individual chains to form filler particles is achieved by a simple modification in the strength of the minimum in the Lennard-Jones potential governing pair-wise intramolecular interactions within a filler particle. Even when completely collapsed, the filler particles retain mobility in their internal degrees of freedom. Their centers of mass are also mobile. The filler particles can be collapsed completely to dense, impenetrable objects, but they can also be collapsed incompletely to produce permeable filler particles.There is no evidence for spontaneous aggregation of impermeable filler particles, but sufficiently permeable filler particles can aggregate. The parameters used in the simulations insure that the aggregation cannot be energetically driven. Matrix chains that fill space within a permeable filler particle have severe restrictions placed on their available conformations. The reduction in the conformational entropy of the matrix chains can be alleviated if the permeable filler particles interpenetrate, or aggregate. Then fewer matrix chains must enter the permeable filler particles in order to maintain the density of the system. The simulation detects no aggregation of impermeable filler particles because it is not necessary for matrix chains to enter completely collapsed particles.     

大涡模拟方法模拟鼓泡床内气固两相流动

采用大涡模拟（LES）方法模拟气相湍流,颗粒动理学方法考虑颗粒相碰撞产生的动量和能量传递和耗散,采用颗粒相大涡模拟方法（LESp）模拟颗粒脉动导致的能量耗散,同时考虑介观尺度对颗粒相压力的影响,建立了气体-颗粒LES-θ-LESp双流体模型,研究鼓泡流化床内气固两相流动的特性。数值模拟与文献实测颗粒速度和实测颗粒浓度结果具有相同的变化趋势。     

Three-dimensional, rapid shear flow of particles with continuous size distributions

Rapid granular flows occur in nature and industry and often contain particles of many sizes. Over the last two decades, significant theoretical and experimental effort has been directed at rapid granular flows with monodisperse or binary particle-size distributions. In contrast, the behavior of rapid granular flows with more than two particle sizes has received only limited attention. The particle-size distributions in many natural and industrial granular flows may be represented as continuous distributions (e.g., Gaussian or lognormal distributions), providing incentive for the investigation of rapid granular flows with these particle-size distributions. As an extension of previous work for two-dimensional simulations of rapid shear flows with Gaussian and lognormal particle-size distributions, this work is directed at three-dimensional flows with continuous size distributions. Event-driven, discrete-particle (“molecular dynamic”) simulations are employed for the three-dimensional simple shear flow of smooth, spherical particles with Gaussian and lognormal particle-size distributions. The results parallel those found previously in two dimensions and demonstrate the effect of distribution width on the stress tensor and granular energy.     

Axial segregation in bubbling gas‐fluidized beds with Gaussian and lognormal distributions of Geldart Group B particles

Bubbling, gas‐fluidized bed experiments involving Geldart Group B particles with continuous‐size distributions have been carried out. Sand of various widths of Gaussian or lognormal distributions were completely fluidized, then axial concentration profiles were obtained from frozen‐bed sectioning. Similar to previous works on binary systems, results show that mean particle diameter decreases with increasing bed height, and that wider Gaussian distributions show increased segregation extents. Surprisingly, however, lognormal distributions exhibit a nonmonotonic segregation trend with respect to distribution widths. In addition, the shape of the local‐size distribution is largely preserved with respect to that of the overall distribution. These findings on the nature of local‐size distribution provide experimental confirmation of previous results for granular and gas‐solid simulations. Lastly, an interesting observation is that although monodisperse Geldart Group D particles cannot be completely fluidized, their presence in lognormal distributions investigated still results in complete fluidization of all particles. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Filter efficiency as a function of nanoparticle velocity and shape

The filtration efficiency of a conventional fibrous filter was investigated with particular emphasis on the removal of particles with different shapes. A previous study has shown that particles of spherical shape are removed from the gas carrier with efficiencies which are higher when compared to cubic particles of the same aerodynamic size. In this project, to challenge our previously made explanation, spherical PSL and cubic MgO particles were tested along with particles of sodium chloride (NaCl) of intermediate shape (cubic particles with rounded edges) at a range of filtration velocities from 5 to 20 cm/s. It was found that particles of NaCl are removed with efficiencies lower then those for PSL particles but higher than the efficiencies for cubic particles of MgO, at the lowest filtration velocity when inertial effects are negligible. The rounded NaCl particles, depending on the geometry of the contact, could either land on the rounded corner and hence roll, land on a sharp edge and hence tumble, or slide. This range of options alters the probability of detachment of the particle. The difference between the filter efficiencies for cubic MgO particles and intermediate shaped NaCl particles is decreasing with the increase in velocity. With increasing velocity, the filtration efficiency of the cubic MgO particles, exceeds the filtration efficiency for the intermediate shaped NaCl particles, due to the dominating inertial effects of the denser, and hence heavier, MgO particles. This paper shows the results of these experiments and, we hope, will ignite the interest of the aerosol community towards further theoretical analysis of the phenomenon.     

Electrostatic phenomena and molecular motion at interfaces of glass/polymer composites

A boundary zone of filler-affected polymeric network is a possible element in the microstructure of composites. The intensity of adsorption potentials for polymeric material on the filler and therefore its surface energy should be an important variable in boundary zone properties. This work has involved the modification of surface energy in a glass filler material through the introduction of externally induced electrostatic charge that is through the creation of a ‘synthetic’ zeta potential on filler particles. The interactions of charged and uncharged glass surfaces with a polymeric matrix were studied by thermally stimulated discharge (TSD), and also by contact angle measurements. The experimental system studied was an aluminosilicate glass as the filler material, and poly(tetraethylene glycol dimethacrylate) as the organic matrix. Contact angle measurements revealed enhanced wettability for the matrix-forming monomer on glass surfaces charged negatively by electric fields. TSD analysis was also carried out on pure polymer, and composite materials containing either uncharged or bipolar filler particles (particles exposed to an external electrical potential). TSD spectra suggest a suppressed level of molecular motion in composites with fillers of high electrostatic surface energy. Also, activation energies calculated from TSD data are higher in bipolar filler composites. The higher activation energies are consistent with the possibility that a less mobile interfacial zone polymerizes around higher surface energy filler particles.     

Numerical predictions of 3-D filler orientation and elastic compliance for reinforced plastics containing fillers with aspect ratio distribution

In the injection molding of parts containing 30 wt% short-glass-fiber or glass-flake, filler orientation distribution functions and elastic constants are predicted, taking into account the aspect ratio distribution of fillers. The filler orientation distribution functions and the elastic compliance tensors are estimated by using Advani's method and Wakashima's method, respectively. The estimated filler orientation distributions in composite parts reinforced with short-glass-fiber or glass-flake agree with soft X-ray photograph observations. The fiber orientation distribution function, predicted for interaction coefficient C_I = 0.01, is close to the experimental results. Based on this orientation distribution, the elastic compliance tensor distributions are predicted on the assumption that the filler aspect ratio can be presented by a circumscribed filler aspect ratio or an equivalent filler aspect ratio. As a result, the vibration behavior predicted by adopting the equivalent aspect ratio agrees with the experimental results. Polym. Compos. 25:194–213, 2004. © 2004 Society of Plastics Engineers.     

A proposal for discrete modeling of mechanical effects during drying,combining pore networks with DEM

A discrete modeling approach is introduced to investigate the influence of liquid phase distributions on damage and deformation of particle aggregates during convective drying. The approach is illustrated on a simple 3D aggregate structure, in which monosized spherical particles are arranged in a cubic packing and bonded together at their contacts; the mechanical behavior of this aggregate is simulated by discrete element method (DEM). Liquid phase distributions in the void space are obtained from drying simulations for a pore network. In a one‐way coupling approach, capillary forces are computed over time from the filling state of pores and applied as loads on each particle in DEM. A nonlinear bond model is used to compute interparticular forces. Simulations are conducted for various drying conditions and for aggregates with different mechanical properties. Microcracks induced by bond breakage are observed in stiff material, whereas soft material tends to shrink reversibly without damage. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Design and characterization of a novel single-particle polar nephelometer

A new polar nephelometer (PN) has been developed to measure simultaneously the scattering angular distributions from 11.7° to 168.3° for individual particles in planes parallel and perpendicular to the polarization of the incident laser beam. Each detection plane had 21 silicon photodiode detectors to detect scattered light at a rate of 100 Hz. Laboratory experiments to validate the performance of the instrument were conducted using nearly mono-disperse spherical particles (polystyrene latex [PSL] and nigrosine) and nonspherical particles (sodium chloride [NaCl] and soot). The observed scattering angular distributions for individual PSL particles were in good agreement with the results of simulations based on Mie theory. Complex refractive index values for nigrosine particles were determined by comparing the observed scattering angular distributions with the results of simulations. Clear differences between the measured scattering angular distributions and the results of simulations based on Mie theory assuming spherical particles were observed for NaCl particles (mobility diameters of 500 and 700 nm) and propane soot particles (mobility diameters of 300, 500, and 700 nm). These results are reasonably explained by theoretical predictions. We also conducted initial observations of ambient particles in Nagoya city, Japan. Scattering angular distributions for particles with a mobility diameter of 500 nm and an average effective density of 1.4 or 0.3 g/cm³, which were selected with a combination of differential mobility analyzer and aerosol mass particle analyzer, were measured using the PN. As results, scattering angular distributions for nearly spherical inorganic and organic particles with an average effective density of around 1.4 g/cm³ were found to be distinguishable from nonspherical particles with an average effective density of around 0.3 g/cm³. This study has demonstrated that our PN has the potential to distinguish between spherical and nonspherical particles.

Copyright © 2016 American Association for Aerosol Research     

Polypropylene during crystallization from the melt as a model for the rheology of molten-filled polymers

Polarized light microscopy shows that polypropylene crystallizes from the melt into a well-distinguished spherulitic structure. Therefore, it provides a useful model for molten-filled polymers, where the growing spherulites are considered to be filler particles dispersed in a matrix fluid. Although spherulites are randomly dispersed in the space, two dispersion models (simple cubic and centered cubic) are discussed to correlate the transformed fraction α(t) with the volume fraction of filler ϕ(t). The combination of these results with those of differential scanning calorimetry (DSC) shows that the transformed fraction α(t) is a direct indication of the volume fraction of filler ϕ(t). The rheological study, using oscillatory experiments coupled with DSC results, shows the relative sensitivity of the rheological functions to structural changes of the liquid during crystallization. Furthermore, they reveal the existence of a yield effect above a certain criticl value of the filler content (ϕ_c = 0.4). In the absence of this yield effect, a model is proposed to predict the variation of the rheological functions with the filler content. This model shows not only a variation of the plateau modulus, but also the modification of the characteristic times of relaxation of the polymer matrix, whereas the shape of the relaxation spectrum remains unchanged. © 1996 John Wiley & Sons, Inc.     

Uncovering the critical factor in determining the residual stresses level in Si3N4–GM filler alloy–42CrMo joints by FEM analysis and experiments

The influence of gradient materials (GM) filler alloy on the distribution of thermal stresses and on the bending strength of the brazed Si₃N₄–42CrMo steel joints was examined by using finite element modeling (FEM) computations in combination with experiments. In order to form a smooth thermal expansivity change across the whole joint, a novel GM filler alloy was fabricated by stacking each layer with different content of Mo particles (Ag–Cu–Ti+Mo) addition together. We examined the effect of GM compositions, layer numbers and thicknesses on the residual stresses in the brazed joint. In particular, the monolayer composite filler produced by incorporating 10 vol% Mo particles induced the minimum residual stresses in the joint, agreeing with the experimental results. The results indicated that the CTE mismatch between the joined materials and the ability of plastic deformation in the filler alloy were two factors that determine the residual stresses level in a brazed joint. The results reported here will provide us guidance to choose an appropriate filler alloy for improving the ceramic–metal joint performance.     

Response of matrix chains to nanoscale filler particles

A new generation of on-lattice MC simulations for dense melts of coarse-grained POE chains has been developed so that the MC simulations include nanoscale filler particles. In this novel approach, filler particles and polymer chains are built from the same chemical structural building unit. Early simulations pointed an ambiguous behavior for the response of the matrix chains to the introduction of the nanoparticles. When the size of nanoparticles is comparable to that of matrix chains, or even smaller, a significant amount of chain expansion (for matrix chains) is always the case, which challenges the current theoretical considerations in this field. Our recent simulations show that the chain expansion behavior is not triggered by an artificially created “extra volume” effect. Furthermore, the relation between chain expansion behavior and a potential enhancement in the free volume is found to be irrelevant based on our analysis on the pair correlation and scattering functions.     

MODELING OF DRYING IN CAPILLARY-POROUS MEDIA: A DISCRETE APPROACH

Drying experiments are carried out in two-dimensional etched networks under quasi-isothermal conditions. The evolution of phase distributions within the network are visualized and compared to numerical discrete simulations. The phase evolution determined by numerical simulations agrees very well with experimental results. However, the comparison between numerical and experimental drying kinetics does not show good agreement. The differences are explained by the presence of liquid films on the micromodel walls and edges during drying. These films are not taken into account in the numerical model.     

Filtration of nanosized particles with different shape on oil coated fibres

In our previous work it has been shown that perfectly spherical polystyrene latex (PSL) particles have higher filtration efficiency compared to cubic magnesium oxide (MgO) particles of the same electrical mobility as PSL particles. This disparity was ascribed to the different nature of motion of the spherical and cubic particles along the fibre surface, following the initial collision. After touching the fibre surface and before coming to rest, the spherical particles could either slide or roll compared to the cubic ones, which could slide or tumble. During tumbling, the area of contact between the particle and the fibre changes significantly, thus affecting the bounce probability, whilst for the spheres, the area of contact remains the same for any point of particle trajectory. In this project, the polypropylene filter was coated with a thin layer of mineral oil that was used to absorb the energy and, respectively, to minimize particle motion along the fibre after collision. The filtration efficiency of spherical PSL, and cubic MgO particles was measured in the size range of 50–300 nm, for filtration velocity of 10 and 20 cm/s. It was found that, regardless of shape, both particle types have very similar filtration efficiency. The theoretical predictions are in good agreement with our experimental results. Therefore, the conclusion can be drawn that the oil coating minimizes the amount of particle motion along the fibre after initial collision, making results for all particle shapes similar.     

A new model for the influence of particle arrangement and interphase on the stiffness of particulate composites

In this work, the stiffness of a composite containing spherical particles surrounded by an inhomogeneous interphase embedded in an isotropic matrix is evaluated. The elastic constants of the interphase are modeled as continuous radial functions. It is assumed that this third phase developed between the polymeric matrix and the filler particles contains both areas of absorption interaction in polymer surface layers onto filler particles and areas of mechanical imperfections.It can be said that the concept of boundary interphase is a useful tool to describe quantitatively the adhesion quality between matrix and particles and that there is an effect of this phase on the thermomechanical properties of the composite. The thickness and volume fraction of this phase were determined from heat capacity measurements for various filler contents.On the other hand, it is assumed that the particle arrangement (distribution) and their interactions should affect the thermomechanical constants of the composite.The theoretical predictions were compared with experimental results as well as with other theoretical values derived from expressions given in the literature and in some cases, they were found to be in a reasonable agreement.     

Particle dynamics simulations of a piston-based particle damper

A piston-based particle damper geometry is proposed and investigated using experiments and particle dynamics simulations. In particle damping, energy is dissipated through the inelastic collisions and friction between granular particles. Due to their temperature-independent performance, particle dampers are promising alternatives for use in extreme temperature conditions. Using the appropriate inter-particle force models, the simulations agree well with the experimental results. Using simulations, many parameters are investigated in this work for their effects on the damping performance, including material properties, particle size, device geometry, and excitation level. These results provide new understanding of particle damping and may help in the design of next generation particle dampers.