A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Numerical simulations of single and multiple scattering by fractal ice clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4≤R≤10 cm and fractal dimensions D_f=2.5 and 3.We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D_f=2.5, but the differences can increase somewhat for D_f=3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.     

各向异性扩散DLA的标度性质

本文利用坐标变换的方法讨论了各向异性扩散对DLA集团标度行为的影响。对二维正方形点阵,解析计算了各向异性扩散DLA集团的Hausdorff维数。结果表明,此时生长集困的Hausdorff维数D随各向异性扩散概率p连续变化,其最大值为5/3,最小值为3/2,还将这里所得到的理论结果与Jullien等人的数值结果进行了比较,发现它们符合得很好。最后,还解析讨论并计算了各向异性扩散DLA的广义维数D_q(p)。     

各向异性扩散DLA集团的豪斯道夫维数与标度性质

讨论了DLA集团的各向异性扩散效应.计算机模拟证实了具有各向异性扩散规则的DLA集团有严格的菱形结构.导出了一个粒子的各向异性扩散的新方程，计算了各向异性扩散DLA集团的豪斯道夫维数，结果表明，有效外半角β_eff=min(β_ix,β_iy).讨论了各向异性扩散DLA集团的广义维数，使用修改的楔模型得到了广义维数D_q的表达式. 关键词：     

Formation of an ensemble of nanoclusters under rapid deposition of atoms on a surface

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D _f ≈ 1.2–1.4 at d ≈ 1.5 nm to D _f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.     

On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates

Several methods to measure the structures of coal aggregates are compared. Loose and compact coal aggregates were generated through flocculation of ultrafine coal particles (mean volume diameter of 12 μm) under specific shearing conditions. Aggregate structure in terms of mass fractal dimension, D_f, was determined using various methods; namely 2D and 3D image analysis, interpretation of intensity patterns from small angle light scattering, changes in aggregation state through light obscuration, and settling behavior. In this study, the measured values of D_f ranged from 1.84–2.19 for coal aggregates with more open structures, and around 2.27–2.66 for the compact ones. All of these approaches could distinguish structural differences between aggregates, albeit with variation in D_f values estimated by the different techniques. The discrepancy in the absolute values for fractal dimension is due to the different physical properties measured by each approach, depending on the assumptions used to infer D_f from measurable parameters. In addition, image analysis and settling techniques are based on the examination of individual aggregates, such that a large number of data points are required to yield statistically representative estimations. Light scattering and obscuration measure the aggregates collectively to give average D_f values of the particulate systems; consequently ignoring any structural variation between the aggregates, and leaving possible small contaminations undetected (e.g. by dust particles or air bubbles). Appropriate utilization of a particular method is thus largely determined by system properties and required data quality.     

基于分形多孔介质三维网络模型的非混溶两相流驱替数值模拟

提出了一个描述多孔介质孔隙尺寸分布的三维分形网络模型,利用该模型对多孔介质中的非混溶两相流驱替进行了数值模拟,研究了孔隙尺寸分布分维D_f和两相流黏滞比M对驱替前沿指进型的影响,结果表明指进型容量维数D_h随着孔隙尺寸分布分维D_f以及黏滞比M的增大而减少,并通过曲线拟合得到了它们之间的定量关系. 关键词： 多孔介质 三维网络 黏滞指进 非混溶两相流     

Additivity and non-additivity of dissociation energies in intermolecular interactions. Theoretical studies on (H2)n,n = 2-8, (CO2)n,n = 2-6 and (HF)n,n = 2-8

CCSD(T) and MP2 results using the aug-cc-pV5Z basis set are reported for chain, cyclic and other structures of the clusters (H₂)_n, n?=?2-8, (CO₂)_n, n?=?2-6 and (HF)_n, n?=?2-8. In chain-like structures of (H₂)_n and (CO₂)_n, with the bonding type of the dimer maintained, the dissociation energy D_e of the dimer doubles for the trimer, triples for the tetramer, and so on. Due to these systems being dominated by short-range forces, interactions are essentially restricted to neighbouring monomers. For other types of (H₂)_n and (CO₂)_n structures, the multipliers relative to the dimerisation energy can be much higher. Dissociation energies for the hexamers in S₆ symmetry of both H₂ (379?cm^?1) and CO₂ (4925?cm^?1) are over ten times the respective dimerisation energies. For the chain-like trimer of HF, however, D_e is in excess of double the dimer value. Mainly due to longer-range dipolar forces, the interactions reach beyond the neighbouring monomers. The interaction energy between HF monomers in chains follows an approximate R^?2 (R being the F–F distance) relationship, The calculated dissociation energies of the HF octamer are 15,985?cm^?1 (factor of 10.4) for the chain, and 21,003?cm^?1 (factor of 13.7) for the C_6h cyclic structure.     

A new example of the diffusion-limited aggregation: Ni-Cu film patterns

The mechanism of the growth of the dendrites in the Ni-Cu films is studied by comparing them with the aggregates obtained by Monte Carlo (MC) simulations according to the diffusion-limited aggregation (DLA) model. The films were grown by electrodeposition. The structural analysis of the films carried out using the x-ray diffraction showed that the films have a face-centered cubic structure. Scanning electron microscope (SEM) was used for morphological observations and the film compositions were determined by energy dispersive x-ray spectroscopy. The observed SEM images are compared with the patterns obtained by MC simulations according to DLA model in which the sticking probability, P between the particles is used as a parameter. For all samples between the least and the densest aggregates in the films, the critical exponents of the density-density correlation functions, α were within the interval 0.160 ± 0.005-0.124 ± 0.006, and the fractal dimensions, D_f, varies from 1.825 ± 0.006 to 1.809 ± 0.008 according to the method of two-point correlation function. These values are also verified by the mass-radius method. The pattern with α and D_f within these intervals was obtained by MC simulations to DLA model while the sticking probability, P was within the interval from 0.35 to 0.40 obtained by varying P (1-0.001). The results showed that the DLA model in this binary system is a possible mechanism for the formation of the ramified pattern of Ni-Cu within the Ni-rich base part of the Ni-Cu films due to the diffusive characteristics of Cu.     

Effect of water–methanol content on the structure of Nafion in the sandwich model and solvent dynamics in nano-channels; a molecular dynamics study

Continuing an ongoing study, molecular dynamics (MD) simulations were performed to investigate the effects of methanol concentration on Nafion morphology, such as the size of solvent cluster, solvent location, and polymer structure via the sandwich model. Our survey shows that high methanol concentrations resulted in increment of solvent cluster size in Nafion membrane. The sulfonic acid clusters also befall much in order as subsequent layers of such ionic clusters are formed. The number of neighbouring hydronium ions around a sulfur atom is independent of methanol concentration, but the first shell of hydronium and water around sulfonic acid clusters is broader. Although methanol would prefer to interact with water molecules rather than sulfonic acid groups, gathering of methanol molecules via hydrophobic self-aggregation is preferred. Methanol is located closer to the hydrophobic part of the polymer than water, while water is located closer to the hydrophilic part of the polymer. It was found that methanol distributes specifically more than water in nano-channels. Investigation of solvent dynamics in nano-channels shows that diffusion coefficients (D) of water, methanol, and hydronium decrease with increasing methanol concentration and they may be ordered as follows: D _Water?>?D _Methanol?>?D _Hydronium (D _Water?≈?1.6–2.0D _Methanol and D _Methanol?≈?2.1–3.0D _Hydronium).     

Structural properties and scaling of the radius of gyration of two-dimensional star-branched polymers grown by diffusion

We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3,6 and 12 branches with a total of 30,000 monomer units. We investigated their structural properties by calculating the monomer-monomer correlation functions. A detailed finite size scaling analysis of the radius of gyration was also performed to determine the exponent and the corrections to scaling. From these results we calculated the fractal dimension of the branched aggregates and obtained: d_f=1.222(7), for the linear chain, d_f=1.2305(8), d_f=1.247(8) and d_f=1.261(8) for the three, six and twelve branches polymer, respectively.     

Novel metal-encapsulated caged clusters of silicon and germanium

We report the recent findings of metal (M) encapsulated clusters of silicon from computer experiments based on ab initio total energy calculations and a cage shrinkage and atom removal approach. Our results show that using a guest atom, it is possible to wrap silicon in fullerenelike (f) structures, as sp² bonding is not favorable to produce empty cages unlike for carbon. Transition M atoms have a strong bonding with the silicon cage that are responsible for the compact structures. The size and structure of the cage change from 14 to 20 Si atoms depending upon the size and valence of the M atom. Fewer Si atoms lead to relatively open structures. We find cubic, f, Frank-Kasper (FK) polyheral type, decahedral, icosahedral and hexagonal structures for M@Si_n with n = 12-16 and several different M atoms. The magic behavior of 15 and 16 atom Si cages is in agreement with experiments. The FK polyhedral cluster, M@Si₁₆ has an exceptionally large density functional gap of about 2.35 eV calculated within the generalized gradient approximation. It is likely to give rise to visible luminescence in these clusters. The cluster-cluster interaction is weak that makes such clusters attractive for cluster assembled materials. Further studies to stabilize Si₂₀ cage with M = Zr, Ba, Sr, and Pb show that in all cases there is a distortion of the f cage. Similar studies on M encapsulated germanium clusters show FK polyhedral and decahedral isomers to be more favorable. Also perfect icosahedral M@Ge₁₂ and M@Sn₁₂ clusters have been obtained with large gaps by doping with divalent M atoms. Recent results of the H interaction with these clusters, hydrogenated silicon fullerenes as well as assemblies of clusters such as nanowires and nanotubes are briefly presented.     

Grain size and composition effects on the cathodoluminescent characteristics of sprayed zinc oxide thin films

The cathodoluminescent (CL) property of 1?µm-thick sprayed ZnO films is here reported versus the sample mean grain size (D) resulting from the spraying flow rate (f) parameter. The deposition process, performed at T _s?=?723?K, leads to hexagonal packed structure of [002] preferred growth orientation, regardless of the f value. The CL-spectra are typical of the film's growth rate (r) and the intensity (I) of the three main emission lines (λ?≈?386, 497 and 644?nm) is greatly affected by D that is ranged between 0.40 and 0.90?µm. Their (I???D) curves have a similar profile that presents a common critical point, D _c?=?0.57?µm, depicting two different luminescent behaviours of the material. Smaller grains exhibit optimal intensities. Their band-edge near UV line (λ?≈?386?nm) proceeds from a phonon replica phenomenon; excess of interstitial Zn explains the result of their blue–green line (λ?≈?497?nm) while deep-level interactions effect is the relevant interpretation for the red one (λ?≈?644?nm). A decrease of luminescent properties from D?=?0.45?µm till D _c is assigned to the sample microstructure degradation. The bell-shaped profile of CL-intensity for D>D _c reflects a competition between the increase of the material reactive part and the collapse of crystallites quality due to higher content of Cl and S impurities in bigger grains. A limit of the two approaches appears at D?=?0.65?µm.     

Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set of paths is complete for the complexity class CC, the subset of P characterized by circuits composed of comparator gates. CC-completeness is believed to imply that, in the worst case, growing a cluster of size n requires polynomial time in n even on a parallel computer. A parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths, and then corrects defects in the guessed cluster through a nonlocal annihilation process. The parallel running time of the relaxation algorithm for two-dimensional internal DLA is studied by simulating it on a serial computer. The numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n. Thus the computational resources needed to grow large clusters are significantly less on average than the worst-case analysis would suggest. For a parallel machine with k processors, we show that random clusters in d dimensions can be generated in ((n/k+logk)n ^2/d ) steps. This is a significant speedup over explicit sequential simulation, which takes (n ^1+2/d ) time on average. Finally, we show that in one dimension internal DLA can be predicted in (logn) parallel time, and so is in the complexity class NC.     

Exploration of fractal nature of WO3 nanowire aggregates

The morphology of WO₃ aggregates formed by irregular nanoparticles (D∼40 nm) and nanowires of different aspect ratios (2, 4, 6, and 10 μm nominal lengths) dispersed in commonly used polar solvents without dispersant agents is investigated using a small-angle light scattering technique and by means of fractal theory. Nanoparticles form compact spherical aggregates (D_f∼2.6), whereas 2 μm nanowires with low aspect ratio (L/D∼10) follow a slow cluster-cluster aggregation mechanism with no discernable change in fractal dimension (D_f=2.1) monitored in an extended period of 6 months, despite a notable growth in size (R_g=2.3-3.1 μm). For higher aspect ratio nanowires, scattered intensity profiles, which migrate towards the Porod regime, qualitatively obey the Lorenz-Mie theory predictions. The 10 μm nanowires with very high aspect ratio (L/D∼250) are observed to form stable dispersions in a time span of 6 days. Analytical methods based on spherical primary particle formulations predict D_f=1.9, 1.7, and 1.4 for 4, 6, and 10 μm nanowires, respectively.     

Morphology Development in Multi‐Component Polymer Blends: I Composition Effect on Phase Morphology in PP/PET Polymer Blends

The relationship of the phase morphology of polypropylene/polyethylene‐terephthalate (PP/PET) blends and their corresponding compatibilized blends with composition was investigated using digital image analysis. A diameter, d _g , was defined and calculated to discuss the phase morphology of this polymer blend system. A figure‐estimation method was introduced to determine the width of the distribution of d _g . Based on the method, it is proven that the distribution of d _g obeys a log‐normal distribution and consequently, the distribution width, σ was calculated. Further, a fractal dimension, D _f , was introduced to describe the distribution of main sizes of the particles of the dispersed phase. The results showed that, while d _g increased with the concentration of the dispersed phase, σ and D _f show different dependence relations on composition;σ increases monotonously but D _f shows a maximum at a PET content of 30%, indicating that, even though the whole size distribution is much broader, the distribution of the main body of size becomes more uniform when the content of PET is less than 30%.     

Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection ind euclidean dimension of a random fractal of dimension D_F and a multifractal distribution of probabilities of dimensionsD _q (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensionsD' _q =D _q +D _F -d, for a finite interval ofq.     

Computational analysis of factors influencing thermal conductivity of nanofluids

Numerical investigations are conducted to study the effect of factors such as particle clustering and interfacial layer thickness on thermal conductivity of nanofluids. Based on this, parameters including Kapitza radius and fractal and chemical dimension which have received little attention by previous research are rigorously investigated. The degree of thermal enhancement is analyzed for increasing aggregate size, particle concentration, interfacial thermal resistance, and fractal and chemical dimensions. This analysis is conducted for water-based nanofluids of Alumina (Al₂O₃), CuO, and Titania (TiO₂) nanoparticles where the particle concentrations are varied up to 4 vol%. Results from the numerical work are validated using available experimental data. For the case of aggregate size, particle concentration, and interfacial thermal resistance, the aspect ratio (ratio of radius of gyration of aggregate to radius of primary particle, R _g/a) is varied from 2 to 60. It was found that the enhancement decreases with interfacial layer thickness. Also the rate of decrease is more significant after a given aggregate size. For a given interfacial resistance, the enhancement is mostly sensitive to R _g/a < 20 indicated by the steep gradients of data plots. Predicted and experimental data for thermal conductivity enhancement are in good agreement. On the influence of fractal and chemical dimensions (d _l and d _f) of Alumina–water nanofluid, the R _g/a was varied from 2 to 8, d _l from 1.2 to 1.8, and d _f from 1.75 to 2.5. For a given concentration, the enhancement increased with the reduction of d _l or d _f. It appears a distinctive sensitivity of the enhancement to d _f, in particular, in the range 2–2.25, for all values of R _g/a. However, the sensitivity of d _l was largely depended on the value of R _g/a. The information gathered from this study on the sensitivity of thermal conductivity enhancement to aggregate size, particle concentration, interfacial resistance, and fractal and chemical dimensions will be useful in manufacturing highly thermally conductive nanofluids. Further research on the refine cluster evolution dynamics as a function of particle-scale properties is underway.     

SIMULATION OF FRACTAL GROWTH OF THIN FILMS AT LOW TEMPERATURE

Fractal growth of thin films at low temperature (50－175 K) is simulated by Monte Carlo method. It is shown that the thin film growth is quite different from the diffusion-limited aggregation (DLA) model when the coverage is larger than 0.1 ML. The average branch width of clusters increases with increasing temperature and it usually larger than the branch width (1.9 atom) in the classic DLA model. The average fractal dimension of clusters increases also with increasing coverage while the fractal dimension of DLA model remains constant. This difference comes from the weak screening effect during the late stage of thin film growth. The relationship between the saturation island number n_s and deposition interval Δt is described in a power law: n_s∝Δt^γ, where γ=-0.332 is very close to the theoretical value -1/3 of rate equations from nucleation theory.