Numerical computations of molecular reactions in associated systems caused by the formation of fractal structures

The interaction between particles in a system containing fractal clusters has been computationally simulated. The fractal structure of the system has been demonstrated to determine the kinetic characteristics of particle interaction. If a system in an N-dimensional space (N = 2, 3, 4) contains fractal clusters with the fractal dimension D > N-1, the rate of interaction of a free particle with particles belonging to clusters depends on their concentration according to the power law. The exponent gamma of this power law formally corresponds to the kinetic order of the reaction with respect to the concentration of particles belonging to the clusters. Its value is determined by the free surface of the clusters and depends on its fractal dimension D. The results of simulation qualitatively agree with the data on high, non-integral orders of many liquid phase molecular reactions characterized by self-organization of the medium via weak intermolecular interactions, such as hydrogen bonds.     

The Evolution of Microstructure in Nonhydrolytic Alumina Xerogels

The effect of drying, aging and thermal treatment of alumina xerogels prepared by the nonhydrolytic route was investigated using SAXS, BET and HR-SEM techniques. The microstructure of the fresh xerogels prepared under different procedures varied drastically, ranging from aerogel-like mass fractals to narrow pore size distribution materials. By variation of the drying conditions the N2-BET surface area was varied from an immeasurable low level up to 600 m2/g. The initial microstructure has a significant influence on the xerogel behaviour during the post-drying heating stage. The ability to produce aerogel-like mass fractal materials from the nonhydrolytic systems is discussed. Finally, a brief theoretical treatment of the drying process of mass fractals is presented as well.     

Structures and their influence factors of three‐dimensional fractal cadmium layer formed by electrodeposition

Three‐dimensional fractal structure of the electrodeposited cadmium layer was investigated. The results suggested that the fractal growth begin with nanometer scale aggregate within which the atoms arrange in hexagonal close‐packed lattice (the normal cadmium lattice). The fractal structure is correlated to the current density. The higher the current density is, the larger the size of fractal growth will be. Fractal structures can emerge in both the complete diffusion‐limited process and the combination‐limited process of the electrochemical reaction and diffusion. The fractal structure obtained from the simple hydrated ion electrolyte is different from that obtained from the complex ion electrolyte, which indicates they grow in different modes. The fractal dimensionality of deposit from the simple hydrated ion electrolyte is 2.592, smaller than that (2.608) from the complex ion electrolyte.     

金属线电极分形生长的模拟

电沉积金属过程中,阴极沉积的金属边缘会出现包括枝晶生长在内的许多复杂形态,这会严重影响电沉积产品的质量和加工过程中的电流效率. 对枝晶分形生长的过程以及形貌进行研究,可以实现对沉淀物的可控生长. 本研究使用Python和Matlab软件相互结合,基于扩散限制凝聚（DLA）模型,建立平行线电极电沉积的模型. 通过分析不同粒子数、沉积概率、电极间距、运动步长、定向漂移条件下的分形生长的变化规律,以及模拟参数与实际电沉积因素对分形生长影响的内在联系,发现只要合理控制模拟的粒子数、沉积概率、线电极间距、运动步长、定向漂移概率参数即可与实际电化学体系的浓度和沉积时间、还原概率、两极间距、温度和电压、电极的相对位置和形状一一对应,从而模拟得到跟实际电沉积接近的分形图,最终可实现对分形生长的可控操作,对分形生长在工业电沉积等方面应用有很大的意义.     

A Study of Relationship Between Universality in Fractal Colloids Aggregation and Time-dependent SERS

The relationship between the rule of time-dependent surface-enhanced Raman scattering (SERS) intensity of adsorbed pyridine in AgBr sol and silver bromide colloidal fractal aggregation is studied in this paper. The experimental results support the view of universality in colloidal aggregation and suggest that SERS may be a useful tool in the study of kinetics of colloidal aggregation.     

金属锌电沉积过程的分形研究

对金属锌电沉积过程中的二维枝晶生长进行了研究,分析了外加电压、电解质浓度以及温度等实验条件对电沉积产物形貌及其分形维数的影响.结果表明,随着外加电压的增大,沉积产物形貌的变化趋势为由开放的分枝结晶向较为致密的生长形貌转变;随着硫酸锌浓度的增大,沉积产物具有分叉结构的致密纤维状枝晶簇和较为粗壮的开放型规则的分叉状枝晶,分形维数发生相应的变化;随着温度的升高,沉积产物的枝晶呈均匀化、致密化,沉积产物分形维数呈明显增大的趋势.     

Elastic properties of networks of fractal clusters

Elastic properties of casein gels were followed by dynamic measurements for various volume fractions of casein micelles far above the percolation threshold. Elastic and loss storage moduli versus volume fractions obey a power law with an exponent close to 3. The previous theoretical models for networks made of a homogeneous packing of fractal flocs do not predict the observed behavior. A model is proposed to estimate the vectorial contribution to the network elasticity. This model is in agreement with our experimental results. The value of the fractal dimension of the flocs derived from this analysis is discussed as a function of the volume fraction of primary particles.     

Fractal phenomena in molecular mechanics calculation

It is proposed that in molecular mechanics calculation points belonging to various stable or meta-sta-ble conformtrs are mixed up and form fractal structures in conformation space.The calculation results show the following two phenomena:(i)Two levels of structure with fractal feature were observed.Around the conformer without mirror symmetry points belonging to the conformer and its enantiomer are mixed up and form the first level of fractal structure; on the boundary of the attractive basin o{ each atlractor,points belonging to different attractors form the second level of fractal structure.(ii) The variation of molecular mechanics parameters will influence the structure and area of each attractive basin significantly The above phenomena may become the basis of a new method for solving the troublesome multi-minimum-point problem in molecular mechanics calculation.     

介孔吸附剂表面分形分析

用自溶液中吸附的方法测定了介孔硅胶和活性炭的分形维数D.结果表明:(1)硅胶自四氯化碳或环已烷中吸附脂肪醇、酮、酯和含氧芳香化合物,活性炭自水中吸附芳香化合物的等温线均服从Langmuir方程.用极限吸附量n_m^s和表观分子面积σ_a,根据方程log n_m^s=-(D)/(2)log σ_a+常数,可计算出分维D. n_m^s和σ_a是根据Langmuir方程和吸附剂比表面数据求出的.(2)用液相吸附法求出的介孔硅胶的分维值与由气体吸附法求出的值相同,并均近于2.当表面曲率半径大于吸附分子大小时,吸附剂表面可是低分维的.(3)由液相吸附法得到的介孔活性炭的分维也近似为2.可能的解释是,活化作用改变了原始炭的微孔结构,使其成为介孔和大孔.介孔活性炭也可是低分维表面.     

Kinetics on Diffusion-Controlled Reactions in a Fractal Medium

The kinetics are investigated for diffusion-controlled reactions in a fractal medium described by a Smoluchowski equation. A class of model potentials are taken into account so as to solve the time-dependent Smoluchowski equation. Corrections to the standard solution are proposed for the fractal geometry of the medium.     

催化剂表面分形结构对催化反应的影响

用溶胶－凝胶方法制备了ＳｉＯ２并以其及另一种ＳｉＯ２气凝胶作载体,用浸渍法制备了两种铑基催化剂。以ｎ－Ｃ５～Ｃ８烷烃为探针分子,测得两种催化剂的表面分形维数Ｄ分别为３和２。在两种催化剂上,ＣＯ加氢和丙烷氢解反应的选择性没有显著差别,但在Ｄ＝２的催化剂上,ＣＯ加氢和丙烷氢解反应的速度显著高于Ｄ＝３的催化剂     

Chemical-physical aspects of formation and evolution of phase structure in multi-polymers: Intensity fluctuation, phase structure and its fractal characteristics in blends of isotactic polypropylene with poly(cis-1,4-butadiene) rubber

This paper studies the formation and evolution of phase structure of isotactic polypropylene/poly(cis-1,4-butadiene) (iPP/PcBR) blends during molten and mixing in a visual mixer by on-line analysis of the small angle light back scattering. The density fluctuation of iPP/PcBR blends during molten and mixing is discussed using the integral-intensity Js, of the scattering intensity of the blends. The "invariant" Q, which shows fluctuation of the system, is calculated by data of the small angle light back scattering, and the variation of Q with the blending time, temperature and shear rate during molten and mixing in iPP/PcBR blends is discussed. The structure parameters which characterize dimensions of phase in the blends, as the correlation distance ac, and the average chord lengths of two-phase, as li PP and lP cBR, are calculated by data of scattering intensity. The average diameters dp of dispersed phases are calculated from SEM images. The variation of ac, dp, li PP and lP cBR with the blending time and compositions in the blends during molten and mixing is discussed. The scale law is analyzed to find multi-scale characteristics in this system. The generalized fractal dimension Dp is calculated and the relation of Dp with generalized entropy function is discussed to determine that Dp is state function and the physical significance of Dp is the same as that of the generalized entropy function.     

Fractal notation for nearly-symmetrical dendrimers

Dendrimeric and related molecules that have the same atomic connectivity from exterior to core, P-C₁-J₁-C₂- … Z (P peripheral group, J juncture, C connector, Z core) can be described completely by a highly compact fractal notation, which is of the general form Pf _{J1,J2 …} (C₁.C₂ …)Z. In this paper, we show how to describe molecules that deviate slightly from the symmetry of a related parent molecule, by use of parenthetic expressions (iX), (dX), and (YrX) which designate atoms or molecular groups that are inserted, deleted, or replaced by other groups in the parent. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2979–2983, 1998     

Diffusion of a passive impurity through a porous media: fractal model in an unsaturated medium

The theory of fractal sets is used to describe convective diffusion of a passive impurity in a partly-saturated porous medium.     

An analysis of fractal geometry of macromolecular gelation

With fractal geometry theory and based on experiments, an analysis of fractal geometry behavior of gelation of macromolecules was carried out. Using the cross-linking copolymerization of styrene-divinylbenzene (DVB) as an example, through the determinations of the evolution of the molecular weight, size and the dependence of scattering intensity on the angle of macromolecules by employing laser and synchrotron small angle X-ray scattering, respectively, this chemical reaction was described quantitatively, its fractal behavior was analyzed and the fractal dimension was also measured. By avoiding the complex theories on gelation, this approach is based on modern physical techniques and theories to perform the analysis of the behavior of fractal geometry of macromolecular gelation and thus is able to reveal the rules of this kind of complicated gelation more essentially and profoundly.     

Fractal Measures of Fluid Mixing and Filtering of Inflow Noise in a Biological Reactor

For -galactosidase production by a recombinant strain of Escherichia coli, fractal dimensions have been computed for two intra-cellular and two extra-cellular variables under three kinds of Guassian noise. The fractal dimensions changed significantly with both fluid mixing and noise, indicating their usefulness as discriminating indexes to optimize mixing intensity and filtering of inflow noise.     

Monolayer physical adsorption in narrow pores. Apparent surface dimension

Monolayer physical adsorption has been considered, taking into consideration the intrinsic volume of the adsorbate molecules. Since an adsorbed molecule occupies not only the site on the surface but also some of the neighboring volume, it creates steric difficulties for the adsorption of other molecules and leads to underestimation of the measured surface area. As a result, this value depends on the size of the adsorbate molecules and the apparent surface dimension can be introduced, even if the surface of narrow pores has no irregularities of atomic scale size. This effect was shown by simulation of adsorption on the surface of Menger sponge. Experimental data for measuring D-values on silica gels with different pore size distributions are in line with this effect.     

多孔介质中气体水合物降压分解的分形理论研究

通过将水合物的分解过程看作是无固态产物层生成的气固反应过程, 结合粒径缩小的收缩核反应模型和分形理论, 建立了多孔介质中水合物降压分解的分数维动力学模型, 提出了基于水合物分解实验数据计算多孔介质分形维数的方法. 分别利用前人的甲烷水合物和CO2水合物降压分解实验数据, 对上述分数维动力学模型进行了验证. 计算结果表明, 用提出的方法所计算得到的多孔介质分形维数与前人的测定结果基本符合; 对甲烷水合物和CO2水合物的降压分解过程, 提出的分数维动力学分解模型得出了和实验结果基本一致的预测, 绝对平均误差(AAD)小于10%.     

Studies on the Spontaneous Evolution of Small Particle Aggregations

On the basis of the criteria for spontaneous evolution of small particle aggregations, which are described by D. Zhaojing, L. Yiping, and L. Cunye [J. Colloid Interface Sci.173,79 (1995)], and according to the results of the experiments and simulations, the spontaneous evolution process of small particle aggregations is further discussed in detail.