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This new book explores the consideration of relationships that connect the structural and basic mechanical properties of polymeric mediums within the frameworks of fractal analysis with cluster model representations attraction. Incidentally, the choice of any structural model of medium or their combinations is defined by expediency and further usag
This book provides an important structural analysis of polymer solutions and melts, using fractal analysis. The book covers the theoretical fundamentals of macromolecules fractal analysis. It then goes on to discuss the fractal physics of polymer solutions and the fractal physics of melts. The intended audience of the book includes specialists in c
Using fractal analysis, irreversible aggregation models, synergetics, and percolation theory, this book describes the main reactions of high-molecular substances. It is the first to give the structural and physical grounds of polymers synthesis and curing based on fractal analysis. It provides a single equation for describing the relationship betwe
Using fractal analysis, irreversible aggregation models, synergetics, and percolation theory, this book describes the main reactions of high-molecular substances. It is the first to give the structural and physical grounds of polymers synthesis and curing based on fractal analysis. It provides a single equation for describing the relationship between the reaction rate constants and the equilibrium constants with the nature of the medium.
One important area in materials science and engineering is the relationship between spatial and temporal scales and its influence on constitutive properties. Fractal functions can be useful in studying materials where self-similarity across scales, often seen in nature, also influence engineered materials. Examples of fractals commonly found in nature include clouds, snowflakes, broccoli, arteries, and coastlines. All these objects exhibit self-similar structures over a finite scale range. Fractals have been found to better describe many natural phenomena relative to more conventional Euclidean geometry. Further, it is also known that fractional derivatives are better equipped to quantify dynamics and mechanics of fractal structures. The use of fractal functions along with the application of fractal or fractional operators can be useful when modeling complex phenomena such as viscoelasticity. Incorporating fractional order calculus into models of fractal materials can more accurately describe the complex phenomena of these materials and allow for the advancement of applications in various fields of study. We will demonstrate how these relations apply to dielectric elastomers (VHB 4949 and VHB 4905) and auxetic (negative Poisson ratio) foams. We find that the fractional order of viscoelasticity is important in obtaining accurate prediction of rate dependent deformation in uncalibrated regimes. We will demonstrate its effectiveness by comparing the models to experimental data and quantifying parameter uncertainty using Bayesian methods.
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses, and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.
This monograph deals with the structural aspects of transport processes of gases, physical ageing and thermo-oxidative degradation of polymers in detail. Fractal analysis, cluster models of the polymer structurea ‘s amorphous state as well as irreversible aggregation models are used as main structural models. It is shown that the polymer structure
In the present monograph, theoretical structural analysis of the main processes of gas transport in polymeric materials (diffusion, solubility, permeability and selectivity) was offered. The mentioned analysis uses fractal (multifractal) analysis and cluster model of polymers amorphous state structure, based on the local order notions, as a tool for polymeric materials structure description. Besides, for the mentioned gas transport processes description, such modern physical treatments as a multifractal model of fluctuation free volume and the conception of anomalous (strange) diffusion were used. Such approach allows the quantitative description of gas transport processes and their prediction as a function of testing temperature, degree of crystallinity, cross-linking and grafting, and so on. Special attention is given to gas transport processes in multicomponent polymeric systems. A number of practical aspects of theoretical structural analysis application was considered in cases of thermal degradation, interfacial layers formation in polymer composites, stability to cracking in active environments and chemical reactions.
Fractal Analysis of Polymers - From Synthesis to Composites