The concepts of mass and surface fractals are introduced, and the corresponding small-angle scattering (SAS; X-rays, neutrons) intensities are computed. It is shown how to resolve the fractal structure of various complex systems from experimental scattering measurements, and how obtained data are related to specific features of the fractal models. We present and discuss various mass and surface fractal structures, including fractals generated from iterated function systems and cellular automata. In addition to the fractal dimension and the overall fractal size, the suggested analysis allows us to obtain the iteration number, the number of basic units which form the fractal and the scaling factor.

This book addresses the basic physical phenomenon of small-angle scattering (SAS) of neutrons, x-rays or light from complex hierarchical nano- and micro-structures. The emphasis is on developing theoretical models for the material structure containing self-similar or fractal clusters. Within the suggested framework, key approaches for extracting structural information from experimental scattering data are investigated and presented in detail. The range of parameters which can be obtained pave the road towards a better understanding of the correlations between geometrical and various physical properties (electrical, magnetic, mechanical, optical, dynamical, transport etc.) in fractal nano- and micro-materials.

Proceedings of the NATO Advanced Study Institute, Como, Italy, May 12--22, 1993

This 2-volume set includes extensive discussions of scattering techniques (light, neutron and X-ray) and related fluctuation and grating techniques that are at the forefront of this field. Most of the scattering techniques are Fourier space techniques. Recent advances have seen the development of powerful direct imaging methods such as atomic force microscopy and scanning probe microscopy. In addition, techniques that can be used to manipulate soft matter on the nanometer scale are also in rapid development. These include the scanning probe microscopy technique mentioned above as well as optical and magnetic tweezers.

We review the basic theoretical methods used to treat small-angle scattering from porous materials, treated as general two-phase systems, and also the basic experimental techniques for carrying out such experiments. We discuss the special forms of the scattering when the materials exhibit mass or surface fractal behavior, and review the results of recent experiments on several types of porous media and also SANS experiments probing the phase behavior of binary fluid mixtures or polymer solutions confined in porous materials. Finally, we discuss the analogous technique of off-specular scattering from surfaces and interfaces which is used to study surface roughness of various kinds.

Scattering Methods and their Application in Colloid and Interface Science offers an overview of small-angle X-ray and neutron scattering techniques (SAXS & SANS), as well as static and dynamic light scattering (SLS & DLS). These scattering techniques are central to the study of soft matter, such as colloidal dispersions and surfactant self-assembly. The theoretical concepts are followed by an overview of instrumentation and a detailed description of the evaluation techniques in the first part of the book. In the second part, several typical application examples are used to show the strength and limitations of these techniques. - Features the latest input from the world-leading expert with personal experience in all the fields covered (SAXS, SANS, SLS and DLS) - Includes unified notation throughout the book to enhance its readability - Provides—in a single source—scattering theory, evaluation of techniques and a variety of applications

The structural characterization of deterministic mass fractals at nano- and microscales is presented in this chapter using two complementary techniques in both reciprocal and real spaces. In the former case, fractal and geometrical features are obtained from the small-angle scattering (SAS) (neutrons, X-rays, light) spectrum in the reciprocal space. The lacunarity technique is considered to extract structural properties and differentiate textures of fractals in real space. We present and discuss various types of mass fractals, such as thin and fat fractals, as well as fractals generated with the Chaos game representation (CGR). We show how the main structural properties of the fractals, such as the fractal dimension, the iteration number, the scaling factor, the overall size of the fractal, and the size of the basic units of the fractal, can be extracted by using SAS and lacunarity techniques.

This book focuses on the widely used experimental techniques available for the structural, morphological, and spectroscopic characterization of materials. Recent developments in a wide range of experimental techniques and their application to the quantification of materials properties are an essential side of this book. Moreover, it provides concise but thorough coverage of the practical and theoretical aspects of the analytical techniques used to characterize a wide variety of functional nanomaterials. The book provides an overview of widely used characterization techniques for a broad audience: from beginners and graduate students, to advanced specialists in both academia and industry.