Thermodynamic theories of adhesion

Adhesion is a steady or firm attachment of two bodies, and as such it can be characterized by the thermod3mamic work of adhesion, i.e., by the work which is needed to separate two different bodies in contact with each other rmder equilibrium conditions. The action of the molecular forces at an interface forms fundamental reasons for the adhesive forces between a substrate and an adhesive. 

Initial premises for the thermod3mamic description of adhesion are the characteristics of two surfaces their surface tension and interfacial tension at the interface between the two bodies in contact. In the simplest case of two liquids with surface tension y and 7,2 their surface tension at the interface (interfacial tension) is always lower than the highest sruface tension at the interface with saturated vapor  

This empirical Eq 2.1 has been referred to as Antonov s rule. The separation of two surfaces (their breaking away from each other in the direction perpendicular to the interface) requires work per unitary sruface area, Wa  

2 is applicable in any case, including the case when one of the components is a solid body. Accordingly, the cohesion energy is the work of destruction of a body, or the work needed to form a unitary surface area in this body. If the only result of the isothermal process here is the formation of 2 cm of new surface area of the body, having surface tension, 7, the thermodynamic work of cohesion can be expressed as  

On wetting, a droplet of liquid forms a definite contact angle on the solid. The state of mechanical equilibrium of the droplet on the surface is determined 

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The adhesion properties of all types of polyolefins are not easy to explain because these properties are affected by different phenomena. Using of a single theory or mechanisms based on the physical and chemical adhesion manifestations is difiicult for the description of interdisciplinary nature and diversity. There is considerable information to discuss each of the adhesion mechanisms. Therefore, it is not possible to select only the thermodynamic theory of adhesion that is the best to describe the surface free energy of the polyolefin. All mechanisms and adhesion theories are implied by the diversity of polymer systems, which are embraced in combination with research for the analyses of adhesion properties. The physical and chemical composition in the first atomic layers dictates the adhesion and some other properties of the polymer materials. This layer represents underneath layer and this subsurface partially controls the outer layers. The double bonds and cross-linked stmctures limit the mobility macromolecules of polyolefins in the subsurface layers, which results in the functional group stabilization on the surface. Other basic research is necessary for an examination of the polymer subsurface layer and explanation of its effect changes of the surface properties. Moreover, for the improvement of quantitative measurements of adhesion, additional investigation is required. 

The adhesion is proportional to particle size only if the dominant forces are molecular. If (apart from these forces) electrical, capillary, or Coulomb forces predominate, the overall force of adhesion may very well not be proportional to particle size. Deryagin s thermodynamic theory of adhesion regards adhesion as a reversible equilibrium process, and the force of adhesion as a function of the gap separating the contiguous bodies. When this gap is zero, the force of adhesion is proportional to the sizes of the contiguous bodies, as indicated in Eq. (1.39). 

For an aqueous medium, the experimental data on the relationship between adhesive force and particle size are in agreement with theoretical values, thus providing practical support for Deryagin s thermodynamic theory of adhesion (see Section 3). 

In a liquid medium, for which there is a liquid interlayer between the contiguous bodies, and the effects of capillary, electric, and Coulomb forces are excluded (see 11-13), adhesion is due solely to the molecular forces fthe disjoining pressure opposes adhesion). The value of the molecular forces is directly proportional to the dimensions of the particles [see Eqs. (1 47) and (1.49)]. For an aqueous medium the experimental results relating to the dependence of the adhesive forces on particle dimensions coincide with the theoretical data, and Deryagin s thermodynamic theory of adhesion is practically confirmed (see 5). 

The most-often cited theoretical underpinning for a relationship between practical adhesion energy and the work of adhesion is the generalized fracture mechanics theory of Gent and coworkers [23-25] and contributed to by Andrews and Kinloch [26-29]. This defines a linear relationship between the mechanical work of separation, kj, , and the thermodynamic work of adhesion ... 

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

When the surfaces are in contact due to the action of the attractive interfacial forces, a finite tensile load is required to separate the bodies from adhesive contact. This tensile load is called the pull-off force (P ). According to the JKR theory, the pull-off force is related to the thermodynamic work of adhesion (W) and the radius of curvature (/ ). 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form a true interpliase. The solubility parameter, the square root of the cohesive energy density of a material, provides a measure of the intemiolecular interactions occurring witliin the material. Thermodynamically, solutions of two materials are most likely to occur when the solubility parameter of one material is equal to that of the other. Thus, the observation that "like dissolves like." In other words, the adhesion between two polymeric materials, one an adherend, the other an adhesive, is maximized when the solubility parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubility between adhesive and adherend. The diffusion theory is not applicable to substantially dissimilar materials, such as polymers on metals, and is normally not applicable to adhesion between substantially dissimilar polymers. 

From the DMT theory [7], which establishes a relationship between the adhesion force F and the thermodynamic work of adhesion Wo P=2tiRWq, R=tip... 

Q Fig. 3.4 Thermodynamic work of adhesion deduced from the DMT theory, versus surface energy of SAMs grafted on wafers. 

A. Surface Free Energies. Surface free energies must dominate any explanation of the adhesion between different phases which are not mechanically linked. Current levels of understanding of adhesiveness are such that actual adhesive strengths are always much less (1-0.1%) than those predicted by thermodynamic analysis, and often there is apparently little correlation between the two. Further refinement of the theory of adhesiveness will require understanding of the importance of flaws in an adhesive joint and of the relative contributions of polar and dispersive Van der Waal s interactions. The following is an analysis of adhesion in terms of surface free energies. 

The importance of the surface polarity and the surface characteristics for polymer adhesion has been considerably discussed in scientific literature [87]. A useful generalized theory of adhesion, however, can be built upon the basis of electrical attractions. The electrical attractions, resulting from uneven surfaces, which are not normally considered to be electrical, participate easily in attractive interactions if adhesives can be found that will wet them. Thus the reason that polyethylene and poly(tetrafluoroethylene) are difficult to bond is simply that available adhesives are thermodynamically more stable if their molecules attract one another than if they interact with low energy surfaces. The solution to this problem would... 

It needs to be noted here that since the surface tension fundamentally originated from the intermolecular forces and can be related to the thermodynamic work of adhesion and cohesion, the slip length can be estimated by appealing to the pertinent molecular theories as [8]... 

The first truly reversible adhesion cracking experiments were carried out by Obreimoff in 1930 on mica and by Johnson et al in 1971 using smooth elastic rubber spheres. The diameter of the black contact zone was measured in reflected light, and plotted against the applied force to compare with the thermodynamic cracking theory. The results were reasonably reversible and fitted the thermodynamic work of adhesion theory. These experiments are described more fully in Chapters 4 and 9. 

The thermodynamic model of adhesion, generally attributed to Sharpe and Schonhom [1], is certainly the most widely used approach in adhesion science nowadays. This theory considers that the adhesive will adhere to the substrate because of interatomic and intermolecular forces established at the interface, provided that an intimate contact between both materials is achieved. The most common interfacial forces result from van der Waals (London, Debye and Keesom) and Lewis acid-base interactions. The magnitude of these forces can generally be related to fundamental thermodynamic surface characteristics, such as surface free energies y, of both materials in contact. 

Adhesion is the thermodynamic work of adhesion , i.e. intrinsic interaction across the interface. Several theories of adhesion have been su ested and these may be classified into three categories (1) Adsorption theories, (2) diffusion theories and (3) electrostatic theories. 

Deryagin developed a theory of adhesion in [57] he established that adhesion took place under the influence of surface forces and could be considered as a thermodynamic equilibrium and reversible process, provided that the radius of curvature of both the surfaces greatly exceeded the radius of action of the surface forces. 

The thermodynamic Deryagin theory of adhesion considers adhesion as an equilibrium and reversible process and the adhesive force as a function of the gap separating the contiguous surfaces. When this gap equals zero, the adhesive force is proportional to the dimensions of the bodies in contact [see (1.64)]. 

Unfortunately, problems of the adsorption or molecular theory of adhesion are in most instances solved exclusively at the qualitative level and are limited to consideration of a role of the polarity of components in adhesion (the so-called polarity rule high adhesion cannot be achieved between a polar substrate and apolar adhesive, and vice versa). It is very unfortunate that in many books on adhesion the description of adhesion is not given at the molecular level, which is now accessible for the description of intermolecular interactions in liquids and solids. At the same time, it is obvious that from a physical point of view the adsorption theory presents a rather correct concept of interfacial phenomena and agrees with thermodynamics. Within this context, adhesion can be regarded as a particular case of adsorption, inasmuch as the formation of molecular bonds at... 

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. 

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