Work of adhesion: contact angles and contact mechanics
D.E. Packham
School of Materials Science, University of Bath,
Bath, BA2 7AY
Abstract
The thermodynamic definitions of work of adhesion and of surface energy are stated and their influence on 'practical' adhesion emphasised. The work of adhesion has long been estimated via contact angle measurements. This paper discusses its measurement via contact mechanics experiments often using the surface forces apparatus, SFA, the results of which are analysed using the JKR or DMT equations. Some recent work using these techniques to study monolayers and thermoplastic films is reviewed.
Key words: surface energy, work of adhesion JKR equation, DMT equation, surface forces apparatus, adhesion hysteresis, Good-Girifalco parameter, critical surface tension, surface energy components, contact angles.
Introduction
The science of adhesion has developed enormously over the past 30 years. In the United Kingdom this development has been closely associated with the name of Keith Allen. It was in 1963 that he, together with David Alner, had the foresight to set up the first of the annual series of adhesion conferences which have continued ever since. In a real sense science does not become science until it is published, so that it may be exposed to open criticism. The adhesion conferences and their written proceedings[1] have played an important part in providing opportunities for work on adhesion to be published and in developing the area as one of serious scientific study in this country.
Since the '60's Keith Allen has contributed a stream of papers covering a range of subjects to the literature on adhesion. An early paper of his was at the 1963 adhesion conference on 'Theories of adhesion surveyed' [2] This is a theme he has returned to from time to time, recent examples being in 1993 [3, 4]. Central to a discussion of 'theories of adhesion' is the concept of work of adhesion: it is this that is considered in this review.
Work of Adhesion
The work of adhesion, WA, is a nineteenth century concept to be found in physical chemistry texts in discussions of the wetting of solids by liquids. Its obvious relevance to the wetting of solids by adhesives ensured that it has featured in many discussions of adhesion [5]. In the period during which Allen's interests in adhesion started, there was confusion over the significance of work of adhesion, and early commentators had to pointed out with great gravitas that WA was not the same as adhesion measured in a mechanical test [6]. A measured fracture energy, G, comprised plastic and other work dissipated in the deformation of the test specimen, y, as well as a thermodynamic term, such as WA:
G = WA + y [1]
Simple calculations showed that y was orders of magnitudes greater than any reasonable estimate of work of adhesion. This led de Bruyne to comment [7]
'those of us who are interested in the fundamental interfacial forces responsible for adhesion can get little, if any, information from destructive tests'.
If this was the situation 30 years ago, what is it now? In particular, can the work of adhesion be measured? Can it be related to 'destructive tests' of adhesion? This paper is mostly concerned to review some of recent work on direct measurement of work of adhesion using the surface forces apparatus, but before doing this, it is necessary to look carefully at the relevant definitions.
Definitions
Thermodynamics deals with ideal systems which it treats by way of unambiguous definitions. Thus the work of adhesion, WA, refers to the free energy difference between two defined states, the first of two phases, 1 and 2 in contact in equilibrium and the second comprising the two phases separate in equilibrium in vacuo [i.e. in equilibrium with their own vapour], figure 1. It is defined in terms of surface free energies, g, as
WA = g1 + g2 - g12 [2a]
where g1 and g2 refer respectively to phase 1 and phase 2 in vacuo [5, 8]. By analogy, work of cohesion refers to the situation where there is only one phase and so is defined as
WC = 2g1 [2b]
Confusion can easily occur because 'work of adhesion' is sometimes used to designate the free energy difference, not between two phases, 1 and 2 in contact in equilibrium and the two phases separate in equilibrium in vacuo, but between two phases, 1 and 2 in contact in equilibrium and the two phases separate in the same enclosure in equilibrium with the vapour present [4, 5, 10]. Designating this as WA*, the definition is now
WA* = glv + g2v - g12 [2c]
g1 differs from glv by the 'spreading pressure', p which represents the lowering of the surface energy of material in vacuo by adsorption of the vapour v
p1 = g1 - glv [2d]
\ WA - WA* = p1 + p2 [2e]
It is necessary here to remember how the surface energies g are defined. Formally they may be taken to be either Gibbs G or Helmholtz F free energies. In the former case the change considered in figure 1 takes place at constant pressure, in the latter at constant temperature. The surface energy, like other surface thermodynamic functions, are defined as the surface excess[9, 10], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. For sake of illustration taking g as being Gibbs energy,
surface energy = g = GS = [G - Gb]/A [3]
where A is the area of the surface, G is the total value of the Gibbs free energy in the system and Gb is the value the total Gibbs free energy would have if all the constituent particles (atoms, molecules etc.) were in the same state as they are in the bulk of the phase.
Such a definition circumvents difficulties which arise from any naïve picture of a surface's in a real material being a two dimensional surface of pure geometry. The purturbations of structure that may extend many atomic spacings from any arbitary one dimensional surface are all accounted for in the 'total minus bulk' formula.
But what about area A in equation 3? We are so used to using the concept of area that we forget that it is a mental abstraction, the product of two linear dimensions, themselves mental constructs, not amenable to precise measurement nor absolute definition outside the realms of pure geometry. Such esoteric considerations can usually be ignored by practical scientists and engineers. In the present context, however, we have to give them some attention.
If the interface between phases 1 and 2 is 'perfectly' flat, there is no problem in defining the interfacial area, A. Cleaved mica provides one of the very few atomically smooth surfaces known to science, so most of the surfaces we work with are to a degree rough. If the roughness was not considered very great we might simply take it into account. Thus if figure 2 represents a section through a nominal square centimetre of surface, we might calculate the true area using the concept of the Wenzel roughness factor,
r = A/Ao [4]
where A is the 'true' surface area, Ao the nominal area. For the surface represented in the figure, measurement of the length of the curved interface suggests a roughness factor of about 1.6 . In such a case we could substitute a corrected area into equation 3 for surface energy and thence via equation 2 evaluate work of adhesion.
Can we do this if the surface is very much rougher? Can we do it for an abraded surface, represented by the Talysurf trace in figure 3? This could be attempted, but what about the surface of anodised aluminium or a microfibrous dendritic surface on zinc, figure 4? As the scale of roughness becomes finer, such the utilisation of a simple roughness factor becomes increasingly unrealistic and unconvincing. It becomes unconvincing not just because of increasing practical difficulty in measuring the 'true' area of such surfaces , it is unconvincing because the roughness itself is an essential feature /characteristic of the surfaces. As we approach molecular scale roughness, indeed long before we get there, the energy of the surface molecules is a consequence of the topological configurations they take up. They will take up these configurations as a consequence of the molecular interactions at the interface: they are an essential feature of bringing together the two phases 1 and 2.
While not wishing to question the value of the roughness factor concept for taking into account modest departures from the flatness of a surface, I would suggest that the area, A, to be used in equation 3 (and thence in calculating the work of adhesion through equation 2), should be the ideal, geometric i.e. macroscopic area of the interface.
In summary, work of adhesion is defined by equation 2. It gives the free energy difference (per unit nominal area) between the two phases concerned in contact at equilibrium and entirely separate, formally in vacuo.
The work of adhesion and practical adhesion
In the past 30 years our understanding of the way in which fundamental interfacial forces influence the outcome of destructive adhesion tests has advanced considerably. There are now examples in the literature where a quantitative relationship between work of adhesion and practical bond strengths have been demonstrated with plausibility. Thus Andrews and Kinloch [11] working with a mechanically simple adhesive and showed that the measured fracture energy G was related to work of adhesion by
G = WA × f [5]
where f is a temperature and rate dependent viscoelastic term. This multiplicative relationship shows that although WA is generally much smaller than G, small changes in the work of adhesion cause large changes in practical adhesion (G). This may be generally true,although the mathematical relationship given in equation 5 is by no means always followed [12,13].
Measurement of work of adhesion
In order to make comparisons between fundamental and practical adhesion, it is clearly necessary to be able to measure values of work of adhesion. This is usually done via contact angle measurements which by use of Young's equation enable estimates of surface energies and of interfacial energies to be made. This area has been much discussed [14, 15, 16], and the details will not be repeated here. It is important to note that this approach is not without its problems. Various, ultimately questionable, simplifications have to be incorporated in order to make progress, consensus is absent over the answers to many questions. Thus the spreading pressure, equation 2d, is usually assumed to be zero [4, 15]. Is the critical surface tension, gc, a charactersitic of the surface? Can the Good and Girifalco interaction parameter f be taken as unity? Many approaches assume that the surface energy can be expressed as a sum of components associated with different types of force acting across an interface. Where non-dispersion forces are involved controversy has raged, and to some extent still rages, as to how they should be treated [14, 17]. Is a geometric mean or a harmonic mean of polar components appropriate? Is the concept of a 'polar component' of surface energy misleading? Should it be replaced by 'acid-base' interactions, and, if so, how should they be calculated?
Having said this, the contact angle approach gives values of surface energies and of works of adhesion that can be usefully applied in the context of the theory of adhesion. Different analyses yield reasonably consistent values, especially where the dispersion contribution is expected to dominate.
A different approach yielding values of work of adhesion involves sensitive measurements of detachment force and contact radius between two surfaces involving the surface forces apparatus, S.F.A. This the main area of this review.
The surface forces apparatus.
The surface forces apparatus was first developed by Tabor, Winterton and Israelachvili for direct measurement of van der Waals forces between molecularly smooth sheets of mica. A good description of a modern version can be found in Israelachvili's book Intermolecular and surface forces [18]. The apparatus uses crossed cylinders of molecularly smooth cleaved mica between which forces may be measured with a sensitivity of 10-8 N (10-6 gf ). This is achieved by sensitive detection of small movements in force measuring springs. It is capable of a distance resolution of 0.1nm by application of multiple beam interferometry. The positions and shapes of the interference fringes give the distance between the surfaces and also the shape of the area of contact.
The basic experiment by which surface forces apparatus is used to deduce surface energy values involves bringing the two surfaces concerned into contact and observing either the load necessary to cause them to separate, or the relationship between the radius of the contact zone and the applied load. The most common analysis used is one put forward by Johnson, Kendall and Roberts in a classical paper in 1971 on surface energy and the contact of elastic solids [19].
Surface energy and the contact of elastic solids
If two elastic bodies come into contact the size of the area of contact will depend on the load and the elastic moduli of the bodies concerned. A whole range of problems of this kind of contact between two spheres, between spheres and planes and so forth were treated by Hertz in the nineteenth century in a manner which is still widely applied to such problems in engineering [18]. As Johnson, Kendall and Roberts pointed out, Hertz did not take surface forces into account: the adhesion forces between the two bodies in contact will cause a small, but observable, increase in contact area. They allowed for surface forces and produced the JKR equation, which for two elastic spheres, of radii R1 and R2, in contact takes the form:
a3 = [ F + 3pRW12 + Ö{6pR W12 F + (3pR W12)2}]R/K [6]
where
a is the radius of the area of contact,
R = R1 R2/( R1 + R2),
F is the normal load,
K is an elastic constant.
The term W12 is a surface energy term and will be discussed below.
Several general points should be noticed about the JKR equation. If the surface energy term is put to zero, the equation reverts to the Hertz relationship. For zero normal load (F = 0), there is a finite contact area - this is the consequence of the surface forces. Contact will remain with a small pull-off force (F< 0). As the pull-off force is increased (F becoming more negative) the contact area will reduce, and suddenly the sphere will jump free. Johnson et al. pointed out that there will only be real roots for a if
F ³ - 3pR W12 /2 [7]
and identified the critical adhesion or 'pull-off' force as
Fs = - 3pR W12 /2 [8]
The JKR analysis is of course an elastic analysis, indeed a linear elastic analysis, which means that the deformations involved must be kept small for most materials if the assumptions of the analysis are not to be invalidated.
The JKR equation is easily modified for particular cases. If the two spheres are made of the same material, K is simply related to the Young's modulus, E, and Poisson's ratio, n:
K = 2E / 3(1 - n 2) [9]
For a sphere on a flat surface, we can put R1 = R and let R2 become infinite, so the form of the equation remains as equation 6.
Let us return to the 'surface energy' term W12. The essential basis of the JKR theory is extremely simple.The total energy of two spheres in elastic contact is the sum of the surface energy loss, the stored elastic energy caused by their deformation and the potential energy of the applied load (figure 5). At equilibrium the differential of this sum with respect to radius of contact willbe zero. W12 enters the derivation by saying that the loss in surface energy consequent upon producing a circle of contact of radius a is
Us = - pa2 W12 [10]
Johnson et al. rather loosely called W12 the 'surface energy'. Israelachvili [20] regards it as 'by definition reversible work of adhesion', and if the two materials are the same, puts W = 2gs
How does W12 in the JKR theory relate to the thermodynamic terms defined above (equn 2) ? By analogy with equn 2a and figure 1 one could write
W12 = glv + g2v - g12 = WA/v [11]
where glv refers to the surface energy of material 1 in the presence of whatever vapour v is in equilibrium with the spheres in the SFA. Similarly for g2v . WA/v can be termed the work of adhesion in the presence of vapour v. It is similar to WA* (equation 2c) except that for WA*, the vapour phase is simply the vapours of phases 1 and 2. If the spheres are both of the material 1, equation 11 reduces to
W = 2 glv [12]
The terms glv and g2v will be lower than the surface energies gl and g2 (cf. equation 2d) by whatever lowering of energy is associated with the adsorption of v on the surfaces of 1 and 2. Thus equns 11 and 12 only define the thermodynamic work of adhesion and of cohesion respectively, if the 'vapour' v is vacuum.
A further issue, at present unresolved, is that there are other theories of adhesion which predict a different Fs / W12 relation from that of equation 8. In particular the Derjaguin, Muller and Toporov [DMT] theory predicts [20, 21]
Fs = - 2pR W12 [13]
The DMT theory accounts for the effects of surface forces just outside the area of contact. Maugis has described a theory which comprehends both the theories as special cases [22]. In principle a decision between equations 8 and 13 could be made by experimental measurement, but at present this has not proved possible, despite the 25% difference between their predictions. It is Israelachvili's opinion that the pull off force probably lies between the values predicted by equations 8 and 13 [20].
Adhesion of thin layers and hysteresis
Israelachvili and his colleagues have published a number of studies of adhesion between thin layers which have used the sufrace forces apparatus [20, 23-27]. Typically they have deposited monolayers, or very thin layers of surfactants or liquid hydrocarbons on the surfaces of cleaved mica and have evaluated adhesion under different conditions from the relationship between radius of contact and applied force (cf. equation 6) or by measurement of the pull-off force (equations 8 and 13). As the layers deposited on the two surfaces are usually the same for a particular experiment, the W12 term in the JKR equation reduces to the W of equation 12. They express their results in terms of this W, or, more usually the 'surface energy' which is a half of W (equation 12).
Their results are at first sight startling because they report that W when measured on separating the surfaces, W , is greater than that measured as the surfaces approach, W¯ thus
W > W¯ [14]
DW = (W - W¯) > 0 [15]
A typical example is shown in figure 6 [27]. The graphs show radius /load curves plotted according to the JKR equation. The separate lines for separating, marked gR and approach (gA) in figure 6a show the hysteresis commonly found. Different conditions gave the results of figure 6b which show almost no hysteresis.
Such results are startling because work of adhesion is supposed to represent a change in free energy between two defined equilibrium states, and the properties of such states, according to the tenets of thermodynamics, depend on the states themselves not on how they are approached [9].
The phenomena which the SFA reveal on very thin layers has potential application in all adhesion systems. How does Israelachvili account for this hysteresis? He acknowledges that contact angle hysteresis, which of course implies hysteresis in apparent surface energy and work of adhesion, is widely attributed to surface roughness or surface heterogeneity, but maintains that such explanations do not apply to these molecularly smooth, chemically homogeneous surfaces. He considers that there are two other sorts of hysteresis inherent in many adhesion situations: he calls them mechanical and chemical hysteresis.
Mechanical hysteresis.
In practice the force between two surfaces cannot be measured (e.g. in the SFA) at the surfaces themselves, S, but some distance away, say S', figure 7a. In effect the force is applied to the surfaces via a spring of stiffness Ks. Now consider the schematic atomic force separation curve in figure 7b. A straight line has been drawn on this with a slope representing the 'spring' stiffness Ks. During the SFA experiment described above, the area of contact either increases or decreases so the separation at the edge of the area of contact might be thought of as travelling one way or the other along the force/distance curve. On approach the curve will be followed up to point DA where the gradient of the force curve becomes equal to Ks. At this point the surfaces will jump to DB and then continue down the curve. On separation the curve will be followed upto about DO whence the surfaces will jump to DR.
These mechanical instabilities mean that the 'surface energy' measured as the contact area grows will be less than that when the surfaces are separating. This mechanical hysteresis will not occur where the attractive forces are very weak, or the backing material very stiff.
Chemical Hysteresis.
The basis of this is that the molecules at the interface may relax or change their configuration when the surfaces come into contact arriving, over a period of time, at an equilibrium configuration different from that when the surfaces were isolated. Thus the chemical nature of the surface on contact is different from that on separation. This reorganisation can take various forms. It may involve interdiffusion, reorientation of polar molecules, or the exchange of chemical species from bulk to surface.
Israelachvili has found evidence for these effects in his studies of thin surfactant layers. Many of these have been postulated, and occasionally demonstrated in studies of adhesive bonding in a 'practical' context.
Israelachvili has classified his surface layers as crystalline, amorphous solid and liquid-like (figure 8). The first tend not to reorganise, so hysteresis is low. The liquid-like surfaces reorganise very quickly both on loading and unloading, so again hysteresis tends to be low. It is the solid amorphous surfaces where reorganisation may take place over a significant time scale, that hysteresis is generally greatest.
On a simplistic level, the analogy with viscoelastic loss is obvious, and it is not surprising to find that adhesional hysteresis is considered to have a temperature / rate dependence, figure 9. Thus the 'adhesion energy' of CTAB (hexadecyltrimethylammonium bromide) monolayers measured by unloading was found to increase by 60% if the layers were left in contact at 15 °C for 6 minutes. At higher temperatures the layer became more fluid and by 35 °C, no increase in energy with time was observed [20]. CTAB layers also show rate effects, with greater hysteresis for a fast load/unload loop than for a slow one [20].
The results in figure 6 refer to CaABS (a calcium alkyl benzene sulphonate) monolayers. They show the effects that ambient vapour can have on adhesion. In an atmosphere of dry air or nitrogen, the layers behave as amorphous solid and show significant hysteresis, but when exposed to nitrogen saturated with decane vapour, the hysteresis is lost, the surface energy value corresponding closely to that expected for decane, 24 mJ/m2. It is considered that the hydrocarbon molecules condense onto the surfactant layers, penetrate the outer regions and fluidise the surface [24, 26, 27].
Application to elastomers
The JKR analysis assumes linear elasticity, so may be successfully applied where the forces are small (low surface energy) and deformations are modest (small contact area compared with the radius of curvature). The surface forces apparatus is well suited to these restrictions. Elastomers have low modulus and are elastic, linearly elastic at small deformations. The JKR technique has been used with these materials for some years. The low modulus enables contact areas to be monitored relatively easily by conventional microscopic techniques. Some illustrative examples are discussed.
Barquins used a JKR analysis to study time effects in the adhesion of a glass sphere to a polyurethane rubber [28]. The work of adhesion calculated increased with time t according to a t0.1 relationship. He argued that this was the wrong function for diffusion of chain ends to be responsible, and attributed the increase in adhesion to the relaxation of stored stress associated with surface roughness.
Shanahan and Michel worked with glass microscope slides and polyisoprene hemispheres [29], and studied the variation of contact radius with time for two types of contact. In'touch on' contact, oscillating contact was made with the light slide (0.1g): after oscillation ceased an essentially constant contact radius was observed after a few minutes. The value of work of adhesion W derived form the JKR theory was ca. 115 mJ/m2, independent of crosslink density and somewhat higher than expected for a thermodynamic work of adhesion.
The other experiment, 'forced contact' involved placing a 50g weight on the slide for 10 minutes: on removal of the weight, the contact radius decreased over an extended period reaching apparent equilibrium by 15 days. The work of adhesion calculated from the 'equilibrium' radius was larger than the 'touch on' value and increased approximately linearly with the sub-chain molecular weight of the crosslinked rubber. Thus there is a difference, an hysteresis, between the values of W inferred from the two experiments. Shanahan and Michel suggest an explanation in terms of essentially kinetic models, based on slip-stick adhesion as the crack length changes during the experiment. While this may apply to the situation where the crack is moving, the hysteresis persists when the crack lengths have long stopped changing. This would seem to imply some difference in surface structure consequent upon the application of considerable different contact pressures in the two experiments. This would correspond most closely to the 'chemical hysteresis' described in the previous section.
Table 1
Comparison of surface energy results (mJ/m2)
measured by different methods for modified siloxane surfaces [30]
Method for Surfaces
Surface energy -CH3 -OCH3 -CO2CH3
JKR 20.8 26.8 33.0
Contact angle
Geometric mean:
dispersion component 20.6 30.8 36.0
polar component 0.09 6.4 6.4
total 20.7 37.2 42.4
Harmonic mean:
dispersion component 23.5 32.2 36.7
polar component 0.4 10.9 11.5
total 23.9 43.1 48.2
Chaudhury has studied alkylsiloxane monolayers of different functionality on the surface of polydimethyl siloxane elastomer using a sphere on plane configuration [30]. He compared the JKR surface energy with values calculated from contact angle measurements, table 1. From the contact angles (of only two liquids) he calculated the dispersion , gd, and polar, gp, components of surface energy using both a geometric mean and an harmonic mean relationship. The correlation between the JKR surface energy and the dispersion component, rather than the total surface energy is remarkable. Chaudhury claims that the JKR method 'provides a direct estimate of surface energy' and that the results show that the interaction between the surfaces 'originates entirely from dispersion forces'. As the discussion earlier in this paper shows, it is at the best debatable to say that the JKR method directly measures surface energy. It is difficult to understand why polar interactions should not act across some of the surfaces listed in table 1. An explanation of the results might be that the surfaces in the two experiments were actually different, because of change in configuration in response to the test liquids used.
Silberzan, Perutz and Kramer, working with Chaudhury, have recently published some interesting results for siloxane elastomers without deposited monolayers [31]. In contrast to Chaudhury's earlier paper [30], considerable hysteresis was found between the loading and unloading a3 vs. F curves (cf. equation 6). What is particularly interesting is that 'no satisfactory fit could be obtained by using the same value for [the elastic constant] K for the analysis of the loading and unloading regimes'. As a consequence they express caution over the uncritical use of the JKR equation in these circumstances. They rationalise their findings by suggesting that the surface energy itself may be changing according to the position as a consequence of a pressure induced surface reaction.
Application to other polymers
Most polymers have much more complex mechanical behaviour than elastomers, making difficult the experimental techniques used by the authors in the previous section. A group working in Minneapolis-St. Paul (at the Univeristy of Minnesota and 3Ms) have successfully used the surface forces apparatus to study the surface energies of thermoplastic films. This group, which comprises Merrill, Pocius, Thakker, Tirrell and Mangipudi, published their first report of the work in 1991 [32]. They used films about 5mm thick of polyethylene terephthalate (PET) which they successfully glued to the lens of the SFA. They calculated the 'surface energy' of the PET from the pull-off force, comparing the results from the JKR analysis with that of DMT (equations 8 and 13). They have extended the work to cover polyethylene (PE), the PET/PE interface [33] and PE after successive corona discharge treatment [34].
In some cases surface energies have been found to increase with contact time (PE/PE), attributed to interdiffusion, and in some cases (PE/PET) the calculated surface energy increases with pull-off rate. For most of their results, however, they claim that time effects are small.
A valuable feature of the papers is a comparison of the 'surface energy' calculated from the pull-off force in the SFA with that calculated from contact angles. In the earlier papers on PET [32, 33] they find a large difference between the JKR surface energy of 61.2 mJ/m2 and that derived from contact angles, about 43 mJ/m2. Both techniques give a value of about 33 mJ/m2for PE. It does seem questionable whether the contact angle analysis they use in these papers adequately takes into account non-dispersion interactions [35]. In the 1995 paper on corona treatment of PE they include analyses of contact angle results using geometric mean and harmonic mean equations. It is very interesting to see that these, particularly the former, agree quite closely with the JKR surface energies.
Conclusions
Work of adhesion and surface energies play a vital rôle in adhesion and in understanding theories of adhesion. Even modest changes in their values can cause large changes in practical measured adhesion. For many years their values have been deduced via contact angle measurements. The contentious issues associated with these measurements should be well recognised as they have been discussed often enough. The JKR equation, especially in combination with measurements on the surface forces apparatus, gives an alternative method of obtaining values for these energy terms. It enables subtle changes in interfacial layers to be studied, changes which change work of adhesion significantly, and which consequently have great potential in understanding and modifting adhesion in an engineering context. If we allow the SFA experiment to be called a 'destructive test', we can certainly answer de Bruyne now by saying that valuable information about interfacial forces can be obtained from destructive tests.
Strictly work of adhesion and surface energy are thermodynamic quantities. In practice experimental limitations mean that the 'true' thermodynamic values are unlikely to be obtained from either wetting or SFA measurements. Assertions by some of the authors reviewed that the JKR surface energy is a true thermodynamic quantity should not be accepted uncritically. Israelachvili is quite clear on this. Indeed he raises the interesting point as to whether adhesion is ultimately a thermodynamic process, whether adhesive bonds usually (ever?) exist in 'true' equilibrium.
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33. V. Mangipudi, M. Tirrell and A.V. Pocius, J. Adhesion Sci. Tech. 8, 1251(1994).
34. V. Mangipudi, M. Tirrell and A.V. Pocius, Langmuir 11, 19(1995).
35. In paper 32 it is only Zisman's critical surface tension analysis which is used. In 33 Mangipudi et al. use a relationship (their equation 11) which neglects spreading pressure and which seems to assume either that the Good-Girifalco parameter is unity or that non-dispersion force interactions are zero. for more detail, this equation should be compared with equation 7 p. 353 of Shanahan loc. cit. 14.
Figure captions
Figure 1
The change from two phases in contact at equilibrium to the two phases separate in vacuo for which the work of adhesion is defined.
Figure 2
An interface showing a small degree of roughness. If the nominal area were 1 cm2, the 'true' area would be 1.6 cm2
Figure 3
A typical Talysurf trace of surface profile of a metal.
Figure 4
Scanning electron micrograph showing a microfibrous surface consisting of zinc dendrites.
Figure 5
Contact of two spheres.
Figure 6
JKR curves for calcium alkyl benzene sulphonate monolayers. Contact radius cubed is plotted against force, equation 6. Atmosphere: (a) dry air or nitrogen, (b) nitrogen saturated with decane [27].
Figure 7
Mechanical hysteresis. (a) In practice a force cannot be applied directly to a surface S, but is applied at some distance from it, S'. (b) Schematic force/ distance curve for interatomic forces., after 20.
Figure 8
Schematic representation of solid-like (crystalline), amorphous solid, and liquid-like surface layers [23].
Figure 9
Effect of temperature on adhesion hysteresis, after 27.
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