Adhesion deformable solids

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

Various continuum models have been developed to describe contact phenomena between solids. Over the years there has been much disagreement as to the appropriateness of these models (Derjaguin et al. [2 ] and Tabor [5-7]). Experimental verification can be complex due to uncertainties over the effects of contaminants and asperities dominating the contact. Models trying to include these effects are no longer solvable analytically. A range of models describing contact between both nondeformable and deformable solids in various environments are discussed in more detail later. In all cases, the system of a sphere on a plane is considered, for this is the most relevant to the experimental techniques used to measure nanoscale adhesion. 

Initially, the adhesive must be either a liquid or a readily deformed solid so that it can be applied and formed to the required geometry within the assembled joint. It is necessary for the adhesive to flow and conform to the surface of the adherends on both micro- and macroscales. Small air pockets caused by the roughness of the substrate must be easily displaced with adhesive. 

The adhesion is now a function of the modulus E of the deformable solid for smooth contacts this is not the case. Where is small, Le, for low modulus and smooth surfaces, the adhesion is greatest and vice versa. The form of has been derived and Figure 4 shows a comparison of theory and experiment. The enhanced adhesion at small values of is notable but the mechanism which produces this effect is not properly resolved. " ... 

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. 

Finally, an important feature of gels made of adhesive emulsions arises from the deformation of the droplets. Indeed, as the temperature is lowered the contact angles between the droplets increase [27,28] (see Chapter 2, Section 2.3). Consequently, the structure of the final floes depends on the time evolution of the strength of the adhesion. Initially, the adhesion results in the formation of a random, solid gel network in the emulsion. Further increase of adhesion causes massive fracturing of the gel, disrupting the rigidity of the structure and leading to well separated, and more compact floes [27,28]. 

Decreased mobility of adsorbed chains has been observed and proved in many cases both in the melt and in the solid state [52-54] and changes in composite properties are very often explained by it [52,54]. Overall properties of the interphase, however, are not completely clear. Based on model calculations the formation of a soft interphase is claimed [51], while in most cases the increased stiffness of the composite is explained by the presence of a rigid interphase [55,56]. The contradiction obviously stems from two opposing effects. Imperfection of the crystallites and decreased crystallinity of the interphase should lead to lower modulus and strength and larger deformability. Adhesion and hindered mobility of adsorbed polymer chains, on the other hand, decrease deformability and increase the strength of the interlayer. 

Since n is less than unity, the apparent viscosity decreases with the deformation rate. Examples of such materials are some polymeric solutions or melts such as rubbers, cellulose acetate and napalm suspensions such as paints, mayonnaise, paper pulp, or detergent slurries and dilute suspensions of inert solids. Pseudoplastic properties of wallpaper paste account for good spreading and adhesion, and those of printing inks prevent their running at low speeds yet allow them to spread easily in high speed machines. 

New insights into solid/solid adhesion have been provided by Chaudhury and Whitesides [12] who have directly studied the adhesion forces between various silicone surfaces. They analyzed the deformations occurring on contact of small... 

Because of increased production and the lower cost of raw material, thermoplastic elastomeric materials are a significant and growing part of the total polymers market. World consumption in 1995 is estimated to approach 1,000,000 metric tons (3). However, because the melt to solid transition is reversible, some properties of thermoplastic elastomers, eg, compression set, solvent resistance, and resistance to deformation at high temperatures, are usually not as good as those of the conventional vulcanized mbbers. Applications of thermoplastic elastomers are, therefore, in areas where these properties are less important, eg, footwear, wire insulation, adhesives, polymer blending, and not in areas such as automobile tires. 

So far we have assumed that the interacting surfaces are not deformable. In reality all solids have a finite elasticity. They deform upon contact. This has important consequences for the aggregation behaviour and the adhesion of particles because the contact area is larger than one would expect from infinitely hard particles. 

The adhesion force increases linearly with the particle radius. Surprisingly, it is independent of the elasticity of the materials. This is because of two opposing effects. In a hard material the deformation of the solid is small. As a result the contact area and the total attractive surface energy are small. On the other hand, the repulsive elastic component is small. Both effects compensate each other. Soft materials are strongly deformed. Thus both the attractive surface energy term and the repulsive elastic term are high. 

Food rheology is mainly concerned with forces and deformations. In addition, time is an important factor many rheological phenomena are time-dependent. Temperature is another important variable. Many products show important changes in rheological behavior as a result of changes in temperature. In addition to flow and deformation of cohesive bodies, food rheology includes such phenomena as the breakup or rupture of solid materials and surface phenomena such as stickiness (adhesion). 

In principle, an equality between the thermodynamic work of adhesion of liquid-solid systems and the work needed to separate an interface might be expected for simple systems and this has been observed for failure of adhesive-polymer interfaces bonded by van der Waals forces, (Kinloch 1987). Similarly, empirical correlations of interfacial strengths and work of adhesion values of solidified interfaces have been reported for some nominally non-reactive pure metal/ceramic systems. However, mechanical separation of such interfaces is a complex process that usually involves plastic deformation of the lattices, and hence their works of fracture are often at least ten and sometimes one hundred times larger than the works of adhesion, (Howe 1993). Nevertheless, for non-reactive metal/ceramic couples, it is now widely recognised that the energy dissipated by plasticity (and as a result the fracture energy of the interface) scales with the thermodynamic work of adhesion (Reimanis et al. 1991, Howe 1993, Tomsiaet al. 1995). 

The main difference between a solid and a liquid is that the molecules in a solid are not mobile. Therefore, as Gibbs already noted, the work required to create new surface area depends on the way the new solid surface is formed [ 121. Plastic deformations are possible for solids too. An example is the cleavage of a crystal. Plastic deformations are described by the surface tension y also called superficial work, The surface tension may be defined as the reversible work at constant elastic strain, temperature, electric field, and chemical potential required to form a unit area of new surface. It is a scalar quantity. The surface tension is usually measured in adhesion and adsorption experiments. 

When attempting to relate the adhesion force obtained with the SFA to surface energies measured by cleavage, several problems occur. First, in cleavage experiments the two split layers have a precisely defined orientation with respect to each other. In the SFA the orientation is arbitrary. Second, surface deformations become important. The reason is that the surfaces attract each other, deform, and adhere in order to reduce the total surface tension. This is opposed by the stiffness of the material. The net effect is always a finite contact area. Depending on the elasticity and geometry this effect can be described by the JKR 65 or the DMT 1661 model. Theoretically, the pull-off force F between two ideally elastic cylinders is related to the surface tension of the solid and the radius of curvature by... 

Zhang F, Busnaina A. The role of particle adhesion and surface deformation in chemical mechanical polishing processes. Electrochem Solid-State Lett 1998 1 184-187. 

A more recent hypothesis is that the craze tip breaks up into a series of void fingers by the Taylor meniscus instability - . Such instabilities are commonly observed when two flat plates with a layer of liquid between them are forced apart or when adhesive tape is peeled from a solid substrate jjjg hypothesis in the case of a craze is that a wedge-shaped zone of plastically deformed and strain softened polymer is formed ahead of the craze tip (Fig. 3 a) this deformed polymer constitutes the fluid layer into which the craze tip meniscus propagates whereas the undeformed polymer outside the zone serves as the rigid plates which constrain the fluid. As the finger-like craze tip structure propagates, fibrils... 

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