International Journal of Adhesion & Adhesives 38 (2012) 95–116 Contents lists available at SciVerse ScienceDirect International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh Adhesion phenomena in bonded joints A. Baldan n Department of Metallurgical and Materials Engineering, Mersin University, 33343 Ciftlikkoy Campus, Mersin, Turkey a r t i c l e i n f o abstract Article history: Accepted 18 April 2012 Available online 8 May 2012 Adhesive bonding is a key joining technology in many industrial sectors including the automotive and aerospace industries, biomedical applications, and microelectronics. Adhesive bonding is gaining more and more interest due to the increasing demand for joining similar or dissimilar structural components, mostly within the framework of designing lightweight structures. When two materials are brought in contact, the proper or adequate adhesion between them is of great importance, so it is necessary to device ways to attain the requisite adhesion strength between similar or dissimilar materials including the different combinations of metallic materials, polymers, composite materials and ceramics. To make adhesion possible, it is necessary to generate intrinsic adhesion forces across the interface. The magnitude and the nature of those forces are very important. From a thermodynamic standpoint the true work of adhesion (or intrinsic property) of the interface create free surfaces from the bonded materials. Adhesion mechanisms have been known to be dependant on the surface characteristics of the materials in question. The intrinsic adhesion between the adhesive and substrates arises from the fact that all materials have forces of attraction acting between their atoms and molecules, and a direct measure of these interatomic and intermolecular forces is surface tension. Atomic/molecular understanding of adhesion should be extremely beneﬁcial in selecting or creating the appropriate materials to attain the desired adhesion strength. In the present paper, the following topics are reviewed in detail: (a) the surfaces or interfaces of similar and dissimilar materials, (b) adhesion or bonding mechanisms in the adhesive joints (c) thermodynamic theory of adhesion: surface tension or surface free energy concepts including the wetting, wetting criteria, wettability, and thermodynamic work of adhesion, (d) dispersion and polar components of surface free energies, and ﬁnally (e) effect of surface roughness on wettability or adhesion. & 2012 Elsevier Ltd. All rights reserved. Keywords: Adhesion Adhesive bonding Bonding mechanims Wetting Wettability Thermodynamic work of adhesion Surface free energy Contact angle Surface roughness 1. Background Adhesion is concerned whenever solids are brought into contact, for instance, in coatings, paints, varnishes, multilayered sandwiches, polymer blends, ﬁlled polymers, adhesive joints, and composite materials. To make adhesion possible, it is necessary to generate intrinsic adhesion forces across the interface. Because the ﬁnal performance or use properties of these multicomponent materials depend signiﬁcantly on the quality of the interface that is formed between the solids, it is understandable that a better knowledge of adhesion phenomena is required for practical applications. Although the study of adhesion mechanisms can be traced back to the 1930s, the ﬁeld of adhesion began to create real interest in scientiﬁc circles only about 60 years ago. Even though considerable research has been carried out since then, the fundamental knowledge about adhesion mechanisms is n Tel.: þ90 324 361 00 01x7500; fax: þ 90 324 361 0032. E-mail address: [email protected] 0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijadhadh.2012.04.007 still not well developed and no single global theory or model can explain all the phenomena or mechanisms. This is mainly due to the fact that adhesion is a very complex phenomenon since it involves multidisciplinary knowledge of polymer and surface chemistry, fracture mechanics, mechanics of materials, rheology and other subjects. Fourche  in his review, described some important adhesion models with the explanation of corresponding mechanisms in detail. These models can help us to better understand the phenomena that occur between two substrates. Therefore, adhesion became a scientiﬁc subject in its own right, but it is still a subject in which empiricism and technology are slightly ahead of science, although the gap between theory and practice has been narrowed considerably . It should be noted that the term ‘intrinsic adhesion’ is often used when referring to the direct molecular forces of attraction between the adhesive and the substrates, to distinguish this phenomenon from the ‘measured adhesion’; i.e., from the measured strength or toughness of an adhesive joint . As Kinloch pointed out , even when using a fracture mechanics approach, and interfacial failure of the joint does occur, the value of the adhesive fracture energy, Gc, will usually not be equivalent to the 96 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 energy associated with the rupture of the intrinsic adhesion forces, since the value of Gc will also encompass the energy dissipated in viscoelastic and plastic deformation processes which occur in the vicinity of the crack tip. Thus, the value of Gc is typically orders of magnitude greater than the energy associated solely with the intrinsic adhesion forces. From a practical standpoint, this emphasizes the need not only to establish good intrinsic adhesion across the adhesive/substrate interfaces but also to develop tough adhesives, where the plastic, or process, zone in the vicinity of the crack tip will be relatively large. The adhesion phenomanon is relevant to many scientiﬁc and technological areas and has become in recent years a very important ﬁeld of study. The main Application of adhesion is bonding by adhesives. The adhesion plays an important role in various complicated structures that require adhesive joining from high technology industries such as aeronautics, aerospace, electronics, and automotive to traditional industries such as construction, sports, health and packaging, as a result of time and cost savings, high corrosion and fatigue resistance, crack retardance and good damping characteristics (i.e., ). Adhesives have also been introduced in such areas as dentistry and surgery. The automotive and aerospace industries have been investigating adhesives and the associated adhesion mechanisms for more than 50 years . In recent years, the interest from the sector in adhesion has been directed towards polymers and epoxy resins due to their advantageous bulk and surface properties, low cost and good mechanical properties [5–12]. For example, adhesion between the polymer surface and the paint substrate layer is controlled by the chemical groups at or near the interface . A common example of an adhesive system found in the automotive industry is the attachment of a paint coating to a polymer bumper bar. Such bumper bars are frequently made with polypropylene (PP); a material exhibiting poor surface adhesive properties in its native state . Adhesion can be improved by a number of ways including : (a) adding an adhesion promoter such as a chlorinated polyoleﬁn (CPO) , (b) ﬂame surface pretreating the polypropylene compounds , (c) plasma surface pretreating the polypropylene to promote the creation of polar functional groups at the surface [15–20], and (d) by blending in ethylene–propylene rubber (EPR) which in turn forms a thermoplastic polyoleﬁn (TPO) [21–24]. Most industrially applied polymer resins and composites have low surface free energy, relative inertness and lack polar functional groups on their surface, resulting in inherently poor adhesion properties [2,5,25]. There has been tremendous R & D activity in the arena of polymer surface modiﬁcations to render them adhesionable. Therefore, atomic/molecular understanding of adhesion should be extremely beneﬁcial in selecting or creating the appropriate materials to attain the desired adhesion strength . As Awaja et al.  pointed out, a strong research momentum to understand polymer adhesion in the last decade has been motivated by the growing needs of the automotive and aerospace industries for beter adhesion of components and surface coatings. Also, an understanding of adhesion mechanisms is of growing importance in the biomedical ﬁeld. For example, in studies of the fracture of bonds between human hepatoma cell lines and polymers such as polystyrene, polymethylmethacrylate and polycarbonate [26–29], it has been shown that the dominant factor in cell adhesion to polymer substrates is the surface free energy of the polymer, irrespective of whether the surface has been covered by a protein layer [5,29,30]. There are more than 200 different methods for measuring adhesion, suggesting it to be material, geometry and even industry speciﬁc . This availability has exploded at least partly due to the arrival of dissimilar material interfaces (i.e., adhesive joints) and thin ﬁlms and the ease with which microfabrication techniques apply to silicon technology. The emphasis is on measuring thin ﬁlm adhesion from the standpoint of fracture mechanics, when the ﬁlm is mechanically or by other means removed from the substrate, and the amount of energy necessary for this process is calculated per unit area of the removed ﬁlm. According to Volinsky et al. , this tends to give values approaching the true work of adhesion at small thickness and greater values of the practical work of adhesion at larger thickness, all being in the 30–30,000 nm range. Therefore, the resulting large range of toughnesses depends on the scale of plasticity achieved as controlled by ﬁlm thickness, microstructure, chemistry and test temperature. Although viscoelastic polymers are widely used for adhesive applications, the fundamental nature of the adhesion of these materials remains poorly understood (i.e., ). There are many factors that determine how a polymer adheres to a particular surface. The most important physical characteristics when one considers the adhesive performance of a polymer are its viscoelasticity, molar mass distribution M, the glass transition temperature Tg, and the distribution of functional groups on the surface . Other external factors that are important in evaluating the adhesion between two surfaces include temperature, humidity, surface roughness, the surface free energy of the substrates, and the total interfacial contact time. 2. Interfaces (or surfaces) Interfaces usually constitute a weak link in the chain of load transfer in bonded joints. Also, the discontinuity of the material properties causes abrupt changes in stress distribution, as well as causing stress singularities at the edges of the interfaces . It is very desirable to optimize the substrate surface topography at the interfaces to maximize the load bearing capacity of bonded joints, and to improve their deformational characteristics. Therefore, the use properties of the adhesive joints depends signiﬁcantly on the quality of the interface that is formed between the substrates. A concept that has been gaining much support among adhesion scientists is the existence of an ‘‘interphase’’, loosely deﬁned as a region intermediate to two contacting solids that distinct in structure and properties from either of the two contacting phases. The interphases exist in many macrosystems such as adhesive joints, coating-substrate systems, and ﬁber- or particulate-reinforced composites; that they may control the overall mechanical behavior of these systems; and that failure to take them into account is likely to lead to ﬂawed models. Surfaces are also important to the study of microstructures, friction and wear, the joining of all materials by all means, the catalysis of chemical reactions, oxidation, corrosion, the mechanical behavior of small or thin bodies, the design of electronic devices, and a wide variety of other phenomena. The surfaces of phases always differ in behavior from the bulk of the phases themselves, because of the rapid structural changes which must occur at and near phase boundaries. If the forces on a molecule in the bulk are compared to the forces on a molecule at the surface, the forces on the bulk molecule cancel whereas the forces on the surface molecule are unbalanced. As a result of this unbalance force, equilibrium bonding arrangements are disrupted, leading to an excess energy (i.e., surface free energy, c), which is deﬁned as the energy necessary to form a unit area of new surface or the energy necessary to move a molecule from the bulk to the surface. The excess energy (or surface free energy) may be minimized by minimizing surface area. This tendency is called surface tension if the surfaces are liquid and a vapor, glv. Surface free energy may also be lowered by segregation of the various components to and from the surface; such behavior is called adsorption. The magnitude A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 of g may be estimated for metallic and covalent materials by considering the number and enegy of the bonds which must be broken to form the surface. Similarly, calculations of work done against the Coulomb force lead to approximate values of g for ionic materials. In both cases, g depends on crystallographic orientation. Direct measurement of g is possible by force equilibrium, if the phases are sufﬁciently mobile. At the interface between two phases, the crystal structure, or the state of aggregation, or the composition must change in a fairly abrupt manner. As mentioned above, the atoms in the vicinity of the surface are not in equilibrium states, since they are neither one phase nor the other. The excess energy due to the perturbed material at the interface is proportional to the surface area. Thus, a drop of liquid will tend to assume a spherical shape in order to minimize its surface area and, thereby, its surface free energy. In single-phase solids, similar surfaces exist. These are the grain boundaries, which exist beteen grains of different crystallographic orientations. Polymer surfaces and interfaces play an essential role in many commercial applications of polymers, such as coatings, adhesives, blends, packaging and resists. Understanding the molecular processes taking place at interfaces is, therefore, increasingly important for the wide ranging uses of polymers. For example, as Bucknall pointed out , the properties of composite materials are dominated by the structure of the interfaces between their constituents, since the interfaces between different phases are more susceptible to deformation, fracture and chemical reactions. In many cases the success of the use of a polymeric material in delivering the required properties depends on the possibility of modifying the interfacial properties. Therefore, the nature of the interface between immiscible polymers is important to investigate, both because these interfaces provide model systems to elucidate fundamental problems of the statistical mechanics of surfaces and interfaces, and also because an understanding of the microscopic structure of the polymer interface will help to address technological questions connected to the adhesion of polymers and the properties of multiphase polymer systems. Interfaces are ubiquitous in engineering materials and materials systems, and often play a determining role in mechanical performance. For example, the development of new classes of highperformance composite systems has resulted to a large degree from advances in interfacial modiﬁcation and associated property enhancements . The adhesion, or fracture resistance, of an interface is determined by many factors. At the ﬁnest length scale, interfacial bond strength sets the intrinsic resistance to fracture and provides the foundation upon which other dissipation processes may operate. At intermediate scales, near-crack process zones comprising of a variety of damage processes dissipate energy. At the coarsest scale, bulk loss processes may operate and provide a major component of resistance to interface separation. As pointed out by Rahul-Kumar et al. , all these processes are coupled and may be dependent on rate, temperature and ambient reactivity. Mechanical energy dissipation via mechanisms operating at larger length scales often results in a specimen size and geometry dependent fracture resistance that precludes the use of a welldeﬁned fracture resistance parameter to specify performance. The surface characteristics of polymers determine their interfacial properties and technological applications. There have been many attempts to modify the surfaces of polymers to improve wettability, dye printing, and adhesion to other materials [37,38]. For example, plasma technology, high-energy ion beam irradiation, corona discharge, chemical treatment and other techniques have been used to improve the surface morpholgy of the polymer surfaces to provide solutions for poor polymer adhesion. However, rough and/or damaged surfaces (through bond scission, carbonization, cross-linking, etc.) are produced by the above 97 methods. The coating of a surfactant [39,40] was found to be relatively successful in enhancing the wettability of polymers, but the lifetime of the surfactant is too short for practical use. Therefore, as Koh et al. pointed out , new surface modiﬁcation methods are required to obtain polymer surfaces free of surface damage and having good wettability with a long lifetime. Koh and co-workers [42–46] have successfully modiﬁed polymer surfaces such as PMMA, PC, and PVDF by a combination of low-energy ion beam and reactive gas environment; they named this surface modiﬁcation method ‘ion-assisted reaction (IAR)’. They also reported that the polymer surface irradiated by energetic ions induced a chemical reaction between the reactive gas and the free radicals in the polymeric chains, and that the new functional groups formed, such as carboxyl, carbonyl, hydroxyl, and ester radicals, improved wettability and adhesion to other materials. Polymer surfaces are often difﬁcult to wet and bond, due to the low surface energy, incompatibility, chemical inertness, or the presence of contaminants and weak boundary layers . As mentioned above, surface pretreatments are therefore used to change the chemical composition, increase in surface free energy, modify the crystalline morphology and surface topography, or remove the contaminants and weak boundary layers [25,48,49]. There are two main approaches reported to measure the surface free energy (i.e., ). First approach employs an equation of state (i.e., thermodynamic theory of adhesion (see Section 4 for more details)) such that surface free energy may be calculated using only one contact angle measurement [9,50–52]. The second approach is the components approach, whereby the surface tension or surface free energy is considered to be a combination of (a) dispersion forces (van der Waals forces), and (b) polar forces (hydrogen bonding) (see Section 5 for more details). 3. Adhesion mechanisms: adhesion theories Adhesion is the interatomic and intermolecular interaction at the interface of two surfaces . Adhesion mechanisms have been known to be dependant on the surface characteristics of the materials in question since the early beginnings of both the aerospace and automobile industries. Since then, and especially in the last 30 years, the understanding of adhesion mechanisms has increased signiﬁcantly as both industries have sought lighter and cheaper alternatives to metals and metal components . This drive has been the major inﬂuence in the need to understand polymer adhesion and to resolve the debate over how the interfaces are actually adhering [54–59]. Adhesion is a multi-disciplinary topic which includes surface chemistry, physics, rheology, polymer chemistry, mechanics of materials (i.e., stress analysis), polymer physics, fracture analysis and other subjects. Describing the mechanism of adhesion in simple terms is difﬁcult due to the complexity and evolving understanding of the subject . The ultimate goal is to identify a single mechanism that explains adhesion phenomena [53,60–65]. A range of adhesion mechanisms, based variously on diffusion, mechanical, molecular and chemical and thermodynamic adhesion phenomena, are currently the subject of debate in the literature . This debate warrants their detailed explanation [49,66,54,55,63]. The study of the adhesion mechanism began in the 1920s when MacBain and Hopkins introduced the mechanical interlocking model . As mentioned above, in spite of numerous papers that have reported on the problems with adhesives made of plastic materials, fundamental knowledge about the adhesion processes is still not well developed, and no single global approach or theory describes all adhesion phenomena or mechanisms in detail (e.g., [68,69]). 98 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Despite the wide use of adhesives, a good deal of controversy surrounds the nature of the bond. There are six main mechanisms or models (or theories) that could explain the adhesion process, have some support, each seems to be particularly useful in explaining certain phenomena associated with adhesive bonding . These theories are (i.e., [71,55,1,69]): (a) Mechanical interlocking model, (b) Electronic theory or electrostatic theory, (c) weak boundary layer theory, (d) Adsorption theory, (e) Diffusion or interdiffusion theory, (f) Chemical bonding theory. Although Lee  in the past had some criticism the weak boundary layers model explains some cases of poor adhesion. Fourche  in his review, described some important adhesion models with the explanation of corresponding mechanisms in detail. These models can help us to better understand the phenomena that occur between two substrates. It is wortwhile to review these because they indicate procedures commonly followed for optimal bonding. Fig. 2. Three types of surface irregularities . 3.1. Mechanical interlocking model The mechanical interlocking or coupling (or hooking) model is the one of earliest adhesion theories; it was introduced by MacBain in 1925 . The mechanical interlocking model or theory proposes that the main source of intrinsic adhesion is the mechanical keying of the adhesive into the irregularities of the adhered surface (see Fig. 1) [5,73]. In other words, this oldest adhesion theory considers adhesion to be the result of the mechanical interlocking of a polymer adhesive into the pores and other superﬁcial asperities of a substrate . The roughness and porosity of substrates are generally suitable factors only in so far as the wettability by the adhesive is sufﬁcient. Therefore, mechanical adhesion is related to the degree of roughness and as a consequence friction of the adherend surface. A certain amount of bonding can be expected purely from the mechanical interlocking, increased total surface area available for chemical bonding and creating a convoluted failure path where the adhesive penetrates crevices on the adherend surface. Although the tensile strength of the bond can depend on the crevice angles on the adherend surface, shear strength increases signiﬁcantly with increased roughness. However, mechanical interlocking is not a mechanism at the molecular level. It is merely a technical means to increase the adsorption of the adhesive on the substrates. The model involves the mechanical (physical) interlocking between irregularities of the substrate surface and the cured adhesive at the macroscopic level. As van Leeden and Frens  suggested, three types of irregularities are possible (see Fig. 2), although only type b may form mechanical interlocking . In the case of surface irregularities of the types a or b, the adhesive strength depends on the direction of the applied force because only mechanical hooking is present. Therefore, from the foregoing discussion the main factors affecting the mechanical interlocking are the roughness, porosity, and irregularities of the surface, but only under sufﬁcient wetting Fig. 1. Illustration of mechanical coupling between two substrates . Fig. 3. (a) Sufﬁcient wetting and (b) poor wetting (after Fourche ). of the substrate by the adhesive (see Fig. 3a). In fact, the nonwetting of substrate’s surfaces can prohibit adhesive bonds from forming at all. Therefore, as Maeva et al.  pointed out, for strong adhesion the adhesive must not only wet the substrate but also have the proper rheological characteristics for penetrating into pores in a reasonable time. Low adhesive viscosity promotes greater interfacial strength due to its faster and more complete penetration into the microvoids and pores. Despite its obvious appeal, the model of the mechanical interlocking can not be considered as a universal adhesion theory because good adhesion can occur even between perfectly smoothsurfaced substrates. Moreover, this theory does not consider any factors that occur on the molecular level at the adhesive/substrate interface. Mechanical interlocking should only be considered as a composite attribute in the overall view of adhesion mechanisms. This model can be effectively applied in situations where the substrates are impermeable to the adhesive and where the surface of the substrate is sufﬁciently rough . 3.2. Adsorption theory The adsorption theory is the most generally accepted model; it was introduced by Sharpe and Schonhorn . The adsorption theory states that the materials will adhere because of the interatomic and intermolecular forces that are established between the atoms and molecules in the surfaces of the adhesive and the substrate after their intimate contact [74,69]. These forces between adhesive and substrate include (i.e., [71,69]); (a) Secondary bonds: (i) van der Waals forces, and (ii) Hydrogen bonds, (b) Primary bonds: (i) Covalent, (ii) Ionic, (iii) Metallic and (c) Donor–acceptor interactions which are intermediate in strength between secondary and primary bonds (acid–base interaction). The theory includes several models that sometimes are considered as separate theories: wetting, rheological, and chemical adhesion models. The adsorption theory is also known as the thermodynamic theory (also referred as wettability and acid–base theory). A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 It is well known that for good adsorption, effective wetting is essential to provide close contact between two substrates . Several comprehensive reviews (i.e., [72,75,76]), have presented major results regarding wetting and wettability studies of polymers. As described in detail in Section 4, the measurement of contact angles is a means of investigating adhesion by physical adsorption. These are the weakest forces that contribute to adhesive bonds, but are quite sufﬁcient to make strong joints. In conclusion, this theory states that to be successful, an adhesive must wet the surface to be bonded (called the adherend). This theory has led to the development of materials with lower surface tension than that of the adherend. Supporting this theory is the fact that epoxy wets steel and provides a good bond, whereas it does not wet the oleﬁns PE, PP, and PTFE and does not bond them . 3.3. Diffusion or interdiffusion theory [71,69] The diffusion theory was proposed by Voyutski , who explained adhesion as being the result of interdiffusion of the macromolecules of the two polymeric materials at the interface as illustrated in Fig. 4. According to the diffusion theory both the adhesive and substrate must be polymers, which are mutually miscible and compatible . The diffusion theory states that adhesion of two macromolecules in intimate contact results from the interdifﬁusion of the molecules of the superﬁcial layers . This interdiffusion forms a transition zone or ‘‘interface’’ as shown in Fig. 4. In the case of polymer autohesion, i.e., two samples of identical polymers, adhesion, under a constant assembly pressure, is a function of temperature and contact time following Fick’s law. Thus, the average interpenetration depth, x, of one phase into another is given as : E xpexp t 1=2 ð1Þ 2RT where E is the diffusion activation energy, t the contact time, R the molar gas constant, and T is the temperature. The application of this model is limited to the adhesion of compatible polymers as well as the welding of thermoplastics. For the case of intrinsic adhesion of polymer to a metal mutual, diffusion across the polymer/metal interface occurs when certain metals are evaporated onto polymeric substrates. The diffusion theory assets that two specimens of polymers that are placed in contact under a constant assembly pressure will diffuse together following Fick’s laws of diffusion. In the case where concentration remains constant with time (steady state diffusion: Fick’s ﬁrst law of diffusion), ﬂux (Fx) in the direction x is proportional to the concentration c gradient, @c ð2Þ F x ¼ D @x where D is the diffusion coefﬁcient. Fig. 4. Diffusion theory of adhesion (a) Interdiffusion of adhesive and (b) substrate molecules (after Fourche) . 99 When concentration c varies with time, Fick’s second law determines the diffusion constant to be ! @c @2 c @2 c @2 c ¼D þ þ @t @x2 @y2 @z2 ð3Þ The molecular diffusion coefﬁcient D can be calculated using the following expression : DZ ¼ ArkT 36 R2 M ! ð4Þ where Z is the bulk viscosity, A is Avogadro’s number, r is the density, k is Boltzmann’s constant, M is the molar mass distribution and T is the absolute temperature. It was demonstrated in Refs. [79,80]that interdiffusion is optimal when the solubility characteristics of both polymers are equal. The chain length of the macromolecule, the concentration c, and the temperature T all have a signiﬁcant inﬂuence on the mobility of the macromolecules and, therefore, on the interdiffusion process and on the adhesive strength . Although increasing attention is being paid to the study of the interdiffusion process, the kinetic performance of the diffusion mechanism is still difﬁcult to predict and not completely understood at present. Vasenin  developed the kinetic concept of adhesion based on Fick’s ﬁrst law. This quantitative model states that the amount of material diffusion in a given direction across an interface is proportional to the constant time and gradient of concentration. Later, the diffusion kinetics were rewritten in light of the reptation theory of de Gennes  and later extended by several authors (i.e., [83,84]). As Maeva et al. pointed out in their work , the reptation theory has made much progress in the fundamental understanding of the molecular dynamics of polymer chains and it has been applied to study the tack, green strength, healing, and welding of polymers. From contact time, t, and the gradient of polymer concentration parameters, it is possible to evaluate the depth of interpenetration, x, and the number of macromolecular chains crossing the interface Lo(t)  xðxÞ t 1=4 N1=4 ð5Þ Lo ðtÞ t 3=4 N 7=4 ð6Þ where N is number of monomers per chain in the polymer. A direct relation exists between the concentration gradient and the contact time. Vasenin  studied the peel energy for joints bonded with polyisobutylenes of different molecular weights and established that peel strength is proportional to the contact time t1/2. Finally, Maeva et al.  concluded that the diffusion model of adhesion is not thought to contribute to adhesion if the substrate polymers are crystalline or highly cross-linked or if contact between two polymeric phases occurs far below their glass transition temperature. It has also been found to be of limited applicability if the adhesive and substrate are not soluble. As most polymers, including those with very similar chemical structures such as polyethylene and polypropylene are incompatible, the theory is generally only applicable in bonding like rubbery polymers, as might occur when surfaces coated with contact adhesives are pressed together, and in the solvent-welding of thermoplastics . There are a small number of polymer pairs made compatible by speciﬁc interactions. One pair is poly(methyl methacrylate) and poly(vinyl chloride), which permits the possibility of interdiffusion when structural acrylic adhesives are used to bond PVC. 100 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 3.4. Electrostatic attraction theory The electrostatic attraction theory (or the electrical adhesion mechanism) is also known as electrical double, or electronic, or parallel plate capacitor theory. This mechanism is based on the two materials joining at the interface having two different band structures such that at contact there is a mutual sharing of electrons . This model treats the adhesive–substrate system as a plate capacitor whose plates consist of the electrical double layer that occurs when two materials of different nature are brought in contact, see Fig. 5. This model is only applicable in the case of incompatible materials, e.g., a polymer and a metallic substrate. This theory postulates that as a result of the interaction of the adhesive and the adherend, an electrostatically charged double layer of ions develops at the interface . In another words, forces of attraction occur between two surfaces when one surface carries a net positive charge and the other surface a net negative charge as in the case of acid–base interactions and ionic bonding. The fact that electrical discharges are observed when an adhesive is peeled from a substrate is cited as evidence of these attractive forces. A difference in electrostatic charge between constituents at the interface may contribute to the force of attraction bonding. The strength of the interface will depend on the charge density. This attraction is unlikely to make a major contribution to the ﬁnal bond strength of the interface. The bonding of this type will explain why silane ﬁnishes are especially effective for certain acidic or neutral reinforcements like glass, silica and alumina. 3.5. Model of weak boundary layer The theory of weak boundary layers is important as it was initially thought that the interface between adhesive and substrate would not fail, but that failure was due to the formation of a weak boundary layer . This has been rebutted vigorously as real adhesives are generally polymeric and that the interface contains chain entanglements and cross links, resulting in a much greater force being required for interfacial failure [60,85]. Although recently it must be noted that surface morphology including plasma treatment can often degrade polymeric substrates, causing the formation of a weak boundary layer [5,86,87]. The weak boundary layer theory holds that for an adhesive to perform satisfactorily, the weak boundary layer should be eliminated. For example, in the case of the metals with a scaly oxide layer, failure takes place at the boundary. The problem does not exist for aluminum, which has a coherent oxide layer . Similarly, in the case of polyethylene, a weak, low-molecularweight additive is present throughout the structure, and this leads to a weak interface. In both case the potentially weak layers can be removed by surface pretreatments. Bikerman  showed that, in the separation of an assembly, the propagation of the failure is very unlikely to take place exactly at the interface. The fracture is, in fact, cohesively propagated in either solid in contact. Thus, whatever the mechanism governing Fig. 5. Electrical double layer at polymer–metal interfaces . Fig. 6. Seven classiﬁcations of weak boundary layers . the assembly formation, the strength of the assembly only depends on the bulk properties of the substrates. Bikerman also indicated that another failure mechanism may occur when the fracture moves forward in a weak interfacial layer located between two materials. Fig. 6 illustrates graphically the seven classes of weak boundary layers that were considered by Bikerman. The Bikerman model is simple, but was criticized in the past. It is now, however, admitted that many cases of poor adhesion can be attributed to these weak interfacial layers . 3.6. Chemical or molecular bonding theory The chemical bonding theory is the oldest and best known of all bonding theories [89–91]. The nature of the chemical bonding is the key to the physical and chemical behavior of matter. Molecular bonding is the most widely accepted mechanism for explaining adhesion between two surfaces in close contact . It entails intermolecular forces between adhesive and substrate such as dipole–dipole interactions, van der Waals forces and chemical interactions (that is, ionic, covalent and metallic bonding). It is easily understandable that chemical bonds formed across the adhesive–substrate interface can greatly enhance the level of adhesion between the two similar or dissimilar materials (substrates) . These bonds are generally considered as primary bonds in comparison with physical interactions, such as van der Waals, which are called secondary force interactions. The term primary and secondary stem from the relative strength or bond energy of each type of interaction. Molecular or chemical bonding mechanisms require an intimate contact between the two substrates. However, intimate contact alone is often insufﬁcient for good adhesion at the interface due to the presence of defects, cracks and air bubbles . A chemical bond is formed between a chemical grouping on the adhesive surface and a compatible chemical group in the adherend. The strength of the chemical bond depends on the number and type of bonds and interface failure must involve bond breakage . The processes of bond formation and breakage are in some form of thermally activated dynamic equilibrium. Atomic or molecular transport, by diffusional processes, is involved in chemical bonding. Solid solution and compound formation may occur at the interface, resulting a reaction zone with a certain thickness. This encompasses all types of covalent, ionic, and metallic bonding. Chemical bonding involves primary forces and the bond energy in the range of approximately 40–400 kJ/mol. For example, a chemical reaction at the interface is of particular interest for polymer matrix composites because it offers the major explanation for the use of coupling agents on glass ﬁbers and porabably the surface oxidative treatments on carbon ﬁbers for application with most thermoset and amorphous thermoplastic matrices. A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Surface treatments often involve chemicals which produce surfaces with different chemical compositions and oxide stoichiometries. These morphological changes inﬂuence the nature of the chemical bonds. Subsequently, a relationship exists between chemical composition of the surface and the bond durability. The mechanical behavior of the adhesive joint heavily depends on the adhesion at the adhesive/substrate interface; indeed the occurrence of delamination and/or debonding is critical to the overall integrity of built-up structures. As a consequence, one of the most important step in the design and fabrication of adhesive bonds is to use adhesion promoter molecules, generally called coupling agents to improve the joint strength between adhesive and substrate and/or suitable surface pretreatments [25,4]. The coupling agents are able to react chemically at both ends, with the substrate on one side and the polymer on the other side, thus creating a chemical bridge at the interface. Coupling agents based on silane molecules are the most common type of adhesion promotors. They are widely employed in systems involving glass or silica substrates, particularly in the case of polymer-based composites reinforced by glass ﬁbers. In addition to the improvement in joint strength, a signiﬁcant enhancement of the environmental resistance of the interface or durability of adhesive joints, in particular to moisture, can be achieved in the presence of such coupling agents at elevated temperature . The structure of the silane primer is shown in Fig. 7. Theories proposed in an attempt to explain the mechanism by which silane coupling agents function are numerous. According to the chemical bonding theory, the coupling ability of silanes is attributed to their unique hybrid chemical structure . A ﬁlm of oxide or of organic contamination may greatly reduce the adhesion performance of the adhesive joints . Organofunctional silanes are commonly used as coupling agents to enhance adhesion between polymeric and inorganic materials [95–97]. The silane coupling agents have the general structure of X3Si(CH2)nY, where X is a hydrolyzable (generally alkoxy) group capable of reacting with the substrate and Y is a organofunctional group selected for bonding to the polymer. In the past, extensive efforts have been devoted to demonstrate the effectiveness of organofunctional silanes as coupling agents between polymers and metals [98–110]. When a silane coupling agent is used to modify a polymeric– inorganic interface, the two different groups of the coupling agent can interact with both the polymer and the inorganic surface . It forms oxane bonds with the hydroxyl groups of inorganic surfaces, which are reversible in nature, and it may also interact with the polymer matrices to form covalent bonds with the reactive functional groups of the polymer or form interpenetrating polymer networks, or a combination of the two. According to Rider et al.  a silane coupling agent will perform two functions in order to improve the environmental durability of a bonded joint. First, it will increase the density of strong bonds between the oxide and the adhesive. Second, it will improve the hydrolytic stability of the inorganic surface such as 101 the aluminum oxide. Formation of a weak hydrated layer on the aluminum surface is signiﬁcantly hindered by the formation of a cross-linked multilayer ﬁlm [112–114]. Organo-functional silanes RSi(OR0 )3 are reactive molecules which are widely used as crosslinkers for moisture curing silicone elastomers . The curing proceeds at room temperature by hydrolysis of silicon–oxygen bonds followed by condensation of silanols in the presence of tin or titanium organometallic compounds. Silicone elastomers are used in many different applications such as waterprooﬁng seals in construction, adhesives in structural glazing, gaskets in car engines, adhesives for electronic devices, antifouling coatings, etc. Three main classes of silane crosslinkers have been developed, based on acetoxysilanes, oximinosilanes and alkoxysilanes . Variations of the silicon atom substituents may inﬂuence the cure rate and the properties of the silicone elastomer. It is, therefore, of interest to know the relationship between the chemical structure of the silane and the properties of the silicone materials to be able to design speciﬁc formulations. The curing of silicone elastomers has been described in the past (i.e., [115–117]). 4. Thermodynamic theory of adhesion 4.1. Surface tension or surface free energy (solid, liquid) The intrinsic adhesion between the adhesive and substrates arises from the fact that all materials have forces of attraction acting between their atoms and molecules, and a direct measure of these interatomic and intermolecular forces is surface tension . Therefore, Kinloch  underlined the fact that the tension in surface layers is the result of the attraction of the bulk material for the surface layer, and this attraction tends to reduce the number of molecules in the surface region resulting in an increase in intermolecular distance. This increase requires work to be done, and returns work to the system upon a return a normal conﬁguration. This explains why surface tension exists and why there is a surface free energy. The basic concept of surface free energy is that it is the excess energy associated with the presence of a surface. It is expressed per unit area. In formal treatments it is necessary to recognize that they may be deﬁned in terms either of Gibbs G or Helmholtz F free energies [118,119]. Distinction is also drawn between the ‘surface energy’ GS and the surface tension g, in which they are numerically the same but different dimensions [120,121]. In adhesion science and technology the interest is usually in complex solid surfaces for which very precise measurements of surface free energy are not generally possible. As Packham pointed out , it is therefore common, even universal, in this context to gloss over the formal distinctions between these terms and to take g and GS as being the same referring to both as ‘surface free energy’. Let us now consider an island on a planar, rigid (or nondeformable) substrate (or isotropic solid surface), as shown in Fig. 8. In the absence of elastic stresses, interfacial thermodynamics deﬁnes  the equilibrium angle y in the conﬁguration of Fig. 8 to satisfy the Young equation. When a liquid drop of known surface tention is on a solid surface in the equilibrium state as shown in Fig. 8, the relationship between the surface free energies (or the equilibrium balance of forces at the contact between three materials phases) from Young’s equation is as follows (i.e., [123,4]): gs ¼ gsl þ gl cos y ðYoung’s equationÞ ð7Þ 2 Fig. 7. The structure of g-glycidoxypropyltrimethoxy silane. where gs is the surface free energy of a solid substrate (mJ/m ), gl is the surface free energy of a liquid drop (or the surface tension of the liquid, mN/m), gsl is the interfacial free energy between the 102 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Fig. 8. Liquid drop on solid surface in equilibrium state showing the equilibrium force balance according to Young’s equation. solid substrate and the liquid drop, and y is the wetting (Young– Dupré) or contact angle between the solid–liquid interface. Therefore, the angles describing the intersection of three interfaces, separating different material phases are known as wetting angles. This term has its origins in the ﬂuid-mechanics literature [122,88], where it is used to describe the angle at which an isolated, liquid island meets the solid substrate on which it rests (see Fig. 8). In equilibrium, the wetting angle is determined by energy minimization at the triple line (i.e., the corner). In analyses of islands and other three-phase systems, the wetting angle provides the key boundary condition in determining three-phase interface morphologies . This same approach is routinely used to describe morphologies where intersections of solid–solid interfaces occur, e.g., a solid island on a substrate . Contact angle distribution may be obtained from the SEM or AFM image analysis . Usually, surface tension and (or) interfacial tension parameters are substituted for free energy. The angle chosen serves as a boundary condition on the shape of the interface for equilibrium conﬁgurations even in dynamic situations, as long as the departure from equilibrium is sufﬁciently small . In principle, the Young’s equation applies only to one-dimensional spreading and becomes invalid if the substrate is not rigid and motion of the contact-line takes place in both horizontal and vertical directions. The force equilibrium ignores the vertical component of the surface tension which acts along the line of contact. As the capillary forces are not balanced, external forces must be applied to the solid to achieve equilibrium. Palasantzas and Hosson  suggest that these forces may produce even deformation in highly deformable solids, such as gels and rubber, destroying the co-planarity of interfacial tensions that is assumed in Young’s equation and causing ridge formation at the interfacial region. With the use of the Young’s equation, it has to be stressed that only a ‘‘quasi-equilibrium’’ exists within the window of time when observations are made, provided that the solids deformation rate is small . However, wetting of solid surfaces is extremely sensitive to surface geometrical/chemical (roughness/ contaminants) disorder which manifests itself by the contact angle hysteresis phenomenon [126–130]. Considerations of surface energetics are usually regarded as fundamental to an understanding of adhesion . Surface energies are associated with formation of the adhesive bond. A prerequisite for adhesion is contact between the phases (i.e., solid and liquid) forming the bond. Commonly the adhesive is applied as a liquid, and its angle of contact y with the solid is related to the surface energies by Young’s equation . About two centuries after the foundation of the ﬁeld of contact angles and surface energetics there is practically no handbooklevel collection of contact angles data, except the collection by Wu  and the limits and the validity of the available experimental data are always quite unclear and a matter of discussion. The literature on contact angles and surface energetics has repeatedly indicated the lack of complete information on analyzed surfaces as one of the main problems in this ﬁeld. Therefore, as pointed out by Volpe et al. , it is very uncommon to ﬁnd papers in the literature where both the morphology and the chemistry of surfaces have been analyzed taking into account the roughness and chemical composition of those surfaces whose contact angles with common liquids are available. Although surface energies of liquids may be measured relatively easily by methods such as the du Nouy ring and Wilhelmy plate , those of solids present more problems. Many of most widely used methods for the surface free energies of solids are based on measuring the contact angles of a series of test liquids on the solid surface, and evaluating the surface energies via Young’s equation. Some of the methods used to evaluate the surface free energies in the literature are presented below. The contact angle (or wetting angle) can be measured by the sessile drop method  as shown in Fig. 9. A small drop of double distilled, deionized water (W) is put on the surface with a microsyringe and observed through a microscope . The height (h) and radius (r) of the spherical segment is measured and the angle is calculated by the following equations [47,48]. Contact angle ðyÞ ¼ sin 1 2 rh 2 r2 þ h ð8Þ At least 10 readings should be taken at different places and an average is determined. For example, in their study Deshmukh et al.  have found that the error in the measurement was found to be 721. Similarly, the angle of contact can be measured with respect to two different liquids [i.e., glycerol (G) and formamide (F)] to ﬁnd out polar ðgPs Þ and disperse ðgds Þ components of solid surface free energy and hence the surface free energy (S. E.) by Fowkes equation . In order to calculate the surface free energy of substrate, Deshmukh et al.  have used the three liquids of known polar and disperse components and are given in Table 1 . The surface energy is then calculated by using Fowkes equation (see Section 5 for more details about the Fowkes equation) as follows: sﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃ gPl qﬃﬃﬃﬃﬃd 1þ cos y gl P x qﬃﬃﬃﬃﬃ ¼ gs x þ gs ð9Þ 2 gdl gd l p l d l where g and g are the polar and disperse components of surface free energy of liquids, respectively. Eq. (9) is in the form: YðLHSÞ ¼ m ðRHSÞ þ C ð10Þ Where the value of LHS can be obtained by calculating y for liquid used. Value of gpl and gdl are given in literature (Table 1). Similarly, RHS is calculated by using polar and disperse components of surface free energy for liquid used from Table 1. The plot of LHS vs RHS would give a straight line with intercept on Y-axis as shown in Fig. 10. Slop and intercept obtained from the plot are squared and added up to give a total surface free energy. Surface free energies are also associated with failure of an adhesive bond. Failure involves forming new surfaces and the appropriate surface free energies have to be provided. The surface free energy term may be the work of adhesion, Wa; or the work of cohesion, Wc; depending on whether the failure is adhesive or Fig. 9. Sessile drop method for calculation of contact angle or wetting angle (y) (Ref. ). A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 103 Table 1 Surface free energy of liquids for polar (gpl ) and disperse (gdl ) components[47,4], Wetting liquids gl (mJ/m2) gpl (mJ/m2) gdl (mJ/m2) Water (W) Glycerol (G) Formamide (F) 72.8 63.4 58.2 51.0 26.2 18.7 21.8 37.2 39.5 Fig. 11. Relation between the thermodynamic work of adhesion Wa and the surface free energy gS of the two adjacent phases A (gA) and B (gB) . Fig. 10. A plot of Fowkes equation to determine the surface free energy from the polar and disperse components . cohesive . These are deﬁned as follows : W a ¼ gs þ gl gsl ð11Þ W c ¼ 2gs ð12Þ Eq. (11) (i.e., the Dupré equation) is called the thermodynamic work of adhesion,Wa (i.e., ). Before Eqs. such as (11) and (12) can be used, values for the surface energies have to be obtained using the single contact angle measurement or surface free energy component approach (i.e., dispersion and polar forces approach), as mentioned previously. The contact angle of a liquid on a surface can be related to the thermodynamic work of adhesion, Wa, which is directly related to the surface energy of the two adjacent phases A and B (see Fig. 11). In 1869, Dupré  deﬁned work of adhesion (Wa) leading to equation: W a ¼ gl ð1 þ cos yÞ ð13Þ Provided both gl and y can be measured experimentally, it is possible to calculate the work of adhesion of ‘‘liquid’’ to the solid under water. Although the interfacial tension can be measured accurately, the experimenter must be aware of complications due to hysteresis in contact angles, especially due to solid surfaces being rough or chemically heterogeneous. A more important aspect of such an experimental approach is that the use of Eq. (13) requires gl and y to be obtained for all systems of interest. This method of determining the thermodynamic work of adhesion Wa is an important consideration for predicting the success of the adhesion promoters such as the surface pretreatment and/or a silane coupling agent for increasing the bond strength, since the work of adhesion determines the work required to separate the unit area of two phases in contact (i.e., ). (See Section 3.6 for more details about the silane coupling agents.) Eq. (13) may be derived from Eqs. (7) and (11) by substitution. Eq. (13) provides a more useful expression for the work of adhesion. Adamson  outlines the origin and relationship between these equations and comments that Eqs. (11) and (7) are often both referred to as the Young–Dupré equation [134,140]. Eq. (13) provides a simple formula for Wa in terms of the measurable contact angle and the known surface tension of the test liquid . As stated above, in principle, the work of adhesion, as deﬁned in Eq. (13), should be a useful measure of the strength of adhesion in the particular system. Therefore, it would clearly be useful to be able to use Eq. (13) to predict values for the work of adhesion if it were possible to estimate all three interfacial tensions from some other source of data. This would require the use of combining rules that allow any interfacial tension to be predicted from ‘‘surface tension components’’, and the determination of such components for solid surfaces. In a real system, however, macroscopic surface roughness and surface chemical heterogeneity (non-uniform surface chemistry) may give rise to contact angle hysteresis; the advancing contact angle measured as the test ﬂuid expands the sessile drop and advances of over new surface area is greater than the receding contact angle measured as the sessile drop retreats . This behavior introduces a measure of ambiguity in the determination of contact angle and is a source of conjecture in the application of Eqs. (7) and (13) [5,9,50,142]. Often the polymeric material is adhesively bonded to primary metal structures. But unfortunately, these polymers exhibit insufﬁcient adhesive bond strength due to low surface energy. The poor bondability owing to the low surface energy of some polymers has limited the widespread use of these materials . For example, the poor bondability of propylene (PP) is attributed to its nonpolar characteristics with low surface energy. It is shown that a high polar component with a simultaneously high overall surface energy of the substrate can lead to a better adhesion strength . Therefore, the surface modiﬁcation of polymers, while leaving the bulk intact, becomes very important from an industrial point of view. Hence, surface modiﬁcation of polymers is often carried out to enhance their surface energy for improved adhesion, for greater joint strength in polymer to metal joints. 4.2. Wetting, wetting criteria, and wettability Wetting of liquids on solid surfaces is a topic of fundamental interest with widespread technological implications [126–130]. 104 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Examples include coating technology, thin ﬁlm technology but also gluing and lubrication. Adhesives that have surface energies less than that of the adherend will readily wet the surface and form good bonds. If sufﬁciently intimate contact is achieved between the adherend and adhesive a physical interaction develops between the atoms of the two surfaces, which results in wetting. The formation of a physical interaction or bond results from highly localized intermolecular forces. Wetting may be due to (i.e., ): (a) acid–base interactions, (b) weak hydrogen bonding or (c) van der Waals forces (dipole–dipole and dispersion forces). The extent of wetting depends on the differences in surface free energies of the solid, liquid and subsequent interface. For wetting to occur spontaneously, the condition gsv Z gsl þ glv ð14Þ should apply.where gsv, gsl and glv are the interfacial surface free energies for solid–vapor, solid–liquid and liquid–vapor interfaces, respectively. If the gsl is not signiﬁcant, this criterion can be simpliﬁed (i.e., ) to gsv Z glv or gsubstrate Z gadhesive ð15Þ Eq. (15) once again indicates that the adhesive will spread on the substrate when the surface free energy of the substrate is greater than that of the adhesive. Poor wetting causes less contact area between the substrate and the adhesive and more stress regions at the interface and, accordingly, adhesive joint strength decreases. Sharpe and Schonhorn  have shown that the adhesive joint strength is inﬂuenced by the ability of the adhesive to spread spontaneously on the surface when the joint is intially formed. The energy change (per unit area) when liquid spreads over the surface of solid is called the spreading coefﬁcient or spreading energy, S,  and is also related to the surface energies: S ¼ gsv glv gsl Z0 ð16Þ Eq. (16) also constitutes a wetting criterion. If S is positive, the liquid droplet at equilibrium will be spread completely over the solid (i.e., complete wetting), while if S is negative, partial wetting will occur, leading to a non-zero contact angle y at the junction of solid–liquid–vapor [126–130]. It is worth noting that geometric aspects or processing conditions, such as the surface roughness of the solid and applied external pressure, can restrict the applicability of this criterion. 5. Estimation of surface energy: dispersion and polar components of surface free energies Many theories have been introduced to describe and measure the surface tension of materials with applications to polymer systems. Consideration of the sample surface free energy is a consideration of sample surface tension. Depending on the surface to be examined and the selected test liquids, several methods are available for calculation of the surface energy of a solid (i.e., [141,145]): (a) Good–Girifalco interaction approach [146,147], (b) Zisman plot approach , (c) the Owens–Wendt method , (d) a method proposed by Schultz , (e) Good and van Oss approach , (f) Fowkes and co-workers [136,152,153] and Owens and Wendt  approach, and (g) van Oss, Good, and Chaudhury [155–157] approach. As stated previously in Section 4, the surface free energy of the solid gs can be obtained from equilibrium contact angle measurements of a series of test liquids on the solid surface, providing the relationship between gsl and the solid gs (in vacuo) and liquid glv surface energies is known . Good and Girifalco [146,147] provided the exact relationship (i.e., the Good and Girifalco equation) between surface free energies as pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ gsl ¼ gs þ glv 2| gs glv ð17Þ gs gsv ¼ pe ð18Þ where | is the Good–Girifalco interaction parameter and pe is called the equilibrium spreading pressure. The spreading pressure is difﬁcult to measure, and it is common to neglect it . This may be justiﬁable for a low energy, non-polar (e.g., an alkane), but is difﬁcult to justify where a high surface energy solid is involved. In principle the solid surface energy is calculated by eliminating gsl between Eqs. (7) and (17) giving pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð19Þ glv ð1þ cos yÞ ¼ 2| gs glv The difﬁculty with Eq. (19) is that the Good–Girifalco interaction parameter | is not generally known. Over past decades enormous intellectual effort has been put into devising ways of circumventing the problem of not knowing | and much controversy has been generated in the process . Surface energy is a method of analyzing the interaction between the molecules on the surface of a material and the molecules in the bulk. The surface energies can be calculated by means of the Good– Girifalco–Fowkes–Young (GGFY) equation (i.e., ): rﬃﬃﬃﬃﬃ gs pe 1þ cos yls ¼ 2 ð20Þ gl gl where yls is the liquid–solid contact angle, gs the surface energy of the solid (mJ/m2), pe the equilibrium spreading pressure (mJ/m2) and gl the surface tension of the liquid (mN/m). The work of adhesion can be measured using the combined Young–Dupré equation: W sl ¼ gl ð1þ cos yls Þ þ pe ð21Þ Acid–base interaction is a major factor among short-range (o0.2 nm) intermolecular forces and involves hydrogen bonding, electron donor–acceptor, or electrophile–nucleophile interaction . Fowkes [136,150,152,154] proposed that interfacial tension (or total surface tension) g may be expressed by two terms: a dispersive force component for the surface free energy, gd, and a polar force component (e.g., hydrogen bonding) for the surface free energy, gp g ¼ gd þ gp ð22Þ The dispersive component contains all the London forces such as dispersion (London–van der Waals), orientation (Keesom–van der Waals), induction (Debye–van der Waals) and Lifshitz–van der Waals (LW) forces; while the polar component represents all the short-range nondispersive forces, including hydrogen (acid/base) and covalent bonds (i.e., [5,71]). The Fowkes method has been discussed widely in the literature (i.e., [29,52,158,73,159–162]). Owens–Wendt  used the previous equation (i.e., Eq. (22)) to derive a relation for the work of adhesion (Wa): W a ¼ W da þ W pa ð23Þ W da W pa derived from the London dispersion forces and derived from the non-dispersive, i.e., acid–base interaction. As Fowkes considered only the dispersion force interaction at the solid liquid interface, Eq. (22) can be further developed by taking into account the geometric mean of the dispersion components of both liquids, resulting in Eq. (24): qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð24Þ gsl ¼ gs þ gl 2 gds gdl ðFowkes equationÞ Substituting Young’s equation, Fowke’s equation becomes qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ gl ð1 þ cos yÞ ¼ 2 gds gdl ð25Þ A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 This equation when applied to calculating surface free energies only takes into account the dispersive interactions of the system and as such is not reliable for calculations of complex systems . However, for simple systems its application can provide useful approximations . When there are only dispersion forces involved, the work of adhesion can be expressed by the geometric mean of the dispersion component: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ W da ¼ 2 gds gdl ð26Þ Many workers including Fowkes and co-workers [136,152,153] and Owens and Wendt  developed a geometric mean approach which is an extension of Fowkes’ models for the interfacial free energy between two phases, which can be applied to a liquid drop on a solid surface. This theory considers also the polar (hydrogen bonding) term. Therefore, they used the geometric mean to combine the polar and dispersive components together as shown in Eq. (27). qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð27Þ gsl ¼ gs þ gl 2 gds gdl 2 gps gpl Similarly, the non-dispersion contribution (deriving from electrostatic, metallic, hydrogen bonding and dipole–dipole interactions) to the equation of the work of adhesion can be deﬁned as the geometric mean of polar contributions. Combining Eq. (27) with Young’s equation generates the following geometric mean equation [145,149,163]. qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð28Þ gl ð1þ cos yÞ ¼ 2 gds gdl þ 2 gps gpl Due to the presence of the polar term, the minimum number of liquids required to calculate the solid surface components is two, of known surface tension [9,154,85]. Thus, the dispersive gds and polar gps components of surface free energy of the substrate can be calculated from the intercept and the slope of the previous expression (for example, see Fig. 12). Owens and Wendt , Kaelble and Uy  proposed, glv ð1 þ cos yÞ ¼ 4gds gdlv gds þ gdlv þ 4gps gplv p p s þ lv g g ð29Þ In an attempt to relate components more closely to the chemical nature of the phases, Good and van Oss  suggested that the polar component could be better described in terms of acid–base interactions. Thus, to better describe the polar component in terms of acid–base interaction this approach was later extended by van Oss, Good, and Chaudhury [155–157] and an 105 interfacial tention can be described as: g ¼ gLW þ gab ð30Þ LW ab where g is the Lifshitz–van der Waals component and g is the acid–base component of the interfacial energy. The acid–base interaction or theory has received signiﬁcant support from many researchers (i.e., [52,165,166]). The adhesion work for dispersive forces is then qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ d d d W LW ð31Þ a ¼ W 12 ¼ 2 g1 g2 where gd1 , gd2 are the dispersive components of the surface free energy of the substrates 1 and 2, while gp1 and gp2 are the polar components of the surface energy for substrates 1 and 2. Unlike gLW, the apolar London–van der Waals component, the acid–base component gab comprises two non-additive parameters. These acid–base interactions are complementary in nature and are the electron-acceptor surface tension parameter (i.e., the Lewis acid–base component of surface interaction) (g þ ) and the electron-donor surface tension parameter (i.e., the Lewis base component of surface interaction) (g ), contribution of the acid–base interaction to the interfacial energy (i.e., [155,167]). The total acid–base component (gab) contribution to the surface tension is then given by pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð32Þ gab ¼ 2 g þ g The acid–base contribution to the interfacial energy can be determined for the substrates 1 and 2 as qﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃ þ þ gab ð33Þ 12 ¼ 2½ g1 g1 ½ g1 g2 If the surface involves both Lifshitz–van der Waals and acid– base interactions, the total interfacial tension between the two phases is expressed as qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ þ LW g12 ¼ g1 þ g2 2 gLW g1 g2þ ð34Þ 1 g2 2 g1 g2 þ The total interfecial tension between condensed phases i and j  is qﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ giþ g g gLW gij ¼ ½ gLW gþ 2 þ 2½ giþ g þ gjþ g i j i j j i j ð35Þ ’ As presented previously, the Young–Dupre equation for a nonspreading liquid (L) on a solid surface (S), is gs ¼ gsl þ gl cos y Fig. 12. Surface free energy measurements on the microwave-treated PP surface using the Owens, Wendt, Rabel and Kaelble method . ð70 Þ 106 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 where y is the contact angle. Expressing the three tensions in Eq. (7) in the form of Eq. (36) gives (i.e., [167,71]) qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ LW þ ð36Þ ð1þ cos yÞgl ¼ 2½ gLW gsþ gl þ gs glþ s gl and the work of adhesion Wa (taking into account the total acid– base component gab and the Lifshitz–van der Waals component gLW) as qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ LW W a ¼ 2½ gLW g1þ g2 g1 g2þ ð37Þ 1 g2 þ Eq. (36) contains three unknowns related to the solid surface, þ gLW S , gS and gS . As a result, contact angle data for at least three different liquids (of which two must be polar) enable all three parameters to be calculated from the various simultaneous equations of type 36. Once these parameters are known for the solid surface, the work of adhesion can be calculated. All imply that the spreading pressure may be neglected. These equations result from assuming that the total surface energy can be split into the sum of components associated with different types of bonding, for example dispersion gd plus polar gp (Eqs. (28) and (29)), or Lifshitz–van der Waals gLW plus acid– base gAB (Eq. (36)). Kim and Lee  calculated the polar component gpS and the dispersion one gdS of the surface free energy of the carbon/epoxy composite using Eq. (27) from the measurement of contact angles of water and glycerol drops, whose surface free energies have been known as listed in Table 2. Then the surface free energy gS of the carbon/epoxy composite was calculated. The surface free energies are inversely proportional to the contact angles of the water and the glycerol drops as shown in Fig. 13. The contact angles of the water drops on both the plasma surface treated carbon/epoxy composite and not-treated one were also studied. The contact angle of the liquid drop on the carbon/epoxy composite decreased after the plasma surface treatment because the surface free energy of the carbon/epoxy composite increased . Zisman plot , and the Owens–Wendt  methods can be used to evaluate the wettability of the differently treated surfaces. Zisman  introduced the concept of critical surface free energy, gc, an empirical parameter, which can be used to assess the wettability of a surface. Zisman used a wide range of homologous and non-homologous test liquids to prove his hypothesis [148,154,169]. Determination of the surface free energy, for the example selected in Fig. 14, gives the critical surface free energy, gc, of a solid, which corresponds to a theoretical contact angle of zero, with complete wetting of the surface. In general, a high value of gc anticipates a surface with good wetting qualities. The critical surface free energy of a solid corresponds to a theoretical contact angle of zero, with complete wetting of the surface . Mirabedini et al.  calculated the critical surface energy, dispersion and polar components of the surface energies from the intercept and the slope values of the Zisman and Owens plots for PP surfaces, as listed in Table 3. In this table, the Polypropylene (PP) samples were surface cleaned using a soft brush. The samples were then dipped in an aqueous solution of 20% H2SO4 for about 5 min. Subsequently, specimens were rinsed with distilled water and then exposed to microwave irradiation in the presence of different Table 2 Surface free energies of water and glycerol [168,4]. Liquid gl (mJ/m2) gdl (mJ/m2) gpl (mJ/m2) Water Glycerol 72.8 63.4 21.8 37.2 51.0 26.2 Fig. 13. Contact angles of water and glycerol drops and the surface free energy of the carbon/epoxy composite calculated from the contact angles . Fig. 14. Critical surface free energy gc of microwave-treated PP surface in the presence of 0.4 mol/l KMnO4 Zisman method . concentrations of KMnO4 (0.2, 0.4 and 0.5 mol/l) for time intervals of 40, 60 and 120 s. For comparison, some samples were degreased and treated with ChA, according to the procedure described in ASTM D 2093. For comparative reasons, some samples were treated with 0.5 mol/l of KMnO4 solution using conventional heating for time intervals of 2, 5, 10,15, 30, 45 and 60 min. Nonirradiation heating was through hot plate system and the temperature of solution was around 95 1C. As expected, the untreated PP sample has the lowest surface energy, with a very low polar value; generally, a surface free energy of 24 mJ/m2 or slightly less, suggests hydrocarbon oil contamination on the surface. For example, triglyceride oils have a surface free energy of about 24 mJ/m2 . Such contaminants accumulate on the PP surface during production and/or migration of additives to the surface from the polymer bulk. The surface free energy values increased for the microwave and chromate-treated samples. For such surfaces, probe liquids exhibit tendency to spread and, consequently, potentially high adhesive strengths may be achieved. The results show that the polar component of the surface free energy of PP increased considerably by the microwave treatment. No signiﬁcant difference was observed between the dispersion components of the degreased and microwave-treated PP, which indicates that the polar component is responsible for the increase in total surface energy due to microwave treatment. A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Table 3 Critical surface free enery gc and surface energy values of the differently treated PP Films . Pretreatment Acid cleaned 0.2 M/ PPM, 40 s 0.2 M/PPM, 60 s 0.2 M/PPM, 120 s 0.4 M/PPM, 40 s 0.4 M/PPM, 60 s 0.4 M/PPM, 120 s 0.5 M/PPM, 40 s 0.5 M/PPM, 60 s 0.5 M/PPM, 120 s ChA treated PP 0.5 M/PPM, 2 min, conventional heatinga 0.5 M/PPM, 10 min, conventional heating 0.5 M/PPM, 20 min, conventional heating 0.5 M/PPM, 30 min, conventional heating a Zisman (mJ/m2) Owens and co-worker (mJ/m2) gc gps gds gs 27.6 29.2 30.3 30.4 30.8 32.6 33.7 30.9 33.3 33.9 34.8 29.2 29.6 30.0 30.9 0.1 0.1 0.1 0.6 0.6 9.9 12.0 1.3 10.8 12.3 14.5 0.6 1.1 1.4 1.7 32.8 33.8 34.4 33.4 33.2 28.7 27.8 34.7 28.7 28.7 28.6 29.8 30.2 30.9 31.7 32.9 33.9 34.5 34.0 33.8 38.6 39.8 36.0 39.5 41.0 43.1 30.4 31.3 32.3 33.4 Heating was carried out using a hot plate. 107 It is evident from Table 3, despite long treatment times, those specimens treated with conventional heating showed low surface free energy compared to microwave irradiated samples. In Fig. 15, the variation of surface free energy of treated samples with exposure time is given and it shows that the increasing rate of surface free energy of microwave-treated samples is higher than that of conventionally heated specimens. For example, the surface free energy of microwave irradiated sample becomes 41 mJ/m2 in just 2 min whereas the surface free energy of samples exposed to conventional heating only just reaches 33 mJ/m2 after 30 min. Clint and Wicks  have used contact angles to determine the components of the solid surface energies for a set of probe liquids on solid surfaces. They treated the crown glass surfaces with 1% solutions of various surface modifying agents. They then determined the contact angles on these surfaces using the probe liquids. From these the values, gdS and gpS were calculated and these values used to predict the work of adhesion of the oil under water. When combined with the appropriate form of the Young equation this allowed the expected contact angle for oil under water to be calculated. To test these predictions, the contact angles for squalane (a C30 hydrocarbon oil) were measured with the modiﬁed surfaces under water. The experimental contact angles are compared with the theoretical predictions in Fig. 16 where it can be seen that the agreement is good. An interesting feature of the results is that the different treatments fall into different zones depending on the chemical type of the surface-modifying agent. For example, the functionalised siloxanes promote adhesion of the oil under water whereas perﬂuoro compounds have the opposite effect. One of the perﬂuoro compounds, FC129 (from 3 M), a potassium perﬂuoroalkyl carboxylate, gave a contact angle of 1801 indicating no tendency for oil to adhere at all, as predicted by the surface energy components. The ﬂuorosilanes give results intermediate between those of the functionalised siloxanes and the perﬂuoro compounds. 6. Effect of surface roughness on wettability (or adhesion) Roughness of adherend surfaces has frequently been used as a design parameter for adhesive joints . A number of Fig. 15. Variation of surface free energy of microwave irradiated (MV) and conventional treated samples with exposure time . Fig. 16. Experimental contact angles for squalane under water on various modiﬁed glass surfaces plotted against values calculated using components of solid surface energy. Circle—untreated glass; triangles—functionalised siloxanes; diamonds—ﬂuorosilanes; squares—perﬂuorocompounds . 108 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 researchers have examined its effect on the strength and durability of adhesive joints using various adherends and adhesives (i.e., [172–178]). There are, however, no much published quantitative data, which relates surface roughness parameters to the strength of joints. An examination of the adherend surfaces using scanning electron microscopy (SEM) and proﬁlometry reveals that when the molecular scale is approached, all engineering material surfaces are always rough . In fact, based on structural and chemical studies we can conclude that the surfaces of engineering materials almost never have the same structure or composition as the bulk. Consequently, both the chemical and the physical nature of a surface are crucial in adhesion. It is often difﬁcult to separate these two effects. The chemical nature inﬂuences the reactivity of the surface towards the adhesive . The surface free energy and fundamental wetting characteristics also affect the strength and stability of adhesion. As Sancaktar and Gomatam  pointed out, many surface treatments that improve adhesion have the effect of roughening the surface involved. For example, surface pretreatments, such as abrasion and etching, also remove weak boundary layers, increase the reactivity of the surface, and improve its wetting behavior. For efﬁcient bonding, liquid adhesives need to be spread over the whole surface to be joined. The capillary forces play an important role in adhesive penetration into the surface crevices. The viscosity of the adhesive also plays an important role in its surface penetration behavior. However, spreading and penetration do not ensure the removal of air from the cavities present on the surface. Some form of substrate surface pre-treatment is almost always necessary to achieve a satisfactory level of bond strength . As Shahid and Hashim pointed out , almost all surface pretreatment methods do bring some degree of change in surface roughness but grit-blasting is usually considered as one of the most effective methods to control the desired level of surface roughness and joint strength. Grit-blasting does not only remove weak boundary layers but can also alter the chemical characteristics of the adherends . For example, an earlier work on steel cleavage specimens showed the effectiveness of grit-blasting over diamond polishing in achieving improved cleavage strength . The relationship between roughness and adhesion is not very simple. Optimum surface proﬁle varies from one adhesive to another, and depends upon the type of stress applied . Of possible positive effects of surface roughness [181–183], increase in surface area results in increasing intermolecular bonds and keying for mechanical adhesion. This in turn can divert the failure path away from the interface into the bulk of the adhesive . However, the actual microscopic distribution of stress at the rough interface is complex. Bikerman  states that when a liquid advances into a surface topographical valley, the air initially present there can escape without experiencing any serious resistance. If the spreading liquid adhesive covers a surface crevice without penetration and forms an air pocket, the surface forces usually cease to affect the position or motion of this air pocket. For efﬁcient bonding, care must be taken to ensure that the adhesive makes intimate contact with the adherend surface. The surface roughness can affect the spreading of the adhesive, either because the adhesive can not penetrate the adherend or because it gels before it completes the penetration. The effects of surface roughness on wettability have been studied by many researchers using surface roughness factors such as the Wenzel roughness factor [125,184] and so on [185,186]. Cassie and Baxter  discussed the inﬂuence of a porous surface on wettability, and proposed an equation describing the contact angle changes for composite materials [188,189]. As for the experimental technique for changing the roughness of a solid surface, many researchers used powders , photoresist micropatterns [191,192], a porous surface [187,190], etc. However, their roughness factors depend on each other which makes a precise discussion difﬁcult. To solve this difﬁculty, in their study, Nakae et al.  adopted two kinds of surface models, a hemispherical close-packed model and a hemiround-rod closepacked model. By using these models, the height roughness can be varied with the radius of the spheres and the rods. This means that the Wenzel roughness factors are constant for both of these models. Their work describes the effect of surface height roughness on wettability without changing the Wenzel roughness factors. For the hemispherical close-packed models, the effect of height roughness on wetting can be explained by the change in the radius of curvature, R, of the liquid in trapped air pockets at the solid–liquid interface. In the case of the hemi-round-rods close-packed models, they determined that the contact angles, measured from the direction parallel to the rods, resemble the advancing and receding angles of contact angle hysteresis. There have been attempts to model the effect of surface roughness on the contact angle with liquids. The best-known treatment is by Wenzel . Wenzel proposed a parameter ‘r’ to characterize a surface as follows: r¼ total surface area apparent geometric area ð38Þ Wenzel assumed that the value of r increased as the roughening increased. It is generally believed that the apparent contact angle decreases with increasing roughness values . The wetting of a surface, however, is a kinetic phenomenon and the liquid must ﬁrst advance on the surface. Even if the ultimate equilibrium contact angle may be zero, the advancing contact angle is never zero but is a function of the rate of movement of the liquid . Not only the average roughness, but also the geometry of the adherend surface topographies is expected to affect the resulting joint strength . For example, Pugh  showed ﬁve different surface proﬁles, all with the same roughness values but different topographies. Johnson and Dettre  modeled the rough surface by a sine wave. They postulated that further roughening would maintain the wavelength but would increase the amplitude to increase Wenzel’s ‘r’ parameter. Some theories suggest that roughening should be regarded as a situation in which both the amplitude and the wavelength are varied in a ﬁxed ratio [66,179]. This is done by considering the surface as an array of (n number of) pyramids in which the array height and base (a) of the pyramid are equal. This leads to a total surface area of n(5)1/2a2. If we consider the corresponding apparent surface area, n a2, the Wenzel parameter, r, characterizing the surface complexity  can be calculated as r ¼(5)1/2. This theory is offered mostly for polycrystalline substrates . Upon roughening, the crystalline structure is likely to remain intact, but with a different crystal size. This suggests that roughness is related not only to the amplitude, but also to the underlying adherend structure . Sancaktar and Gomatam  note that in this case Wenzel’s parameter is independent of the actual surface topographical dimensions and it is not altered upon surface roughening. Based on a thermodynamic analysis, Wenzel  introduced an apparent contact angle yW, where yW ¼ cos1 ðDr cos yÞ ð39Þ Dr represents the ratio of the average area of the actually attached interface to its projected part. In his approach, as mentioned above, the rough surface was supposed to be completely wetted and unwetted sharp grooves were ignored. A similar A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 model was proposed by Cassie and Baxter  taking into account the area fraction Df of an uncontected solid-liquid interface on the solid. Unfortunately neither of these theories can predict correctly the experimental contact angles . Further, the parameters Dr and Df are not easily experimentally accessible. Moreover, the corresponding equations are only correct for radial grooves with a liquid droplet spreading radially, for which an equilibrium state can be reached . Wenzel’s equation predicts that with increasing roughness the apparent contact angle yW decreases for y o901, while yW increases for y 4901. In other words a transition occurs for theoretical contact angles equal to 901, whereas experimental results [125,197] indicated that such a transition takes place at contact angles smaller than 901. PALASANTZAS and HOSSON  derived for radial grooves a more general equation cos yr ¼ Dr ð1Df Þcos yDr . Another way of measuring the surface roughness is using the ‘arithmetic mean roughness’ parameter, Ra, which is deﬁned as follows (i.e., ): Ra ¼ 1 Lm Z x ¼ Lm 9y9dx ð40Þ x¼0 where Lm is the total scanned length in the x (horizontal) direction (see Fig. 17). The Hommel tester also provides ‘mean peak-to-valley height’, Rz, values, and ‘maximum individual peak-to-valley height’, Rmax , values. The Rz value is the arithmetic mean from the peak-tovalley heights of ﬁve successive sampling lengths (see Fig. 10). The Rmax value is the absolute maximum peak-to-valley height within the overall measuring length. A comparison of this value with Rz provides insight into the variability of peak heights. A comparison of Rz with Ra, for example Rz/2Ra, provides information on the effect of the proﬁle wavelength, and the shape of the wave, since larger wavelengths and small height–roughness distribution within this wavelength result in smaller Ra values and large Rz/2Ra values . Shahid and Hashim  studied the inﬂuence of surface roughness of a steel adherend on cleavage strength. They attempted to relate the surface roughness parameters Ra and Rlo to cleavage strength. To produce varying degrees of surface roughness, steel specimens were diamond polished and grit-blasted with four sizes of alumina grit. Pre-treated surfaces were examined using measured surface parameters like Ra, Rlo and root mean square slope, Rdq. Rlo is deﬁned in ISO 4287 1984. It is the measured length of the proﬁle surface within the evaluation length, i.e., the length obtained if the proﬁle, within the evaluation length was to be drawn out into a straight line . Mathematically it is represented as follows: sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 Z ln dy Rlo ¼ dx ð41Þ 1þ dx 0 A graphically representation of Rlo is given in Fig. 18. Rdq is deﬁned in ISO 4287 1997 paragraph 4.4.1. It is the root mean square value of the ordinate slope dz/dx within the sampling length. The mathematical representation for this is sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Z 1 L Rdq ¼ ½yðXÞy2 dx ð42Þ L 0 where y is the slope of the proﬁle at any given point and Z 1 y¼ yðXÞdx ln ð43Þ Graphically, this is explained in Fig. 19. In their study, Shahid and Hashim  constructed the relationship between the average cleavage strength and the Ra value of the steel adherend surfaces in Fig. 20. It can be seen that cleavage strength appears to increases linearly with the Ra value. The increase in cleavage strength may be attributed to an increase in surface area by forming of mini scarf joints on adherend surfaces at micro level. Harris and Beever , Thery et al.  and Critchlow and Brewis  found no appreciable change in joint strength with increasing adherend surface roughness by mechanical treatment.These contrasting ﬁndings may be due to the fact that each researcher used a different set of adherend, adhesive and joint geometry . Moreover, the overall effect of grit blasting is not limited to the removal of contamination or to an increase in surface area.This also relates to changes in the surface chemistry of adherends  and to inherent drawbacks of surface roughness, such as void formations and reduced wetting . The inﬂuence of surface irregularities on the interaction between the adhesive and substrate have also been investigated by numerous workers, including the shape of pits, the effects of surface topography on peel adhesion, the average roughness, the width of the valleys, and peaks on the strength of joints etc (i.e., [201–204]). For example, De Bruyne  studied the shapes of pits into which the adhesive would not penetrate if the contact angle, y, with the material walls was greater than a certain value. He gave the expression for the capillary driving pressure P as (see Fig. 21). P¼ Fig. 17. Calculation of the average surface roughness, Ra, and the mean peak-tovalley height, Rz, values . 109 2g 2 g sinðy þ|Þ r o 2ðx cot |Þ R ð44Þ where g is the surface energy of the adhesive. As long as sinðy þ jÞs is positive, a driving pressure exists, implying that (y þ f) is less than 1801. As Sancaktar and Gomatam  pointed out, If instead of this (ﬂower pot) shape, f becomes greater than 901 and the depression contains reentrant angles, then y need not be very large to prevent the adhesive from ingression. If the trapped air opposes the capillary pressure of the liquid, the situation worsens. Khrulev  proposed an alternative analysis for describing the inﬂuence of surface irregularities on the interaction between the adhesive and the substrate. His aim was to determine the optimum thickness of the adhesive layer and how this layer was affected by the ﬂow property of the adhesive. Khrulev assumed that the continuous layer of adhesive that withstood shear would 110 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Fig. 18. Graphical representations of linear proﬁle length, Rlo (). Fig. 19. Graphical representation of Rdq . be less due to the penetration of the adhesive into the surface irregularities. By assuming the surface irregularities as surface furrows of 601 sides, Khrulev deduced an expression according to which the depth of penetration into the pits depended mainly on the pressure used in combining the joint members . He also gave the example that the differences in optimum adhesive thickness between wood and metals were due to the irregularities in the surface of the wood, and the metals were assumed to be smooth compared with wood. Arrowsmith  studied the effect of surface topography on peel adhesion by performing peel tests on electroformed copper foil to epoxide laminates. Arrowsmith showed that not only the average surface roughness, but also the particular geometry of the surface topography including the presence of a secondary (dendritic) superposed structure had an inﬂuence on the peel strength. Keisler and Lataillade  studied the effects of average roughness, the width of the valleys, the dominance of valleys, and peaks on the strength of joints in lap shear conﬁguration. They used high strain rates to evaluate the impact resistance of adhesive joints under shear loading. They reported that the joint shear strength was lower with a ‘stochastic’ proﬁle. They argued that ‘excessive roughness, sharper asperities, and narrow-spaced valleys contributed to poor wettability, leading to the initiation of fracture’ [204,179]. A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 Fig. 20. Variation of cleavage strength with average roughness, Ra . adhesion’ (or practical work of adhesion Wap; i.e., from the measured strength or toughness of an adhesive joint [211,212]. Even when using a fracture mechanics approach, and interfacial failure of the joint does occur, the value of the adhesive fracture energy, Gc, will usually not be equivalent to the energy associated with the rupture of the intrinsic adhesion forces, since the value of Gc will also encompass the energy dissipated in viscoelastic and plastic deformation processes which occur in the vicinity of the crack tip . Thus the value of Gc is typically orders of magnitude greater than the energy associated solely with the intrinsic adhesion forces. From a practical standpoint, this emphasizes the need not only to establish good intrinsic adhesion across the adhesive/substrate interfaces but also to develop tough adhesives, where the plastic, or process, zone in the vicinity of the crack tip will be relatively large . To make adhesion possible, it is necessary to generate intrinsic adhesion forces across the interface. The magnitude and the nature of those forces are very important. From a thermodynamic standpoint the true work of adhesion (or intrinsic property) of the interface is the amount of energy required to create free surfaces from the bonded materials : W a ¼ gf þ gs gf s Fig. 21. De Bruyne’s model for capillary penetration [179,201]. 7. Thermodynamics work of adhesion The concept of measuring the strength of adhesion in terms of the ‘‘work of adhesion’’ was ﬁrst introduced by Harkins . The increase in surface energy [206–208] is an indication of the increase in adhesion force through the relationship between surface free energy and work of adhesion  [see Eq. (11)]. It is evident that if the surface free energy of a plastic substrate is raised by surface pretreatment to a higher level, then adhesion properties can be improved. Most of the test methods measure adhesion by delaminating thin ﬁlms (or adhesives) from the substrate. While debonding from the substrate, the thin ﬁlm and/or the substrate usually experience plastic deformation, so it is difﬁcult to extract the true adhesive energy from the total energy measured . What is measured is the practical work of adhesion Wap, or interfacial toughness : W ap ¼ W a þ U f þ U s þ U f ric ð45Þ where Uf and Us are the energy spent in plastic deformation of the ﬁlm and the substrate, respectively, and Ufric is the energy loss due to friction. Although the last three terms appear to be simply additive, it should be noted that both Uf(Wa) and Us(Wa) are functions of the true work of adhesion Wa  and in many cases Ufric(Wa) will be as well. As pointed out by Kinloch , the term ‘intrinsic adhesion’ (or true work of adhesion) is often used when referring to the direct molecular forces of attraction between the adhesive and the substrates, to distinguish this phenomenon from the ‘measured 111 ð46Þ where gf and gs are the speciﬁc surface energies of the ﬁlm (or adhesive) and the substrate respectively, gfs is the interfacial surface free energy of ﬁlm–substrate interface. As mentioned above, true work of adhesion is an intrinsic property of the ﬁlm/ substrate pair; that depends on the type of bonding between the ﬁlm and the substrate, and the level of initial surface contamination. For the idealized case of Grifﬁth fracture , the interfacial toughness, GI, is assumed to be equal to the thermodynamic work of adhesion, Wa: !I ¼ W a . In practice, even brittle fracture is accompanied by some sort of energy dissipation either through plastic deformation at the crack tip , or friction. In this regard, even relatively thin ﬁlms on the order of 100 nm can exhibit plasticity during interfacial fracture resulting in an elevated work of fracture . As known, the true work of adhesion is often determined by contact angle measurements (i.e., [124,215]) (see Eq. (46)). The most common interaction at the adhesive–substrate interface results from van der Waals forces (i.e., ). These are longrange forces (effective from a distance of much less than 10 nm), which consist of dispersion and polarization components. They all fall off in proportion to r 6. Van der Waals forces directly relate to fundamental thermodydamic parameters, such as the free energies of the adhesive and substrate, and allow a reversible work of adhesion of the materials to be calculated for the materials in contact . In addition to the other factors, the rate of seperation, time and temperature of dissipation are the factors affecting the the adhesion (i.e., ). As it is now well known, the measured adherence energy is a complex function of the adhesion (interfacial strength) and of the energy dissipated in the materials during viscoelastic and plastic deformation processes [216–218]. An illustration of the contribution of the dissipation phenomena is the inﬂuence of the rate of separation on the measured adhesive strength . The dependence of the failure energy G on the separation rate V has been initially proposed by Gent and Schultz with the following expression : G ¼ W a FðaT VÞ ð47Þ where Wa is the thermodynamic energy of adhesion, F is the dissipative function and aT the time/temperature translation factor (i.e., the Wlliam–Landel–Ferry (WLF) shift factor). Maugis and 112 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 example plastic deformation- which occur during fracture : Barquins  proposed a derived equation: GW a ¼ W a FðaT VÞ ð48Þ The energy dissipation is a function of temperature and time and increases generally when the separation rate is increased. When the separation rate decreases and reaches zero, the viscoelastic dissipation is considered to be negligible and, in that case, the measured failure energy G (called Go) is considered, to a ﬁrst approximation, to be theoretically equal to the reversible energy of adhesion W . Experimentally, separation tests or adherence tests at low rates are difﬁcult to perform, and the Go value is determined by extrapolation of the G/V curve to the zero rate value. Adherence tests (generally consisting of the mechanical separation of the assembly) are used in order to quantify the adherence level between an adhesive (usually a polymer-based material) and a substrate . Guillemenet and Bistac  have investigated the adhesive strength of steel/polymer/steel assemblies using a wedge test. Their main aim was to analyze the effect of the wedge introduction speed V, both on adherence energy G and of the crack propagation rate. From Fig. 22 the extrapolated value of G at a zero speed was determined to be Go ¼30,000 N/m. Considering that Go could be equal to Wa, Eq. (48) becomes GGo ¼ Go FðaT VÞ ð49Þ The dissipation function F(aTV) is then equal to F(aTV)¼ (G Go)/Go. Eq. (49) presents the plot of F(aTV)¼(G Go)/Go versus the introduction speed V. It can be seen that the dissipation function is globally increased when the speed V increases, in agreement with the literature results . Elsewhere, the transition is still present and the inﬂexion point occurs around V ¼30 mm/min. There is also a link between the thermodynamic work of adhesion (Wa) and the interfacial toughness (G(c)) . For example, when the thin ﬁlm yield stress is low, and Wa is high, ductile fracture is the most likely failure mechanism. Conversely, when the ﬁlm yield stress is high, and the true adhesion is low, brittle fracture occurs [124,220–222]. In the case of a metal ﬁlm on a brittle substrate, one may improve the interfacial toughness by decreasing the ﬁlm yield stress (annealing), or by using the interlayers that may increase the thermodynamic work of adhesion term Wa. The practical adhesion, for example fracture energy G, will comprise a surface energy term Go (Wa or Wc) to which must be added a term c representing other energy absorbing processes- for G ¼ Go þ c ð50Þ Usually c is much larger than Go. This is why practical fracture energies for adhesive joints are almost always orders of magnitude greater than works of adhesion or cohesion . However, as Packham  stated, a modest increase in Go may result in a large increase in adhesion as c and Wa are usually coupled. For some mechanically simple systems where c is largely associated with viscoelastic loss, a multiplicative relation has been found : G ¼ Go 1 þ fðc,TÞ Go x fðc,TÞ ð51Þ where f(c,T) is a temperature and rate-dependent viscoelastic term [211,212,223]. In simple terms, stronger bonds (increased Go) may lead to much larger increases in fracture energy because they allow much more bulk energy dissipation (increased f) during fracture. Fracture mechanics approach uses the strain energy release rate, or the crack driving force R as a measure of the practical work of adhesion: GZR ð52Þ For the ﬁlms, the resistance to crack growth is deﬁned as G(c), the interfacial fracture resistance for mixed mode crack growth. This along with strain energy release rate, as deﬁned for the case of ﬁxed-grips loading condition gives  @U E G¼ Z GðcÞ ¼ R ð53Þ @A U o where U is the total energy of the system, and A is the crack area, and R is the resistance to crack propagation. Let us ﬁrst address the tests to determine G, and later consider various resistance terms and several possible ways to interpret that resistance, e.g., phase angle, friction and plastic energy dissipation. The amount of energy dissipation depends on mode mixity (phase angle), a relative measure of the amount of shear and normal stress components at the crack tip ðc ¼ tan1 ðt=sÞ ¼ tan1 ðK II =K I ÞÞ. Where KI and KII are the stres intensity factors for mode I and mode I, respectively. The concept of mode mixity is presented in Fig. 23, which shows that the amount of energy dissipation is higher in pure shear compared to the pure opening fracture mode. Several criteria/phenomenological relationships have been proposed to characterize interfacial fracture energy as a function of the phase angle of loading . There are results Fig. 22. Evolution of the adherence energy G as a function of the wedge introduction speed . A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 in the literature, both experimental and theoretical that exhibit similar behavior [225–229]. The most realistic phenomenological descriptions of the functional dependence of the interfacial toughness on the mode mixity are given by Hutchinson and Suo : 2 GðcÞ ¼ Go ½1 þ tan cð1lÞ 2 gðcÞ ¼ Go ½1 þ ð1lÞtan c ð54Þ ð55Þ In these expressions Go is the mode I interfacial toughness for, and l is an adjustable parameter (Fig. 24). Strictly speaking, there is always a mode mixity effect in the case of a crack propagating along the interface between two dissimilar materials just due to a mismatch in their elastic properties [31,230]. Interfacial fracture mechanics considers an interface between two different isotropic materials. In determining fracture toughness through the use of a complex stress intensity factor for bimaterials, this can be expressed as : P M p ie K ¼ ðK I þ iK 2 Þ ¼ pﬃﬃﬃ i 3=2 pﬃﬃﬃ h eio ð56Þ 2 h h where h is the ﬁlm thickness, M is the bending moment due to qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 load P, o is a real angular function p ¼ ð1aÞ=ð1b Þ, and e is a Fig. 23. Interfacial fracture toughness as a function of the mode mixity angle . Fig. 24. Phenomenological functions for GðcÞ  113 bimaterial real constant: e ¼ ð1=2pÞln½ð1bÞ=ð1 þ bÞ ð57Þ The Dundurs parameters a and b for plane strain are : ðm1 =m2 Þð1n2 Þð1n1 Þ ðm1 =m2 Þð1n2 Þ þ ð1n1 Þ 1 ðm1 =m2 Þð12n2 Þð12n1 Þ b¼ 2 ðm1 =m2 Þð1n2 Þ þð1n1 Þ a¼ ð58Þ where the mi, ni are shear moduli and Poisson’s ratios for substrates 1 and 2. For bimaterials the phase angle c is then deﬁned as follows: " # pﬃﬃﬃ 1 Ph sin o2 3M cos o pﬃﬃﬃ ð59Þ c ¼ tan Ph cos o þ2 3M sin o The crack path depends on the phase angle, residual stress and the modulus mismatch between the ﬁlm and the substrate . In the case of a weakly bonded ﬁlm on a substrate, the interface will be the most likely crack path. There will be cases when the crack can kink either into the substrate or into the ﬁlm itself . When testing thin ﬁlm adhesion, knowledge of the fracture interface and the phase angle is necessary in order to interpret the results correctly. 8. Concluding remarks Adhesion is a complex phenomenon and a number of factors affect adhesion, including the type of adherends and adhesive, surface pre-treatment, adhesive thickness and bonding and testing conditions (i.e., [25,231,232]). There are many unresolved issues in adhesion. This is understandable because the subject is highly interdisciplinary and this often leads to different interpretations of the same phenomenon by workers from different disciplines . Almost all research areas in adhesion science are heading for two basic aims. The ﬁrst aim is to understand the mechanical properties of an adhesive joint and the second is to allow predictions about the long-term durability of a joint. Even though these two aims are of purely macroscopic nature, the research also has to focus on much smaller dimensions, e.g., the interface of a joint. Adhesion is a surface physico-chemical phenomenon. Since adhesion is a surface phenomenon, it follows that the physical properties of the adhesive joint depend strongly on the character of the surface of the substrate and how the adhesive interacts with that surface. Thus, a substrate with an improper surface could lead to lower joint strengths than might be predicted from the mechanical properties of the adhesive and the substrate . The phenomena of wetting and adhesion are intrinsically related. Most liquids display surface tensions and interfacial tensions with solids or other (immiscible) liquids, depending mainly on secondary, physical bonds of the van der Waals category (although the importance of acid–base interactions and hydrogen bonding is being increasingly recognized and should not be overlooked) . The molecular origin of the work of adhesion are the intermolecular attractive interactions . When two smooth polymer surfaces approach each other within a distance of a few nanometers, they jump into contact because of such intermolecular interactions as the universal van der Waals interactions and other types of speciﬁc molecular interactions such as polar interactions, hydrogen bonding and acid–base interactions . The work of adhesion can be estimated from the van der Waals interaction in terms of equilibrium separation distance (D0 E0.2 nm) and Hamaker constant A12 , whose value depends on the surface chemistry of materials in contact. It is well known that materials in contact with each other inﬂuence the structure and/or the composition and/or the 114 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116 properties of one or both materials in the near-interface regionmost often called the interphase . These interphases depend on the combinations of adhesive and adherend surface and on the process of contact formation as well. Due to its distinct structure, the interphase possesses properties that can be much different from the behavior of the bulk adhesive . The mechanisms that produce interphases are many and varied and it is probably true that interphases are almost always present where two materials join. Therefore, it is generally misleading to speak about such parameters as the ‘‘interfacial shear strength’’ of a composite material or a structure such as an adhesive joint. The quality of the contact between the adhesive and the substrates results from the interplay of interactions at different length scales . On the molecular scale, it results generically from van der Waals interactions . Surface chemical bonds , macromolecular interdigitation  or macromolecule elongation , however, may enhance signiﬁcantly the strength of the interface for speciﬁc substrates–adhesive pairs. Surface treatments and cleaning are also essential. On the micrometer scale, solid substrates usually display some degree of surface roughness  that may reduce the degree of intimacy of the contact with the adhesive if the adhesive material is not very soft. For very soft adhesives, however, the surface roughness of the substrates may paradoxically enhance the strength of the interface, as small air bubbles trapped at the interface may generate suction effects upon traction . There are a number of surface characterization techniques utilized for investigating the physical and chemical properties of the adhering surfaces related to adhesion mechanisms and adhesion strength. These surface characterization techniques include : (a) time-of-ﬂight secondary ion mass spectrometry (ToF-SIMS), (b) X-ray photoelectron spectroscopy (XPS), (c) atomic force microscopy (AFM), (d) scanning electron microscopy (SEM), (e) attenuated total reﬂectance infrared spectroscopy (ATR-IR), and (f) other microscopy techniques plus methods sensitive to surface energy such as optical contact angle analysis. Using all these thechniques numerous studies have been made to investigate the surface properties such as roughness, polarity, chemical composition and surface free energies to describe and explain adhesion phenomena at a surface or interphase [13,9–11,53,66,248–254]. As stated previously, adhesion research is a multi-faceted science that encompasses and requires knowledge of chemistry, materials and mechanics. Understanding the roles that these factors play in adhesion requires knowledge of complex processes that occur on multiple scales, from atomic to molecular to macro length scales. Numerous testing techniques have been and are continuing to be developed to characterize adhesion using nanomechanical instrumentation. These techniques all use some combination of the capability to actuate normal and lateral to the sample surface while measuring both force and displacement. References  Fourche G. An overview of the basic aspects of polymer adhesion. Part I: Fundamentals. Polym Eng Sci 1995;35:957–67.  Adhesion Promotion Techniques: Technological Applications, 2002. Mittal KL, Pizzi A, editors. Marcel Dekker, Inc., New York, p. 37, Part 1: Theories and Mechanisms of Adhesion, by J. Schultz and M. Nardin, p. 1.  Kinloch AJ, 1996. Adhesives in Engineering. In: Proceeding of the Institution of Mechanical Engineers. 84th Thomas Hawksley Memorial Lecture in Institution of Mechanical Engineers, London IMechE, Lecture Presented at An Ordinary Meeting of the Institution Held in London on Wednesday 11 December 1996, Preprint no. 8.  Kinloch AJ. Adhesion and Adhesives. New York: Chapman and Hall; 1987 pp. 18–100.  Awaja F, Gilbert M, Kelly G, Fox B, Pigram PJ. Prog Polym Sci 2009;34:948–68.  Sargent JP. Int J Adhes Adhes 2005;25:247–56.  Swadener JG, Liechti KM, Lozanne A. J Mech Phys Solids 1999;47:223–58.  Dixon DG, Unger W, Naylor M, Dublineau P, Figgures CC. Int J Adhes Adhes 1998;18:125–30.  Clint JH. Curr Opinion Colloid Interface Sci 2001;6:28–33.  Grundmeier G, Stratmann M. Annu Rev Mater Res 2005;35:571–615.  Brockmann W, Huther R. Int J Adhes Adhes 1996;16:81.  Hutchinson AR, Iglauer S. Int J Adhes Adhes 2006;26:555.  Pijpers AP, Meier RJ. J Electron Spectrosc Relat Phenom 2001;121:299–313.  Tomasetti E, Daoust D, Legras R, Bertrand P, Rouxhet PG. J Adhes Sci Technol 2001;15:1589.  Nihlstrand A. Int Congr Adhes Sci Technol 1995:285–305.  Occhiello E, Morra M, Morini G, Garbassi F, Humphrey P. J Appl Polym Sci 1991;42(2):551–9.  Noeske M, Degenhardt J, Strudthoff S, Lommatzsch U. Int J Adhes Adhes 2004;24:171.  Nowack H, Muhlhan C. Surf Coat Technol 1998;98:1107.  Hegemann D, Brunner H, Oehr C. Nucl Instrum Methods Phys Res, Sect B 2003;208:281.  Nihlstrand A, Hjertberg T, Johansson K. Polymer 1997;38:3581.  Wong TL, Barry CMF, Orroth SA. J Vinyl Add Tech 1999;5:235–40.  Morris HR, Munroe B, Ryntz RA, Treado PJ. Langmuir 1998;14:2426–34.  Tang H, Martin DC. J Mater Sci 2002;37:4783–91.  Kumar CR, George KE, Thomas S. J Appl Polym Sci 1996;61:2383–96.  Baldan A. J Mater Sci 2004;39:1–49.  Alexander W, Eric G. Biomed Microdevices 2002;4:33.  Lampin M, Warocquier-Clérout R, Legris C, Degrange M, Sigot-Luizard MF. J Biomed Mater Res 1997;36:99–108.  Ohashi KL, Dauskardt RH. J Biomed Mater Res 2000;51:172–83.  Zhao Q, Liu Y, Abel EW. J Colloid Interface Sci 2004;280:174–83.  Schakenraad JM, Busscher HJ, Wildevuur CR, Arends J. Cell Biophys 1988; 13:75–91.  Volinsky AA, Moody NR, Gerberich WW. Acta Mater 2002;50:441–66.  Israelachvili JN. Handbook of Surface Imaging Visualization. In: Hubbard AT, editor. Boca Raton, FL: CRC Press; 1995. p. 793–816.  Pickering JP, Van der DW, Van der Meer DW, Vancso GJ. J Adhes Sci Technol 2001;15:1429–41.  Liu J, Toshiyukisa WA. J Adhes Sci Technol 2001;15:43–61.  Bucknall DG. Prog Mater Sci 2004;49:713–86.  Rahul-Kumar P, Jagota A, Bennison SJ, Saigal S, Muralidhar S. Acta Mater 1999;47:4161–9.  Mittal KL, editor. Polymer Surface Modiﬁcation: Relevance to Adhesion. Utrecht: VSP; 1996.  Mittal KL, editor. Polymer Surface Modiﬁcation: Relevance to Adhesion, Vol. 2. Utrecht: VSP; 2000.  Rauser J, Knudsen G. EP 85919; 1983.  Gibbsons CE, Whillock AA. EP 293098; 1998.  Koh SK, Cho JS, Kim KH, Han S, Beag YW. J Adhes Sci Technol 2002;16: 129–42.  Koh SK, Song SK, Choi SK, WK SN, Han SN, Jung HJ. J Mater Res 1995;10: 2390.  Koh SK, Choi WK, Cho JS, Kim YM, Jung HJ, Koh SK. J Mater Res 1996;11: 2933.  Cho JS, Choi WK, Yoon KH, Koh SK. J Vac Sci Technol 1998;B16:1110.  Han S, Koh SK, Yoon KH. J Electrochem Soc 1999;146:4327.  Choi SC, Choi WK, Jung HJ, Park JG, Chung BC, Yoo YS, Koh SK. J Appl Polym Sci 1999;73:41.  Deshmukh RR, Bhat NV. Mater Res Innovat 2003;7:283–90.  Rossier JS, Bercier P, Schwarz A, Loridant S, Girault HH. Langmuir 1999;15:5173.  Qin R-Y, Schreiber HP. Colloids Surf 1999;156:85–93.  The equation of state for interfacial tensions. In: Neumann AW, Spelt JK, editors. Applied Surface Thermodynamics. New York: Marcel Dekker; 1996. pp. 239–92 [chapter 5].  Tavana H, Neumann AW. Adv Colloid Interface Sci 2007;132:1–32.  Della Volpe C, Maniglio D, Brugnara M, Siboni S, Morra M. J Colloid Interface Sci 2004;271(2):434–53.  Pukanszky B, Fekete E. Adv Polym Sci 1999;139:109–53.  Been JL, Bikales NM, Bickerman JJ, Blomquist RF, Moks E, Kovach GP, et al. Adhesion and Bonding. 1st ed. John Wiley and Sons Inc.; 1971.  van Leeden MC, Frens G. Adv Eng Mater 2002;4(5):280–9.  Roberts JC. The Chemistry of Paper. 1st ed. Cambridge, UK: The Royal Society of Chemistry; 1996.  Amouroux N, Leger L. J Adhes 2006;82(9):919.  Lo Chieh-Tsung, Laabs Francis C, Narasimhan Balaji. J Polym Sci, Part B: Polym Phys 2004;42(14):2667–79.  Raghavan J, Wool RP. J Appl Polym Sci 1999;71(5):775–85.  Kinloch AJ. J Mater Sci 1980;15:2141–66.  Yosomiya R, Morimoto K, Nakajima A, Ikada Y, Suzuki T. Adhesion and Bonding in Composites. 1st ed. New York: Marcel Dekker Inc; 1989.  Beholz B, Aronson CL, Zand A. Polymer 2005;46:4604–13.  Brown HR. Mater Forum 2000;24:49–58.  Lippert T, Dickinson JT. Chem Rev 2003;103(2):453–86.  Sathyanarayana MN, Yaseen M. Prog Org Coat 1995;26(2–4):275–313.  Wake WC. Adhesion and the Formulation of Adhesives. 2nd ed. Essex: Applied Science Publishers Ltd., New York; 1982.  MacBain W, Hopkins DG. J Phys Chem 1925;29:88.  Oliver JF, Huh C, Mason SG. Colloids Surf 1980;1:79. A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116  Yang Shuo, Gu Lan, Ronald F. Nondestructive detection of weak joints in adhesively bonded composite structures. Gibson Compos Struct 2001;51: 63–71.  Alisa Buchman, Hanna Dodiuk-Kenig. Laser surface treatment to improve adhesion. In: Mittal KL, Pizzi A, editors. Adhesion promotion techniques: technological applications. New York: Marcel Dekker, Inc.; 2002. p. 206.  Maeva E, Severina I, Bondarenko S, Chapman G, O’Neill B, Severin F, Maev RG. Can J Phys 2004;82:891.  Lee LH. Adhesive Bonding. New York: Plenum Press; 1991.  Georges F. Polym Eng Sci 1995;35(12):957–67.  Sharpe LH, Schonhorn H. Adv Chem Ser 1964;8:189.  Zisman WA. In: Lee LH, editor. In Adhesion Science and Technology, vol. A. New York: Plenum Press; 1975. p. 55.  Mittal KL. In: Lee LH, editor. In Adhesion Science and Technology, vol. A. New York: Plenum Press; 1975. p. 129.  Richard A, Flinn, Trojan Paul K. New York: John and Wiley, Inc.; 1995. p. 595.  Voyutski SS. Autohesion and Adhesion of High Polymers. New York: WileyInterscience; 1963.  Pravatareddy H, Dillard JG, McGrath JE, Dillard DA. J Adhes 1999;69:83.  Hansen CM, Just L. Int Eng Chem Res 2001;40:21.  Vasenin RM. Adhesion: Fundametals and Practice. London: McLaren; 1969 p. 29.  de Gennes PG. J Chem Phys 1971;55:572.  Doi M. Introduction to Polymer Physics. Oxford: Clarendon Press; 1995.  Graessley WW. Adv Polym Sci. 47 1982:76.  Lipatov Y. Polymer Reinforcement. ChemTec Publishing; 1995.  Zukiene K, Jankauskaite V, Mickus KV. J Adhes 2008;84(7):601–18.  Muhlhan C, Weidner ST, Friedrich J, Nowack H. Surf Coat Technol 1999; 116–119:783.  Bikerman JJ. The Science of Adhesive Joints. New York: Academic Press; 1961.  Walker P. J Adhes Sci Technol 1991;5:279.  Plueddemann EP. J Adhes Sci Technol 1991;5:261.  Chen R, Boerio FJ. J Adhes Sci Technol 1990;4:453.  Shultz J, Nardin M. Theories and mechanisms of adhesion. In: Mittal KL, Pizzi A, editors. Adhesion Promotion Techniques: Technological Applications. New York: Marcel Dekker, Inc.; 2002. p. 19.  Horner MR, Boerio FJ, Cleariﬁeld HM. In: Mittal KL, editor. Silanes and Other Coupling Agents. Utrecht: VSP; 1992. p. 241–62.  Song J, van Ooij WJ. Bonding and corrosion protection mechanisms of g-APS and BTSE silane ﬁlms on aluminum substrates. J Adhes Sci Technol 2003; 17(16):2191–221.  Plueddemann EP. Silane Coupling Agents. New York, NY: Plenum Press; 1991.  Mittal KL, editor. Silane and Other Coupling Agents, vol. 2. Utrecht: VSP; 2000.  van Ooij WJ, Sabata A. Surf Interface Anal 1993;20:475.  Pape PG, Plueddemann EP. J Adhes Sci Technol 1991;5:831.  Allen KW. J Adhes Sci Technol 1992;6:23.  Tutas DJ, Stromberg R, Passaglia E. SPE Trans 1964;4:256.  Pohl ER, Blackwell CS. In Controlled Interphases in Composite Materials. In: Ishida H, editor. New York, NY: Elsevier; 1990.  Boerio FJ, Ho CH. J Adhes 1987;21:253.  Kinloch AJ, Dukes WA, Gledhill RA. Adhesion Science and Technology. In: Lee LH, editor. New York, NY: Plenum Press; 1975. p. 597.  Theidman W, Tolan FC, Pearce PJ, Morris CEM. J Adhes 1987;22:197.  Boerio FJ, Ondrus DJ. J Colloid Interface Sci 1988;124:349.  Boerio FJ, Dillingham RG. Adhesive Joints: Formation, Characteristics, and Testing. In: Mittal KL, editor. New York, NY: Plenum Press; 1984. p. 541.  Ogarev VA, Selector SL. Prog Org Coat 1992;21:135.  Petrunin MA, Nazarov AP, Mikhailovski YN. J Electrochem Soc 1996;143: 251.  Underhill PR, Duquesqay DL. In: Mittal KL, editor. Silane and Other Coupling Agents, vol. 2. Utrecht: VSP; 2000. p. 149.  Beccaria AM, Chiaruttini L. Corros Sci 1999;41:885.  Rider AN, Arnott DR, Wilson AR, Vargas O. Mater Sci Forum 1995;189/190: 235–40.  Kinloch AJ. Proc Inst Mech Eng 1997;211:307–35.  Rider AN, Arnott DR. Surf Interface Anal 1995;24:583–90.  Arnott DR, Wilson AR, Rider AN, Lambriandis LT, Farr NG. Appl Surf Sci 1993;70/71:109–13.  Pujol Jean-Marc, Prébet Christiane. Functional silanes: crosslinkers for silicone elastomers. J Adhes Sci Technol 2003;17(2):261–75.  Schoenherr W, Falender J. ACS Polym Prepr 1981;22(1):190.  de Buyl F, Comyn J, Shepard NE, Subramaniam NP. Paper presented at Third International Symposium on Silanes and Other Coupling Agents. Newark, New Jersey ; 2001.  Packham DE. Int J Adhes Adhes 2003;23:437–48.  Srolovitz DJ, Davis SH. Acta Mater 2001;49:1005–7.  Lewis GN, Randall M. Thermodynamics. In: Pitzer KS, Brewer L, editors. 2nd ed. (revised). New York: McGraw-Hill; 1961. p. 472.  Somorjai GA. Principles of Surface Chemistry. Englewood Cliffs, NJ: PrenticeHall; 1972.  Dussan EB. Annu Rev Fluid Mech 1979;11:371.  Young T. Philos Trans R Soc 1805;95:65.                                                           115 Lipkin DM, Clarke DR, Evans AG. Acta Mater 1998;46:4835. Palasantzas G, Th. J, Hosson MDE. Acta Mater 2001;49:3533–8. de Gennes PG. Rev Mod Phys 1984;57:827. Asthana R, Sobczak N. JOM-e 2000;52:1. Leger L, Joanny JF. Rep Prog Phys 1992;55:431. Eustathopolous N. Acta Mater 1998;46:2319. Meier A, Javernick JA, Edwards GR. JOM 1999;51:44. Padday JF. Handbook of Adhesion. In: Packham DE, editor. New York: Longman; 1992. p. 82. Wu S. Polymer Interface and Adhesion. New York, NY: Marcel Dekker; 1982. Della Volpe C, Siboni S, Maniglio D, Morra M, Cassinelli C, Anderle M, Speranza G, Canteri R, Pederzolli C, Gottardi G, Janikowska S, Lui A. J Adhes Sci Technol 2003;17:1425–56. Adamson AW. Physical Chemistry of Surfaces. 5th ed. New York: Wiley; 1990. Wavhal DS. PhD thesis. India: University of Mumbai; 1998. Fowkes FM. J Phys Chem 1963;67:2538. Jones DA, Lelyveld TP, Mavro.dis SD, Kingman SW, Miles NJ. Resour Conserv Recycl 2002;34:75. Dupré A. Théorie mécanique de la chaleur. Paris: Gauthier-Villars; 1869. Molitor P, Young T. Int J Adhes Adhes 2004;24:127–34. Tg C-M, Jrn M, Br Granqvist, Jrnstrm J, Peltonen J, Rosenholm JBr. Holzforschung 2007;61(5):516–22. Mirabedini SM, Rahimi H, Hamedifar Sh, Mohseni SM. Int J Adhes Adhes 2004;24:163–70. Renton WJ, Vinson JR. Trans ASME J Appl Mech 1977;44:101–6. Schultz J, Nardin M. Handbook of Adhesive Technology. In: Pizzi A, Mittal KL, editors. New York: Marcel Decker; 1994. Lugscheider E, Bobzin K. Surf Coat Technol 2001;755:142–4. Oosting R. PhD thesis. The Netherlands: Delft University of Technology; 1995. Girifalco LA, Good RJ. J Phys Chem 1957;61:904. Girifalco LA, Good RJ. J Phys Chem 1960;64:561. Zisman WA. In: Gould RF, editor. Advances in Chemistry Series, vol. 43. Washington: American Chemical Society; 1964. Fox HW, Zisman WA. J Colloid Sci 1950;5:514. Schultz J, Tsutsumi K, Donnett JB. J Colloid Interface Sci 1977;59:277. Good RJ, van Oss CJ. Modern Approach to Wettability: Theory and Application. In: Schrader ME, Loed G, editors. New York: Plenum Press; 1991 [chapter 1]. Fowkes FM. J Adhes Sci Technol 1987;1:7. Allara DA, Fowkes FM, Noolandi J, Rubloff GW, Tirrell MV. Mater Sci Eng 1986;83:213. Owens DK, Wendt RC. J Appl Polym Sci 1969;13:1741–7. Good RJ, Chaudhury MK, van Oss CJ. Fundamentals of Adhesion. In: Lee LH, editor. New York: Plenum Press; 1991 [chapter 4]. van Oss CJ, Good RJ, Chaudhury MK. Langmuir 1988;4:884. van Oss CJ, Good RJ. Interfacial Forces in Aqueous Media. New York: Marcel Dekker; 1994. Oss CJv, Chaudhury MK, Good RJ. Adv Colloid Interface Sci 1987;28:35–64. Vasconcellos AS, Oliveira JAP, Baumhardt-Neto R. Eur Polym J 1997;33(10–12): 1731–4. Bhowmik S, Jana P, Chaki TK, Ray S. Surf Coat Technol 2004;185(1):81–91. Oss CJV, Ju L, Chaudhury MK, Good RJ. J Colloid Interface Sci 1989;128(2): 313. Blum F, Metin B, Vohra R, Sitton O. J Adhes 2006;82(9):903. Comyn J. Int J Adhes Adhes 1992;12:145. Kaelble DH, Uy KC. J Adhes 1970;2:50. Mathieson I, Bradley RH. Int J Adhes Adhes 1996;16:29. Watts JF, Chehimi MM. Int J Adhes Adhes 1995;15(2):91–4. Clint JH, Wicks AC. Int J Adhes Adhes 2001;21:267–73. Kim JK, Lee DG. Compos Struct 2002;57:37–46. Hafrin EG, Zisman WA. J Phys Chem 1960:51964 1960:519. Hansen CM. Eur Coat J 1994;11:839. Shahid M, Hashim SA. Int J Adhes Adhes 2002;22:235–44. Critchlow GW, Brewis DM. Int J Adhes Adhes 1995;15(3):173–6. Gilibert Y, Verchery G. Infuence of surface roughness on mechanical properties of joints. In: Mittal KL, editor. Adhesive Joints Formation, Characteristics, and Testing. New York: Plenum Press; 1982. Jennings CW. Surface roughness and bond strength of adhesive. Am Chem Soc Div Org Chem 1971;31(2):184–92. Sargent JP. Int J Adhes Adhes 1994;14(1):21–30. Katona TR, Batterman SC. Surface roughness effects on the stress analysis of adhesive joints. Int J Adhes Adhes 1983;3(2):85–91. Matsui K. Size-effects on average ultimate shear stresses of adhesivebonded rectangular or tubular lap joint under tensionshear. J Adhes 1990; 10(2):81–9. Harris AF, Beevers A. Grit blasting of surfaces for adhesive bonding. Conference and Proceedings of Structural Adhesives in Engineering V. Bristol: Institute of Materials; 1998. Sancaktar E, Gomatam R. A study on the effects of surface roughness on the strength of single lap joints. J Adhes Sci Technol 2001;15(1):97–117. Shahid M, Hashim SA. Cleavage strength of steel/composite cleavage joints. J Adhes 2000;73:365–84. Sykes JM. Surface treatments for steel. In: Brewis DM, editor. Surface Analysis and Pretreatment of Plastics and Metals. London: Applied Science Publishers; 1982. p. 153–74. 116 A. Baldan / International Journal of Adhesion & Adhesives 38 (2012) 95–116  De Bruyne NA. Aero Research Technical Notes. Bulletin no. 168. Cambridge: Aero Research Ltd.; 1958.  Packham DE. Roughness of surfaces. In: Packham DE, editor. Handbook of Adhesion. New York: Longman Group (FE) Ltd.; 1992.  Wenzel RN. Ind Eng Chem 1936;28:988.  Shuttleworth R, Bailey GL. Discuss Faraday Sot 1948;3:16.  Johnson Jr. RE, Dettre RH. Surf Colloid Sci 1969;2:85.  Cassie ABD, Baxter S. Trans Faraday Sot 1944;40:546.  Cassie ABD. Discuss Fradq Sot 1948;3:11.  Drelich J, Wilbur JL, Miller JD, Whitesides GM. Langmuir 1996;12:1913.  Mori N, Ukita M, Ohgi K. J Jpn Inst Metals 1991;55:820.  Hitchcock SJ, Carroll NT, Nicholas MG. Some effects of substrate roughness on wettability. J Mater Sci 1981;16:714–32.  Kawai A, Nagata H. Jpn J Appl Phys 1994;33(Pt. 2, No. 9A):L1283.  Nakae H, Inup R, Hirata Y, Saito H. Effects of surface roundness on wettability. Acta Mater 1998;46(7):2313–8.  Weast RC. Handbook of Chemistry and Physics, vol. 69. Florida: CRC Press; 1988–1989.  Pugh B. Friction and Wear. London: Newnes-Butterworths; 1973.  Johnson RE Jr., Dettre RN. In: Contact angle, wettability and adhesion. Adv Chem Ser 43, p. 112. American Chemical Society,Washington, DC (1964).  Bussher HJ, van Pelt AWJ, De Boer P, De Jong HP, Arends J. Colloids Surf 1984;9:319.  ISO 4287. Help ﬁle of Ultra Software. Taylor and Hobson, 1984.  Harris AF, Beevers A. Grit blasting of surfaces for adhesive bonding. Int J Adhes Adhes 1999;19:445–52.  Thery S, Legros A, Balladon P. Study of parameters inﬂuencing the mechanical behaviour of and damage to steel polymer interfaces. In: Baptiste D, editor. Mechanics and mechanisms of damage in composites and multimaterials, ESIS11. London: Mechanical Engineering Publications; 1991. p. 339–50.  De Bruyne NA. J Appl Chem 1956;6:303.  Khrulev VM. Mekh Polim 1965;6:103.  Arrowsmith DJ. Trans Inst Met Finish 1970;48:88.  Keisler C, Lataillade JL. J Adhes Sci Technol 1995;9:395.  Harkins WD. Z Phys Chem 1928;139:647.  Nie HY, Walzak MJ, Berno B, McIntyre NS. Appl Surf Sci 1999;145:627.  Nie HY, Walzak MJ, Berno B, McIntyre NS. Langmuir 1999;15:6484.  Garbassi F, Morra M, Occhiello E. Polymer Surfaces: from Physics to Technology. Chichester: Wiley; 1994.  Garbassi F, Morra M, Occhiello E. Polymer Surfaces from Physics to Technology. New York: Wiley; 1998.  Jokl ML, Vitek V, McMahon CJ. Acta Metal 1980;28:1479.  Andrews EH, Kinloch AJ. Mechanics of adhesive failure I. Proc R Soc London 1973;A332:385.  Andrews EH, Kinloch AJ. Mechanics of adhesive failure II. Proc R Soc London 1973;A332:401–14.  Grifﬁth AA. Philos Trans R Soc London 1920;A221:163.  Orowan E. Trans Isnt Eng Shipbuilders Scot 1945;89:89.  Furuya A, Hosoi N, Ohshita YJ. Appl Phys 1995;78:5989.  Gent AN, Schultz J. J Adhes 1972;3:281–94.  Maugis D, Barquins M. J Appl Phys D 1978;11:1989–2023.  Chun H, Gent AN. J Polym Sci Part B: Polym Phys 1996;34:2223–9.  Guillemenet J, Bistac S. Crack propagation in adhesively bonded steel assemblies. Int J Adhes Adhes 2001;21:77–83.  Rice JR In: Yokobori T, Kawasaki T, Swedlow JL, editors. Proceedings of the 1st International Conference on Fracture, Sendai, Japan; 1966:309.  Lipkin DM, Beltz GE. Acta Mater 1996;44:1287.  Lipkin DM, Clarke DR, Beltz GE. Acta Mater 1996;44:4051.  Gent AN, Kinloch AJ. J Polym Sci 1971;9(A29):659–98.  Hutchinson JW, Suo Z. Mixed mode cracking in layered materials. Adv Appl Math 1992;29:63–191.  Blackman BRK, Kinloch AJ. Determination of the mode I adhesive fracture energy, GIc of structural adhesives using the double cantilever beam (DCB) and the tapered double cantilever beam (TDCB) specimens. ESIS TC4 Protoc 2000.  Liechti KM, Chai YS. J Appl Mech 1992;59:295.  Cao HC, Evans AG. Mech Mater 1989;7:295.  Wang JS, Suo Z. Acta Metall Mater 1990;38:1279.  Jensen HM, Thouless MD. Int J Solids Struct 1993;30:779.  Dundurs J. J Appl Mech 1965;32:400.  Lees, WA. Adhesives in Engineering Design (The Design Council, 1984.  Harris, AF and Beevers, A. In: Proc. Structural Adhesives in Engineering V Conf (Institute of Materials, Bristol, 1998).  SHARPE LOUISH. J Adhes 1998;67:277–89.  Adhesion and adhesives Technology, by Alphonsus V. Pocius, Second Edition, by Hanser, 2002.  Shanahan MER, Caree A. Langmuir 1995;11:1396–402.  Kendall K. Molecular adhesion and its application. Kluwer Academic/ Plenum Publishers; 2001 p. 46.  Boxin Zhao, Kwon Hyock Ju. J Adhes Sci Technol 2011;25:557–79.  Israelachvili JN. Intermolecular and surface forces. London: Elsevier; 1992 pp. 201–4.  Sharpe Louis H. The interphase in adhesion. J Adhes 1972;4:51–64.  Possat Wulff, editor. Adhesion: current and applications, WileyVCH, editor 2005.  Gay Cyprien. Biofouling, Vol 19. Taylor and Francis; 2003 (Supplement), pp 53–57.  Israelachvili J. Intermolecular and surface forces. 2nd ed. London & New York: Academic Press; 1992.  Gent AN, Schultz J. Effect of wetting liquids on the strength of adhesion of viscoelatic materials. J Adhes 1972;3:281–94.  Raphael E, de Gennes P-G. Rubber–rubber adhesion with connector molecules. J Phys Chem 1992;96:4002–7.  Lake GJ, Thomas AG. The strength of highly elastic materials. Proc R Soc London, Ser A 1967;300:108–15.  Greenwood JA, Williamson JBP. Contact of nominally ﬂat surfaces. Proc R Soc London, Ser A 1966;295:300–19.  Gay C, Leibler L. Theory of tackiness. Phys Rev Lett 1999;82:936–9.  Komvopoulos K. J Adhes Sci Technol 2003;17:477–517.  Wool RP. C R Chimie 2006;9:25.  Brovko O, Rosso P, Friedrich K. J Mater Sci Lett 2002;21:305.  Jones R, Pollock HM, Cleaver JAS, Hodges CS. Langmuir 2002;18:8045–55.  Basin VE. Prog Org Coat 1984;12:213–50.  Court RS, Sutcliffe MPF, Tavakoli SM. Int J Adhes Adhes 2001;21:455–63.  Tanahashi M, Yao T, Kokubo T, Minoda M, Miyamoto T, Nakamura T, et al. J Mater Sci: Mater. Med 1995;6:319.