Contact mechanics

From the decrease in the lattice constant in small crystals caused by the compression due to the surface stress The lattice spacings can be measured with the help of X-ray diffraction or by LEED (low-energy electron diffraction) experiments. 

From the work necessary for cleavage We measure the work required to split a solid. The problem is that often mechanical deformations consume most of the energy and that the surfaces can reconstruct after cleaving. 

From adsorption studies with the help of inverse gas chromatography. 

From mechanical measurement of the surface tension If the surface tension of a solid changes, the surface tends to shrink (if Y increases) or expand (if T decreases). This leads, for instance, to the deflection of bimetallic cantilevers or a contraction of ribbons. 

From the heat generated upon immersion Material in the form of a powder with known overall surface is immersed in a liquid. The free surface enthalpy of the solid is set free as heat and can be measured with precise calorimeters. 

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A second detennining factor in the Femii contact mechanism is the requirement tliat the wavefrmction of the bonding orbital has a significant density at each nucleus, in order for the nuclear and the electron magnets to interact. One consequence of this is that K correlates with nuclear volume and therefore rises sharply for heavier nuclei. Thus the constants m the XFI series with X = Si, Ge, Sn and are... 

Although the Femii contact mechanism dominates most couplings, there are smaller contributions where a nuclear dipole physically distorts an orbital, not necessarily of s type [18]. There are many useful compilations of J and K values, especially for FIFI couplings (see [9], eh 4, 7-21 and [12, 13,14 and 15]). 

Frantz P ef al 1997 Use of capacitance to measure surface forces. 2. Application to the study of contact mechanics Langmuir 2 5957-61... 

The new approach to crack theory used in the book is intriguing in that it fails to lead to physical contradictions. Given a classical approach to the description of cracks in elastic bodies, the boundary conditions on crack faces are known to be considered as equations. In a number of specific cases there is no difflculty in finding solutions of such problems leading to physical contradictions. It is precisely these crack faces for such solutions that penetrate each other. Boundary conditions analysed in the book are given in the form of inequalities, and they are properly nonpenetration conditions of crack faces. The above implies that similar problems may be considered from the contact mechanics standpoint. 

Supersaturation is modest and secondary nucleation occurs by contact mechanisms througout run... 

Seed crystals grow and participate in secondary nucleation by contact mechanisms throughout run... 

Tube-type. These separators are typically divided into two sections (I) precharging and (2) separation. The precharging section is designed to create or enhance the charge difference between particles to be separated (typically by some form of contact mechanism or external pretreatment to render one constituent positive or negative in comparison to the other materials present. The separation section consists of two vertical walls of tubes opposing each other. Each tube... 

The technique of contact mechanics has also been applied to the direct mechanical determination of solid-fluid interfacial energies, and the results compare favorably with those obtained by contact angle measurements [19]. 

Contact mechanics, in the classical sense, describes the behavior of solids in contact under the action of an external load. The first studies in the area of contact mechanics date back to the seminal publication "On the contact of elastic solids of Heinrich Hertz in 1882 [ 1 ]. The original Hertz theory was applied to frictionless non-adhering surfaces of perfectly elastic solids. Lee and Radok [2], Graham [3], and Yang [4] developed the theories of contact mechanics of viscoelastic solids. None of these treatments, however, accounted for the role of interfacial adhesive interactions. 

Dutrowski [5] in 1969, and Johnson and coworkers [6] in 1971, independently, observed that relatively small particles, when in contact with each other or with a flat surface, deform, and these deformations are larger than those predicted by the Hertz theory. Johnson and coworkers [6] recognized that the excess deformation was due to the interfacial attractive forces, and modified the original Hertz theory to account for these interfacial forces. This led to the development of a new theory of contact mechanics, widely referred to as the JKR theory. Over the past two decades or so, the contact mechanics principles and the JKR theory have been employed extensively to study the adhesion and friction behavior of a variety of materials. 

The Hertz theory of contact mechanics has been extended, as in the JKR theory, to describe the equilibrium contact of adhering elastic solids. The JKR formalism has been generalized and extended by Maugis and coworkers to describe certain dynamic elastic contacts. These theoretical developments in contact mechanics are reviewed and summarized in Section 3. Section 3.1 deals with the equilibrium theories of elastic contacts (e.g. Hertz theory, JKR theory, layered bodies, and so on), and the related developments. In Section 3.2, we review some of the work of Maugis and coworkers. 

As mentioned earlier, the contact-mechanics-based experimental studies of interfacial adhesion primarily include (1) direct measurements of surface and interfacial energies of polymers and self-assembled monolayers (2) quantitative studies on the role of interfacial coupling agents in the adhesion of elastomers (3) adhesion of microparticles on surfaces and (4) adhesion of viscoelastic polymer particles. In these studies, a variety of experimental tools have been employed by different researchers. Each one of these tools offers certain advantages over the others. These experimental studies are reviewed in Section 4. 

Section 4.1 briefly describes some of the commonly employed experimental tools and procedures. Chaudhury et al., Israelachvili et al. and Tirrell et al. employed contact mechanics based approach to estimate surface energies of different self-assembled monolayers and polymers. In these studies, the results of these measurements were compared to the results of contact angle measurements. These measurements are reviewed in Section 4.2. The JKR type measurements are discussed in Section 4.2.1, and the measurements done using the surface forces apparatus (SFA) are reviewed in Section 4.2.2. 

Some of the recent work in contact mechanics is focused on understanding the adhesion of viscoelastic polymers and dynamic contributions to the adhesion energy this work is summarized in Section 5. Sections 6.1 and 6.2 include some of the current applications of contact mechanics in the field of adhesion science. These include possible studies on contact induced interfacial rearrangements and acid-base type of interactions. 

Contact mechanics deals with the deformation of solids in contact. Consider two elastic bodies, shown schematically in Fig. 3, of radii of curvature R[ and Rt, Young s moduli E and E2, and Poisson s ratios and V2. Define... 

The classical theory of contact mechanics, due to Hertz, treats the bodies in contact with a hard wall repulsive interaction, i.e. there is no attractive interaction whatsoever, and a steep repulsion comes into play when the surfaces of the bodies are in contact. The Hertzian theory assumes that only normal stresses exist, i.e. the shear stress in the contact region is zero. Under these conditions, the contact radius a), central displacement (3) and the distribution of normal stress (a) are given by the following expressions ... 

The surfaces of all materials interact through van der Waals interactions and other interactions. These interfacial forces, which are attractive in most cases, result in the deformation of the solid bodies in contact. In practice, the radius of the contact zone is higher than the radius predicted by the Hertzian theory (Eq. 7). Johnson et al. [6] modified the Hertzian theory to account for the interfacial interactions, and developed a new theory of contact mechanics, widely known as the JKR theory. In the following section, we discuss the details of the JKR theory. The details of the derivation may be obtained elsewhere [6,20,21]. 

Fig. 4. Schematic of the JKR treatment of contact mechanics calculations. The point (, a, P) corresponds to the actual state under the action of interfacial forces and applied load P. P is the equivalent Hertzian load corresponding to contact radius a between the two surfaces, ( o, P) and (S], a, P ) are the Hertzian contact points. The net stored elastic energy and displacement S are calculated as the difference of steps 1 and 2.

Contact mechanics of elastic solids with interfaces in non-equilibrium... 

As mentioned earlier, the contact-mechanics-based experimental studies on interfacial adhesion primarily include ... 

Fig. 8. (ii) Geometry and interferometry in the SFA. The distance between the surfaces is determined from the wavelengths of FECO. (a) The PECO fringes when the surfaces are in contact. The separation profile, D versus r, can be measured from the fringe profile, and compared to that predicted by the JKR theory of contact mechanics, (b) The FECO when the surfaces are separated. By measuring the wavelengths of the fringes when the surfaces are in contact and when they are separated, we can determine the distance between the two surfaces. 

Given the importance of surface and interfacial energies in determining the interfacial adhesion between materials, and the unreliability of the contact angle methods to predict the surface energetics of solids, it has become necessary to develop a new class of theoretical and experimental tools to measure the surface and interfacial energetics of solids. Thia new class of methods is based on the recent developments in the theories of contact mechanics, particularly the JKR theory. 

Effect of phase state of monolayers of hexadecylsiloxane supported on oxidized PDMS-hysteresis in interfacial energetics as determined by contact mechanics and contact angles... 

A comparision of contact mechanics and contact angle data... 

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