Theories of reinforcement

Glickman SE, Schiff BB (1967) A biological theory of reinforcement. Psychol Rev 74 81-109. 

It will be recognized that Eqs. (30) to (32) do not constitute a theory of reinforcement - they merely provide inter-relationships between the variables Hb, Ub and eb. Since there is no way as yet to calculate eb and Hb from first principles, prediction of the breaking energy remains inaccessible. 

Dannenberg19 summarized the phenomena which must be explained by a theory of reinforcement. One of these is the reversed modulus-temperature dependence shown by the rubber on the addition of carbon black, and is closely linked to the observations by Oono et al.66. The modulus of crosslinked, unfilled rubber increases with temperature addition of carbon black reduces this tendency until, at sufficient concentration, the modulus-temperature gradient is reversed. This effect may be explained qualitatively by the saltation mechanism the more rapid thermal motions... 

Reinforcement, however defined, depends upon the size, surface chemistry, state of aggregation, and quantity of filler. The influence that these characteristics have on physical and mechanical characteristics will be explored. Current theories of reinforcement, both thermodynamic and viscoelastic, will be developed, in order to summarize the state of the art in this area. 

This is Volume 2 of Natural Rubber Materials and it covers natural rubber-based composites and nanocomposites in 27 chapters. It focuses on the different types of fillers, the filler matrix reinforcement mechanisms, manufacturing techniques, and applications of natural rubber-based composites and nanocomposites. The first 4 chapters deal with the present state of art and manufacturing methods of natural rubber materials. Two of these chapters explain the theory of reinforcement and the various reinforcing nanofillers in natural rubber. Chapters 5 to 19 detail the natural rubber composites and nanocomposites with various fillers sueh as siliea, glass fibre, metal oxides, carbon black, clay, POSS and natural fibres ete. Chapters 20-26 discuss the major characterisation techniques and the final ehapter covers the applications of natural rubber composites and nanoeomposites. By covering recent developments as well as the future uses of rubber, this volume will be a standard reference for scientists and researchers in the field of polymer chemistry for many years to come. 

Theory of Reinforcement by Rigid (Fractal) Aggregates and Agglomerates of Filler Particles... 

The influence of the filler surface and in the case of CB the proven presence of an active site, with a surface energy directly proportional to the specific surface of the filler, tends to show also the importance of the interactions between the surface and the elastomeric chains. However, theories of reinforcement have been diverging and recall the main proposals and in the last years there is a strong trend to accept the Payne proposals the carbon surface lastomer interaction being a part of a total phenomenon, at the nanoscale. 

The theory of reinforcement of polymers and elastomers refers to the Guth-Gold-Smallwood equation (Equation (23.1)) to correlate the composite initial modulus Efi with the filler volume fraction (0) ... 

In Section 23.2 was discussed the theory of reinforcement of polymer and elastomers which refers to the Guth-Gold-Smallwood equation (Equation (23.1)) to correlate the compound initial modulus (E ) with the filler volume fraction ( ). Moreover, it was already commented on the key roles played by the surface area and by the aspect ratio (/). Basic feature of nanofillers, such as clays, CNTs and nanographites, is the nano-dimension of primary particles and thus their high surface area. This allows creating filler networks at low concentrations, much lower than those typical of nanostructured fillers, such as CB and silica, provided that they are evenly distributed and dispersed in the rubber matrix. In this case, low contents of nanofiller particles are required to mutually disturb each other and to get to percolation. Moreover, said nanofillers are characterized by an aspect ratio /that can be remarkably higher than 1. Barrier properties are improved when fillers (such as clays and nanographites) made by... 

Wilczynski, A.P. (1990) A basic theory of reinforcement for unidirectional fibrous composites. Comp Sci. Tech., 38, ill. 

All theories of reinforcement of plastics by particrdate fillers and corresponding equations (see Chapter 5) assume the statistical distribution of the discontinuous phase in a continuous matrix, although this has not been experimentally verified. The assumption that during distribution in the dispersion process, the particles or dispersed phase become statistically distributed, is identical to the increase of entropy. If we treat such systems as equilibrium, as proposed by Wessling, their properties should be predictable. But experimental data show that most polymeric systems, including filled ones, exhibit unpredictable behavior, sudden change in properties, and even totally unexpected phenomena. 

Weiss, B. (1970) The fine structure of operant behavior during transition states. In W.N. Schoenfeld (ed). The Theory of Reinforcement Schedules, Appleton-Century-Crofts, New York, pp. 277-311. 

This observation was expanded into a thermodynamic argument [42] for the prediction of exfoliation of montmorillonite as a function of the surface treatment and the hydrophilic-hydrophobic balance of the polymer continuous phase. More work needs to be done in matching the hydrophilic-hydrophobic balance of fluorinated polymers with the hydrophilic-hydrophobic balance of the organomontmorillonite in order to achieve full exfoliation of the montmorillonite in the polymer. Full exfoliation of the montmorillonite in the polymer will allow for a valid examination of the mechanical properties of fluorinated polymer-montmorillonite composites in relation to the theory of reinforcement developed in Chapter 5. 

---