Theories of Fundamental Adhesion

Abstract

The historical development and current status of the four classical theories of adhesion are first reviewed. The adsorption theory emphasizes the point that once adhesive and substrate come into contact forces of attraction will act between them. As long as the extent of wetting is good, these forces, whether primary bonds, such as covalent, or secondary van der Waals forces, are generally considered sufficient to give a high bond strength. Primary bonding may be necessary to achieve bond durability in a hostile environment.

The mechanical theory focuses on interlocking between adhesive and a rough substrate surface. Again good wetting is required, or surface roughening is likely to lead to poor bond strength. It has been shown to apply to some surfaces rough on a macroscale as well as to microfibrous and microporous surfaces, such as anodized aluminum. The enhanced adhesion is associated with increasing plastic energy dissipation during fracture in the bulk adhesive.

The electrostatic theory points to electrical phenomena such as sparking, which may be observed during the destruction of an adhesive bond, and consider the transfer of electrostatic charge between the adhesive and substrate. It regards the adhesive-substrate system as analogous to a parallel plate condenser. Estimates of the energy associated with this process are generally small compared with adhesion fracture energies, and the theory is much less vigorously supported than was the case some 50 years ago.

The diffusion theory has attracted increasing interest since the development of reptation theory of polymer chain dynamics. It provides a model for polymer-to-polymer adhesion, and gives an explanation of the time and molecular weight dependence of adhesion to polymers of various compatibilities.

The role of weak boundary layers is discussed with emphasis on the importance of careful investigation of the locus of failure of an adhesive bond.

In conclusion it is argued that the classical theories are best regarded as emphasizing a different aspect of a more comprehensive model which, in principle, relates molecular dispositions in the region of the interface to macroscopic properties of an adhesive joint.

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1 Introduction

1.1 Practical and Fundamental Adhesion

The phenomenon of adhesion has been of interest for tens of thousands of years. Our remote ancestors were concerned to stick pigments to walls for cave painting and flint and bone to wood for tools and weapons (Pascoe 2005; Wadley et al. 2009). Aristotle remarked on the gecko’s ability to adhere to vertical surfaces; both Galileo and Newton were fascinated by the high forces of adhesion that could be observed in certain surfaces in intimate contact.

As Newton realized, there are two different types of question to be asked about the phenomenon of adhesion. The first type asks about the forces and so on which have to be applied to separate the bonded components; the second concerns what holds the components together in the first place. These two types of question respectively concern practical and fundamental adhesion. Some authors have written as if they thought that fundamental and practical adhesion were the same. This tendency was more prevalent in the past, but is still occasionally encountered.

Practical adhesion, then, is concerned with the magnitude of mechanical force or the quantity of energy which has to be applied to break an adhesive bond. It is relevant whether an adhesively bonded component breaks under load in service, or in some test machine in the laboratory. Practical adhesion is clearly of enormous importance and is considered in detail in this Handbook in Chaps. 20, “Fracture Tests,” 21, “Impact Tests,” 22, “Special Tests,” and 23, “Constitutive Adhesive and Sealant Models.” This chapter is concerned with fundamental adhesion. It is concerned with forces and mechanisms on, or approaching, the molecular scale, which are involved in holding together the different components of an adhesive bond. Newton recognized that the forces concerned in fundamental adhesion could be very large and challenged “experimental philosophy” to discover what they were! (Newton 1730).

Serious scientific concern with fundamental adhesion is usually dated back to the classic work of McBain and Hopkins in the 1920s, and to the various theories were advanced during the middle part of the last century. There was a strong tendency during much of this period to regard different theories as rival explanations of the same phenomena, rather than as complementary aspects of a broader rationalization. Much of the literature of the time, and even some of the literature today, reflects this approach, and therefore it is appropriate, if somewhat anachronistic, in this chapter first to consider different theories individually. A synthesis will be given in the conclusions.

It is obvious that adhesion at the fundamental level is a prerequisite for the existence of practical adhesion. What is the relationship between fundamental and practical adhesion? The answer to this question is by no means simple; indeed some authorities in the past have considered that there was no relation between the two. It is not appropriate here to attempt a detailed answer, but a simple, indeed simplified, account will be presented now.

Practical adhesion is generally assessed in the laboratory by loading an adhesive joint and observing the force required to produce failure, cf. Chaps. 20, “Fracture Tests,” 21, “Impact Tests,” and 22, “Special Tests.” In some tests, the numerical value representing practical adhesion is a fracture energy (per unit area); in other tests, a fracture stress. Let us consider each in turn.

1.2 Fracture Energy

When an adhesive joint fails energy will have to be supplied to break the bonds where the joint fails, creating two new surfaces. These bonds broken may be, according to circumstances, primary or secondary bonds. This energy required to form new surfaces is surface energy. If the failure is at the interface between phases 1 and 2, the appropriate surface energy term is the work of adhesion, W_A,

$$ {W}_{\mathrm{A}}={\gamma}_1+{\gamma}_2-{\gamma}_{12} $$

(1)

where γ₁ and γ₂ are the surface energies of materials 1 and 2 respectively in contact with air, and γ₁₂ is the interfacial energy between phases 1 and 2.

An adhesive joint often fails cohesively within one component, rather than at the interface. Under these circumstances, the corresponding term will be the work of cohesion, W_C, given (for failure in phase 1) by

$$ {W}_{\mathrm{C}}=2{\gamma}_1 $$

(2)

The work of adhesion and work of cohesion have been defined and discussed more fully in Chap. 5, “Spreading of Liquids on Substrates.”

In practice the magnitude of the fracture energy, G, is (almost) always considerably greater than that of the surface energy term W_A or W_C (now written as G₀), given by Eqs. 1 or 2. G₀ may be some average of W_A or W_C, depending on the locus of failure. These Eqs. 1 and 2, are thermodynamic equations; however, fracture of an adhesive bond will rarely, if ever, be reversible as thermodynamics require. Moreover, during the fracture process other energy absorbing processes occur, for example, plastic and viscoelastic deformation. Thus

$$ G={G}_0+\psi $$

(3)

where ψ represents these other energy absorbing processes.

From a simple standpoint, Eq. 3 can be taken as representing the relationship between practical adhesion (represented by the measured G) and fundamental adhesion associated with molecular forces at the interface, G₀. To repeat, usually ψ is very much larger than G₀, and so practical fracture energies for adhesive joints are almost always orders of magnitude greater than work of adhesion or work of cohesion.

It might be thought from this that the surface energy term G₀ was not important as its magnitude was small. However G₀ and ψ are coupled: as G₀ increases ψ gets larger as well. Put simply, a very weak interface (low G₀) would not be able to transmit a high stress needed to produce high ψ, say by plastic deformation. In some mechanically simple adhesive bonds, the loss term is directly proportional to the surface energy term. If G₀ is doubled, ψ also is doubled, so the overall fracture energy, G, becomes twice as large.

1.3 Fracture Stress

Where the measure of practical adhesion is a fracture stress, similar considerations apply. A simple treatment of the physics of fracture (Griffith-Irwin theory, v. Good 1972) shows that the fracture stress σ_f also depends on the fracture energy G:

$$ {\sigma}_{\mathrm{f}}=k{\left( EG/l\right)}^{\frac{1}{2}} $$

(4)

where k is a constant, l is the length of the critical crack which leads to fracture, and E is the effective modulus. When this equation was first put forward, it was considered that the term G was the surface energy, but is was soon recognized that this led to strength predictions which were much too low. It was realized that G represented the sum of all the energy absorbing processes involved in the fracture, i.e., once again Eq. 3 applied. Practical adhesion (now represented by σ_f) is related to fundamental adhesion through Eqs. 3 and 4.

1.4 Structure of This Chapter

Contemporary discussion of the fundamentals of adhesion generally reflects the historical development of the subject. For convenience, this approach will be adopted here. Early work in the 1920s discussed two kinds of adhesion. Where surfaces were smooth what would now be described as Adsorption Theory applied, with rough or porous surfaces Mechanical Theory. The next two Sects. 2 and 3, of this chapter discuss these in turn.

These theories were challenged by work originating in the Soviet Union. The Electrostatic Theory, considered in Sect. 4, laying emphasis on the transfer of charge across an interface, was put forward by Deryagin in the 1940s. A different challenge came from a different Soviet school which insisted on the fundamental importance of diffusion across an interface. The Diffusion Theory is the subject of Sect. 5.

The weak-boundary-layer theory is essentially a theory of fracture, rather than of fundamental adhesion. However it is frequently discussed along with these other theories, so consideration is given to it here in Sect. 6.

A great deal has been discovered about the mechanisms of adhesion since the middle years of the last century when the “classic” theories of adhesion were first proposed. The concluding section of the chapter will reassess them in the light of present understanding and question whether emphasis on one theory at the expense of another is still a useful way of rationalizing the results of experimental research in adhesion.

2 Adsorption Theory

2.1 Contact and Bond Formation

It is clear that the adhesive and substrate must come into contact for the possibility of the formation of an adhesive bond to exist. By far, the most common situation is one where a liquid adhesive comes into contact with a solid substrate. (That obviously means close contact on a molecular scale.) Factors that affect the extent of wetting and spreading of a liquid drop on a solid surface are, therefore, of primary importance in any consideration of theories of adhesion. It is appropriate, then, that two other chapters in this handbook are devoted to these considerations.

As these other chapters show, there is a well-developed thermodynamic theory of wetting and spreading This relates surface energies and surface tensions to contact angles and extent of wetting. Where the relevant surface energies and contact angles are known, or can be deduced, the extent of contact between a specific adhesive and substrate at equilibrium can be predicted. The essential idea of the adsorption theory of adhesion is that whenever there is contact between two materials at a molecular level, there will be adhesion.

When two materials come into contact, there will be forces of attraction between them. What those forces will be will depend on the chemical nature of the surfaces of the materials concerned. If this is known, it may be possible to postulate, or even to prove experimentally, the formation of a specific type of bond. Thus, metallic bonds may be involved in contact between a metallic solder and substrate metal (Some authors discuss secondary bonding in adhesion under the heading “Adsorption Theory,” and treat primary bonding under a different heading, e.g., “Chemical Adhesion.”).

Strong evidence for the presence of covalent bonds has been found, e.g., from some studies of the action of organosilane adhesion promoters used in bonding epoxies and other adhesives to metal and glass surfaces. It has long been suggested that the effectiveness of silanes was, in part, associated with covalent bond formation between the silane and a metal or glass surface, as indicated schematically in Fig. 1. Secondary ion mass spectroscopy (SIMS), which enables molecular fragments from an interface to be examined, has produced evidence of the presence of such silicon-oxygen-metal covalent bonds.

Fig. 1

Typical structure (a) and postulated mode of action (b) for a silane adhesion promoter

Using high-resolution X-ray photoelectron spectroscopy (XPS), small changes can sometimes be detected in the molecular bonding of a chemical group at the interface. Leadley and Watts (1997) used the technique to examine the interface between polymethylmethacrylate (PMMA) and oxidized surfaces of metals or silicon. They found evidence for hydrogen bonding, ionic bonding, and ion-dipole interactions, depending on the strength of the acid or basic nature of the mineral surface (Fig. 2). All three are examples of electron donor–acceptor (i.e., Lewis acid–base) interactions.

Fig. 2

Interaction between PMMA and surfaces of differing acidic and basic nature (After Leadley and Watts (1997)). ^aIndicating hydrolysis of the ester and adsorption through the carboxylate anion

A broadly similar conclusion was reached by a different route by Schneider et al. (2002). Maleic anhydride is used as a curing agent for some types of epoxy resin. The authors studied its interaction with a model system consisting of a thin aluminum layer deposited on a silicon wafer. The aluminum was allowed to oxidize and was then equilibrated with a laboratory atmosphere, before a monolayer of maleic anhydride was deposited from solution in acetone. Reflection–absorption intra-red spectroscopy indicated that the anhydride was hydrolyzed to the acid and adsorbed onto the oxidized aluminum surface . As a result of comparing the observed absorption frequencies with those calculated by quantum mechanical modeling for various plausible structures, the authors argued for the presence of three different adsorption structures (Fig. 3) in the ratio 6:1:1 for Fig. 3a–c. The dominant structure involved a carboxylate ion adsorbed on two neighboring aluminum ions. Figure 3b shows similar carboxylate ion adsorption with additional hydrogen bond adsorption involving the second carboxylic acid group of the maleic acid molecule. The third structure, Fig. 3c, involves interaction between the carbonyl oxygen and aluminum in the substrate surface. All three structures again involve electron donor–acceptor (i.e., Lewis acid–base) interactions.

Fig. 3

Adsorption of maleic acid on model-oxidized aluminum surface (After Schneider et al. (2002))

Weak, secondary forces, resulting from molecular dipoles, also act between materials. They are often classified according to the nature of the interacting dipoles. Keesom orientation forces act between permanent dipoles, London dispersion forces between transient dipoles, and Debye induction forces between a permanent and an induced dipole, see Tables 1 and 2. These are collectively known as van der Waals forces (but note alternative usage of this term, Table 2) and occur widely between materials. They are much less dependent upon specific chemical structure than primary bonds. Indeed, dispersion forces are universal. They only require the presence of a nucleus and of extranuclear electrons, so they act between all atomic and molecular species.

Table 1 Classification of secondary forces

Table 2 Alternative classification of secondary forces (N.B. some authors, especially in earlier literature, have used t upon specifi to include hydrogen bonding and other electron donorersion forces are universal. They only require

Thus, whenever there is contact between two materials at a molecular level, there will be adhesion. Physical adsorption or chemical adsorption (chemisorption) will occur. Specific types of bonding may be present, but there will always, at least, be London dispersion forces. That is the essential idea of the adsorption theory of adhesion.

2.2 Strength of the Adhesive Bond

Elementary chemistry books give bond dissociation energies for bonds of different types. Primary bonds are typically of the order of hundreds of kilojoules per mole, van der Waals bonds tens of kilojoules per mole. It is natural then that many have supposed that an adhesive bond involving primary bonds at the interface will be stronger than one relying simply on van der Waals interactions. However, Eq. 3 above implies that the situation is not so simple. The “strength of an adhesive bond ” (practical adhesion) depends not just on the interfacial forces (reflected in G₀) but also on other energy terms (ψ), and these latter are usually much greater in magnitude.

It is possible to calculate the energy of interaction between model molecules, representing adhesives, and model surfaces. When the results of such calculations are compared with corresponding practically measured adhesion, the predicted strength is found to be much higher than the measured strength. Even when dispersion forces are the only interactions considered, the calculated value is generally an order of magnitude higher than the measured strength. This has led to the conclusion that dispersion forces alone are more than sufficient to account for practical strengths of adhesive bonds. The question to be answered when considering the strength of adhesive bonds is not “why are they so strong?” but “why are they not stronger?” Of course, an analogous question occurs when considering the strength of materials in general, and much of the science of materials is devoted to answering it!

2.3 Environmental Stability

The discussion so far points to the critical importance of wetting in the formation of an adhesive bond. Once wetting occurs, there are adhesive–substrate interactions – adsorption of some sort has occurred, and dispersion forces alone will be sufficient to give a strong bond.

In a practical context, van der Waals adsorption may not form the basis for a satisfactory adhesive bond. The bond may not be stable in the service environment. This can be seen from a discussion of the work of adhesion considered above.

If the work of adhesion (as defined in Eq. 1) is positive, the adhesive will make contact with the adhesive and adsorption will take place. However, in the presence of a medium m, Eq. 1 has to be modified, and the work of adhesion now becomes

$$ {W}_{\mathrm{A}/\mathrm{m}}={\gamma}_{1\mathrm{m}}+{\gamma}_{2\mathrm{m}}-{\gamma}_{12} $$

(5)

where γ_1m is the surface energy of material 1 in the presence of the medium m. If = γ_1m and/or γ_2m are sufficiently low, the work of adhesion (Eq. 5) may now become negative, and the bond fails.

A widely encountered “medium” is water, either liquid or vapor, and this is strongly adsorbed onto many high-energy surfaces, lowering their surface energy. There are many examples of adhesive bonds that fail in a humid environment because the adhesive is displaced by this mechanism from the substrate.

Thus dispersion force adsorption may be sufficient, in principle, to provide good fundamental adhesion. In practice, it is often necessary to produce stronger bonds that are less susceptible to attack by medium m, e.g., less susceptible to hydrolysis. Silane adhesion promoters, discussed above, increase the hydrolytic stability of interfaces between adhesives and glass or metals through covalent bond formation.

2.4 Kinetic Effects

At the start of Sect. 2, it was pointed out that thermodynamic theories of wetting (cf. Chap. 6, “Thermodynamics of Adhesion” ) enable a prediction to be made of the extent of contact between a liquid adhesive and a given substrate, provided information relating to interfacial energies and contact angles was available. Obviously a thermodynamic theory predicts the equilibrium state, and in practice, it is important to consider whether equilibrium will be attained.

Typically, adhesives are liquids that solidify following application to the substrate. There is no reason to suppose that equilibrium wetting will always be achieved before they set. Whether equilibrium will be attained will depend on the relation between such factors as the forces causing the adhesive to spread and the rate of increase in viscosity with time. Moreover, the surface energy of the solidified adhesive will differ from that of the liquid, changing the equilibrium conditions. Such considerations are relevant to the application of the adsorption theory of adhesion.

2.5 Rough Surfaces

Rough surfaces are central to the concept of the mechanical theory of adhesion, discussed in Sect. 3. However, practical surfaces are always rough to some degree, and the discussion of the adsorption theory so far has tacitly assumed that the surface to be bonded was smooth.

If this roughness is not very great, its effect on wetting will be small, but some of the surfaces used in adhesion technology are extremely rough on a macro or microscale. Significant roughness can seriously reduce the extent of wetting achieved at equilibrium. If wetting is reduced, adsorption, and as a consequence fundamental adhesion, will be reduced also. The extent of this effect depends on the roughness features. It is possible, with plausible assumptions about surface tension and contact angle, to calculate equilibrium contact with model rough surfaces. Figure 4 shows some results after the classic work of de Bruyne (1956). Obviously a reentrant (“ink bottle”) pore is particularly difficult to wet.

Fig. 4

Equilibrium penetration of a liquid into cylindrical and g will be small, but some de Bruyne (1956)

The calculations on which Fig. 4 is based assume that equilibrium will be established. Considerations of the rate of setting of the adhesive and of its effect on viscosity and contact angle are relevant here. Depending on these factors, contact between an adhesive and a particular rough surface may be further inhibited by kinetic effects (Packham 2002).

3 Mechanical Theory

3.1 Macro and Microroughness

Many of the features of the adsorption theory of adhesion, just discussed, can be traced back to McBain and Hopkins’ classical work in the 1920s, where they are referred to it as “specific adhesion” (McBain and Hopkins 1925; Packham 1998, 2002, 2003). They also described “mechanical adhesion” to porous substrates, such as wood, unglazed porcelain, pumice, and charcoal. They regarded it as obvious “that a good joint must result whenever a strong continuous film of partly embedded adhesive is formed in situ.” This is, in essence, the mechanical theory of adhesion.

Clearly, this mechanical adhesion relies on contact between adhesive and substrate, and therefore adsorption forces, described in Sect. 2, will act between the two materials.

Despite the “obvious” nature of the mechanical theory of adhesion, by the 1950s, the validity of the mechanism was largely denied by scientists working on adhesion. This denial was based on the results of studies in which adhesion to similar surfaces with different degrees of roughness was reported. These generally showed an inverse relationship between roughness and practical adhesion.

These results, no doubt, bore witness to the difficulty of obtaining good wetting of a rough surface by a viscous adhesive, cf. Fig. 4. Thus, many joints to rough surfaces have voids at the interface and asperities will act as points of stress concentration, which can lower the practical adhesion with a brittle adhesive. However, there are now many examples in the literature where good wetting is obtained with rough surfaces, and, indeed, stress concentrations can even enhance practical adhesion with a ductile adhesive, but initiating local plastic deformation, which increases the energy dissipated during failure – ψ in Eq. 3.

Many successful prebonding treatments produce rough, microfibrous, or microporous surfaces. Some of these are shown in Fig. 5. The integrity of a sizable proportion of the world’s civil aviation fleet relies on adhesive bonding to anodized aluminum (Fig. 5a). A black, microfibrous oxide coating on copper is often used as a pretreament for bonding in electronic applications (Fig. 5c). PTFE is notoriously difficult to bond. Figure 5d shows the surface resulting from a successful bonding pretreatment involving irradiation by argon ions. Figure 5e shows an example, on a somewhat coarser scale, where the poor adhesion of copper to silica has been overcome by anchoring the copper to the silica surface using titanium tungstide “keys.”

Fig. 5

Some rough surfaces resulting from pretreatment prior to adhesive bonding: (a) porous anodic oxide on aluminum (schematic); (b) dendrites of zinc electrodeposited onto a zinc surface; (c) black CuO layer produced on copper; (d) PTFE irradiated by argon ions (After Koh et al. 1997); (e) adhesion of copper to silica using a mechanical key (van der Putten 1993). (i) TiW islands deposited; (ii) Pd activator adsorbed and HF etching; (iii) electroless Cu deposited; (iv) Cu electrodeposited

Control experiments have shown scientifically that very rough surfaces, such as those illustrated in Fig. 5, give high adhesion under circumstances where adhesion to a corresponding smooth surface is low. So it could reasonably be said that the mechanical theory of adhesion applies in these cases. Of course, this does not necessarily mean that the high adhesion is the only technological reason for using the pretreatment. For example, the anodization of aluminum enhances durability of an adhesive bond in humid environments: in the aviation context, this is more important than the actual level of practical adhesion achieved .

3.2 Mechanism of Adhesion to Rough Surfaces

On the phenomenological level, it is clear that there are many rough surfaces known to adhesion science and technology where the surface roughness plays an essential role in adhesion: the mechanical theory of adhesion applies. Rather than simply ascribing adhesion to “mechanical effects,” it is useful to explore why roughness can lead to good adhesion.

Consider again Eq. 3. The surface energy term G₀ is, from the standard definition of surface energy, the excess energy in the surface of the material, over that in the bulk material. In a simple way, this excess energy can be thought of as the energy necessary to break those bonds needed to produce the surface. Compare the bulk atom (B) in Fig. 6, with an atom S on a plane surface. In this schematic two-dimensional diagram, where the material is represented as a close-packed array of spherical atoms, B is bonded to six nearest neighbors, but S is only bonded to four. By extension of this argument, it can be seen that an atom (A) on an asperity will have a still higher surface energy. Thus, a rough surface, especially a very rough surface such as those illustrated in Fig. 5b–d, will have a higher surface energy than a corresponding smooth surface.

Fig. 6

Local environment of an atom in the bulk of a material (B), on a plane surface (S), and on an asperity on a rough surface (A) (Schematic representation)

Returning to Eq. 3, it must be remembered that the fracture energy G is fracture energy per unit area. Obviously, G₀ and ψ are also energies per unit area. The area relevant here is the formal (ideal) area, i.e., the macroscopic area of the interface, assuming that there was no roughness. For a rough surface, the “true” area will be greater and the surface energy term (G₀) will consequently be higher. For moderate increases in surface roughness, a proportional increase in adhesion (practical adhesion) has been demonstrated (Gent and Lai 1995).

For very rough microporous and microfibrous surfaces, the effective increase in area becomes enormous: G₀ can be raised to a very high value indeed. Many engineering surfaces are fractal in nature: for such surfaces, the “area” is, in principle, indefinitely large. The practical adhesion to such surfaces does not become indefinitely large, because a joint with a strong interfacial region will fail cohesively in some other region where G₀ is locally smaller.

The results presented in Table 3 show this effect in practice. Much higher fracture energies are found for adhesive bonds made to microfibrous surfaces than to corresponding smooth surfaces. For the smooth surfaces, stresses are concentrated at the interface, and failure occurs at or close to the interface with little plastic energy dissipation (Fig. 7a); for the microfibrous surfaces, the stresses are concentrated at the fiber or dendrite tips causing yielding, which moves into the polymer, giving cohesive failure and higher fracture energy associated with the plastic deformation involved (Fig. 7b). It is interesting to note that, even with the brittle unmodified epoxy resin, cohesive failure occurs showing signs of plastic deformation associated with the dendrite tips (Fig. 8).

Table 3 Adhesion of low density polyethylene (LDPE) to copper and of epoxy resin to electroformed zinc, assessed, respectively, by peel and single edge notched (SEN) tests (Evans and Packham 1979; Hine et al. 1984)

Fig. 7

Adhesion of polyethylene to copper. Substrate surface after peeling from (a) polished copper and (b) copper with a microfibrous oxide surface

Fig. 8

Zinc with a dendritic surface bonded with unmodified epoxy resin: fracture surface showing plastic deformation of the epoxy just above the dendrite tips (Hine et al. 1984)

Thus, the basic ideas, related by McBain and Hopkins in the 1920s, underlying both the adsorption and mechanical theories of adhesion still provide useful models for rationalizing observations in adhesion science. Two further adhesion theories, the electrostatic and diffusion theories, emerged from the Soviet Union in the middle of the twentieth century. We now turn to consider them, and how they are regarded today.

4 Electrostatic Theory

4.1 Early Formulation

The electrostatic theory was put forward in the 1940s by Deryagin (alternative transliteration Derjaguin) and colleagues in the Soviet Union (Deryagin and Krotova 1948). The interface is seen as analogous to the plates of an electrical condenser across which charge transfer occurs. A physical model was introduced representing the electric double layer as a three-dimensional region at the polymer–solid contact (Deryagin et al. 1973).

The basis of the theory is that free charges exist to some extent in any condensed material, even in the best dielectrics, and there will always be an electrochemical potential difference across the interface between two materials in contact, e.g., adhesive and substrate. Free electronic or ionic charge carriers will tend to move across the contact interface, and an electric double layer is established. This mechanism is considered quite distinct from any charge transfer, which may be associated with bonding at the interface, as discussed in Sect. 1.1.

Electrical phenomena (e.g., sparking) can often be demonstrated to accompany the destruction of an adhesive bond. The work of separation of the plates of a condenser depends upon rate of separation and ambient gas pressure. Measured peel energy certainly depends on rate of separation, and some published results indicate a dependence upon gas pressure. Deryagin argued that this supported the electrostatic theory of adhesion. He published results showing good correlation between measured peel energy and condenser discharge energy, but the details of his argument have been the subject of adverse criticism, see, e.g., Wake (1982) and Kinloch (1987).

More recently, Possart has used potential contrast scanning electron microscopy to study electric double layer formation associated with the interface between a thin layer of solvent-cast low-density polyethylene and aluminum (Possart 1988). While arguing that the electrical discharge energy of the double layer makes a contribution to the fracture energy, this study accepts that many other energy mechanisms also contribute. The work spent in mechanical testing surmounts the electrostatic interaction energy in the double layer by several orders of magnitude. The work of peeling was measured to be 1 J/m². The specific electrostatic work of separation was calculated as 247 J/m².

There was a period in the mid-years of the last century when its supporters presented the electrostatic theory as a comprehensive theory of adhesion, replacing the adsorption theory. Many critics of the theory pointed out examples where a change of filler or of polymer might lead to the absence of electrical phenomena, despite there being similar levels of measured adhesion: most cases of conventional adhesion, it was argued, could be explained without recourse to the electrostatic theory. By the 1970s, Deryagin himself was prepared to accept that “an adhesive bond is always caused by either the forces of chemical bonding or by so-called van der Waals forces.” (Deryagin et al. 1978). The present writer’s perception is that the widely held view is that electrostatic contributions in conventional adhesion are likely to be small; this view, however, is not universally accepted.

4.2 Particle Adhesion

Although the detailed mechanism is distinct from that just discussed, it is relevant to note that electrostatic forces are still considered to be of relevance in adhesion of small particles. An advantage of this sort of adhesion is that it may be possible to manipulate the charged particles by external electric fields. Electrostatic precipitation is a well-established industrial technique. It is used to remove dust particles from a gas flow, e.g., from flue gases in a power station. Electrically charged dust particles are attracted to an electrode surface and are thus removed from the gas stream. In a similar way, the application of a strong field across the open base of a silo can be used to prevent the egress of charged dust particles.

The modern photocopier relies for its function on both electrostatic and van der Waals forces. Charged toner particles initially adhere to charged regions on a moving photoconductor belt and are subsequently transferred by electrostatic forces to a paper sheet on which they are fused (Kendall 2001).

5 Diffusion Theory

5.1 Origins: Voyutskii and Colleagues

The second adhesion theory to emerge from the Soviet Union in the mid-years of the twentieth century was the diffusion theory. The basic principles were set out by S.S. Voyutskii and his colleagues. Their compatriot, R.M. Vasenin, contributed to its quantitative development using Fickian diffusion theory (Voyutskii 1963; Wake 1982).

Much of Voyutskii’s original work was done on the self-adhesion (called autohesion) of unvulcanized rubbers. It was subsequently extended to polymer adhesion, more generally. The theory postulates that the molecules of the two parts of the specimen interdiffuse, so that the interface becomes diffuse and eventually disappears. For polymers in contact, Voyutskii studied the effects on adhesion of such variables as time, temperature, contact pressure, molecular weight, polarity, and crosslinking. He argued that the results proved that the adhesion was associated with the interdiffusion of polymer chains.

Voyutskii’s 1963 book, Autohesion and Adhesion of High Polymers, is the locus classicus for the exposition of his ideas in English. Here he takes a robust, comprehensive view of the scope of the diffusion theory arguing that it is superior both to adsorption theory and electrostatic theory. He even argues for its application to the adhesion of polymers to metals.

As already indicated, the mid-decades of the twentieth century were the time when many authorities in the field of adhesion took an exclusive approach to theories of adhesion: if one theory was correct, another must be incorrect. In contrast, it is now much more widely recognized that different theories may have different areas of applicability, or even be better regarded as emphasizing a particular feature of a broader, overarching understanding.

Consistent with the spirit of the 1950s and 1960s, the diffusion theory generally got an unsympathetic reaction among supporters of the adsorption theory, i.e., mainly workers in the West. But attitudes changed, and by 1970, the position could probably be summarized by saying that diffusion was generally accepted as a mechanism for adhesion between samples of the same polymer (autohesion) or between very similar polymers (Wake 1982), but it was not more broadly accepted, even for polymer–polymer adhesion.

The reluctance to accept the applicability of diffusion theory to adhesion between chemically different polymers was because mutual solubility (emphasized by Voyutskii) was regarded as an essential feature of the mechanism, and most polymer pairs were known to be incompatible.

5.2 Polymer–Polymer Compatibility

It is often important to know whether two phases are mutually soluble, i.e., will mix on the molecular level to form a true solution. The question of mutual solubility – compatibility – can be approached in terms of thermodynamic criteria. The two phases will be compatible if the Gibbs free energy for mixing is negative. The Gibbs free energy of mixing ΔG_m is related to the enthalpy (heat) of mixing ΔH_m and entropy of mixing ΔS_m by the usual second Law equation:

$$ \Delta {G}_{\mathrm{m}}=\Delta {H}_{\mathrm{m}}{-} T\Delta {S}_{\mathrm{m}} $$

(6)

where T is the absolute temperature. As mixing always increases disorder, ΔS_m is positive, it follows that the – TΔS_m term is always negative, and therefore favors mixing. However, where polymers are involved, the long chain molecules mean that the entropy gain is much smaller than when compounds with small molecules are mixed. The – TΔS_m term, although negative, tends to be small in magnitude.

One approach to the discussion of compatibility in polymer systems is the Flory-Huggins theory (Berg 2002). This considers the number of ways in which chain segments of the polymers may be distributed among identical unit cells in a hypothetical lattice. The theory gives an expression for the free energy of mixing of polymers 1 and 2 (volume fractions ϕ₁ and ϕ₂, degrees of polymerization x₁ and x₂) in terms of the Flory-Huggins interaction parameter, χ. It may be written as:

$$ \Delta {G}_{\mathrm{mix}}= kT\left[{\chi \phi}_1{\phi}_2+\left({\phi}_1/{x}_1\right)\ln {\phi}_1+\left({\phi}_2/{x}_2\right)\ln {\phi}_2\right] $$

(7)

$$ {\displaystyle \begin{array}{c}\Delta {G}_{\mathrm{mix}}/ kT={\chi \phi}_1{\phi}_2+\left({\phi}_1/{x}_1\right)\ln {\phi}_1+\left({\phi}_2/{x}_2\right)\ln {\phi}_2\\ {}\mathrm{enthalpy}\,\, \mathrm{configurational}\ \mathrm{entropy}\end{array}} $$

(8)

where k is Boltzmann’s constant and T absolute temperature. In this particular form of the equation, the free energy change is expressed per total number of polymer chain segments. The interaction parameter, χ, is a dimensionless temperature-dependent parameter.

The last two terms in Eqs. 7 and 8, involving ln ϕ, represent the configurational entropy of mixing. This is negative and so favors the formation of a solution, but, as explained, it is small in magnitude because of the limited potential gain in entropy in mixing long chain molecules. The first term, involving χ, was originally conceived as expressing the enthalpy of mixing and is usually positive, meaning that for most polymer–polymer combinations ΔG_mix overall is positive, and so the mixture is heterogeneous. Even polymers as similar as polyethylene and polypropylene are incompatible: the value of χ at 140 °C has been calculated to be 0.011.

Such thermodynamic treatments point to the incompatibility of most polymer/polymer combinations, and practical studies with polymer blends lead to the same conclusion. Mutual solubility, regarded as an essential feature of the diffusion theory, would rarely be achieved, restricting the applicability of the theory to autohesion, and perhaps to adhesion between polymers of closely similar chemical structure.

5.2.1 Developments in Molecular Dynamics

Following the work on molecular dynamics by de Gennes (1998) and by Doi and Edwards (1986) leading to the development of reptation theory, a much more detailed description of the motion of polymer chains can now be given (Wool 1995, 2002, 2005). Consider two samples of an amorphous polymer brought into contact above the glass transition temperatures. The conformations of the chains at the interface will tend to relax. Five different mechanisms of relaxation can be identified, corresponding to five different time scales. In order of increasing relaxation time, they are: (1) short-range Fickian diffusion of individual chain segments, (2) Rouse relaxation between chain entanglements, (3) Rouse relaxation of the whole chain, (4) reptation diffusion, and (5) Fickian long-range diffusion.

It is the reptation region (4) of diffusion of chain segments to a depth of the order of the radius of gyration that is considered to be the most important in discussing the development of strength of interfaces. This is illustrated for the autohesion of polystyrene at 118 °C by the data of Table 4 (Wool 2005). It can be seen that reptation leads to considerable interpenetration of the chains and, as discussed below, to significant strength.

Table 4 Chain relaxation and diffusion mechanisms: relaxation time (τ) and molecular weight (M) relationships. M_c is molecular weight between chain entanglements, τ_e is the Rouse relaxation time between chain entanglements, τ_RO is the Rouse relaxation time of the whole chain, T_r is the reptation relaxation time

The reptation model envisages the polymer chain to be enclosed within an initial tube out of which it gradually escapes by wriggling in a snake-like manner (“reptating”: reptare to creep). The reptation relaxation time Tr corresponds to the time when about 70% of the chain has escaped from the initial tube. During this time, the interfacial thickness increases with time t, in proportion to t¼, in contrast with the t½ relationship for Fickian diffusion. The relaxation time Tr is proportional to the cube of molecular weight.

5.3 Interfacial Strength and Interdiffusion

The fracture strength of a polymer depends on molecular weight, the chain length, and in a similar way, the fracture of a polymer–polymer adhesive bond depends on the length of the chain, which has diffused across the interface.

Figure 9 shows the molecular weight dependence of the fracture energy for polystyrene. It can serve as a focus for consideration of the mechanisms involved in polymer–polymer adhesion. Two characteristic molecular weights are involved in this discussion: Mc and M^*. Mc is the average molecular weight between chain entanglements, the critical entanglement molecular weight. It represents the onset of the well-known zero shear viscosity law

$$ \eta \sim {M}^{3.4} $$

(9)

and the molecular weight at which the dynamics change from Rouse to reptation. In contrast, M^* is the value above which the molecules are too long for chain disentanglement (or pullout) to occur. They are related approximately by:

$$ {M}^{\ast}\approx 8{M}_{\mathrm{c}} $$

(10)

Fig. 9

Fracture energy versus molecular weight for polystyrene in the virgin state (After Wool 2005). M_c is the average molecular weight between chain entanglements; M* is the average molecular weight above which the molecules are too long for chain disentanglement (or pull-out) to occur

Low molecular weight When M < M_c (region A, Fig. 9) only short lengths of polymer chain are involved in the fracture process, which occurs by chain pullout. The fracture energy is low, up to about 1 J/m².

Fracture behavior in this region can be treated using the “nail solution” where the weak interface is modeled as if the two sides were nailed together with Σ nails per unit area, each of length L. The analysis shows that the fracture energy associated with chain pullout, G, increases with L2 and with Σ. To this “friction” term must be added a surface energy term, so that

$$ {G}_{1\mathrm{c}}\sim 2 S\gamma +{kL}^2\varSigma $$

(11)

where S depends on surface roughness (S = 1 for a perfectly flat fracture surface) and k is a constant related to the “friction” involved in chain pullout. The term “friction,” of course, refers to inter- and intramolecular attractions, such as van der Waals forces.

Intermediate molecular weight When M_c < M < M^* (region B, Fig. 9), the chains are long enough for entanglement to occur and the fracture energy rises progressively. Fracture in this region occurs by disentanglement and chain pullout: bond rupture is not considered to be significant.

Fracture in this region can be treated by the vector percolation theory, which models the polymer as a three-dimensional network, the links of which are progressively broken (here by chain disentanglement) until a critical value, the percolation threshold, is reached, and the whole net fractures (Wool 2005).

High-molecular weight Here, M > M^* (region C, Fig. 9) and the dominant facture mechanism becomes bond rupture. Vector percolation theory predicts extensive bond rupture throughout a significant volume of the polymer before failure occurs. With glassy polymers, this is often associated with crazing. The fracture energy is high tending to a limit, according to the Flory equation for molecular weight dependence:

$$ {G}_{1\mathrm{c}}/{G_{1\mathrm{c}}}^{\ast }=\left[1-{M}_{\mathrm{c}}/M\right] $$

(12)

where G_1c^* represents the fracture energy at high molecular weight.

To summarize, for autohesion (polymer–polymer welding), there will be rapid (Rouse) interdiffusion, which occurs to distances comparable to the radius of gyration of the entanglement molecular weight, M_c, say 3 nm (Table 4). The interface is very weak and could be described in terms of the nail solution, with chain pullout being the dominant fracture mechanism.

As welding proceeds, chains diffuse by reptation diffusion, and the failure mechanism then involves chain disentanglement and, with more extensive diffusion at longer times, bond rupture dominates. When bond rupture begins to dominate, the weld will appear fully healed, even in the absence of full interpenetration. There is a rate effect here. At high test rates, chains may not have time to disentangle and may rupture instead. This will give a high fracture toughness, G_1c, but at much lower deformation rates, weld weakness may be apparent. Wool (2002) cites, as an example, welding of a particular polystyrene at 125 °C, where essentially full (short time) weld strength would be obtained in 156 min, but the fatigue strength would be about one-fifth of its virgin value. For complete welding, a reptation time of 435 min, the relaxation time for reptation, would be needed. The importance of this observation for the molding of thermoplastics is obvious.

5.4 Interfaces Between Incompatible Polymers

Despite macroscopic thermodynamic incompatibility, Sect. 5.2, an atomically sharp interface between two such polymers will not be stable. Although there is an enthalpy debt to be paid if a chain of polymer 1 starts to diffuse into polymer 2, there is an entropy gain. Helfand and Tagami 1972, Helfand 1992) introduced a model, which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterized by the parameter χ. They predicted that at equilibrium, the “thickness,” d_∞, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows

$$ {d}_{\infty }=2b/{\left(6\chi \right)}^{\frac{1}{2}} $$

(13)

Thus, despite the argument in Sect. 5.2, some interdiffusion can be expected between formally incompatible polymers. The extent will depend on the extent of incompatibility, e.g., on the value of the interaction parameter: the smaller the χ, the greater the possibility of interdiffusion.

Different mechanisms were discussed above (Sect. 5.3) in the context of autohesion. Depending on the extent of interdiffusion, fracture may occur at low energy by chain pullout or by chain disentanglement with bond rupture accompanied by crazing giving the highest fracture energies corresponding to the greatest extent of interdiffusion. In principle, the same considerations should apply to adhesion between different polymers.

The toughness of an interface will be expected to be related to the depth of interpenetration of the chains. Wool (1995) has argued that the fracture energy, G, for chain pullout, is proportional to the square of the interface thickness, which, via Eq. 6, gives

$$ G\propto {d_{\infty}}^2\propto 1/\chi $$

(14)

cf. Eq. 13 above.

For higher fracture energies, a linear relationship with the number of chain entanglements, N_ent, has been found for a range of polymer pairs, Fig. 10.

Fig. 10

Fracture energy G_1c of bonds between a range of immiscible polymers as a function of number of entanglements (After Wool 2005)

5.5 Copolymer Compatibilizers

Much higher adhesion may be obtained between incompatible polymers through the use of copolymer compatibilizers . If an AB diblock copolymer is introduced at the interface between two incompatible polymers A and B, the interface may be toughened by diffusion of the copolymer ends into the respective homopolymer. Much ingenuity has been employed in developing this type of compatibilizer.

A range of fracture toughness values (G_c) may be obtained. The general principles are similar to those discussed in Sect. 5.3. For diblock copolymers, both surface density (Σ) and degree of polymerization (N) of the blocks are important. For example, if the degree of polymerization of the A block were shorter than the entanglement length, but that of the B block longer, interdiffusion could occur at the interface, but the bond would be weak with chain pullout of the A part of the copolymer from polymer A. Typical results are illustrated schematically in Fig. 11 (cf. Creton et al. 1994a): strength of the bond increases both with surface density of copolymer and with segment chain length (here segment A). However, as all the lengths of segment A are below the entanglement length, the fracture energy corresponds to chain pullout and is low.

Fig. 11

Adhesion between incompatible polymers A and B. Interface reinforced by diblock copolymer AB, with A-block length below entanglement length

With greater degrees of polymerization, chain entanglement can take place, Fig. 12. At low surface density (Σ), chain scission will occur close to the junction of the diblock, with each fragment remaining on the “correct” side of the interface. The fracture energy is low. As the copolymer surface density increases, fracture energy rises steeply with plastic deformation, e.g., crazing, occurring in the polymer followed by chain scission or pullout . If an increase in copolymer surface density continues, eventually the surface becomes saturated and a weak layer forms at the interface with fracture energy falling toward a limiting value (cf. Creton et al. 1994b).

Fig. 12

Adhesion between incompatible polymers A and B. Interface reinforced by long chain length diblock copolymer

Toughening of a polymer–polymer interface with random copolymers can sometimes be more effective than with diblocks, provided the polymers are not too incompatible. This is of industrial, as well as of scientific, interest as random copolymers are usually cheaper to produce.

Each molecule in diblock copolymers will form a single, strong chemical linkage across the interface. However if the incompatibility between the homopolymers is not too large, a molecule of a random copolymer will form coils wandering many times across interface, forming many “stiches.” At larger incompatibilities, the random copolymer will no longer describe coils, but the homopolymers will still be linked by “loops.” If the incompatibility is too large, the copolymer will simply form collapsed globules at the interface, a weak boundary layer giving no enhancement of adhesion, cf. Fig. 13.

Fig. 13

Schematic representation of a random copolymer at the interface between two incompatible homopolymers. Incompatibility increases in the order (a), (b), and (c)

As with block copolymers, the important parameters are the surface density and length of the copolymer chains. Toughening of the interface may occur as a result of pullout or scission of the connector chains, or of fibril or craze formation in the matrix. This last mechanism gives the highest fracture toughness, G, and tends to occur at high surface density of chains.

Needless to say, implicit in the general discussion of Sects. 5.4 and 5.5 is that the time and temperature of contact are such that the degree of interdiffusion discussed can occur. The lowering of temperature, and the shortening times will lead to kinetic inhibition.

5.6 Diffusion Theory: Conclusion

The ideas advanced by Voyutskii and his colleagues over half a century ago have now been developed far beyond what was possible at the time. It is now possible to relate with some clarity the circumstances where interdiffusion plays a significant part in adhesion, and plausible molecular models have been developed, which go a long way to describe it, relating joint strength to interfacial structure. These scientific developments have important technological implications for the development of new multicomponent polymer materials and for the recycling of mixed plastics waste.

6 Weak-Boundary-Layer Theory

6.1 Practical Adhesion

This article is concerned with theories of fundamental adhesion, i.e., with theories concerned with the reasons for two materials holding together in an adhesive bond, however weak. In contrast, a weak boundary is a cohesively weak layer in the interfacial region (some authors use the term “interphase”) of an adhesive joint, which may cause the joint itself to be weak, i.e., to fail at a low stress or with low fracture energy. So the question of weak boundary layers occurs when the level of practical adhesion is under consideration, and may form part of an answer to a question such as “why did this joint fail at such and such a stress?”

However, 50 years ago, when there was considerably less basic understanding, and more confusion, in the study of adhesion than there is now, “weak boundary layer theory” would often be discussed alongside theories such as the adsorption theory and the electrostatic theory. The tendency to group theories of adhesion in this way has persisted, and so it may now be useful to discuss the significance of weak boundary layers.

6.1.1 Need for Pretreatment

At one level, the existence of weak boundary layers and their deleterious effect on adhesion is obvious. Surface pretreatments, prior to adhesive bonding, are almost always a prerequisite for success. That is, because almost all surfaces will be contaminated to some degree from the environment to which they have been exposed. Generally speaking, extensive cleaning under conditions of ultrahigh vacuum is required to remove such contamination and to maintain a molecularly “clean” surface. Good adhesion is aided by high-substrate surface energy, partly to aid wetting (see Chap. 4, “Wetting of Solids,” 5, “Spreading of Liquids on Substrates,” and 6, “Thermodynamics of Adhesion”) and partly to increase fracture energy G, see Eqs. 1 and 3. The universal tendency for high-energy states to move toward lower-energy states is manifested here by adsorption onto a high-energy substrate surface of extraneous material. This can come from other solids or liquids with which the surface has been in contact, as well as from the atmosphere. Thus the surface of a metal, which, outside the realms of surface science might be described as “clean,” will be covered by complex layer including an oxide, probably partly hydrated, perhaps carbonated, adsorbed water, residual lubricant, and processing aids. Such a layer, in molecular terms, will be thick. It is unlikely to have good wetting properties and is likely to be cohesively weak. Unless removed by pretreatment, it is likely to form a weak boundary layer and to give poor practical adhesion. A successful pretreatment is very unlikely to produce a molecularly “clean” surface, but the surface produced will not suffer from the same cohesive weakness and lyophobicity of the original. Polymers are also likely to require pretreatment, because their surfaces usually carry complex layers, chemically different from the bulk material. The formation of these layers is now considered.

6.2 Polymer Surfaces

Few, if any, polymers in commercial practice are used without the incorporation of a range of additives. These may include antioxidants, processing aids, perhaps plasticizers and lubricants. Elastomers are likely to be based on even more extensive formulations including a complex vulcanization mixture.

In Sect. 5.2, the question of polymer–polymer compatibility was considered, and it was argued that the majority of binary polymer blends will be two phased because the component polymers are incompatible, the free energy of mixing, Δ G _m, will be positive. Essentially, the same argument applies when polymer additive solutions are considered. The physical chemistry is similar: the entropy term will be small compared with that for a low-molecular-weight solvent–solute combination, and the enthalpy term is likely to be positive (cf. Eqs. 6–8). Most polymer-additive systems are thermodynamically unstable: the additive will tend to migrate out of the polymer. Loss of plasticizer from PVC (polyvinyl chloride) is a widely experienced phenomenon. The mode of action of antistatic agents depends on their progressive migration to the polymer surface.

Most adhesives are polymeric and set during the bonding process by loss of solvent, by solidifying from the melt, or by some form of cross-linking or polymerization reaction. In all of these solidification processes, there is the potential for low-molecular-weight additives to migrate to the substrate–adhesive interface and to form a weak boundary layer. Moreover, almost all polymers have a distribution of molecular weights, and there will be a similar tendency for low-molecular-weight fractions of the polymer itself to be rejected to the interface during solidification, especially during cooling from the melt.

6.3 Formation of Weak Layers During Bonding

The need for pretreatment to remove weak surface layers is widely understood. More subtly, other weak layers can form during the bonding process by the migration of low-molecular-weight species to the interface: sometimes these can lead to poor joint performance.

Many examples in the literature show that these effects occur. Classic experiments include removing low-molecular-weight fractions from a polymer, and observing increased adhesion, and complementarily, adding low-molecular-weight fractions, and observing a reduction in adhesion (Bikerman 1961). In Sect. 5.5, examples were given of weak boundary layers formed by copolymer compatibilizers.

6.4 The Legacy of Bikerman

Much of the early work on weak boundary layers was done by Bikerman and his colleagues in the 1950s and 1960s. His frequent observation of cohesive failure close to the interface, combined with direct demonstration of a weak boundary layer mechanism in specific examples, led him to take up an extreme position (Bikerman 1961). This insisted on (1) the widespread occurrence of weak boundary layers, (2) the impossibility of adhesive (i.e., interfacial) failure, and (3) the practical strength of an adhesive bond depended on the rheology of the joint, not upon the forces at the interface.

Although Bikerman’s position would not be supported today, it stimulated developments in the understanding of theories of adhesion, which can, to some extent, be regarded as his legacy. The potential for the formation of weak boundary layers (1) is well established, and much of the technique of adhesive bond preparation is designed to avoid them.

Locus of failure Where weak boundary layers exert an effect on adhesion behavior, failure typically occurs within the weak layer, close to the adhesive–substrate interface. The boundary layer will often be very thin, in macroscopic terms, and there are large numbers of examples where workers have reported the adhesive (i.e., interfacial) failure of a joint, when in fact it could be shown that failure was cohesive within a boundary layer. Bikerman’s insistence (2) that adhesive failure could not occur had the beneficial effect of concentrating attention on the locus of failure. Careful examination of locus of failure is an important technique – still sometimes neglected – in the study of adhesive bonds. Modern methods of surface analysis are appropriate here. They have established that, although adhesive failure may be rare, it does occur sometimes.

In considering locus of failure, it must be emphasized that observation of cohesive failure close to the adhesive–substrate interface does not, itself, prove the presence of a weak boundary layer. The idea that an adhesive joint “fails at its weakest link” is naïve. The locus of failure of a joint depends in a complex way on the chemical and physical properties of the materials in the joint, and on the way the stress is applied to them. Cohesive failure close to an interface is entirely possible in the complete absence of weak interfacial layers (Good 1972). Dillard has demonstrated how failure can change between cohesive, interfacial, and oscillating for exactly the same joint, depending on how the stress is applied (Chen and Dillard 2002).

Practical bond strength Bikerman was right (3) in insisting on the importance of joint rheology in determining the practical strength of an adhesive bond. It was an important point to make at the time. However, he was wrong to say that interfacial forces were irrelevant. The connection between the two, expressed in a simple form in Eq. 3, is discussed in detail elsewhere in this handbook (Chap. 3, “Forces Involved in Adhesion” ).

7 Conclusions

A theory in science is a model that aims to order the experimental results in a field and, for a fruitful theory, to suggest new experiments and their outcome. We do not look to theories for immutable truths: we expect them in time to be modified and discarded (Popper 1959; Khun 1970).

In the light of our present understanding of adhesion, what can be said about the “classical” adhesion theories? On one level, it could be said that the adsorption, mechanical, and diffusion theories (and some would add electrostatic theory) maintain their importance undiminished. It is still acknowledged that adsorption plays a vital role, that there are examples where diffusion is crucial and so forth. However, the classic theories originated at a time when there were few, if any, experimental techniques available to study surfaces and interfaces at the nanometer level. We now benefit from several decades of results from scanning probe technologies and surface analysis and theoretical advances in contact mechanics and molecular chain dynamics. We have direct evidence for the presence of particular groups on a surface, for the effects of variations of topography and chemical nature over small distances on a surface. Consequently, in many cases, we have a much clearer understanding of what is happening in the interfacial region, and of how it affects adhesion.

One consequence of this understanding is that we can often make plausible suggestions about adhesion mechanisms without having to hide behind broad-brush statements about “mechanical effects” or “chemical activation.” We should also recognize now that the mechanisms characteristic of classical theories are not completely distinct. This is our contemporary answer, no doubt provisional, to Newton’s challenge (Sect. 1.1).

A good example of such an approach to theories of adhesion is provided by a recent extensive review of fracture and adhesion of soft materials by Creton and Ciccotti (2016). Nowhere in their review of adhesion mechanisms do Creton and Ciccotti find it necessary to refer to “classical” theories of adhesion, adsorption, mechanical, and so on. However, they discuss the use and range of validity of equations for fracture energy applicable to some of the soft materials which is their concern. These include equations which are much more specific versions of the general Eqs. 3 and 4 above.

It is recognized that the practical surfaces used in adhesion are always to a degree rough: the only question is “how rough?” As the roughness of a surface changes, so must the chemical environment of its surface atoms and molecules. Thus, changing the roughness changes the local chemistry, which will affect the adsorption properties of the surface. The scale of roughness of surfaces encountered in adhesive joints varies from the macroscopic through to the nano- and molecular scale, from the classic realm of the mechanical theory to that of the diffusion theory. The energy expended in peeling strands of rubbery polymer from a macroporous surface has been successfully analyzed in essentially the same way as the pullout of individual polymer chains by the “nail” model in diffusion theory (Sect. 5.3) (Gent and Lin 1990). In principle, the range of types of forces that may act between adsorbate and adsorbed molecule on a nominally flat surface are the same as those that may act between diffusing molecules.

Moreover, the way in which adhesion is enhanced is essentially the same whether we think in terms of adsorption, diffusion, or roughening. These provide mechanisms whereby the energy dissipation (ψ in Eq. 3) is enhanced. Whether the focus is on enhanced chemical interaction, surface roughening, or interdigitation of polymer chains, a common consequence is increased plastic or viscoelastic losses and crazing.

Each of the classical theories is best regarded as emphasizing a different aspect of a more comprehensive model, which, in principle, relates molecular dispositions in the region of the interface to macroscopic properties of an adhesive joint. It would be a mistake today to lay too much emphasis on the distinction between classical theories, although this has been valuable at various times during the last 80 years in stimulating the development of new concepts and in suggesting fruitful experiments.