Deformable layer theory

A deformable layer theory—coupling agents produced a tough, flexible layer between glass and 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. 

The Chemical Bonding Theory Deformable Layer Theories... 

Preferential Adsorption Theory (modified from the 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. 

Figure 10-12. The shape of a rising gas bubble as a function of the Weber number, as predicted by small-deformation, boundary-layer theory. We = 0,0.25, 0.5.

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. 

Another view is the inhibition layer theory, which holds that the structure of the stress relaxation transition layer between the matrix and the packing is not a flexible deformation layer, but an interfacial layer with a modulus between that of the matrix and the packing. The treatment agent is a part of the interfacial area, and this part is a substance with a medium modulus that is between that of the high-modulus reinforcing material and the low-modulus matrix. It has the effect of transferring stress uniformly and reducing interfacial stress, so that it can enhance the performance of the composite materials. The inhibition layer theory is not widely accepted because it lacks the necessary experimental basis. ... 

Sugimoto explained the ER effect shown by the ion exchange resin-suspension fluid by using the electric double layer theory. In the electric double layer theory a particle suspended in an electrically insulating oil has an electric double layer due to dissociation of the ionic groups by the adsorbed water on the surface. The dissociated ions are moved by the external electric field and the electric double layer deforms. Shear is applied to the polarization, resistance is created when particles tty to move each other, and, consequently, viscosity increases. 

It has been also shown that when a thin polymer film is directly coated onto a substrate with a low modulus ( < 10 MPa), if the contact radius to layer thickness ratio is large (afh> 20), the surface layer will make a negligible contribution to the stiffness of the system and the layered solid system acts as a homogeneous half-space of substrate material while the surface and interfacial properties are governed by those of the layer [32,33]. The extension of the JKR theory to such layered bodies has two important implications. Firstly, hard and opaque materials can be coated on soft and clear substrates which deform more readily by small surface forces. Secondly, viscoelastic materials can be coated on soft elastic substrates, thereby reducing their time-dependent effects. 

SFA measurements on mica. Horn et al. [68] studied the deformation of mica surfaces in contact. In these studies, Horn et al. established the applicability of Hertz theory of contact mechanics to non-adhering layered solids by measuring... 

A simple explanation of the existence of deformed nuclei in these ranges is provided by the close-packed-spheron theory (J4) it is that the inner core (of two or five spherons) in these ranges has an elongated structure, and that this elongation is imposed by the inner core on the two surrounding layers. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

---