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.

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 usage convenience only. This book presents leading-edge research in this rapidly changing and evolving field. The book presents descriptions of the main reactions of high-molecular substances within the frameworks of fractal analysis and irreversible aggregation models. Synergetics and percolation theory were also used. In spite of the enormous number of papers dealing with the influence of the medium on the rate of chemical reactions (including synthesis of polymers), no strict quantitative theory capable of "universal" application has been put forward up until now. It is now possible to describe the relationship between the reaction rate constants and the equilibrium constants with the nature of the medium in which the reactions take place by means of a single equation. This important book for the first time gives structural and physical grounds of polymers synthesis and curing, and the fractal analysis is used for this purpose. This new book: * Highlights some important areas of current interest in polymer products and chemical processes * Focuses on topics with more advanced methods * Emphasizes precise mathematical development and actual experimental details * Analyzes theories to formulate and prove the physicochemical principles * Provides an up-to-date and thorough exposition of the present state of the art of complex polymeric materials

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 chemistry and physics of polymer synthesis and those in the field of polymers and polymer composites processing.

This text 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 chemistry and physics of polymer synthesis and those in the field of polymers and polymer composites processing.

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 usage convenience only. This book presents leading-edge research in this rapidly changing and evolving field. The book presents descriptions of the main reactions of high-molecular substances within the frameworks of fractal analysis and irreversible aggregation models. Synergetics and percolation theory were also used. In spite of the enormous number of papers dealing with the influence of the medium on the rate of chemical reactions (including synthesis of polymers), no strict quantitative theory capable of "universal" application has been put forward up until now. It is now possible to describe the relationship between the reaction rate constants and the equilibrium constants with the nature of the medium in which the reactions take place by means of a single equation. This important book for the first time gives structural and physical grounds of polymers synthesis and curing, and the fractal analysis is used for this purpose. This new book: * Highlights some important areas of current interest in polymer products and chemical processes * Focuses on topics with more advanced methods * Emphasizes precise mathematical development and actual experimental details * Analyzes theories to formulate and prove the physicochemical principles * Provides an up-to-date and thorough exposition of the present state of the art of complex polymeric materials

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.

The interest in polymer composites study is due to an even greater degree of their application. The filling by hard disperse particulates or fibres gives to polymers a desirable properties number: increases stiffness, reduces thermal expansion coefficient, rises resistance to yield and fracture toughness and so on. Difficulties in research of structure-properties relationships for polymer composites are due to their structure complexity. So, on the elasticity modulus value besides composition a polymer-filler interaction influences. In other words, it is clear even intuitively that for the complete description of such structurally-complex objects as polymer composites it is necessary to account for three groups of factors, namely, polymeric matrix structure, filler structure and level of interaction between them. Up to now the researches of such kind were carried out within the frameworks of continuous mechanics and thermodynamic conceptions. However, these conceptions application does not allow to describe satisfactorily and all the more to predict such materials properties. As a matter of fact, an experimental data set dictates the choice of either structure physical model for macroscopic properties description.

Contents: Structure and Properties of Polymers in Terms of the Fractal Approach; Fractal Kinetics of Radical Polymerisation of Dimethyl Diallyl Ammonium Chloride; Thermodynamics of Polymer Structure Formation in an Amorphous State; A Percolation Model of Brittle-Ductile Transition for Polyethylene; The Dependence of Diffusive Characteristics from the Size of Penetrant Molecules and Structure for Polyenthylenes; Polymer Chain Flexibility and Networks of Macromolecular Entanglements; Estimation of End-to-End Distances for a Polycarbonate Chain within the Framework of the Fractional Derivatives Theory; Molecular Weight Distribution of Poly (Dimethyl Diallyl Ammonium Chloride): Analysis within the Framework of Irreversible Aggregation Models; The Interrelation of Fluctuation Free Volume and Structure for Polymer's Amorphous State; Structural Aspects of Adhesion in Particulate-Filled Polymer Composites; The Fractal Analysis of Curing Processes of Epoxy Resins; Index.

Fractals & Local Order in Polymeric Materials

This book examines polymer nanocomposites filled by inorganic nanofillers. Polymers are considered as nanocomposite matrix only, possessing, as a rule, an invariable structure. In many respects this situation is explained by the absence of a quantitative structural model of polymers amorphous state. This problem becomes particularly important because all structural elements of polymers have sizes of nanometer scale. The development of notions about polymers amorphous state structure within the frameworks of the cluster model of this structure allows to represent amorphous polymer as a quasitwophase system.

The interest in polymer composites research is due to their enlarged application. Filling with hard particles gives to polymers a number of desirable properties: increases hardness, decreases heat expansion coefficient, improves resistance to creep and fracture toughness. Difficulties in structure-properties relationships researching for polymer composites are due to their structure complexity. Till now, composites studies were conducted within the frameworks of continuum mechanics and thermodynamic conceptions. However, these conceptions applications does not allow satisfactory descriptions nor predictions of such materials properties. As a matter of fact, an experimental data set dictates one or another physical model of structure choice for composites macroscopic properties description.

Fractal analysis gives just general mathematical description of polymers, i.e. it does not identify structural units (elements), from which any real polymer is formed. Physical description of thermodynamically non-equilibrium polymer structure in the framework of the local order ideas gives the cluster model of the polymer amorphous state structure that quantitatively identify its elements. Since these models consider the polymer structure somewhat from two sides, they are excellent completing one another. It is common knowledge that structures displaying fractal behaviour on small length scale and being homogeneous on large length scale are named homogeneous fractals. These fractals are percolation clusters at the percolation threshold. As shown below, the cluster structure represents the percolation system and, due to the above-said, the homogeneous fractal. To put it differently, the presence of the local order in the condensed phase of polymers determines fractality of their structures.

Nanochemistry is a science connected with obtaining and studying of physical-chemical properties of particles having sizes on the nanometer scale. This book addresses polymer synthesis which, according to Melikhov's classification, is automatically part of nanochemistry. This is determined as far as polymeric macromolecules (more precisely macromolecular coils) belong to nanoparticles and polymeric sols and gels - to nanosystems. Catalysis on nanoparticles is one of the most important sections of nanochemistry. The majority of catalytic systems are nanosystems. At heterogeneous catalysis the active substance is tried to deposit on carrier in nanoparticles form in order to increase their specific surface. At homogeneous catalysis active substance molecules have often in themselves nanometer sizes. The most favorable conditions for homogeneous catalysis are created when reagent molecules are adsorbed rapidly by nanoparticles and are desorbed slowly but have high surface mobility and, consequently, high reaction rate on the surface and at the reaction molecules of such structure are formed at which desorption rate is increased sharply. If these conditions are realised in nanosystem with larger probability than in macrosystem, then nanocatalyst has the raising activity that was observed for many systems.

Theoretical & Practical Guide to Organic Physical Chemistry