Contact Angles in the Study of
Adhesion
Surface tension in Action
introduction
• It has been recognized for some time that
there is a relationship between the contact
angles which liquids make with surfaces and
the strength of adhesive bonds to the
surfaces.
SURFACE TENSION OF LIQUIDS
• The surface tension of a liquid can be obtained
by measuring the force needed to remove a
metal ring from the surface of the liquid, the
ring-pull method. A correction factor has to be
applied to the measured force; it is a function of
the radius of the ring, the radius of the wire and
the volume of liquid raised above the surface.
For liquids, surface tension and surface freeenergy are numerically the same, but have
different units, which are usually mN m-' and mJ
m-2.
Fmax f r  2 ( 2 rmean )  2 ( rext  rint )
THE LIQUID-LIQUID INTERFACE
Spreading of One Liquid on Another
• It is important that adhesives spread on
substrates, and in the case of liquids
spreading on liquids, spreading depends on
their surface tensions. If a drop of liquid B is
placed on the surface on liquid A, the change
in Gibbs free energy accompanying a change
in the area covered by the drop, at constant
temperature and pressure, is given by:
• If B increases in area it is at the expense of A, and more interface
is formed, i.e.
• The partial differentials are surface or interfacial free-energies, e.g
• Hence equation 8.1 can be written as
• dG/dAA is known as the spreading coefficient of B and A, i.e.
• A positive value of SA,B is the condition for
spreading.
Measurement of Interfacial Tension
• The ring-pull method can be used to measure
the interfacial tension between two immiscible
liquids such as water and an alkane. The
procedure is to float a layer of alkane on water
and place the ring at the interface. When a lifting
force is applied the ring rises above the interface
and draws the meniscus with it. Because of
bouyancy a large volume of water is raised
above the interface and quite a deep layer of
alkane is needed to contain it; the correction
factor is now larger than in measuring surface
tension of liquids.
Fmax f r  2 ( 2 rmean )  2 ( rext  rint )
Measurement of Interfacial Tension
• Interfacial Tension Between Two Non-polar
Liquids
Measurement of Interfacial Tension
• Interfacial Tension Between Two Polar Liquids
– The surface tension of a polar liquid is the sum of
dispersive and polar components, so equations
8.11 and 8.12 apply to polar liquids 1 and 2,
respectively.
THE LIQUID-SOLID INTERFACE
Measurement of Contact Angles
• All adhesive bonds are made by placing an
adhesive, which is a liquid at the time of wetting,
on a solid substrate. If a drop of liquid is placed
on a flat, horizontal solid surface, it will make a
contact angle  with the surface.
• If the contact angle is zero the liquid is said to
wet the surface fully. Small droplets (a few l)
are used to minimize distortion due to gravity.
THE LIQUID-SOLID INTERFACE
Measurement of Contact Angles
• Contact angles can be measured by several
methods including:
(i) Direct measurement by viewing through a
microscope with a goniometer eyepiece.
(ii) Measuring height (h) and radius (r) of the base
of a drop, using a microscope or by projecting an
image on a screen, followed by use of equation:
(iii) The Wilhelmy plate method:
• The Wilhelmy plate method in which a plate
of the test solid is suspended from a
microbalance, and partially immersed in the
liquid. The method can be adapted to
measure contact angles on fibers.
• The measured force is given by the following
equation, where X is the length of the
contact between the plate and the liquid and
L is the surface tension of the liquid.
Contact Angle Hysteresis
• The latter phenomenon described above is
known as contact angle hysteresis, which is
due to surface heterogeneity caused by
roughness, or patchy composition such as
might occur on the surface of a block
copolymer.
• It can be measured on droplets made to grow
or shrink by the addition or removal of liquid,
as is illustrated:
Forces Between a Solid Surface and a
Liquid Drop
• The forces acting at the periphery of a droplet making a contact angle 
with a solid surface are illustrated in Figure 8.6, and are related by
Young’s equation:
The spreading
pressure is πe; this is usually
small and is often neglected.
• The surface energies of both phases are the sum of dispersion (d) and
polar (p) components, as given by equations
Determination of Polar and Dispersive
components
• Equations can be combined to give equation, in
which the spreading pressure is neglected.
• This means that if Lv(1 + cos )/2(Ld)is plotted
against (LP/Ld)1/2, the graph should be linear
with an intercept (sd)1/2 and slope (sp)1/2,
thus permitting the determination of the polar
and dispersive components of the surface freeenergy of the solid.
Determination of Polar and Dispersive
components
• Wu considers that harmonic means give more
consistent results for interactions between low
energy systems (such as liquids and adhesives on
polymers), while geometric means are more
appropriate for high energy systems (such as
adhesives on metals).
• Equation 8.22 is the harmonic equivalent of
equation 8.21, but the fact that there is no simple
way to plot this equation may account for the
greater popularity of the geometric mean
approach.
Determination of Polar and Dispersive
components
• Table 8.2 contains a list of some test-liquids
for which the values of the polar and
dispersive contributions to surface free-energy
are available.
• The liquids are arranged in order of
(LP/Ld)1/2 as this is the abscissa of plots
based on equation 8.21.
Spreading Pressure
• Adsorption of vapour on a solid surface will change the surface freeenergy of the solid. This will be greatest when the contact angle is low,
i.e. when the liquid has a high affinity for the solid.
• The lowering of surface free-energy is known as the spreading pressure,
πe, and is given by equation
• Here s is the surface free-energy of the solid in a vacuum and SVap is
that when in equilibrium with the saturated vapour. The term πe, is
usually negligible when  > 10.
• Spreading pressure can be measured by vapour adsorption using
equation:
• Here p is vapour pressure, p0 is the saturated vapour pressure,  is the
number of moles adsorbed per unit area, and  is the chemical potential
of the adsorbate.
Surface Energies of Adhesives and
Substrates
Complete Wetting of a Solid
• Fox and Zisman have characterized some
polymer surfaces by measuring contact angles
for a series of liquids, and plotting the data in
the form of cos  against the surface tension
of the liquids. When  = 0 (cos  = 1) the
liquid spreads on the surface and the surface
tension of the liquid is then equal to the
critical surface tension c of the polymer. A
plot is shown in Figure 8.9; it is for liquids on
some fluorinated polymers;
• Values of critical surface tension for some polymers are given in
Table 8.5. They are similar to the values of s in Table 8.4.
• Critical surface tension is related to surface tension by equation
8.25, i.e. , is equal to or less than the surface tension.
• Wetting is not a reciprocal property, which means that if A spreads
on B, B does not necessarily spread on A.
• An example of this is that a liquid epoxide resin will not spread on
polyethylene, but if the resin is cured it will then be wetted by
molten polyethylene.
• A solid can induce liquids of lower, but not higher, surface tension
to wet it.
THERMODYNAMIC PREDICTIONS OF JOINT STABILITY
Work of Adhesion
• The thermodynamic work of adhesion ( WA),
that is the work required to separate a unit
area of two phases in contact, is related to
surface free-energies by the Dupre equation.
• If the phases are separated in dry air then
equation:
• But if separation is in the presence of water it
takes the form of equation:
THERMODYNAMIC PREDICTIONS OF JOINT STABILITY
Work of Adhesion
• Equation 8.28 indicates that a stronger bond will be obtained if
the adhesive and substrate are matched in their surface energy
components, as illustrated by the following calculations.
• Suppose both adherend and adhesive have d = 20mJm-2 and p
= 2 mJm-2, then the work of adhesion in dry conditions is 44
mJm-2 and in water it is 65.7 mJm- 2; the higher stability in water is
due to both materials being quite hydrophobic. If the values of the
two parameters for the adhesive are interchanged then work of
adhesion when dry is 25.3mJm-2 and in water it is 31.8mJm-2, i.e.
both are reduced.
THERMODYNAMIC PREDICTIONS OF JOINT STABILITY
Theory and practice
• Table 8.6 is based on one by Kinloch in which
the work of adhesion in air and in some
liquids is compared with the tendency to
debond interfacially in an unstressed
condition. The fact that interfacial
debonding only occurs when the
thermodynamic work of adhesion is negative
is very strong evidence of the validity of
thermodynamics in predicting the durability
of adhesive bonds.
THE END