Adhesion between solids

The JKR theory relates the interfacial-force-induced contact deformation to the thermodynamic work of adhesion between solids, and provides a theoretical... 

One effect of a lubricant is to reduce adhesion between the solids. Adhesion between solids is usually dominated by van der Waals forces. Hydrocarbons have a small Hamaker constant and their presence leads to a reduction in the adhesion and hence friction. Films of only a monomolecular thickness are sufficient to have a pronounced effect. This shows up when we measure friction between solids, which are coated with monomolecular layers (see example 11.1). In that case, friction can be as small as friction with plenty of lubricant. A monomolecular film affects significantly the frictional properties [495], At least with metals it can be shown that the number of microcontacts is not changed by the lubricant. Only the contact intensity is reduced. The reduced van der Waals attraction can thereby diminish the actual contact area. 

It can be derived from Antonow s rule, 15.7.4], applying it to partial wetting but accounting for the adhesion between solid and liquid, assuming it to be dominated by the Van der Waals, or dispersion, parts of the surface tensions, y and y. Various studies have shown that [5.7.5] is quite effective for materials that mainly interact through dispersion forces and that it remains a reasonable approximation for systems in which other interactions also operate. The root in the r.h.s. of [5.7.5] stems from the assumption that Berthelot s principle may be applied. In sec. 2.11b we argued that this principle may be applied only to the energetic part of the interfacial tensions and that a more correct form is... 

Figure 12.11 Diagrammatic representation of adhesion between solid surfaces at rest (a) no adhesive layer (b) a viscous liquid at the interface and (c) a semisolid adhesive layer. On separation, the nature of the intervening film is shown (a) no film, (b) a necking filament of liquid, (c) multiple filaments of the semisolid layer...

The other theory had its origin in ideas put forward in 1834 by Faraday (Ashmor, 1963). He assumed the condition of adhesion between solid and fluid. This condition leads, under favourable circumstances, to the combination of bodies simultaneously subjected to the attraction. The chief evidence that this simple idea is inadequate, is that some substances can decompose to give quite different products in the presence of different catalysts. 

Contact mechanics is both an old and a modern field. Its classical domains of application are adhesion, friction, and fracture. Clearly, the relevance of the field for technical devices is enormous. Systematic strategies to control friction and adhesion between solid surfaces have been known since the stone age [1]. In modern times, the ground for systematic studies was laid in 1881 by Hertz in his seminal paper on the contact between soHd elastic bodies [2]. Hertz considers a sphere-plate contact. Solving the equations of continuum elasticity, he finds that the vertical force, F , is proportional to where S is the indentation. The sphere-plate contact forms a nonlinear spring with a differential spring constant k = dF/dS oc The nonhnearity occurs because there is a concentration of stress at the point of contact. Such stress concentrations - and the ensuing mechanical nonhnearities - are typical of contact mechanics. 

The quality of adhesion between solids, e.g. between a film and its substrate, depends to a large extent on the condition of the interfacial layer that is formed as can be seen in Fig.2. The following types of interfacial layers can be distinguished [15,75,107]... 

If 0 = 0, then Wa = 2y that is, the work of adhesion between solid and liquid is equal to the work of cohesion of the liquid. Thus the liquid can spread indefinitely over the surface, since energetically the system is indifferent to whether the liquid is in contact with itself or with the solid. On the other hand, if 0 = 180°, cos 0 = — 1, and = 0. No Gibbs energy expenditure is required to separate the solid and the liquid. The liquid does not wet the solid and does not spread on it. The spreading coefficient f or one liquid on another is defined in the same way as for a liquid on a solid, Eq. (18.23), except that cos 0 = 1. Thus... 

The relation between equilibrium contact angles at a solid surface, and the adhesion between solid and liquid, is reviewed. The information deducible as to the chemical nature of the groups exposed at the surface is summarized. 

In conclusion, there are many mechanisms which can alter the level of molecular adhesion between solid bodies. Some of these may be elastic and reversible while others are time dependent, leading to drag and hysteresis. Thus, adhesion measurements cannot generally be explained in terms of a simple adhesion energy or range. The mechanisms of adhesion can magnify or reduce the adhesion force by several orders of magnitude. 

H.M. Pollock, D. Maugis, and M. Barquins, "The Force of Adhesion Between Solid Surfaces in Contact," Appl. Phys. Lett., 33, 798 (1978). 

The first ever equation used to describe adhesion between solids was devised by Coulomb in 1773 to explain the movement of soils under load. In a shear box test (Fig. la), a powder is loaded with a normal force N, and sheared with a force F. In general, the plot of F versns N (Fig. 1(b) does not pass throngh the origin but is displaced by an amount A on the horizontal axis. This displacement A represents the adhesive force pulling the particles into contact by Dispersion forces or other molecular attractions. Conlomb s eqnation describing this behavionr may be written as... 

Adhesion Force and Work of Adhesion between Solids. 77... 

The Derjaguin equation for the force of the molecular adhesion between solid particles in a liquid medium can be written as... 

Balachandran [23] analyzed the role of electrostatic forces in the adhesion between solid particles and surfaces. According to the available information this role is not completely clear, the results are contradictory. Electrostatic forces can be significant in the case of polymer and semi-conductor particles. These forces have four main types Coulomb, image charge, space charge and dipole forces. 

In considering the above theories, one has to admit that the most useful concept of adhesion stays within the boundaries of the moleciilar theory and the thermodynamics of interfacial phenomena. At the same time, no one theory of adhesion can predict the real adhesion between solid and polymer or adhesion j oint strength. A large number of theoretical ideas on adhesion do not refer to the phenomena of adhesion but rather to the processes of failure of adhesion joints and their description. A clear distinction between the processes of adhesion and the formation of adhesion contact and failme is a key to rmderstanding this complex set of phenomena, referred to for convenience as adhesion. 

Where r is the distance between the two molecules. It is important to realize that the London interaction is present in all pairs of atoms or molecules. The London dispersion forces, thus, form the basis of adhesion between solid bodies. 

The knowledge of both the strength of acid-base interaction, i.e., the enthalpy of interaction, and the number of moles of acid or base functional groups interacting per unit area across the interface allow the determination of the reversible acid-base work of adhesion. In the particular case of adhesion between solids, it rapidly appears (Israelachvili 1991) that the contribution of the polar interactions (Keesom, Debye) to the thermodynamic work of adhesion could be neglected compared with both dispersive and acid-base contributions as experimentally confirmed (Fowkes et al. 1984). The acid-base component of the work of adhesion can be related to the variation of enthalpy per mole of acid-base interfacial adducts interaction, follows ... 

Bearing this in mind, now a brief look at the work of adhesion between solid adhesive and adherend in the framework of Fowkes general approach is taken. Equation 6.38 is of the form... 

Furthermore, the assumption of rigid bodies is in most cases a too strong simplification to correctly describe adhesion between solids. Bodies in contact will deform due to either external or surface forces. This means for understanding the phenomenon of adhesion, we need to know not only the adhesion energy of the materials but also the deformations. In this chapter, we will first discuss the surface energy of solids and its connection to adhesion. Then, we will give an overview of the classical theories of contact mechanics and finally discuss important parameters influencing adhesion. 

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