Surfaces, chemistry applications

ADHESION SCIENCE

URFACES,
CHEMISTRY
PLICATIONS

Edited by M. Chaudhary and A X Fb&s


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ADHESION SCIENCE AND ENGINEERING - 2

Series Editor

A.V. Pocius

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The cover displays a micrograph of glass particles on a plasticized polystyrene substrate showing
adhesion-induced viscous flow of the substrate and encapsulation of the particle. The crater is the
deformed substrate after a particle had been removed. The micrograph was taken by Ray Bowen
and was supplied by Dr. Donald Rimai.

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ADHESION SCIENCE AND ENGINEERING - 2

SURFACES, CHEMISTRY AND
APPLICATIONS
Edited by
M. Chaudhury
Department of Chemical Engineering
Centerfor Polymer Inter$aces
Leh igh University
111 Research Drive
Bethlehem, PA I81 05
U.S.A.

A.V. Pocius
3M Adhesive Technologies Center
3M Centei; Building 201 -4N-01
St. Paul, MN 55144-1000
U.S.A.

2002

ELSEVIER
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Preface
Volume I of Adhesion Science and Engineering dealt with the mechanics of
adhesive bonds and the rheology of adhesives. Volume I1 deals with the other two
disciplines that make up adhesion science, surfaces and chemistry. In addition,
this volume describes several applications of adhesion science and engineering.
The volume begins with discussions of aspects of surface science and how they
relate to adhesion science. Methods based on surface thermodynamics have been
powerful tools in the hands of adhesion scientists. Berg introduces us to the topics
of interfacial thermodynamic and practical adhesion and shows how the critical
predictive parameters of adhesion can be obtained from wetting, solution theory and

group contribution methods (UNIFAC). It becomes clear from Berg’s presentation
that the predictions of adhesion strengths by the traditional wet chemical methods
are somewhat empirical. This limitation can be partially overcome by the methods
of contact mechanics as pioneered by Johnson, Kendall and Roberts, which allows
direct measurements of the surface energies of deformable solids. These methods,
as shown by Mangipudi and Falsafi, have played a very important role in developing
a deeper understanding of the relationship between adhesion and the chemical
composition of surfaces and complement the chapters describing contact mechanics
found in Volume I. Rimai and Quesnel extend this discussion to the interaction
of powdered solids and give us an in-depth view of the types of intermolecular
forces that control adhesion of solid surfaces. The chapter by Wahl and Syed Asif
explores the behavior of adhesion and contact mechanics at the nanoscopic level.
This chapter not only complements the above three but also describes additional
techniques that may be used to probe the properties of surfaces. Surface roughness,
which could be examined by some of the probe techniques described in Chapter 4,
is discussed by Packham. Spectroscopic techniques useful for examination of the
chemistry of surface and interfaces are described by Boerio (Chapter 6).
Other aspects of interfacial science and chemistry are examined by Owen and
Wool. The former chapter deals with a widely used chemistry to join disparate surfaces, that of silane coupling agents. The latter chapter describes the phenomenon
of diffusion at interfaces, which, when it occurs, can yield strong and durable
adhesive bonds. Brown’s chapter describes the micromechanics at the interface
when certain types of diffusive adhesive bonds are broken. The section on surfaces
ends with Dillingham’s discussion of what can be done to prime surfaces for
adhesive bonding.
The section on chemistry of adhesives evolves from rubber-based adhesives to
semi- structural and finally to structural adhesives. Everaerts and Clemens provide
a thorough description of chemistry and applications of pressure sensitive adhesives and Kinning and Schneider describe an enabling technology for pressure

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vi

Preface

sensitive adhesive tapes, release coatings. Martin-Martinez reviews the chemistry
and physical properties of rubber-based adhesives with an emphasis on the materials properties of the components of those adhesives. Silicone chemistry provides
products that range from pressure sensitive adhesives to sealants to semi-structural
adhesives and is described by Parbhoo et al. in Chapter 14. Progressing into
more semi-structural and structural adhesives, the chapters by Paul and by Frisch
describe the chemistry and properties of hot melt adhesives and polyurethane adhesives, respectively. The remainder of this section deals with structural adhesives
beginning with discussions of acrylate chemistry by Righettini and then Klemarczyk. The adhesives described in these two chapters are some of the most easy
to use structural adhesives available. One of the oldest technologies in modern
adhesive chemistry, phenolic chemistry is described by Detlefson and one of the
newer chemistries, bismaleimides is discussed by Kajiyama.
The final section in this volume deals with applications of adhesion science.
The applications described include methods by which durable adhesive bonds
can be manufactured by the use of appropriate surface preparation (Davis and
Venables) to unique methods for composite repair (Lopata et al.) Adhesive
applications find their way into the generation of wood products (Dunky and
Pizzi) and also find their way into the construction of commercial and military
aircraft (Pate). The chapter by Spotnitz et al. shows that adhesion science finds its
way into the life sciences in their discussion of tissue adhesives.
The editors wish to express their sincere thanks to the contributing authors for
their invaluable contributions to this volume. Their collective expertise represents
many years of industrial and academic experience in the field of Adhesion Science and Engineering. We would also like to thank the employers of each of the
contributors for allowing them to take on the extra tasks associated with the completion of their contribution to this volume. We would also like to acknowledge
the contribution of Mr. Theodore Reinhart of the University of Dayton Research
Center to the initial organization of this volume. An unfortunate illness prevented
him from completing his work on this project. Assistance from the Department of

Chemical Engineering and the NSF sponsored IUCRC of the Polymer Interface
Center at Lehigh University are gratefully acknowledged. Finally, we thank our
spouses for their patience as we compiled and edited this volume.
ALPHONSUS
V. POCIUS
Editor

MANOJCHAUDHURY
Associate Editor

Corporate Scientisl
3M Company
St. Paul, MN, USA

Professor of Chemical Engineering
Directol; Centerfor Polymer Interjkes
Lehigh University
Bethlehem, PA, USA

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Contents
Preface

..................................................................

v

Surface Science

Chapter 1. Semi-empirical strategies for predicting adhesion
J.C. Berg ....................................................

1

Chapter 2. Direct estimation of the adhesion of solid polymers
KS, Mangipudi and A. Faha$. ................................

75

Chapter 3. Particle adhesion
D.S. Rimai and D.J. Quesnel.. ................................

139

Chapter 4. Surface mechanical measurements at the nanoscale
K.J. Wahl and S A . Syed Asif. .................................

193

Chapter 5. Micro-mechanical processes in adhesion and fracture
H.R. Brown.. ................................................

221

Chapter 6 . Surface analysis in adhesion science
EJ. Boerio.. .................................................

243

Chapter 7. Surface roughness and adhesion
D. E. Packham. ...............................................

3 17

Chapter 8. Diffusion and autohesion
R.P. Wool.. ..................................................

351

Chapter 9. Coupling agents: chemical bonding at interfaces
M.J. O w e n . ..................................................

403

Chapter 10. Priming to improve adhesion
G. Uillingham ...............................................

433

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Contents

viii

Chemistry
Chapter 11. Pressure sensitive adhesives
A.I. Everaerts and L.M. Clemens ..............................

465

Chapter 2. Release coatings for pressure sensitive adhesives
D.J. Kinning and H.M. Schneider .............................

535

Chapter 3. Rubber base adhesives
J.M. Martin-Martinez ........................................

573

Chapter 14. Fundamental aspects of adhesion technology in silicones
B. Parbhoo, L.-A. O’Hare and S.R. Leadley ....................

677

Chapter 15. Hot melt adhesives
C.W P a u l . . ..................................................

711

Chapter 16. Chemistry and technology of polyurethane adhesives
K.C. Frisch, Jr. ...............................................

759

Chapter 17. The chemistry of bis-maleimides used in adhesives
M. Kajiyama.. ...............................................

813

Chapter 18. Structural acrylics
R.E Righettini ...............................................

823

Chapter 19. Cyanoacrylate instant adhesives
P. Klemarczyk.. ..............................................

847

Chapter 20. Phenolic resins: some chemistry, technology, and history
W D . Detlefsen ...............................................

869

Applications
Chapter 21. Surface treatments of metal adherends
G.D. Davis and J.D. Venables.................................

947

Chapter 22. Electron beam processed adhesives and their use in composite
repair
VJ. Lopata, A. Puzianowski and M.A. Johnson.. ............... 1009

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ix

Contents

Chapter 23. Wood adhesives
M . Dunky and A . Pizzi ........................................

1039

Chapter 24 . Tissue adhesives and hemostats: new tools for the surgeon
W D. Spotnitz. D . Mercer and S. Burks ........................

1105

Chapter 25 . Applications of adhesives in aerospace
K.D. Pate ....................................................

1129

Author Index .............................................................

1193

Subject Index .............................................................

1195

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Chapter 1

Semi-empirical strategies for predicting
adhesion
JOHN C . BERG‘
Department of Chemical Engineering, University of Washington, Seattle, WA 98105-1750, USA

1. Predicting adhesion: is it a reasonable objective?
1.1. The scope of the question
1.1.1. The meaning of adhesion, adhesive failure arid iriterjkiul strength
Adhesion refers to a complicated set of inter-connected phenomena that is far from
completely understood, and it therefore makes sense at the outset to inquire into
the reasonableness of any attempts to ‘predict’ it using semi-empirical methods.
To preserve the hope of a positive answer, it is first necessary to narrow the scope
of the question. There may be ambiguity with respect to what is to be predicted. It
may refer, on one hand, to the strength of an isolated adhesive joint as determined
by some carefully crafted mechanical test in which the joint is destroyed, or it
may, on the other hand, refer to the strength of a more complex global structure,
such as a multi-layer laminate, or a fiber-reinforced or particle-filled composite.
The present chapter focuses mainly on the individual adhesive joint rather than
on global structures in which interfaces exist. Even when attention is focused on
single joints, it must be noted that these may be stressed to failure in different
modes and at different rates, leading to different results. In fact, understanding of
the different interfacial rate processes involved in adhesion is just beginning to
emerge [I].
Another distinction to be made is illustrated with the peel test shown in Fig. 1.

Application of stress may cause the joint to fail either ‘adhesively’ or ‘cohesively’.
Adhesive failure, shown in Fig. la, is thought ideally to correspond to a perfect

* Corresponding author. E-mail: berg @cheme.washington.edu

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2

J.C. Berg

/

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.

A

adhesive failure

cohesive failure

(4

(b)

Fig. 1. (a) Adhesive vs. cohesive failure. (b) Close-up view of adhesive failure in the presence of
an ‘interphase.’ The locus of failure may be adjacent to or within the interphase (as shown), and
particles of material may be ejected during the debonding process.

separation of the two phases meeting at the interface. Sharpe [2] has argued
persuasively, however, that such ‘adhesive’ or ‘interfacial’ failure almost never
occurs in practice. Owing to the geometric complexity of any real interface at the
microscopic level, it would be highly unlikely for the system to disjoin precisely
along its contours. One would expect instead to find at least fragments of the
opposing material on each of the separated surfaces, and indeed some of the
material may be ejected and lost as microparticles during the disjoining process
[3]. Furthermore, Sharpe argues that true interfaces, in the mathematical sense,
dividing phases which are homogeneous right up to the interfaces, almost never

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Semi-empirical strategies for predicting adhesion

3

exist between joined solid phases. Instead there is generally a transition zone
of finite thickness, perhaps as thin as 1 nm, but possibly as thick as several
micrometers, separating the bulk phases. Called interphases, they may be caused
by the interdiffusion or interdigitation of the materials, or they may be simply
the result of structuring of the adhesive layer adjacent to the interface due to the
asymmetric molecular forces existing at the boundary between the phases. Such
an ‘interphase’ has a structure, and possibly a composition, distinct from that of
either of the bulk phases. Recognizing the ubiquitous presence of interphases, the
following definition of terms will be used in this chapter: when the locus of failure
occurs within or immediately adjacent to the interphase, it will be referred to as
‘adhesive’ or ‘interfacial’ failure, as shown in Fig. lb. The word ‘interface’ is thus
used loosely in that it may be referring to an interphase. When failure of the joint
occurs in material outside the interphase, i.e. in one of the bulk phases, it will
be designated as ‘cohesive’ failure. Even with this distinction having been made,
some cases involve a mixture of adhesive and cohesive failure. The design or
choice of a structural adhesive thus may depend on both high interfacial strength
and high cohesive strength of the adhesive. The present chapter concerns adhesive
failure, and therefore focuses on ‘interfacial strength’ in accord with the above
definition.
It must also be recognized that adhesive interfaces are not static entities, but
may deteriorate or even strengthen over time, and often it is the time course
of interfacial strength or durability under different conditions and in different
environments that is of greatest concern [4].As important as durability issues are,

they too will not be a direct concern of this chapter.
It remains to be determined if even the more modest scope suggested above may
profitably be pursued. To address this question, we note that ‘adhesive interfaces’
refer to those dividing solid phases across which intermolecular forces are engaged
over all or a significant portion of the interfacial area. With the exception of clean,
atomically smooth solid surfaces (as might be obtained when Moscovite mica is
freshly cleaved in vacuo), this cannot be achieved by simply bringing two solid
surfaces together. Their inherent roughness and contaminability prevent it. Thus
at least one of the phases must be a liquid (or a polymer sufficiently above its
glass transition temperature to be fluid-like) when the two materials are brought
together to form the interface. The ‘liquid’ phase is designated as the adhesive,
and the solid surface to which it is applied is the adherend. The adhesive interface
is finally formed when the adhesive ‘cures’. In most cases, curing results in
solidification of the adhesive, although pressure sensitive adhesives may remain
in a viscoelastic state. In most cases, solidification results in the development
of significant internal residual stresses at the interface owing to the mismatch in
thermo-mechanical properties of the adhesive and adherend [5,6].In some cases,
these are great enough to cause interfacial failure without the application of any
external stress at all. In any event, the presence and magnitude of internal residual

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J.C. Berg

4

stresses must be taken into account in the analysis of the results of mechanical
measurements of interfacial strength. Residual stresses do not directly influence
the intrinsic interfacial strength, but instead contribute to the total of the stresses

existing at an interface in a mechanical test.
In a mechanical test, interfacial strength may be quantified in terms of either the
minimum load required for interface disruption or the total integral energy or work
expended. In many situations, due to non-uniformity of chemical or morphological
conditions over the area of the interface or to non-uniformity of the applied stress
in a given test [7], the two criteria are different. The investigator must thus strive to
minimize or deal with both of the above complications, i.e. the interfaces studied
should be chemically and morphologically uniform, and the stresses applied in the
test should be uniform or distributed in way which is quantitatively describable.

1.1.2. Optimizing adhesion
The adhesion scientist or technologist has two general variables at his or her
disposal in seeking to increase or control adhesive interfacial strength: (1) the
chemical formulation of the adhesive; and (2) the chemistry and morphology of
the adherend surface. The adhesive may be chosen, for example, to be made up of
species capable only of Lifshitz-van der Waals (LW) intermolecular interactions
(referring to predominantly dispersion or London’s forces, but also including a
possible small contribution to permanent dipole interactions), or it may be made
to be acidic or basic, or acid-base bifunctional, or it may be designed to interact
covalently with the adherend (reactive adhesion). Its surface tension may be
lowered or its viscosity altered through the use of additives. Most adhesives are
polymeric, and for a given chemistry of the repeat unit, the molecular weight
and the structure (linear vs. branched, etc.) may be important. Thermosetting
adhesives (e.g. epoxies, polyurethanes, bis-maleimides, etc.) are designed to
crosslink internally, leading to enhanced cohesive strength (outside the scope of
the present discussion), but may also produce covalent bonding with the adherend
across the interface [8]. The morphology of the adherend surface may be altered
by roughening or texturizing (e.g. acid-etching, grit-blasting, anodization, etc.),
and its chemistry may be altered through plasma treatment, corona treatment,
etc. or the use of finishes, conversion coatings, primers or coupling agents, either

physically adsorbed, coated onto or covalently bonded to the surface.
It is only in the context of the systematic variation of the properties of the
adhesive and/or the adherend surface in a set of otherwise identical specimens
subjected to a given mechanical testing procedure that it is reasonable to think of
predicting relative interfacial strength.
In the above narrowed context, ‘prediction’ refers to the development of system
descriptors which can be measured independently in some rather simple and
inexpensive way (in terms of time and instrumentation), or it may refer to ab

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Semi-empirical strategies for predicting adhesion

5

initio calculations based on readily available handbook data and requiring no
experimental measurements at all. Both approaches are examined in this chapter.
The objective may be to screen candidate adhesive formulations and/or adherend
surface treatments for the purpose of eliminating unpromising candidates for what
is generally tedious and costly mechanical testing. The results of such attempts
may vary from the formulation of simplistic, but nonetheless useful, ‘rules of
thumb’, to more sophisticated optimization schemes. Such guidelines may be
useful even when all of the above-mentioned caveats are not observed.

1.2. ‘Practical’ vs. ‘ideal’ adhesion

I .2.I . Practical adhesion
The measure of adhesive interfacial strength is the result of a properly conducted
mechanical test which leads to a predominantly adhesive failure of the specimen.

This leads to a measure of what is termed ‘mechanical’, or ‘practical’ adhesion.
Many different such tests are described in detail elsewhere in this text series, as
well as in standard texts on adhesion [9-111. As noted above, however, even for a
given material interface, different tests carried out under the same thermodynamic
conditions, or the same test carried out at different rates (normalized in accord
with WLF theory, described elsewhere in this text series), will in general lead to
different values for the failure stress or for the energy per unit area required to
disjoin the interface. The recent emergence of the method of ‘contact mechanics’,
reviewed recently by Chaudhury [ 121, permits the quantitative mechanical determination, under idealized circumstances, of both the energy required to separate
t :o surfaces as well as the energy gained by adjoining them, and the results
indicate that there is a sizable difference between the two (‘adhesion hysteresis’)
[I 31. Thus any valid comparisons of practical adhesion between material systems
whose properties are varied as suggested above must pertain to the same test,
carried out under the same conditions at the same normalized rate. Even when
these requirements are stringently met, the results may show significant variation,
as has been demonstrated in a round-robin program in 1993 involving 12 different laboratories measuring the interfacial shear strength of the same fiber/matrix
interface with the same set of techniques [14]. Fig. 2 shows the results of this
effort, revealing variations within any given test method of approximately a factor
of two amongst the different laboratories. Thus the objective of predictions must
be recognized as a somewhat blurred target, although it may be hoped that results
for practical adhesion obtained in any given laboratory for a series of properly
conducted tests may be validly compared.

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J.C. Berg

6
120.0

h

B

100.0

80.0

60.0
40.0
20.0

-

I

I

I

I

I

I

I

I

I

I

Fragmentation
Indentation
A

A

-

* *

A

0

1

.

0

0

-

-

m

A

1

0.0

I

4)

-

1

1

1

1

1

1

1

1

1

n

Fragmentation
Indentation

W

2

80.0

c
(

cd

.d

%8

4

,

0.0

0

1

;

2

I

3

,

4

,

5

6

I

,

I

I

7

8

9 1 0 1 1 1 2

Laboratory

co)

Fig. 2. Results of interfacial shear strength measurements of the same fiberlmatrix systems
using four different micro-mechanical tests during a round-robin program involving 12 different
laboratories. (a) Results for untreated, unsized carbon fibers. (b) Results for carbon fibers with the
standard level of surface treatment. Redrawn from ref. [13].

1.2.2. Ideal adhesion
Most of the various strategies which have been proposed to ‘predict’ relative
adhesive interfacial strength are based on thermodynamics. One may define,
without ambiguity, as shown in Fig. 3, a thermodynamic ‘work of adhesion’, W,,

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-

7

Semi-empirical strategies for predicting adhesion

W, = reversible work
= Ys + "h - YSL

interface
of unit area

WA

=

vacuum
S (adherend)

YSm + It"- YSL

fluid medium m

W, = ys + yL - ysL- 'IC,

>

air + vapors of adhesive

(c)
Fig. 3. Definition of thermodynamic work of adhesion, WA: (a) disjoining surfaces in vacuum;
(b) disjoining surfaces in fluid medium m; and (c) disjoining surfaces in presence of vapors from
adhesive.

as the reversible work required to perfectly disjoin a unit area of interface between
an adherend S (solid) and adhesive L (liquid) in some fluid medium m, as given by
the Dupr6 equation:

where y r is the surface or interfacial tension of the adhesive (liquid) in the fluid

medium m. Y," is the interfacial free energy/area of the adherend (solid)/medium

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J.C. Berg

8

interface, and y s ~is the interfacial free energy/area of the adhesive/adherend
interface. WA is thus the free energy/area of the surfaces created minus that of the
interface destroyed in the disjoining event. This is equivalent to the negative free
energy change associated with the contacting event, that is, WA = -AGEadheaion.
It
is seen to depend not only upon the adhesive and the adherend, but also upon the
fluid medium in which the system resides. It is usually assumed that this medium
is air, whose components are assumed to adsorb but negligibly on the surfaces of
either the adhesive or the adherend. While this is generally true, complications
arise when the air contains water vapor or when the adhesive is volatile, and
its vapors adsorb onto the otherwise dry adherend. Water vapor may adsorb to
the adherend surface reducing its energy, so that any accounting of such energy
must take this into consideration.Any adsorption of vapors from the adhesive also
reduces the surface energy of the adsorbent, by an amount at equilibrium termed
the equilibrium spreading pressure, ne,so that the Dupr6 equation becomes:
WA = )/s

+ YL - YSL - ne.

(2)

It is common to neglect the effect of equilibrium spreading pressure, particularly
for ‘low surface energy’ adsorbents [15,16], but there is some evidence that it
may not be negligible even under such circumstances [17,18]. It can certainly
be neglected for polymeric liquids, owing to their non-volatility. Whether ne is
taken into account or not, the work of adhesion is thought to be a measure of the
‘thermodynamic’ or ‘ideal’ adhesion for a given adhesive/adherend system. One
must next inquire: (1) whether WA is conveniently measured; and (2) if it relates
in any meaningful way to practical adhesion, defined earlier.
While the surface tension of the adhesive, n,is easily measured in the
laboratory, the other terms in WA, by themselves, are not. A second easily
measurable property associated with the solid-liquid-air system, however, is the
contact angle, 8 , the angle, drawn in the liquid, between the solid-liquid and the
liquid-air interfaces, drawn in the plane perpendicular to the three-phase interline,
as shown in Fig. 4. Minimization of the free energy of the solid-liquid-air

Fig. 4. Definition of contact angle showing the derivation of Young’s equation, Eq. 3, using a
balance of horizontal forces at the three-phase interline.

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Semi-empiricul strategies for predicting adhesion

9

system with respect to 0 leads to a relationship between the contact angle and the
free energies of the interfaces meeting at the three-phase interline, viz. Young's
equation:
Ys - YSL
cos0 =

(3)

n

Eq. 3 may also be derived heuristically by making a balance of horizontal forces
on a small section of the interline as shown in Fig. 4. This treats the solid surface
and the solid-liquid interface as though they were in states of tension given by
their respective surface energies. The vertical force n sin0 in such a construction
is balanced by stresses in the underlying solid.
If equilibrium spreading pressure is to be included, it must be subtracted from
the right hand side of Eq. 3, i.e.
cos0 =

YS - Y S L

n

(34

-Ire.

Since -1 < cos0 < 1, Young's equation is valid only when the right hand side of
Erl 3 or Eq. 3a lies between these limits, i.e. the observed contact angle is finite.
In le event that the measured contact angle is O", i.e. full spreading occurs, one
may conclude only that
Ys - YSL
Ys - Y S L
or
-ne>l
(4)

VL

M.

Substitution of Eq. 3 into Eq. 1 leads to the Young-DuprC equation:

w,= n(1+cos@,

(5)

which suggests that thermodynamic adhesion is quantifiable in terms of the readily
measured values of VL and 0, at least for the situation in which the contact angle is
finite.
The technique of contact mechanics has also been applied to the direct mechanical determination of solid-fluid interfacial energies, and the results compare
favorably with those obtained by contact angle measurements [ 191.
If equilibrium spreading pressure is to be accounted for, it is added to the right
hand side of Eq. 5, giving:

w, = n(l+cosO)+ne.

(54

Determination of the equilibrium spreading pressure generally requires measurement and integration of the adsorption isotherm for the adhesive vapors on the
adherend from zero coverage to saturation, in accord with the Gibbs adsorption
equation [2O]:

0

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J.C. Berg

10

where r ( p ) is the adsorbed amount (moles/area) as a function of the adsorbate
partial pressure, p , and p s is the saturation value. The needed data are not so
easily obtained as those of contact angle and surface tension. A second difficulty
with using the Young-Dupr6 equation to estimate the work of adhesion is that it
presumes the use of an appropriate stable equilibrium contact angle. In practice,
one measures either an advancing angle or a receding angle, and the hysteresis
between them is significant. Both refer to metastable states [21]. It is common
practice to use the static advanced angle to compute the work of adhesion, but this
cannot be rigorously justified.
One may also be able to determine the work of adhesion for cases in which
the contact angle is zero by using probe liquids, as described later in this chapter.
There are also other ways of determining the work of adhesion, such as inverse gas
chromatography, which do not depend solely on capillary measurements (surface
tension and contact angle). This too will be discussed later.
1.2.3. The relationship between practical adhesion and the work of adhesion, W,
Assuming the work of adhesion to be measurable, one must next ask if it can be
related to practical adhesion. If so, it may be a useful predictor of adhesion. The
prospect at first looks bleak. The perfect disjoining of phases contemplated by Eq.
1 almost never occurs, and it takes no account of the existence of an ‘interphase’,
as discussed earlier. Nonetheless, modeling the complex real interphase as a true
mathematical interface has led to quantitative relationships between mechanical
quantities and the work of adhesion. For example, Cox [22] suggested a linear
relationship between WA and the interfacial shear strength, t, in a fiber-matrix
composite as follows:

where E, and Ef are the elastic moduli of the matrix and the fiber, respectively,
and h is a universal length ( ~ 0 . 5nm). This has led to a number of successful
interpretations of fiber fragmentation tests on these types of systems described
later.
The most-often cited theoretical underpinning for a relationship between practical adhesion energy and the work of adhesion is the generalized fracture mechanics theory of Gent and coworkers [23-251 and contributed to by Andrews and
Kinloch [26-291. This defines a linear relationship between the mechanical work
of separation, w,, and the thermodynamic work of adhesion:
= C(b,T,&)’wA,

(8)
where w, is the work of separation (per unit area) and C is the mechanical loss
factor, which accounts for the effects of geometry and rheology, and depends on
wm

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Semi-empirical strategies for predicting adhesion

11

the crack growth rate (a), temperature ( T ) and maximum strain level ( E ) . The
theory was developed for elastic adhesives against hard (brittle) solid adherends,
and is limited to slow (quasi-equilibrium) rates of detachment [7]. The format
of Eq. 8 has been corroborated with experiments in which only the work of
adhesion factor was changed. For example, Gent and Schultz [25] measured the
peel strength of a polybutadiene film on Mylar under a variety of solvent media
(air, water, butanol, etc.) and found it to vary in proportion to the work of adhesion
as computed using Eq. 1 with contact angle values evaluated in the solvent media.

Similar results have been found more recently for cases involving acid-base
effects [30].
Combination of Eq. 7 or Eq. 8 with the Young-Dupr6 equation, Eq. 3 , suggests
that the mechanical work of separation (and perhaps also the mechanical adhesive
interface strength) should be proportional to (1 cos6') in any series o f tests
where other factors are kept constant, and in which the contact angle is finite.
This has indeed often been found to be the case, as documented in an extensive
review by Mittal [31], from which a few results are shown in Fig. 5. Other
important studies have also shown a direct relationship between practical and
thermodynamic adhesion, but a discussion of these will be deferred until later.
It would appear that a useful criterion for maximizing practical adhesion would
be the maximization of the thermodynamic work of adhesion, but this turns
out to be a serious over-simplification. There are numerous instances in which
practical adhesion is found not to correlate with the work of adhesion at all, and
sometimes to correlate inversely with it. There are various explanations for such
discrepancies, as discussed below.

+

1.3. The mechanisms of adhesion

The above discussion has tacitly assumed that it is only molecular interactions
which lead to adhesion, and these have been assumed to occur across relatively
smooth interfaces between materials in intimate contact. As described in typical
textbooks, however, there are a number of disparate mechanisms that may be
responsible for adhesion [9-11,321. The list includes: (1) the adsorption mechanism; (2) the diffusion mechanism; (3) the mechanical interlocking mechanism;
and (4) the electrostatic mechanism. These are pictured schematically in Fig. 6 and
described briefly below, because the various semi-empirical prediction schemes
apply differently depending on which mechanisms are relevant in a given case.
Any given real case often entails a combination of mechanisms.

1.3.1. Adsorption mechanism (contact adhesion)
In the adsorption mechanism, adhesion is modeled as occurring across a welldefined interface by molecular interaction across that interface, and is often

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J.C. Berg

12

20

Adhesive
Strength
( kg/cm2)

10

-

I

I

I

1
i+cos e

Or,

2

300r----200

-

Bond

Strensth
(psi

0

I

1.810

1.850

I

I

1.890
I+COS

e

(b>

1.930

Fig. 5. Examples of the correlation between measured adhesive strength and (1 +cos@). (a)
Plot of data from Raraty and Tabor [171] for adhesion of ice to various solids. (b) Plot of
data of Barbaris [172] for adhesion of a mixture of epoxy and polyamide resin to low density
poly(ethy1ene) treated in various ways. Both figures from ref. [31], by permission.

referred to as ‘contact adhesion’. Because of the rather short-range nature of
molecular interactions, they occur principally between the outermost molecular
layers of the adherend and the molecules of the adhesive immediately adjacent to
them and are said to be ‘adsorbed’ to the adherend surface. Such adsorption may
be purely physical (physisorption), or it may involve the formation of covalent
bonds across the interface (chemisorption). The mobile molecules or chains
of the adhesive will orient themselves at the interface to maximize whatever
interactions are possible and thereby minimize the free energy of the system.
The types of interactions may be classified as follows. Lifshitz-van der Waals

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