An in-situ Observation on Initial Aggregation Process of Colloidal Particles near Three-Phase Contact Line of Air, Water and Vertical Substrate

The self-assembling process near the three-phase contact line of air, water and vertical substrate is widely used to produce various kinds of nanostructured materials and devices. We perform an in-situ observation on the selfassembling process in the vicinity of the three phase contact line. Three kinds of aggregations, i.e. particle-particle aggregation, particle-chain aggregation and chain-chain aggregation, in the initial stage of vertical deposition process are revealed by our experiments. It is found that the particle particle aggregation and the particle-chain aggregation can be qualitatively explained by the theory of the capillary immersion force and mirror image force, while the chain-chain aggregation leaves an opening question for the further studies. The present study may provide more deep insight into the self-assembling process of colloidal particles.     

Scalings for a Ballistic Aggregation Equation

We consider a mean field type equation for ballistic aggregation of particles whose density function depends both on the mass and momentum of the particles. For the case of a constant aggregation rate we prove the existence of self-similar solutions and the convergence of more general solutions to them. We are able to estimate the large time decay of some moments of general solutions or to build some new classes of self-similar solutions for several classes of mass and/or momentum dependent rates.     

Kinetics of colloidal fractal aggregation by differential dynamic microscopy

We study the kinetics of an aggregation process induced by adding salt to a stable colloidal suspension of 73 nm (diameter) particles. Despite the subdiffraction size of the colloidal particles, the process is monitored via optical microscopy, which is used here to obtain time-resolved scattering information about the colloidal aggregates. The radius of the aggregates is determined as a function of time and their fractal dimension is extracted. Our results are compatible with a diffusion limited aggregation process, as independently confirmed by spectral turbidimetry measurements on the same sample.     

Exact order-parameter distribution for critical mean-field percolation and critical aggregation

We show that the order-parameter distribution for the mean-field percolation at the critical point is the Kolmogorov-Smirnov distribution and that it coincides with the corresponding distribution for a mean-field aggregation process at the critical time. Both processes are known to belong to the same universality class in the sense that they share the same set of critical exponents, but percolation is at the equilibrium while the aggregation is a dynamical critical process. This shows that, in this case, the probability density for order-parameter fluctuations is universal at the critical point of the infinite lattice, independent of the hypothesis of thermodynamic equilibrium.     

Self-focusing dynamics in monopolarly charged suspensions

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power-law to sublogarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a universal scaling form, independent of any parameter included in the theory. The relative width falls off to a universal value sigma(infinity)(r) approximately 0.2017 that is much smaller than in the uncharged case. We conjecture that sigma(infinity)(r) is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.     

Ballistic aggregation for one-sided Brownian initial velocity

We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial velocity on the right side is a Brownian motion that starts from the origin x=0). We consider the cases where the left side is either at rest or empty at t=0. We derive explicit expressions for the velocity distribution and the mean density and current profiles built by this out-of-equilibrium system. We find that on the right side the mean density remains constant whereas the mean current is uniform and grows linearly with time. All quantities show an exponential decay on the far left. We also obtain the properties of the leftmost cluster that travels towards the left. We find that in both cases relevant lengths and masses scale as t² and the evolution is self-similar.     

Aggregation Processes with Catalysis-Driven Decomposition

We propose a three-species aggregation model with catalysis-drivendecomposition. Based on the mean-field rate equations, weinvestigate the evolution behavior of the system with thesize-dependent catalysis-driven decomposition rate J(i;j;k)=J ijk^v and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0≤ v ≤1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value atlarge times, while the total size of the decomposed speciesdecreases exponentially with time and vanishes finally.     

Mechanisms of small clusters production by short and ultra-short laser ablation

The mechanisms involved into the formation of clusters by pulsed laser ablation are studied both numerically and experimentally. To facilitate the model validation by comparison with experimental results, the time and length scales of the simulation are considerably increased. This increase is achieved by using a combination of molecular dynamics (MD) and the direct simulation Monte Carlo (DSMC) methods. The combined MD-DSMC model is then used to compare the relative contribution of the two channels of the cluster production by laser ablation: (i) direct cluster ejection upon the laser-material interaction, and (ii) collisional sticking and aggregation in the ablated gas flow. Calculation results demonstrate that both of these mechanisms play a role. The initial cluster ejection provides cluster precursors thus eliminating the three-body collision bottleneck in the cluster growth process. The presence of clusters thus facilitates the following collisional condensation and evaporation processes. The rates of these processes become considerable, leading to the modification of not only the plume cluster composition, but also the dynamics of the plume expansion. Calculation results explain several recent experimental findings.     

Statistical analysis of aggregation in freeway traffic

We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth--death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition probabilities for the jump processes are reconstructed by using Greenshields' model, and the equation of the mean size of the cluster at any time t is derived from the birth--death equation. Numerical experiments show the clustering behaviours varying with time very well.     

具有幂次相互作用的磁性粒子凝聚过程的数值研究

在扩散限制凝聚模型的基础上引入粒子的自旋自由度(包括自旋向上和向下),并假设粒子间存在幂次Ising磁相互作用,采用Monte Carlo方法研究了在不同相互作用力程情况下磁性粒子的分形生长规律.模拟结果表明,当粒子间以反铁磁方式耦合时,凝聚体中的粒子自旋交替凝聚.当粒子间以铁磁方式耦合时,凝聚体中粒子的自旋分布与相互作用力程有关:对于短程作用系统,凝聚体中存在大小不同的自旋畴块,即为铁磁生长;而对于长程相互作用系统,凝聚体中的自旋出现反常分布,即中心区域是近似反铁磁生长的结构,其外围后续生长的粒子却保持 关键词： 幂次相互作用 扩散限制凝聚模型 自旋     

Kerr effect from fractal aggregates of polystyrene microspheres

Summary We study the slow aggregation of aqueous suspensions of optically isotropic microspheres by means of transient electric birefringence. Aggregating clusters exhibit large Kerr constants, and consequently we provide direct experimental evidence that the clusters do posses form anisotropy. From the birefringence relaxation time we derive information on the average cluster size and on the size distribution, and determine their evolution during the aggregation process. Static and dynamic light scattering data confirm the validity of the transient electric birefringence results. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Time scaling regimes in aggregation of magnetic dipolar particles: scattering dichroism results

We report experimental results on the aggregation kinetics in magnetorheological fluids subject to a constant uniaxial magnetic field using the technique of scattering dichroism. We show that the number of aggregated particles displays a long-time power-law dependence with exponents that correspond to two different aggregation regimes. These regimes coincide with 3D and 1D-like aggregation. We also derive the values of both time exponents for the number of aggregated particles.     

Controlled cell aggregation in a pulsed acoustic field

Cell aggregation in ultrasonic resonators can be obtained in a few seconds. Hundreds even thousands of cells can be levitated in suspension and generate 2D or 3D aggregates. Nevertheless, the aggregation rate and the 2D or 3D configurations of the resultant aggregates are very difficult to control. This work reports on a novel way of generating and controlling particle and cell aggregates using pulsed ultrasound. This technique specifically explores (in addition to the ultrasound wave, frequency and amplitude) the time of ultrasound application, i.e. the number of pulses as well as the pulse repetition frequency. We demonstrate that with pulsed ultrasound, particles and/or cells levitate in suspension, as with continuous ultrasound, and the aggregation rate can be modified in a controlled manner. By carefully tuning the number of pulses and the repetition frequency, the 3-D and 2-D configurations of the aggregates can be selectively generated. In addition, pulsed ultrasound limits transducer heating, thus allowing for higher acoustic energies than those currently employed with continuous ultrasound.     

Kinetics of a Migration－Driven Aggregation－Fragmentation Process

We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K(k;j)=K'(k;j)=λkj^υ and the constant aggregation rates I₁, I₂ and fragmentation rates J₁, J₂. Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions in several cases with different values of index υ. We find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J₁=0 and J₂ =0, the aggregate size distributions a_k(t) and b_k(t) obey the conventional scaling law, while when J₁>0 and J₂>0, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved.     

Hastings–Levitov Aggregation in the Small-Particle Limit

We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Carathéodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web.     

Limit Shapes for Gibbs Ensembles of Partitions

We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation-fragmentation processes. We show, that all possible limit shapes for these ensembles fall into several distinct classes determined by the asymptotics of the internal energies of aggregates.     

Cluster-cluster correlation during irreversible diffusion-limited aggregation

Summary In this paper, we discuss the evolution of the scattered intensityI(q) during irreversible diffusion-limited cluster-cluster aggregation. We analyse twodimensional simulations and interpret the results within the framework of a recently proposed theoretical approach. The theory describes the correlation among different clusters which develops during the irreversible aggregation process. The model is based on two coupled differential equations, controlling the growth of the average cluster mass and the time dependence of the probability of finding pairs of clusters as a function of their distance. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

金属离子对银溶胶的聚集作用及形成的分数维结构

本文研究了一些离子作用于银溶胶而引起聚集的情况。一价金属离子对银溶胶的聚集作用不明显,第Ⅱ主族的金属离子能够引起银溶胶的聚集而形成分形体(Fractal)态,且随着金属离子半径的增大,其聚集能力增强,对于三价金属离子Al³⁺,它也能引起银溶胶的聚集而形成分形体态。酸根阴离子一般不直接引起银溶胶的聚集,但能影响银溶胶的聚集。 关键词：     

无规聚甲基丙烯酸甲酯立构复合的红外光谱研究

用红外光谱研究了无规聚甲基丙烯酸甲酯的丙酮、苯、氯仿溶液成膜样品的立构复合状况。结果表明无规聚甲基丙烯酸甲酯在丙酮和苯中确能形成立构复合结构,结构的形成主要是依靠分子链中间规和等规链段的相互作用。对丙酮样品的退火实验表明,在退火过程中能够发生间规链段的自聚集现象。     

Scaling Behavior of an Aggregation-Migration Model

We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates K_A(i;j)=K'_A(i;j) ∝ij^v₁ and K_B(i;j)=K'_B(i;j) ∝ij^v₂, we find that the evolution behavior of the system depends crucially on the values of the indexes v₁ and v₂. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.