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 free-energy are numerically the same, but have different units, which are usually mN m-' and mJ m-2.

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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.

• 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.

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Measurement of Interfacial Tension

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 INTERFACEMeasurement 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 INTERFACEMeasurement 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 surface energies of both phases are the sum of dispersion (d) and polar (p) components, as given by equations

The spreading pressure is πe; this is usually small and is often neglected.

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/L

d)1/2, the graph should be linear with an intercept (s

d)1/2 and slope (sp)1/2, thus permitting

the determination of the polar and dispersive components of the surface free-energy 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/L

d)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 free-energy

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