Adhesion and wetting: similarities and differences.

Adhesion and wetting: Similarities and differences

When two solids are in intimate, molecular contact, a degree of adhesion generally develops between them. This adhesion depends on the type of interaction which may exist between neighboring molecules of the two phases. Adhesion and indeed adhesives have been recognized since antiquity. It is known that the ancient Egyptians had glues based on eggwhite and the Romans used adhesives containing the skin of fish. The deleterious effects of some species of barnacle (Balanus spp.) which adhere tenaciously to ships' hulls have been recognized for centuries although the mechanism of adhesion is poorly understood[1].

Despite this historical aspect to adhesion and adhesives, it must be admitted that a scientific approach to understanding the various problems and phenomena in the field is relatively recent, dating back only about 70 years. An initial interest in adhesives stems from World War I when wooden aircraft structures were assembled with carpenters' glue. A committee in Great Britain in 1919 pointed out that during 1918 it was believed that aircraft production would be seriously limited by a lack of glue[2]. In the same report it was added that no generally acceptable explanation existed at that time of the action by which glues cause surfaces to stick together. Since that time, several theories of adhesion have been prepounded and will be briefly discussed below.

Wetting, or the propensity of a liquid to cover a given solid surface rather than to stay in a compact droplet minimizing surface contact, is clearly a subject with much in common with adhesion. Not only does the nature of the contact between solid and liquid phases depend on molecular interactions in much the same way as does the solid/solid interface, but in addition, many adhesive bonds are produced while one of the two components is in a liquid state. There are similarities in that adequate initial contact is generally ensured by good wetting. Nevertheless, depending on the type of final adhesion mechanism, there can be significant differences.

The quantitative study of wetting phenomena dates from the beginning of the 19th century when Young in England[3] and Laplace[4] in France considered what happens when a liquid is placed in contact with a solid. Two classic relations resulted describing equilibrium at the contact line solid/liquid/surrounding fluid (contact angle), and relating the local curvature of a static liquid/fluid meniscus to the pressure difference across the interface; these being generally known respectively as Young's and Laplace's equations. Although Gauss also showed an interest in wetting phenomena, the subject as a fundamental study stayed relatively dormant until the second half of the 20th century.

Adhesion theories

It is reasonable to consider three types of theory attempting to explain why things stick, although as pointed out by Wake[1], perhaps we ought really to ask ourselves why things do not usually stick when they are placed together. Good spontaneous adhesion is far rarer than apparent lack of affinity between two solids. One of the major causes of poor adhesion is simply inadequate contact established at a molecular level. This effect, often due to surface rugosity, leads to a real contact area far smaller than expected on a geometric basis. It will be seen later that reasonable adhesion may be ensured simply due to physical interfacial bonding if good contact is possible.

Of the three categories of theory, the first is generally referred to as mechanical adhesion. This is supplemented by a group of concepts considered under the term specific adhesion. Last but not least, we must consider cases in which resistance of the interface is largely dependent on bulk properties of one or both phases near the junction.

Mechanical adhesion

The mechanical theory of adhesion proposes that the strength of an interface is essentially due to mechanical anchoring of the adhesive, after solidification, to the rough surface of the substrate (ref. 5). Pores and asperities represent a geometry to which the adhesive can mold itself and once solid, simpley mechanical blocking prevents separation. Clearly this theory, the first historically, can apply only to such rough surfaces as wood (as used in the aircraft industry at that time), paper or textiles. In fact, surface roughness may be harmful in some circumstances since high stress concentrations may be induced locally due to small radii of curvature at localized spots on the substrate. In addition, if the adhesive does not wet the substrate correctly, anchoring effects may be poor. Trapped air between adhesive and substrate impedes wetting and these zones of poor contact can often be where interfacial failure commences.

Specific adhesion

There are essentially four theories of specific adhesion, i.e. theories attempting to explain the fundamental bonding across the interface of two phases in contact (and not necessarily the resulting interfacial strength). By the term specific, it is understood that we are referring to adhesion where mechanical effects, as discussed above, are not a necessary mechanism for producing adhesion. As will be seen below, the various theories each have their fields of applicability and therefore limitations. There is, at least at the present time, no "universal theory of adhesion."

Electrostatic adhesion - In 1948, Deryagin and Krotova (ref. 6) proposed a theory founded on electrical effects observed during peel tests and evoked since mechanical resistance could not be explained by surface tension phenomena alone. Electrical discharges took place during the peeling of polyvinyl chloride from glass in different atmospheres and works of adhesion were high, typically of the order of 10 [J.m.sup.-2] or more. According to Deryagin and Krotova, the high peel energies were due to dissipation of electrical charges and by comparing the system to a capacitor, the work of adhesion corresponded to the energy necessary to separate the two charged plates as predicted by the Paschen gas discharge curve. These basic ideas were further explored by Skinner et al (ref. 7), but these days it is generally accepted that the essential part of the energy dissipated during peel tests is related to rheological phenomena occurring within the bulk of one or both substrates while the system is deformed near the separation front. Electrical discharges may well be a consequence of the separation process rather than a cause of high peel energies, at least in many cases. A renewed interest in the role played by electrical phenomena in adhesion has nevertheless been shown by Legressus and co-workers in France.

Chemical adhesion - Given the high energies of chemical or primary bonds, typically of the order of 400 [kJ.mole.sup.-1], compared to the relatively low values associated with physical bonding [Mathematical Expression Omitted], it is clear that adhesion due to the former type across an interface will be strong. Unfortunately the detection of such bonds has until recently been difficult due to the inevitably small amount of matter constituting an interface (or more exactly an interphase). Modern techniques of surface analysis such as XPS and SIMS are now aiding adhesion scientists to understand the chemical nature of substrates and bonding.

Nevertheless, as early as 1946, there was evidence for chemical bonding in certain systems. Buchan and Rae (ref. 8) showed that rubber-to-metal bonding achieved by the brass plating process was due to chemical valencies linking the brass to the rubber through a mixed copper sulfide compound.

Other cases of chemical adhesion are now recognized such as in the use of silanes to promote adhesion between glass and polymers (ref. 9). These so-called coupling agents typically have the structure [R - Si - X.sub.3] where R is an alkyl group and X is hydrolyzable (e.g. alkoxy, chlorine). The X groups undergo hydrolysis producing silanols which then react with silanol groups existing on the glass surface (ether linkages). Hydrolyzed silanes autocondense to polysiloxanes. The R groups react with appropriate chemical groups in the polymer substrate and thus finally the silane "bridges" the glass/polymer interface. Other examples of chemical bonding known are those at epoxy/cellulose, phenolic resin/lignocellulose and amine/alkyde interfaces.

Adhesion by diffusion - Originally, this theory was proposed by Voyutskii (ref. 10) to explain adhesion between two blocks of a given polymer and was thus known as autohesion. When two chemically compatible polymers are in intimate contact, molecular movement due simply to thermal processes is sufficient to lead to interdiffusion of macromolecular chains. Clearly the process is more rapid at higher temperatures. As a result of this mutual interdiffusion, an interphase is produced and effectively there are chemical bonds linking the two initial phases. (However whether this process can be considered under the term of chemical adhesion is doubtful since ultimate separation may well be due to chain extraction in a process of "reptation" (ref. 11)). The early work of Voyutskii confirmed that the adhesion of polyisobutylene was a result of diffusion by demonstrating a dependance on contact time, temperature and pressure. Later, the peel strength of systems composed of similar or different materials was considered as a function of time. While good adhesion is virtually inevitable for similar components, when their chemical nature differs, interfacial bonding can be very variable, to such an extent that is has been suggested that adhesion may be used as a test for compatibility (ref. 12).

Developments of this model for adhesion have been made recently both from a theoretical stand point (ref. 11) and using experimental techniques. The elegant work on the "healing" of glassy polymers by the Lausanne school is an excellent example of the latter (ref. 13).

Although the diffusion model is undoubtably valid for the treatment of polymeric substrates, clearly it is difficult to imagine its applicability to impervious materials such as glass.

The adsorption or wetting theory - As previously mentioned, when an adhesive bond develops between two phases, in many cases at least one component passes through a liquid state thus ensuring good intimate molecular contact by wetting. It is thus reasonable to say that adequate wetting at some stage is a necessary condition for good adhesion. Whether the similarity between the processes stops there depends on the materials in question and the type of bonds developed (chemical or physical). These ideas were initially proposed by Huntsberger (ref. 14) and by Schonhorn (ref. 15).

Since the intermolecular forces developed during wetting are basically of the same type as those intervening in adsorption processes, Sharpe and Schonhorn proposed their model of adhesion by wetting or thermodynamic adsorption (ref. 16). The basis of the model is use of the two fundamental wetting equations of Young and of Laplace already evoked in the introduction, together with a third equation due to Dupre (ref. 17) defining the thermodynamic reversible work of adhesion, [W.sub.A]. Fundamental parameters are surface (interfacial) tensions or surface (interfacial) free energies, [upsilon], which result from intermolecular forces of a physical nature (van der Waals). Dupre's equation may be written: (1) [W.sub.A] = [upsilon.sub.1] + [upsilon.sub.2] - [upsilon.sub.12] where [upsilon.sub.1] and [upsilon.sub.2] refer to the surface free energies of the two phases in question and [upsilon.sub.12] represents their interfacial free energy. If phases 1 and 2 are in contact, the free energy associated with their interface will be [upsilon.sub.12]. Thus on separation, [upsilon.sub.12] is recovered (per unit area) while free surface energies [upsilon.sub.1] and [upsilon.sub.2] must be supplied. As a consequence, [W.sub.A] is the minimum energy which must be supplied in order to provoke separation. Clearly, if [W.sub.A] is negative, as can be the case sometimes if an adhesive joint is exposed to severe conditions of moisture (ref. 18), then spontaneous dissociation is favored.

A related parameter is the spreading coefficient, S, of a liquid 2 (an adhesive, for example) on a solid 1. At the triple line solid/liquid/environment (liquid or vapor), there is a tendency for the liquid to spread, given by the spreading force characterized by [upsilon.sub.1] reduced by the two tensions attempting to restrict the contact area of the drop, [upsilon.sub.2] and [UPSILON]12. Thus we may define: (2) S = [UPSILON]1 - [UPSILON]2 - [UPSILON]12 If S is positive the liquid will spread leading to contact over a large area whereas if S is negative, the spreading will stop at some earlier stage with the liquid drop presenting a finite contact angle, [THETA], measured between the solid/liquid and liquid/environment interfaces. Although we shall not present a complete description in this brief review, it is interesting to point out the relationship between [W.sub.A] and S. The energy of cohesion of liquid 1, [W.sub.c], is simply 2[UPSILON]1. Thus using equations (1) and (2) we may write: (3) S = [W.sub.A] - [W.sub.c] and we see that a high value of the spreading coefficient is concomitant with a large intrinsic work of adhesion.

"Bulk" adhesion

This category considers the potential role played by bulk properties of the materials in contact.

Weak boundary layers - Nearly 30 years ago, Bikerman (ref. 19) proposed that the separation of two substrates bonded together would not necessarily take place strictly at the interface but could deviate and progress near the interfaces but actually in the bulk of one of the materials. As a result, the failure is cohesive but occurs in a zone where the mechanical strength is reduced for some reason. Bikerman proposed a list of seven types of weak boundary layer failure. In the first class, "failure" takes place simply in air pockets trapped at the interface. Given the unusual properties of interfaces, it is quite possible to have migration of impurities from the bulk of one or both materials towards the discontinuity. For example, in the case of polymers, these impurities may be simply low molecular weight species and their presence leads to reduced mechanical strength thus favoring failure. This explanation, corresponding to Bikerman's second and third classes, may apply to rubbers where a supplementary degree of crosslinking may occur near the interface leading to fragility.

Classes four to seven - their distinction is a little academic - take into account possible interactions between the presence of air, individual substrates and the three phases altogether. When the adhesive bond is exposed to an aggressive environment, this of course replaces air. As a result, chemical or physical attack may take place at the interface. This effect is well known for the case of cohesive failure of polymers taking place in the presence of a wetting liquid. The liquid may have a chemical affinity for the solid (s) (ref. 20) but physical interactions may suffice (ref. 21).

To summarize, Bikerman's model is simple and has often been criticized in the past, but it is recognized today that weak boundary layers may be important in some cases of so-called adhesive failure.

The rheological theory - This theory, developed by Gent, Andrews and co-workers (refs. 22-24) and later refined by Maugis and Barquins (ref. 25) is particularly relevant to elastomeric adhesion. Even in situations where elastomeric adhesion is governed essentially by secondary, or physical, bonds of the van der Waals type (see section on adsorption theory), there can be great variability in the strength of the interface caused by differing conditions both of assembly of the components and of their separation (refs. 22-26). When a rubber is peeled from a rigid substrate, the apparent energy of adhesion, W, is often several factors of ten greater than the reversible value, [W.sub.A], calculated from Dupre's equation (ref. 1). Despite this enormous discrepancy, it has been observed, at least over certain ranges of peel rate and temperature, that there is a direct proportionality between W and [W.sub.A]. In addition, the failure energy varies considerably with peel rate and temperature. The explanation lies in hysteretic energy dissipation occurring during peeling. When an elastomer is separated from its substrate, energy must of course be supplied to break interfacial bonds but during the process, the elastomer is strained. During the process, the elastomer is strained. During the strain cycle, energy is absorbed by mechanical hysteresis. Clearly if the intrinsic adhesion is feeble, so will be the degree of elastomeric deformation and inversely strong adhesion leads to more bulk elastomeric strain.

We can thus understand why there is a proportionality between the dissipation term and intrinsic adhesion in spite of a difference in orders of magnitude. Dissipation obeys the time temperature superposition principle of Williams, Landel and Ferry (WLF) (ref. 27) well known in the context of elastomeric bulk properties and as a consequence, one form of the above theory may be expressed as (ref. 23): (4) W = [W.sub.A] f(R, T) in which f(R, T) is a function of peel rate, R, and temperature, T. By using the WLF shift factor, experimental curves of the type given by equation (4) at different temperatures may be combined to give a master curve.

Hysteresis effects in adhesion and wetting

Both adhesion and wetting represent fields where research today is very active. Of the various topics of interest, perhaps the most controversial is that of hysteresis. Hysteretic effects exist both in adhesion and in wetting phenomena and we shall consider some, at least apparent, similarities. The rheological theory is capable of explaining large measured values of adhesion energy, W, for dynamic conditions, but as peel rates tend to zero, so should viscoelastic dissipation. However, peel experiments at very low rates do suggest that an asymptotic value of W exists well above the predicted value of [W.sub.A] (ref. 26).

Hysteresis effects in rubber adhesion

Given the limitations of peel experiments for assessing the static adhesion of rubber to a rigid substrate, we have considered a different method developed initially by Johnson, Kendall and Roberts (JKR) (ref. 28). As shown schematically in figure 1, a thin disc of glass (microscope slide) is placed on the summit of a hemisphere of elastomer (ref. 29). The elastomer in question is a synthetic polyisoprene (Cariflex IR305, Shell) crosslinked to various degrees using dicumyl peroxide (DCP) (85 minutes at 150 [degrees] C). Intimate contact between glass and elastomer is assured since the molded hemisphere has an optical finish and the polymer is relatively soft. At equilibrium, the slide compresses the hemisphere slightly leading to a circular contact area of radius a. Equilibrium is established as the result of minimizing the overall free energy of the system, its components being strain energy due to compression of the rubber, gravitational energy (height of the center of gravity of the slide) and adhesion energy ([pi][a.sup.2]W). The JKR analysis leads to the following expression for W: (5)[Mathematical Expression Omitted] where E and R are respectively Young's modulus and the radius of the hemisphere (2 cm) and P is the weight of the glass slide (0.1 gm). Young's modulus was determined both by placing large glass masses on the hemisphere and employing Hertz contact equation (ref. 30) and from independent measurements obtained with a dynamic mechanical tester on rubber samples of equivalent states of crosslinking. Degrees of crosslinking were, in their turn, obtained from swelling measurements in toluene, once the mechanical experiments had been completed. These were interpreted using the Flory-Rehner equation modified for effects due to free chain-ends (ref. 31).

Two types of experiment (refs. 32 and 33) were performed in order to exploit equation (5). In "forced adhesion," the slide was placed on the hemisphere and a force of 50 gm imposed for 5 minutes. After removal, evolution of the (diminishing) zone of contact was monitored (using a low power microscope with camera attachment) until (apparent) equilibrium was attained. The time necessary was variable, being shorter for more highly crosslinked hemispheres, but in all cases a stable state was obtained within 15 days. In the second type of experiment, corresponding to naturally attractive or "touching - on adhesion," osculating contact was made and the (increasing) area of contact monitored until a stable was obtained in the same manner as for "forced adhesion." Experiments were conducted at 24 [+ or -]1 [degree] C and 6% RH.

Although the kinetics of evolution of the hemisphere/slide systems has been considered (ref. 34), we are concerned here with the static, apparently equilibrated state. Energies of adhesion evaluated from equation (5) are referred to as [W.sub.1] for "forced adhesion" and [W.sub.c] for "touching-on adhesion." Figure 2 gives [W.sub.1] vs. [M.sub.c], both on logarithmic scales, where [M.sub.c] is the average inter-crosslink molecular weight of the elastomer. It can be seen that there is a definite correlation with [W.sub.1] increasing approximately linearly with [M.sub.c] (the slope of figure 2 is 0.95 + 0.15).

In contrast, there is no apparent dependence of [W.sub.c] on [M.sub.c], its value being calculated at 115 [+ or -] 30 mJ.[m.sup.-2]. There is thus a very clear hysteresis phenomenon related to rubber adhesion. The value of [W.sub.c] is not only approximately constant but also it is quite close to Dupre's reversible work of adhesion, [W.sub.a], as previously remarked (refs. 32 and 33). It would appear that the process of "growing" adhesion corresponding to a "crack front" of negative rate of propagation invokes essentially surface phenomena. Mechanical, or other, dissipation is seemingly a minor factor although the value of 115 mJ.[m.sup.-2] is perhaps a little higher than would be expected for the physical adhesion of rubber to glass (ref. 35).

Since thermodynamic energy balances are necessarily additive, it may be academically more correct to consider the hysteretic effects as being related to the excess energy of adhesion, i.e. the difference ([W.sub.1]-[W.sub.c]), while assimilating [W.sub.c] to Dupre's value, [W.sub.a]. A regression analysis of 1n ([W.sub.1]-[W.sub.c]) vs. 1n [M.sub.c] leads to a slope of 1.3 [+ or -] 0.2 and so the approximate linearity is retained.

No definite explanation of this effect has yet been obtained although three lines of argument may be pursued to explain this hysteresis related to the direction of movement of the "crack front."

An analogy may be made with the theory of Lake and Thomas for bulk rubber fracture (refs. 36 and 37). During failure (positive rate of propagation of "crack front" in "forced adhesion"), polymer chains will to some extent be oriented in the immediate vicinity of the interface. This effect will presumably be essentially entropic since the forces of physical adhesion are small compared to those involved in bulk rubber fracture (leading to chain extension). To a first approximation, a quantity of energy proportional to [M.sub.c] will be required during this orientation since effects should not extend much further than the nearest crosslink to the surface, on average. This energy will be dissipated following failure. The hysteresis effect can be compared to the behavior of a plate of "magnetic spaghetti." If an electromagnet is placed close to a mass of imaginary ferro-magnetic "spaghetti" and turned on, attraction will arise and the mass as a whole will stick to the electromagnet without dissipation. This corresponds to the "touching-on adhesion" experiment. However, if we try to pull the "spaghetti" away without switching off the electromagnet, there will follow internal movement with disentanglement, and thus frictional losses will occur as the "spaghetti" orientates during the forced separation. This may be compared to the case of "forced adhesion." Clearly the analogy must not be taken too far, but the basic physics of hysteresis are similar.

The second possible explanation, which also has something in common with the "magnetic spaghetti" concept, is related to reptation as originally introduced by de Gennes (refs. 11 and 38). In this model, total failure energy corresponds to the sum of that required to provoke interfacial separation ([W.sub.a]) and that dissipated as "friction" (fracture of van der Waals bonds) during the "extraction" of chains from the bulk (assuming a single primary bond scission to take place somewhere along the chain, on average in the middle, enabling separation of the chain from the network). During "extraction," the quantity of energy dissipated will again be proportional to [M.sub.c] (to within a numerical factor).

Given the same dependence on [M.sub.c], it is at present impossible to opt preferentially for one or other of the above explanations.

As for the third possibility, we note that as [M.sub.c] decreases, so does the hysteresis ([W.sub.1] - [W.sub.c]). At high degrees of crosslinking, the rubber tends towards elastic behavior (rather than viscoelastic). It is therefore conceivable that hysteresis is directly related to the viscoelastic properties of the rubber. Viscoelastic dissipation is still important at low separation rates (ref. 39). The kinetics of evolution towards apparent equilibrium are controlled by, among other things, the loss tangent, tan [Delta], of the elastomer. Let us assume a certain analogy between tan [Delta] and hysteresis. (6) tan [Delta] = f([M.sub.c])g(r) (7) [W.sub.1] - [W.sub.c] = h([M.sub.c])i(r) where f, g, h and i are functions and r is strain rate. If when r [right arrow] O, i(r) [right arrow] O and by analogy, g(r) [right arrow] O, the hysteresis of adhesion is simply an artifact controlled in a similar manner to tan [Delta] by a molecular phenomenon. The results given do not then correspond to true equilibrium even if the evolution of contact radius is imperceptibly slow after ca. 15 days. On the contrary, if when r [right arrow] O, i(r) and g(r) [right arrow] 1, then a different argument holds. Hysteresis would be real and the notion of potential energy barriers at a molecular level should be invoked (stick-slip). This eventuality returns us to the models previously mentioned.

Hysteresis of wetting

Before considering wetting hysteresis, let us first recognize the similarity between a sessile drop on a flat, horizontal solid surface and the JKR experiment described previously. In figure 3 we show an imaginary experiment in which drops of constant volume of a given liquid are placed on two solids such that their interfacial free energy is a constant, [Upsilon] SL, but the free energy solid/vapor has two values [Upsilon] SV and [Upsilon] SV, the latter being greater. At equilibrium, the contact angle, [Theta]', is smaller than [Theta] as a result of Young's equation: (8) [Mathematical Expression Omitted] As a consequence, the contact area in the second case, with [Y'.sub.sv], is greater. Both the work of adhesion, [W.sub.A], given by Dupre's equation, (1), and the spreading coefficient, S, equation (2), are more positive. This is quite comparable to the JKR experiment in which the contact area hemisphere/glass slide, and given by [Pi][a.sup.2] depends on the relative affinity of the two materials (and in this latter case, on hysteretic effects). We therefore have a distinct similarity between solid/solid and solid/liquid contact.

Hysteresis of wetting is a phenomenon that has been recognized for several years and pioneering work on it was done in the 1960s by Johnson and Dettre (refs. 40 and 41). However, a full review will not be presented here since the purpose is simply to show how hysteresis effects may be directly related to the direction of wetting, i.e. an advancing or receding wetting front, in much the same way as static rubber adhesion to glass depends on the direction of the "crack front" propagation.

We shall consider an initially straight triple line solid/liquid/fluid corresponding, for example, to part of the periphery of a large sessile drop on a flat, smooth and horizontal surface. Just outside the liquid mass, there is a small energetic heterogeneity of diameter d and at a distance [Y.sub.o] (see figure 4a). Its free energy is taken as [Upsilon]SV + [Epsilon]). Provided that [y.sub.o] is considerably greater than the range of van der Waals bonds (i.e. [greater than or equal to] 1,000 A), then the system is at equilibrium (we ignore all effects far from our microcosm under consideration, which typically has linear dimensions of the order of a millimeter). Suppose however, that we may "pull" the triple line so that contact is established between the liquid and the heterogeneity. Since the latter's free energy is higher than the surrounding solid surface, there will be a tendency for the liquid to stay in place thus covering the heterogeneity and lowering the free energy of the system as a whole.

However, in so doing, the liquid surface is extended adding a certain quantity of free energy to the system due to the term [UPSILON]LV. (There are also changes due to [UPSILON]SV and [UPSILON]SL but these can reasonably be ignored in the simple argument presented here. For a more complete appraisal of the situation, the reader should consult refs. 42-44). Nevertheless, provided that [y.sub.o] is not too great, the liquid will remain "anchored" on the heterogeneity and the triple line profile will adopt the form (see figure 4b):

(9) y [wave] [Epsilon] d/[Pi][Upsilon]LV [Theta.sub.2] 1n [r.sub.o]/~ x ~ where [r.sub.o] is some macroscopic distance comparable to the contact radius of the sessile drop, and [Theta] is the (low) intrinsic contact angle (cf. figure 3a). The maximum value for [y.sub.o] is given by:

(10) [Y.sub.o] [wave] [Epsilon] d/[Pi][Upsilon]LV [[Theta].sub.2] 1n 2 [r.sub.o]/d

If [y.sub.o] exceeds the value given by equation (10), the triple line will "unhook" and return to its straight line configuration.

Considering again figure 4a, provided [y.sub.o] is inferior, or equal, to its maximum value compatible with the presence of a distorted triple line, the system would be in a state of lower energy in the "anchored" configuration. However, since the liquid does not "know" of the presence of the heterogeneity, the triple line remains unperturbed. We thus have all the ingredients necessary for wetting hysteresis to occur. Suppose the drop in figure 4a rolls towards the heterogeneity (advancing wetting front) deformation of the triple line will not occur (except possibly when it gets to within the range of molecular forces of the heterogeneity). Engulfment of [Epsilon] will ensue smoothly. By contrast if the drop is already covering [Epsilon] and it moves away such as to leave the situation shown in figure 4b (receding wetting front), triple line distortion will occur until [y.sub.o] exceeds the value given by equation (10). We can see that this hysteresis effect depends entirely on the direction of movement of the triple line and thus the overall effect is rather similar to the static hysteresis of rubber adhesion in which apparent adhesion is directly related to the direction of motion of the "crack front." The wetting case is perfectly symmetrical in that if [Epsilon] were to take on a negative value, the protuberance shown in figure 4b would become an indentation on the triple line and the directions of motion corresponding to straight and deformed triple lines would be inversed (i.e. respectively receding and advancing). No equivalent reversal can at present be foreseen for the adhesion case.

Conclusion

We have considered briefly the history of adhesion science and the study of wetting phenomena. In both cases, major progress in understanding dates really from the later part of the 20th century. Several theories of adhesion have been propounded over the years and are briefly reviewed here. Each has its merits and applies in certain domains but there is no "universal theory of adhesion." Wetting phenomena are closely related to adhesion in that in many cases when an adhesive bond is established, one phase is liquid and intimate contact, prerequisite for the formation of good interfacial bonding (be this of a physical or a chemical nature), depends on adequate wetting. In certain cases, final adhesion may also depend on the same physical bonding (van der Waals) as the wetting process, but this is not always so. Electrostatic, chemical and diffusional ties may also have to be considered.

Of modern concern are phenomena related to hysteresis both in adhesion and in wetting. We consider here the hysteresis of adhesion in a rubber/glass system when bonding is only physical, and also wetting hysteresis related to the presence of a heterogeneity on a solid surface. The basic causes of hysteresis are different in the two cases (although in the case of adhesion, the fundamental underlying reason is still not clearly understood) but they have a clear similarity. In both cases, hysteresis can be observed as a consequence of changing the direction of motion of the separation front of the condensed matter phases. [Figures 1 to 4 Omitted]

References

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