Colloidal ZnO nanostructures and functional coatings: A survey

The past research work devoted to ZnO nanocolloidal sol-gel route is reviewed. It highlights the cluster chemistry of alcoholic ZnAc₂ solutions and the results of ZnO colloid growth investigations performed worldwide. Moreover, the role of doping and co-doping in the processing of functional ZnO coatings is discussed. The possibilities of tuning the optical properties are also reported with a particular attention to luminescence. The last part of this paper deals with electrical and photoelectrochemical properties of ZnO nanocrystals and their aggregates. This contribution is dedicated to the 80th birthday of Prof. Arnim Henglein from the Hahn-Meitner-Institut in Berlin and to the memory of Prof. Jacques Mugnier from the Université Claude-Bernard Lyon 1 in France.     

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.     

Monopole charge quantization or why electromagnetism is a U(1)-gauge theory

We obtain Dirac’s classic monopole charge quantization from the point of view of geometric quantization and demonstrate how this leads to the conclusion that the electromagnetic field is a U(1)-gauge field.     

Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.     

Hidden structure in the randomness of the prime number sequence?

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy–Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.     

胶束形成的分形研究

提出了测定胶束质量分维的两种新方法即粘度法和GPC－LALLS联机法，随后从动态光散射数据计算了离子型胶束SDS的分维，这些实验数值之间能互相印证．建立了放束形成过程的Laplace分形理论，计算得分维D＝1.54（二级），作高级计算的分维D＝1.67与前面实测值基本相符，另外，从唯象理论角度，讨论了胶束的多重分形及其热力学行为，发现有两个相变点β_c＝-4和β_c＝-1．并认为这两个转折分别对应着单分子<=>分形胶束<=>经典胶束结构之间的转变．     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Squig sheets and some other squig fractal constructions

Squig intervals are a class of hierarchically constructed fractals introduced by the author. They can be visualized as the final outcome upon a straight interval of a suitable cascade of local perturbative eddies ruled by two processes called decimation and separation. Their theory is summarized and their scope is extended in several new directions, especially by introducing new forms of separation. Squig intervals are generalized in two dimensions, with fractal dimensions ranging from 1.2886 to 1.589. Squig sheets are constructed in three dimensional space with fractal dimensions ranging from 8/3 up. They should prove useful in modeling the fractal surfaces associated with turbulence and related phenomena. Squig intervals are constructed in three dimensions. Nonsymmetric eddies and the resulting squigs are tackled. Squig trees and intervals are drawn on unconventional lattices, either in the plane or in a prescribed fractal surface. Peyriére'sM systems are mentioned: their study includes the proof that the informal renormalization argument (involving a transfer matrix) is exact for squigs.Presented at theThird Conference on Fractals: Fractals in the Physical Sciences, held at the National Bureau of Standards, Gaithersburg, Maryland, on November 20–23, 1983.The reader's attention should be drawn to the fact that the second and later printings of this book include an update chapter and additional references. Though it should not have been necessary, it may be useful also to mention here that most of the material in this book that concerns physics, e.g., polymers and percolation clusters, wasnot found in either of my two earlier Essays on fractals,Les objects fractals: forme, hasard et dimension (Flammarion,     

Electric field driven fractal growth dynamics in polymeric medium

This paper reports the extension of earlier work (Dawar and Chandra, 2012) [27] by including the influence of low values of electric field on diffusion limited aggregation (DLA) patterns in polymer electrolyte composites. Subsequently, specified cut-off value of voltage has been determined. Below the cut-off voltage, the growth becomes direction independent (i.e., random) and gives rise to ramified DLA patterns while above the cut-off, growth is governed by diffusion, convection and migration. These three terms (i.e., diffusion, convection and migration) lead to structural transition that varies from dense branched morphology (DBM) to chain-like growth to dendritic growth, i.e., from high field region (A) to constant field region (B) to low field region (C), respectively. The paper further explores the growth under different kinds of electrode geometries (circular and square electrode geometry). A qualitative explanation for fractal growth phenomena at applied voltage based on Nernst–Planck equation has been proposed.