分形理论及在高分子科学中的应用和发展

介绍了分形理论的主要内容，包括分形定义、特性和测定分形维数的方法，概括和评述了近年来分形理论在高分子链结构、结晶过程、溶液中、高分子材料断裂、磨损以及其他方面的研究和应用，并展望了分形理论今后的发展趋势。     

胶体中的分形

介绍了胶体与界面化学的基础理论和发展以及溶胶-凝胶方法在各个领域中的应用。对分形理论在胶体科学研究中的应用以及各种求算分形维数的方法进行了综述和总结，指出了现有基本模型和理论的不足和片面性，提出将分形理论引入溶胶-凝胶体系，深入胶体基础理论层面的研究。同时，对实验的局限性和胶体生长的非线性进行了对照，引入了计算机模拟这个有效的手段，并对分形与计算机紧密结合的趋势进行了展望。     

分形理论及其在活性炭研究中的应用

活性炭的表面和孔隙具有不规则性,且在一定尺寸范围内表现出自相似性,而分形维数是不规则性的一个量度.本文主要介绍了分形的一些基础理论及其在活性炭中的研究方法,如吸附法、小角X射线散射法、压汞法和电镜法等.这些方法能有效地得出自相似结构和分维,但通过对分维的研究,改善材料性能的研究成果很少.随着分形理论的发展及测度方法的进步,用分形来研究活性炭越来越方便.     

煤焦气化过程中的分形特征

将分形理论的概念应用到煤焦气化研究中 .煤焦气化过程孔结构参数间的变化规律符合一定的分形关系 ,气化速率越大 ,分形维数也越大 ,但是分形理论并不适用于所有煤焦气化过程研究 ,只有那些孔容积绝大部分由中小孔构成的煤焦才符合分形规律 .     

用分形理论研究低渗储层孔隙结构

储集层岩石的孔隙结构非均质性对于油气的渗流规律以及水驱油效率都具有重要的影响。利用分形理论对孔隙结构的非均质性进行研究。结果表明,分形维数不同孔隙结构不同,所研究的储集层具有单一分形（分形维数2.690 7～2.814 0）和分段分形特征（分形维数2.414 8～2.995 2）;以分形维数为基础,可以根据孔喉渗透率贡献判断孔隙结构的非均质性和复杂程度。     

镀层表面形貌的分形维数定量表征

为了定量表征镀层表面的形貌特征,应用当代非线性科学新理论--分形几何学方法,研究了几种镀层的表面形貌,用表面分形维数定量表征了其表面形貌特征.结果表明,用像素点覆盖法计算的表面分形维数介于1～2之间,覆盖法计算的则介于2～3之间,后者较接近表面形貌的真实分形维数;两者计算的相关系教都大于0.99,说明镀层具有分形结构.该方法可为进一步研究镀层表面形貌及优化电镀工艺参数提供一种新的定量依据.     

计算机模拟技术在絮体分形成长研究中的应用

颗粒聚集形成絮体是水处理混凝过程中的中心现象,絮体的结构、行为和性能与混凝效果密切相关。计算机模拟为研究颗粒聚集过程提供了一条新的途径,而分形理论则提供了新的理论观念。本文对絮体的分形结构模型、絮体成长过程的计算机模拟方法和模拟结果的分析方法进行了系统的介绍,以期推动此项技术的应用研究。     

硫化物催化剂结构性质与合成甲醇反应性能的关联(Ⅱ)──表面形貌的分形几何特征

应用分形几何理论研究了硫化物催化剂的表面性质及其与合成甲醇反应性能的关系．由分形维数定量地表征了催化剂表面形貌的几何特征．提出了催化剂表面分形维数具有特定的分布,并用正态分布函数进行了拟合．考察了助催化剂和载体对催化剂表面分形维数的影响,由此探讨了分形维数与催化剂结构和反应性能的关系．对甲醇的时空收率和分形维数进行了关联．     

分形理论在渗流力学中的应用

本文从分形理论基础出发,总结了分形理论的发展历程和其核心内容。在论证了分形理论在渗流力学中应用的可行性后,总结了渗流力学和分形理论结合所产生的成果和研究现状。并进一步指出了分形理论在渗流力学中应用所存在的问题和未来的研究趋势。     

热解温度与煤焦微结构及分形特征关系研究

采用扫描电子显微镜 ( SEM)研究了不同热解温度条件下煤焦的微观结构 .结果表明 ,煤焦结构与煤化程度和热解温度有密切的关系 ,烟煤煤焦的微观结构以孔隙为主 ,无烟煤煤焦以裂隙为主 ,且其微观结构具有良好的统计自相似性 ;并采用分形维数定量表征煤焦在不同温度下的孔隙和裂隙特征 ,研究了煤焦分形维数与热解温度、煤化程度的关系及内在机理 ,发现分形维数随煤化程度增加而减少 ,随热解温度提高而增大 .     

Effects of surface topography of material on nucleation site density of dropwise condensation

Heterogeneous nucleation is very important for the initial droplet formation of dropwise condensation, and it is directly related with the surface properties of materials. In this paper, the relationship of nucleation site density with surface topography in nanometer scale for dropwise condensation was experimentally studied on surfaces of magnesium in view of that magnesium can react with hot water (condensate) and make the chemical compositions of the surface changed, and thus leave the nucleation sites in nanometer on the surface. The differential box-counting was used to calculate the fractal dimension of these magnesium surfaces. And condensation experiments were carried out on the magnesium surfaces with different topography under same subcoolings and condensation time. The results showed that surface topography has a great influence on nucleation site density. The larger the fractal dimensions the more the nucleation sites. A new formula to calculate the nucleation site density was proposed based on the modification of Rose's formula with the experimental data. And this new formula can reflect the effect of surface fractal dimension on the nucleation sites.     

Computer simulation of fractal dimensions of fat crystal networks

The rheological properties of fat-structured products are determined by the microstructure of their fat crystal networks, which can be quantified by using microscopical and rheological techniques. Of particular interest to this study is the quantification of the fractal dimension of the network using these two techniques. Fractal dimensions determined by polarized light microscopy include box-counting, particle-counting, and Fouriertransform fractal dimensions, whereas the fractal dimensions determined by small deformation dynamic rheology exploit the dependence of the storage modulus on the solids' volume fraction. This work reveals that different microscopy fractal dimensions are sensitive to different microstructural factors within the fat crystal network, and thus have different physical meanings. The boxcounting fractal dimension, D _b , increases with increases in crystal size and area fraction of the fat crystals, whereas the particlecounting fractal dimension, D _f , is sensitive to the radial distribution pattern of fat crystals; and the Fourier-transform fractal dimension, D _FT, decreases with increasing crystal size. In the studies on the macroscopic physical properties of fat crystal networks, it is necessary to find the determining structural characteristics and then use the fractal dimensions that are most closely related.     

干馏终温对油砂半焦表面特性的影响

利用氮气等温吸附脱附法和电镜扫描研究了印尼油砂干馏热解过程中半焦表面特性的变化,并利用分形维数来定量描述半焦表面形态的复杂程度。结果表明,半焦BET比表面积与孔容积随干馏终温的变化趋势相近,均呈现先增大后减小的趋势。通过FHH方程回归得到的分形维数能够较好地反映半焦内部孔隙结构的分形特性,挥发分的吸出、塑性变形、气体产物的逸出以及油蒸汽的再凝结造成的闭孔效应的多种作用的交替影响,使分形维数在不同的温度区间有不同的变化趋势。电镜扫描能够直观地观察到半焦表面的孔结构特征,利用Matlab编程分析电镜图片得到的盒子维数与氮吸附数据拟合得到的FHH分形维数变化趋势基本一致。     

Direct image-based fractal characterization of micromorphology of calcium carbonate fouling crystals

Researches on macroscopic fouling behavior and micromorphology are usually conducted separately. In this paper, the relationship between the macroscopic fouling behavior and micromorphology on different materials is established. A direct fractal-characterization approach based on the micrographs of calcium carbonate fouling crystals is presented. The box-counting method is used to characterize the fouling crystals. For fractal measurements, t-distribution tests of linear regression hypothesis are performed at the significance level of 0.01. If all listed absolute t-statistics with the minimum of 164 are higher than the corresponding t value, the fouling crystals are determined as fractal, with a confidence level of 99%. The fractal dimensions obtained from the micrographs of different visual fields of a specimen are demonstrated to be almost identical, with maximum and minimum relative values of 4.42% and 0.75%, respectively, and standard deviations ranging from 0.0062 to 0.0266. The irregularity of the crystal morphology indicates larger fractal dimensions. Comparison and analysis of the relationship between macroscopic fouling behavior and micromorphology show that the larger fractal dimension of crystal morphology suggests a small amount of surface fouling. Thus, the reasons for the differences in the macroscopic fouling behaviors of different materials are revealed geometrically.     

Fractal Dimension Analysis of Flocs in Inline Coagulation-Microfiltration of Natural Organic Matter (NOM)

2D fractal dimension analysis of inline-coagulation (IC) flocs in microfiltration of NOM using power-law relationship and box-counting was done. Different process conditions represented by two types of coagulants (PIX and PAX) at four different hydraulic gradients (G-values of 4, 31, 98, and 300 s^?1) were tested. Fractal dimensions of the flocs formed under the varying process conditions were found to be different. Overall NOM removal was found to be similar for all cases; however, the membrane filtration and fouling phenomenon observed were affected by the process conditions. This study has investigated the relationships between fractal dimensions, aggregate properties, and membrane fouling behavior observed. In general, PIX resulted in higher particle concentrations and the more irregular floc shapes resulted in high irreversible fouling, lower specific cake resistance, and a more compressible cake layer. In contrast, PAX resulted in lower particle concentrations and the more regular floc shapes resulted in a more reversible fouling, higher specific cake resistance and a less compressible cake layer. The fractal dimensions properties were found to be complementary for the analysis of membrane and cake resistances and can be useful tools in membrane fouling elucidation and minimization.     

基于MATLAB对混凝土SEM分形维数的计算

在分形科学的研究中,分形维数的求取方法一直是人们所关注的,因为它直接关系到求解的可操作性和结果的精度。利用MATLAB的图像处理和数值计算功能,通过编写MATLAB程序计算Sierpinski垫圈图形分形维数并与理论值对比,结果表明该方法准确、合理。通过对混凝土扫描电镜(混凝土SEM)进行处理,计算出图像的分形维数(即计盒维数),从而也为分析研究混凝土微观结构提供一种新方法。     

Coagulation Coefficient of Agglomerates with Different Fractal Dimensions

A coagulation coefficient of agglomerates with different fractal dimensions has not been considered in the past, even though there is a possibility of variations in the fractal dimension of agglomerates at any instant. In this study, a Brownian dynamics simulation was performed with simultaneous collision and sintering, and variations in the fractal dimension of agglomerates were observed. A coagulation coefficient expression for agglomerates with two different fractal dimensions was proposed. The coagulation coefficient based on the different fractal dimensions was at most 140% higher than that based on the average fractal dimension. To determine an accurate coagulation coefficient of agglomerates, the fractal dimension of each agglomerate has to be considered.     

中低负荷下脉动热管壁温信号的分形特性分析

运用功率谱、小波分解、相空间重构、关联维数计算等非线性分析方法对脉动热管壁面温度波动信号分析。表明:功率谱呈现连续谱线,时间序列存在自相似性,展现温度波动信号的混沌行为;小波分解表现出温度波动的分形特性;重构吸引子展现出4种不同的空间分形结构,说明温度信号波动属于分形下的混沌行为。计算分形维数与传热性能的关系,发现系统存在3~6个分形维;随嵌入维数的增加,分形速度关系为R134a大于丙酮大于去离子水,基本表现为分形维数越大,传热性能越好。并发现关联维和热阻成负相关关系。     

不同秸秆生物炭的孔隙结构及其差异

基于低温氮气吸附的研究方法,对水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭进行了孔结构研究,用BET方程、BJH方程和t-plot方法分别计算得到生物炭的比表面积、孔径分布和微孔数据,利用FHH模型计算了孔隙分形维数。研究表明：不同温度不同材料都对生物炭的孔结构有较大影响,随着热解温度的升高水稻秸秆生物炭和小麦秸秆生物炭的BET比表面积和总孔容呈先增加后降低的趋势,而玉米秸秆生物炭的孔隙度随着热解温度升高持续增加;3种秸秆生物炭的孔径分布均以中孔为主,孔隙内部以Ⅱ型孔为主;水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭都具有很好的分形特征,分形维数(D)分别为2.545 4~2.669 3、2.629 7~2.689 5、2.577 3~2.597 2,表明这3种生物炭孔隙结构比较复杂,非均质性强,其中水稻秸秆生物炭和小麦秸秆生物炭均在500 ℃条件下有较高的分形维数,分别是2.669 3和2.597 2,玉米秸秆生物炭则在700 ℃条件下有较高的分形维数,为2.689 5。     

玻璃涂层与碳钢基材结合性能及界面分形研究

采用热熔敷法在碳钢基体上制备了玻璃涂层,用落球冲击试验研究了熔敷温度对玻璃涂层与碳钢基体结合性的影响,并利用金相显微镜和扫描电镜分析了涂层与基体的界面形貌,计算了界面形貌曲线的分形维数.结果表明,熔敷温度、界面形貌及其分雏值与结合性存在对应关系.在试验温度范围内,熔敷温度越高,涂层与基体的界面形貌越复杂,其分维值越大,涂层与基体的结合性也越好.