Statistical verification of crystallization in hard sphere packings under densification

The performance of various structure characteristics in the task of indicating structural peculiarities in packings of hard spheres is investigated. Various characteristics based on Voronoi polyhedra, spherical harmonics, and Delaunay simplices are considered together with the pair correlation function and the mean number of r-close triples. They are applied to a set of hard sphere packings of density φ from 0.62 to 0.72. It turns out that all used structure characteristics are able to indicate changes of order from non-crystalline to crystalline packings. However, not all of them are sensitive enough to indicate different stages of structure transformation under densification. The characteristics based on Delaunay simplices turn out to be the most sensitive for this purpose. For the models considered three principal structure classes are found: packings of densities lower than the known critical value 0.64 showing a non-crystalline behavior; packings with considerable crystalline regions for φ up to 0.66–0.67; rather complete crystals although with numerous defects for φ above 0.67.     

Simulation of random packing of spherical particles with different size distributions

A numerical model for a loose packing process of spherical particles is presented. The simulation model starts with randomly choosing a sphere according to a pregenerated continuous particle-size distribution, and then dropping the sphere into a dimension-specified box, and obtaining its final position by using dropping and rolling rules which are derived from a similar physical process of spheres dropping in the gravitational field to minimize its gravity potential. Effects of three different particle-size distributions on the packing structure were investigated. Analysis on the physical background of the powder-based manufacturing process is additionally applied to produce optimal packing parameters of bimodal and Gaussian distributions to improve the quality of the fabricated parts. The results showed that higher packing density can be obtained using bimodal size distribution with a particle-size ratio from 1.5 to 2.0 and the mixture composition around n ₂:n ₁=6:4. For particle size with a Gaussian distribution, the particle radii should be limited in a narrow range around 0.67 to 1.5.     

Modelling local voids using an irregular polyhedron based on natural neighbourhood and application to characterize near-dense random packing (DRP)

A model has been developed for finding local voids in randomly packed monodisperse spheres. The voids are polyhedral in shape and are based on the natural neighbourhood concept. The natural neighbourhood is defined in the same spirit of Sibson, who introduced the concept as a refinement of Voronoi tessellation. The model is basically the construction of a Delaunay star, where the centre of the Delaunay star is an arbitrary point in the void and the vertices of the star are the sphere centres. The method is best suited for sampling study. Since the model does not use the radius of the spheres, it can even be used for point distribution in three-dimensional (3-D) space. The model can be improved by using Voronoi vertices as seed points (instead of the arbitrary points) and can be used for crystallochemical studies, where only the electron density distribution is known. It is applicable to non-spherical atoms/particles also. The method is used to analyze near-dense random packing (DRP) and the statistical properties of void structures, e.g. number of vertices per void, cell volume, void volume and void fraction, which do not change from packing to packing in the limit of DRP. The overall local void properties are insensitive to sampling; repeatedly taking 500 void samples in an ensemble did not show considerable change. Most of the voids have 9–12 vertices.     

Dynamically tessellating algorithm for analysis of pore size distribution in particle agglomerates

We describe a novel physical application of the OctTree data structure [P. Meagher, Comput. Graphics Image Process 19(2) (1982) 129–147] in a dynamically tessellating algorithm, in conjunction with an object-oriented, constructive solid geometry library (DOC), to efficiently determine pore size distributions in large multi-particle systems. We apply the DOC library to investigate the evolving dynamics of pore formation in multi-particle systems, such as a mixture of smooth hard cubes and spheres and a collection of frictional soft spheres. We demonstrate that the algorithm is able to provide insight into the effect of structural changes on the porosity network; for example, during the uniaxial compaction of soft spheres, we find the number density of pores increases while the mean volume of the pores decreases. This trend is responsible for a shift in the distribution of the pore volumes to favour smaller volumes. We anticipate that the DOC method will have wider applications in the area of granular materials for studying the changes in pore structure in both experimental and numerical systems as a complement to the analysis of particle packing.     

DEM simulation of small particles clogging in the packing of large beads

The percolation of small particles through a periodic random loose packing of large beads is studied numerically with the Distinct Element Method. The representativity of periodic mono-sized sphere packing of varying system size was first studied by comparing their pore size distributions and tortuosities with those of a larger system, considered as an infinite medium. The results show that a periodic packing of size as low as 4-grain diameters gives a reasonable representation of the porous medium and allows reducing considerably the number of particles that has to be used in the simulations. The flow and clogging of small particles of varying concentrations and friction coefficients flowing through the former packing are then studied numerically. Results show that a steady state is rapidly reached where the mean velocity and mean vertical velocity of small particles are both constant. These mean velocities decrease with an increase in friction coefficient and in small particle concentration. The influence of the friction coefficient μ is much less marked for values of μ larger than or equal to 0.5. The distribution of small particles throughout the crossed packing becomes rapidly heterogeneous. Small particles concentrate in some pores where their velocity vanishes and where the density can reach values larger than the density of the random loose packing. The proportion of particles blocked in these pores varies linearly with concentration. Finally, the narrow throats of the porous medium responsible for blocking are identified and characterized for different values of the friction coefficient.     

Particle size effects on Wulff constructions

The equilibrium structure of small particles is analysed by minimising the total surface energy of atomistic clusters. Large deviations from the bulk Wulff construction are identified for fairly large (~10 nm) particles due to sphere packing corrections. These act as additional edge terms which can be significantly larger than the true edge terms. For a simplified fcc model, it is shown that the fraction of (100) surface drops markedly as the particle size drops because of these packing effects. This can lead to very large particle size effects for a face sensitive catalytic reaction. It is also pointed out that these packing corrections link very small (< 100 atom) cluster to very large particles.     

Structural characteristics of porous polymers treated by freezing with water or acetone

The pore structure of nine polymers of different origin initial and treated in water and acetone for 24 h and then frozen by liquid nitrogen for 2 h was studied using low-temperature nitrogen adsorption. An average increase in pore volume and surface area is approximately 16 and 8%, respectively, after freezing with water and 19 and 8%, respectively, after treatment with acetone. However, for some samples, this effect is negative but for others, structural changes are significantly greater (up to 106%) than the average one. Certain treated polymers are characterized by shifted pore size distribution which is also accompanied by displacement of nitrogen adsorption energy distribution.     

The Laguerre polyhedral decomposition: application to protein folds

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins. Received 20 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: sadoc@lps.u-psud.fr     

等离子喷涂层原生性孔隙几何结构的分形及统计特性

孔隙是等离子喷涂涂层原生性结构, 对涂层的耐磨损、耐腐蚀、耐高温等性能具有显著影响, 是涂层参数优化的重要指标之一. 因此, 对涂层孔隙结构特征参数的全面表征对于更加精确地评价涂层质量具有重要意义. 本文将概率统计方法、分形方法与数字图像分析技术相结合, 研究了等离子喷涂涂层原生性孔隙数量、形态、尺寸及其分布等结构特征参数表征方法及孔隙的成形机理. 首先通过改变喷涂功率得到不同孔隙状态的Fe基合金涂层, 随后采用数字图像分析技术对涂层截面孔隙的扫描电子显微形貌图进行处理, 最后通过Weibull统计模型分析了孔隙周长及面积的尺寸分布特征, 并利用基于分形思想的面积-周长幂率研究了孔隙不规则形态的定量表征方法. 在实验过程中, 为了分析涂层孔隙的成形机理, 采用Spraywatch在线监测喷涂粒子的飞行状态. 结果表明: 分形维数能够表征孔隙的不规则形态, 分形维数越大, 孔隙面积越大或边界形态越复杂, 并且其与孔隙的成形机理之间存在良好的映射关系; 孔隙面积及周长的尺寸分布均服从明显的两项Weibull分布特征, 孔隙尺寸较小时, 形状参数β 较大, 而孔隙尺寸较大时, 则反之; 喷涂功率对孔隙尺寸的聚集特点产生不同程度的影响, 随着喷涂功率的增加, 粒子的融化状态逐渐改善, 孔隙的尺寸明显降低; 而当孔隙面积(周长)小于特征值时, 相同尺寸的孔隙概率密度值则越来越接近, 说明孔隙功率的变化对小尺寸孔隙出现的概率影响较小.     

超低密度SiO2气凝胶的制备及成型研究

 以正硅酸乙酯(TEOS)为硅源，采用酸碱二步催化溶胶-凝胶法，结合超临界干燥技术制备了超低密度SiO₂气凝胶,最低密度为3.4 mg/cm³；进一步结合成型工艺，在解决了模具设计和脱模技术后制备了具有不同密度的柱状和微型套筒样品，密度10～50 mg/cm³。研究了水、催化剂、稀释剂对二步溶胶-凝胶过程的影响，获得了制备低密度SiO₂气凝胶的最佳条件。利用扫描电镜、孔径分布及比表面积测试仪等对SiO₂气凝胶微结构进行了研究。结果表明，获得的超低密度SiO₂气凝胶具有较好的纳米网络，平均孔径18.9 nm，还具有高比表面积898 9 m²/g。     

Nanoporous carbon spheres and their application in dispersing silver nanoparticles

Monodisperse nanoporous carbon spheres (NCS) were synthesized in large quantities via a facile hydrothermal synthesis. It is found that the NCS have rough surfaces with a large quantity of uniformly distributed protruding and concaving zones. Large quantities of nanopores of about 0.3 nm in diameter are distributed uniformly on the whole sphere surfaces. The effects of reaction parameters on the surface roughness, sphere diameter and pore size of NCS were investigated. Taking the NCS as substrates, silver nanoparticles (NPs) were deposited onto their surfaces using a one-step ultrasonic electrodeposition procedure. The deposited silver NP has a uniform distribution, a high particle density and a narrow size range of 12-16 nm in diameter. This study demonstrates an efficient approach to fabricate noble-metal/carbon nanocomposites.     

Jamming in two-dimensional packings

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-based on several approximations to predict the probability distribution of volumes-suggests the existence of the limiting densities of the jammed packings according to their coordination number and compactivity. This result has implications for the understanding of disordered states in the disk packing problem as well as the existence of a putative glass transition in two-dimensional systems.     

Distributional properties of the three-dimensional Poisson Delaunay cell

This paper gives distributional properties of geometrical characteristics of the Delaunay tessellation generated by a stationary Poisson point process in ³. The considerations are based on a well-known formula given by Miles which describes the size and shape of the typical three-dimensional Poisson Delaunay cell. The results are the probability density functions for its volume, the area, and the perimeter of one of its faces, the angle spanned in a face by two of its edges, and the length of an edge. These probability density functions are given in integral form. Formulas for higher moments of these characteristics are given explicitly.     

Variation of microstructure with carbonation in lime and blended pastes

Carbonation, as a reaction of the curing process of both, cement and lime binders, modifies the microstructure. Several microstructure properties, namely porosity, pore size distribution, surface fractal dimension, and specific surface area have been investigated in this study to describe the effect of carbonation on microstructure. Both carbonated and non-carbonated pastes of lime and blended pastes of lime and cement having varying water/binder (W/B) ratios are studied. Results show that carbonation decreases the porosity, but not with the same intensity in all pore size ranges. The highest modification is between 0.03 μm and 0.01 μm in lime pastes and between 0.2 μm and 0.02 μm in 50% lime pastes, while in 80% lime pastes the modification is very small. It is also observed that carbonation is a function of the binder composition but not of the W/B ratio. Moreover, surface fractal dimension decreases during the carbonation process, while the specific surface area varies depending of the binder composition.     

Study of the pore size distribution and fractal dimension of HNO3-treated activated carbons

In the present work, the effect of the oxidizing treatment with nitric acid on three activated carbon samples has been studied. The influence of the acid treatment on the surface groups of the different samples has been investigated by means of FT-IR spectroscopy. The pore size distributions of the different samples were determined by means of the HK and DFT methods. The HK method points out a moderate increment of the microporosity due to the action of the nitric acid, whereas the DFT method shows an increase in the microporosity range above 17 Å. Finally, the values of the fractal dimension reveal that the treatment of the samples with nitric acid leads to chemical reactions of a limited extent.     

Numerical Simulation of Random Close Packing with Tetrahedra

The densest packing of tetrahedra is still an unsolved problem. Numerical simulations of random close packing of tetrahedra are carried out with a sphere assembly model and improved relaxation algorithm. The packing density and average contact number obtained for random close packing of regular tetrahedra is 0.6817 and 7.21 respectively, while the values of spheres are 0.6435 and 5.95. The simulation demonstrates that tetrahedra can be randomly packed denser than spheres. Random close packings of tetrahedra with a range of height are simulated as well. We find that the regular tetrahedron might be the optimal shape which gives the highest packing density of tetrahedra.     

直径任意分布球填充的数值模拟

提出球填充数值算法的新分类方法.改进原有的松弛算法,使其能够模拟直径任意分布的球填充问题,采用可变循环周期使不同球数情形下的填充率基本保持不变.算例数据表明,该算法的填充率和配位数均高于原算法.由于采用背景网格搜索和双向链表组数据结构,使得邻接球搜索效率有相当大的提高,算法的时间复杂度为O(N)(N为球数).在一台AMD Athlon 3200+PC上,对于10000个等径球的随机密排列,只需217s,填充率即可达到0.64.     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001