International Journal of Adhesion & Adhesives 38 (2012) 95–116
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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
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E-mail address: abaldan@mersin.edu.tr
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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 [1] 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 [2].
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 [3]. As Kinloch
pointed out [3], 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
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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., [4]). 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 [5]. 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 [13]. 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 [5].
Adhesion can be improved by a number of ways including [5]:
(a) adding an adhesion promoter such as a chlorinated polyolefin
(CPO) [14], (b) flame surface pretreating the polypropylene
compounds [13], (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
[2]. As Awaja et al. [5] 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
[31]. 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. [31], 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., [32]). 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
[33]. 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 [34]. 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 [35], 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 [36]. 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. [36], 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 [41], 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 [47].
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., [5]). 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 [53]. 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 [5].
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 [49]. 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 [5]. 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 [67]. 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]).
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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 [70]. 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 [72] in the past had some
criticism the weak boundary layers model explains some cases of
poor adhesion. Fourche [1] 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 [55].
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 [67]. 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 [69]. 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 [55]
suggested, three types of irregularities are possible (see Fig. 2),
although only type b may form mechanical interlocking [55]. 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 [5].
Fig. 3. (a) Sufficient wetting and (b) poor wetting (after Fourche [1]).
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. [71] 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 [71].
3.2. Adsorption theory
The adsorption theory is the most generally accepted model; it
was introduced by Sharpe and Schonhorn [74]. 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 [71].
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 [77].
3.3. Diffusion or interdiffusion theory [71,69]
The diffusion theory was proposed by Voyutski [78], 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 [10].
The diffusion theory states that adhesion of two macromolecules in intimate contact results from the interdiffiusion of the
molecules of the superficial layers [69]. 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 [69]:
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) [1].
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 [72]:
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 [78].
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 [81] 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 [82] and later extended by
several authors (i.e., [83,84]). As Maeva et al. pointed out in their
work [71], 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) [72]
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 [81] 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. [71] 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 [71]. 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.
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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 [60].
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 [69]. 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 [5]. 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 [77].
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 [88] 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 [69].
Fig. 6. Seven classifications of weak boundary layers [88].
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 [69].
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 [5]. 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) [92]. 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 [60].
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 [92]. 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 [93]. 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 [94]. A film of oxide or of organic contamination may greatly reduce the adhesion performance of the adhesive
joints [54].
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 [94].
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. [111] 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 [115]. 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 [115]. 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 [3]. Therefore, Kinloch [3] 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 [118], 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 [122] 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 [119]. This same approach is routinely
used to describe morphologies where intersections of solid–solid
interfaces occur, e.g., a solid island on a substrate [119]. Contact
angle distribution may be obtained from the SEM or AFM image
analysis [124]. 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 [119].
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 [125] 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 [125]. 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 [118]. 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 [131].
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 [132] 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. [133], 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 [134], 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 [135] 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 [47]. 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. [47] 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 [136].
In order to calculate the surface free energy of substrate, Deshmukh
et al. [47] have used the three liquids of known polar and disperse
components and are given in Table 1 [47].
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. [47]).
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) [141].
Fig. 10. A plot of Fowkes equation to determine the surface free energy from the
polar and disperse components [47].
cohesive [118]. These are defined as follows [131]:
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., [137]). 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 [138] 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., [139]). (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 [134] 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 [5].
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 [5]. 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 [143]. 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 [144]. 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., [71]): (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., [71]) 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 [74] 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, [131] 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 [148], (c) the Owens–Wendt method
[149], (d) a method proposed by Schultz [150], (e) Good and van
Oss approach [151], (f) Fowkes and co-workers [136,152,153] and
Owens and Wendt [154] 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 [118]. 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 [118]. 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 [118].
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., [118]):
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
[71]. 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 [149] 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 [5].
However, for simple systems its application can provide useful
approximations [29].
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 [154] 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 [154], Kaelble and Uy [164] 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 [151] 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
[167] 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 [141].
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 [168] 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 [168].
Zisman plot [148], and the Owens–Wendt [149] methods can be
used to evaluate the wettability of the differently treated surfaces.
Zisman [148] 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 [141].
Mirabedini et al. [141] 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 [168].
Fig. 14. Critical surface free energy gc of microwave-treated PP surface in the
presence of 0.4 mol/l KMnO4 Zisman method [141].
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
[170]. 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 [141].
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 [167] 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 [171]. A number of
Fig. 15. Variation of surface free energy of microwave irradiated (MV) and
conventional treated samples with exposure time [141].
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 [167].
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 [179]. 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 [179]. The surface free energy
and fundamental wetting characteristics also affect the strength
and stability of adhesion.
As Sancaktar and Gomatam [179] 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 [25]. As
Shahid and Hashim pointed out [171], 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 [178]. For example, an earlier work on steel cleavage
specimens showed the effectiveness of grit-blasting over diamond
polishing in achieving improved cleavage strength [180].
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 [181]. 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 [171].
However, the actual microscopic distribution of stress at the
rough interface is complex.
Bikerman [88] 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 [187] 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 [190], 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. [193] 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 [184]. 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 [66]. 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 [194].
Not only the average roughness, but also the geometry of the
adherend surface topographies is expected to affect the resulting
joint strength [179]. For example, Pugh [195] showed five different
surface profiles, all with the same roughness values but different
topographies. Johnson and Dettre [196] 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 [66] can be calculated as r ¼(5)1/2. This
theory is offered mostly for polycrystalline substrates [179]. 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 [194]. Sancaktar and Gomatam [179] 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 [184] 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 [187] 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 [68]. 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 [68]. 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 [125] 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., [179]):
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 [179].
Shahid and Hashim [171] 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 [181]. 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 [171] 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 [199], Thery et al. [200] and
Critchlow and Brewis [172] 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 [171]. 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 [178] and to inherent drawbacks of surface roughness,
such as void formations and reduced wetting [191].
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 [201] 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 [179].
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 [179] 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 [202] 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 ([198]).
Fig. 19. Graphical representation of Rdq [198].
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 [179]. 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 [203] 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 [204] 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 [171].
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 [3]. 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 [3].
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 [31]:
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 [205].
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 [209] [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 [31]. What is
measured is the practical work of adhesion Wap, or interfacial
toughness [31]:
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 [210] and in many
cases Ufric(Wa) will be as well.
As pointed out by Kinloch [3], 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 [213], 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 [214], 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 [31]. 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., [71]). 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 [71].
In addition to the other factors, the rate of seperation, time and
temperature of dissipation are the factors affecting the the adhesion
(i.e., [216]). 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 [219].
The dependence of the failure energy G on the separation rate V has
been initially proposed by Gent and Schultz with the following
expression [216]:
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 [118]:
Barquins [217] 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
[219]. 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 [219].
Guillemenet and Bistac [219] 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 [219]. 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)) [31]. 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 [118]. However,
as Packham [118] 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
[118]:
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 [31]
@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 [224]. There are results
Fig. 22. Evolution of the adherence energy G as a function of the wedge introduction speed [219].
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
[224]:
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 [224]:
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 [31].
Fig. 24. Phenomenological functions for GðcÞ [31]
113
bimaterial real constant:
e ¼ ð1=2pÞln½ð1bÞ=ð1 þ bÞ
ð57Þ
The Dundurs parameters a and b for plane strain are [230]:
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 [31].
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
[224]. 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
[233]. 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 [234]. 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) [235].
The molecular origin of the work of adhesion are the intermolecular attractive interactions [236]. 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 [237]. 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 [238], 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 [239]. 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 [240]. 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 [241]. On the molecular scale, it results generically
from van der Waals interactions [242]. Surface chemical bonds
[243], macromolecular interdigitation [244] or macromolecule
elongation [245], 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 [246] 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 [247].
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 [5]:
(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.
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