The theory of weak boundary layers

Among many theories describing the phenomenon of adhesion, the theory of weak bormdaiy layers developed by Bikerman plays a special role. Strictly speaking, it is not a theory, but in considerable degree a display of a pragmatic common sense. Bikerman beheved that his concept was a very practical one but 

In most cases, failure cracks arise in the weak bormdary layers. Bikerman distinguished many groups of weak boundary layers according to their origin. Similar to the formation of the adhesion joint, three phases usually participate in failure adhesive, substrate and air (or other medium). Various admixtru-es form a weak boundary layer, being concentrated at the phase border. The defects in the structure of the substrate and adhesive and admixtures determine 

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Fourth, the criterion that we have derived does not override other well-known criteria, such as that the presence of weak boundary layer material is a sufficient, though not a necessary, condition for poor adhesion. Indeed, our theory may be regarded as showing just when boundary-layer material will qualify as "weak", in a particular system. 

This article is concerned with theories of fundamental adhesion, i.e., with theories concerned with the reasons for two materials holding together in an adhesive bond, however weak. In contrast, a weak boundary is a cohesively weak layer in the interfacial region (some authors use the term interphase ) of an adhesive joint, which may cause the joint itself to be weak, i.e., to fail at a low stress or with low fracture energy. So the question of weak boundary layers occurs when the level of practical adhesion is under consideration, and may form part of an answer to a question such as why did this joint fail at such and such a stress ... 

However, 50 years ago, when there was considerably less basic understanding, and more confusion, in the study of adhesion than there is now, weak boundary layer theory would often be discussed alongside theories such as the adsorption theory and the electrostatic theory. The tendency to group theories of adhesion in this way has persisted, and so it may now be useful to discuss the significance of weak boundary layers. 

Although Bikerman s position would not be supported today, it stimulated developments in the understanding of theories of adhesion, which can, to some extent, be regarded as his legacy. The potential for the formation of weak boundary layers (1) is well established, and much of the technique of adhesive bond preparation is designed to avoid them. 

Weak Boundary Layer Theory. According to the weak boundary layer theory, when bond failure seems to be at the interface, usually a cohesive break of a weak boundary layer is the real event. Weak boundary layers can originate from the adhesive, the adherend, the environment, or a combination of any of the three. When bond failure occurs, it is the weak boundary layer that fails, although failure seems to occur at the adhesive-ad-herend interface. 

If slider (A) is placed on support (B) in air, a film of adsorbed air (plus moisture and numerous impurities) remains between the two solids and no true contact between atoms of A and atoms of B occurs anywhere along the surface of apparent contact. In the modern theory of adhesive joints [6], this film is an example of weak boundary layers [7] which so often lower the final strength of adhesive assemblies. Only because a solid cannot displace air (or another gas) from the surface of another solid, it is necessary to apply adhesives, that is materials which are liquid in the moment of application, are (therefore) able to eliminate the gaseous weak boundary layers, and which later solidify thus giving rise to an unbroken 3"layer solid consisting of first adherend - adhesive -second adherend. 

Weak boundary layer. WBL theory proposes that a cohesively weak region is present at the adhesive-substrate interface, which leads to poor adhesion. This layer can prevent the formation of adhesive bonds, or the adhesive can preferentially form bonds with the boundary layer rather that the surface it was intended for. Typically, the locus of failure is interfacial or in close proximity to the silicone-substrate interface. One of the most common causes of a WBL being formed is the presence of contaminants on the surface of the substrate. The formation of a WBL can also result from migration of additives from the bulk of the substrate, to the silicone-substrate interface. Alternatively, molecular... 

Garnish and Haskins found that exposure of polypropylene to trichloroethylene vapour for 10 s resulted in a sixfold increase in joint strength using an Epoxide adhesives. The authors concluded that the improved adhesion was due to the removal of a weak boundary layer. However, the treatment causes the formation of a very porous surface, and an alternative explanation for the improved adhesion is the mechanical keying of the adhesive into the porous surface (see Mechanical theory of adhesion). Garnish and Haskins found that the optimum treatment time was about 10 s and that after 25 s the adhesion level was similar to that of the untreated polymer. This reduction is probably due to weakening of the surface region of the polypropylene. 

All the studies conducted on fracture of bulk polymers are certainly relevant to the adherence of polymers, the mechanisms of losses at a crack tip being the same viscoelastic losses due to moving stresses, work to extract chains or fibrils, and viscous drag in the presence of a liquid. It is probable that the various theories of adhesion, namely, theory of wetting, theory of the rheological factor, theory of the chemical bond, theory of the weak boundary layer, and theory of interdiffusion, are all valid, each corresponding to an emphasis on a dominant mechanism. 

The idea of a weak boundary layer is a theory of non-adhesion rather than one of adhesion. However, weak boundary layers certainly occur on some substrates. Examples include lubricating oil on metals and rust on iron, but a less obvious case lies in the tendency of foreign material in plastics to diffuse to the surface such materials might be the various additives discussed in Section 2.4 or simply low molar mass polymer. In either case the remedy is to remove the weak boundary layer with a solvent or by abrasion. 

The weak-boundary-layer theory is essentially a theory of fracture, rather than of fundamental adhesion. However, it is frequently discussed along with these other theories, so consideration is given to it here in Sect. 2.6. 

The removal of an electron from an acceptor level or a hole from a donor level denotes, as we have seen, not the desorption of the chemisorbed particle but merely its transition from a state of strong to a state of weak bonding with the surface. The neglect of this weak form of chemisorption (i.e., electrically neutral form) which is characteristic of all papers on the boundary-layer theory of adsorption makes it quite impossible to depict the chemisorbed particle in terms of an energy level, i.e., to apply the energy band scheme depicted in Fig. 10 and used in these papers. ... 

When there is no weak bonding at all, one returns within the frame of the boundary-layer theory. In this case, however, the chemisorbed particles do not produce any levels in the crystal energy spectrum. 

Hall, P. and Malik, M.R. (1986). On the instability of three-dimensional attachment-line boundary layer weakly non-linear theory and numerical approach. J. Fluid Mech., 395, 229-245. 

An apparent weakness of the film model is that it suggests that the mass transfer coefficient is directly proportional to the diffusion coefficient raised to the first power. This result is in conflict with most experimental data, as well as with more elaborate models of mass transfer [surface renewal theory considered in the next chapter, e.g., or boundary layer theory (Bird et al., I960)]. However, if we substitute the film theory expression for the mass transfer coefficient (Eq. 8.2.12) into Eq. 8.8.1 for the Sherwood number we find... 

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