Restrained layer theory

A restrained layer theory—coupling agents developed a highly cross-linked interphase region with a modulus intermediate between that of glass and ihe polymer. 

Many theories have been proposed to account for the profound effect minute proportions of silane coupling agents at the dispersed particle interface have on the performance of composites.These include chanical bonding theory acid—base interactions formation of interpenetrating networks wetting and surface energy effects polymer morphology modification deformable layer theories restrained layer theory. 

At the other extreme to the restrained layer theory is the deformable layer theory where a flexible, deformable phase seems desirable to accommodate stresses set up at the interface due to differential thermal shrinkage between resin and filler when the composite is cooled. There is still considerable confusion and debate over what morphology might be desirable in resin adjacent to treated mineral and metal substrates. The amount of coupling agent in a typical finish is probably insufficient to provide a low-modulus layer at the interface. However, Erickson... 

Historically, many reinforcement theories have been proposed. Those include the chemical bonding theory (28), restrained layer theory (29), deformable layer theory (30), and coefficient friction theory (31). However, only the chemical bonding theory could sufficiently explain the observed results. However, the chemical bonding theory alone is not adequate to explain the necessity of more than a monomolecular equivalent of silane for optimum composite strength. Thus, this concept is coupled with interpenetrating network theory (31,32). These theories have been developed primarily for thermosetting resin composites. Thermoplastic-matrix composites rely on different mechanisms. 

Restrained Layer Theory Coefficient of Friction Theory Surface Wettability Theory... 

Reversible Hydrolyzable Bond Theory (combination of Chemical Bonding Theory, Restrained Layer Theory, and Deformable Layer Theory)... 

The mechanism of chemical adhesion is probably best studied and demonstrated by the use of silanes as adhesion promoters. However, it must be emphasized that the formation of chemical bonds may not be the sole mechanism leading to adhesion. Details of the chemical bonding theory along with other more complex theories that particularly apply to silanes have been reviewed [48,63]. These are the Deformable Layer Hypothesis where the interfacial region allows stress relaxation to occur, the Restrained Layer Hypothesis in which an interphase of intermediate modulus is required for stress transfer, the Reversible Hydrolytic Bonding mechanism which combines the chemical bonding concept with stress relaxation through reversible hydrolysis and condensation reactions. 

Several adhesive mechanisms (see Theories of adhesion) have been proposed to account for the enhancement of interface-dominated properties (such as retained tensile strength after environmental conditioning) (1) the chemical bonding theory (2) the deformable layer hypothesis (3) the surface wettability hypothesis (4) the restrained layer hypothesis (5) the reversible hydrolytic bonding mechanism. 

Where a number of stress components are at work in different planes, their values can be mathematically combined to produce a compound or equivalent stress, Cy. To determine the equivalent stress for a thick-layer elastic adhesive, normal stress theory may be used. This is commonly employed for components that are mechanically restrained from undergoing expansion. 

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