Topic:Measurement of surface tension

3 Surface Tension and Its Measurement Sina Ebnesajjad

3.1 Introduction

Surface science is an important branch of physical organic chemistry that studies the behavior and characteristics of molecules at or near a surface or interface. The interface can form between solids, liquids, gases, and combinations of these states. Complex apparatus has been devel- oped to identify and quantify surfaces and inter- faces. Polymer surfaces are of special interest in industrial and biological applications; examples of the latter include dental implants and body part prosthetic devices. Modification of surfaces of these devices allows formation of controlled interfaces to achieve characteristics such as bondability and compatibility.

Adhesion is an interfacial phenomenon that occurs at the interfaces of adherends and adhe- sives. This is the fact underlying the macroscopic process of joining parts using adhesives. An understanding of the forces that develop the interfaces is helpful to the selection of the right adhesive, proper surface treatment of adherends, and effective and economical processes to form bonds. This chapter is devoted to the discussion of the thermodynamic principles and work of adhe- sion that quantitatively characterize surfaces of materials.

Figure 3.1 Liquideliquid interface and balance of forces on molecules of liquids.

3.2 What is an Interface?

Two solid or liquid phases in contact have atoms/ molecules on both sides of an imaginary plane called the interface. The interfacial particles differ ener- getically from those in the bulk of each phase due to being on the boundary of the respective phase and interacting with the particles of the other phase. The composition and energy vary continuously from one phase to the other through the interface. This region has a finite thickness, usually less than 0.1 mm.1,2

Handbook of Adhesives and Surface Preparation, ed. Sina Ebnesajjad. DOI:

� 2011 Elsevier Inc. All rights reserved. This chapter has been adapted from ‘Surface Tension and Its Measurement’ in

S. Ebnesajjad & C.F. Ebnesajjad � 2006 Elsevier Inc.

3.3 Surface Tension

The molecules of a liquid are held together by attraction forces. The sum of all attractive forces on any molecule present in the bulk of a liquid averages zero. The net force (also known as cohesion force) on a surface molecule is a nonzero quantity in the direction toward the bulk (Fig. 3.1). This is the force that must be counteracted to increase the surface area; the energy consumed by this process is called surface energy. The unbalanced forces on the inter- face cause it to contract to the minimum. Water droplets are spherical because a sphere has minimum surface area for a given volume among all geometric shapes. Although surface tension and surface free energy of a liquid are equal, the same is not true for a solid surface.

Surface tension is defined as the work required to increase the area of a surface isothermally and reversibly by unit amount. Surface tension (g) is expressed as surface energy per unit area and alter- natively as force per unit length. Surface tension of liquids can be measured directly and expressed in the units of work or energy per unit area (erg/cm2), which is then simplified (erg/cm2 ¼ dyne.cm/cm2 ¼

10.1016/B978-1-4377-4461-3.10003-3

Surface Treatment of Materials for Adhesion Bonding,

21

22 HANDBOOK OF ADHESIVES AND SURFACE PREPARATION

dyne/cm) to dyne/cm. There are a number of methods for measuring surface tension of liquids, including ones devised to make measurements for unusual liquids such as molten metal and ionic liquids.

3e5

The challenge has been to find methods to determine the surface tension of solids surfaces.

6

Surface tension of polymers can be divided into two components: polar (g

p) and dispersion (gd), to account for the type of attraction forces at the interfaces.7

Chemical constitution of the surface determines the relative contribution of each component to the surface tension. Polar component is comprised of various polar molecular interactions, including hydrogen bonding, dipole energy, and induction energy, whereas the dispersion component arises from London dispersion attractions. The attractive forces (van der Waals and London dispersion) are additive, which results in the surfacetensioncomponentsbeingadditive:g ¼ gp þ gd.

3.4 Surface Free Energy

A hypothetical example is used to describe the concept of surface free energy. Suppose a box with a sliding cover is filled with a liquid (Fig. 3.2). The sliding cover is assumed to have no interfacial tension with the liquid. If the cover is slid back to uncover a surface area of dA, the necessary reversible work will be (g dA). For a pure substance, the increase in the free energy of the system at constant temperature and pressure is defined by Eqn (3.1).

dG ¼ g dA (3.1) The total free energy of the system is comprised of

the energy of the bulk liquid and the surface liquid. The latter is equal to the surface free energy per unit area (Gs) multiplied by the surface area as shown in Eqn (3.2). Combining Eqns (3.1) and (3.2) results in Eqn (3.3), which illustrates that free surface energy of a pure substance is equal to its surface tension.

Figure 3.2 An “ideal liquid” box.

dG ¼ Gs dA (3.2)

Gs ¼ � dG

dA

� T;P

¼ g (3.3)

In a reversible system, the heat (q) associated with it can be related to entropy (S) or surface entropy (Eqn (3.4)), where Ss represents surface entropy per unit area. Equation (3.5) is a thermodynamic rela- tionship applied to the liquid surface in which T represents absolute temperature. Equation (3.6) is obtained by substituting for Gs from Eqn (3.3).

dq ¼ T dS ¼ T Ss dA (3.4)

� dGS dT

� P ¼ �SS (3.5)

dg

dT ¼ �SS (3.6)

The total surface energy (Eqn (3.7)) can be calculated by applying the enthalpy relationship with Gibbs free energy and entropy to the liquid surface.

HS ¼ ES ¼ GS þ TSS (3.7)

Equation (3.8) is the result of substitution from

Eqn 3.6 into 3.7.

ES ¼ GS � T dg

dT (3.8)

Surface tension of most liquids decreases with increasing temperature in a linear manner. A well- known expression (Eqn (3.9)), defining the relation- ship between temperature and surface tension, has been attributed to EôTVôS.8

gV2=3 ¼ kðTc � TÞ (3.9)

V is the molar volume, k has the same value for most liquids (2.1 erg/K), Tc is the critical temperature of the liquid, and T is the liquid temperature. The expectation is that surface tension of a liquid will approach zero at its critical temperature. There are other equations that express the behavior of liquids as a function of temperature.1,7

3: SURFACE TENSION AND ITS MEASUREMENT 23

Techniques have also been developed for estima- tion of the free surface energy of polymers. For example, a method for measuring the surface energy of solids and resolving the surface energy into contributions from dispersion and dipole-hydrogen bonding forces has been developed. It is based on the measurement of contact angles with water and methylene iodide. Good agreement has been obtained with the more laborious gc (critical surface tension method). Evidence for a finite value of liquidesolid interfacial tension at zero contact angle is presented. The method is especially applicable for the surface characterization of polymers.9

Figure 3.3 Equilibrium contact angle on an ideal surface.

3.4.1 Surface Energy of Solids

A solid is defined as a material that is rigid and resists stress. A solid surface may be characterized by its surface free energy and surface energy. Surface energy (tension) of a solid cannot be measured in a similar manner to that of a liquid due to the diffi- culty caused by the reversible formation of its surface. The methods for the determination of surface energy of solids are described in this chapter.

Solid material surfaces can be divided into two categories of high and low surface energy.10 High surface energy materials include metals and inorganic compounds such as oxides, silicates, silica, diamond, and nitrides. Surface tension of high-energy materials is 200e500 dynes/cm. Low-energy materials are mainly comprised of organic compounds including polymers with critical surface tension <100 dynes. Polymer surfaces have themselves been classified11 as being of low, medium, and high surface energy. Low surface energy solids have critical surface tension in the range of 10e30 dynes/cm, medium energy from 30 to 40 dynes/cm, and high energy >40 dynes/cm.

Low-energy materials, such as oils, are spontane- ously absorbed by the high-energy surfaces because of the reduction in the free surface energy of the system. This means that a clean, high-energy surface exposed to the normal ambient environment will not remain clean for long because of the absorption from the environment of water and organic contaminants thereon. Accordingly, a surface cleaning operation is included in many processes just before the actual application of the adhesive or coating to prevent pro- longed exposure of the cleaned substrate (adherend) to the factory environment. Another approach is to apply a protective film to the clean surface, which is removed immediately prior to the adhesive coating step.

3.4.2 Work of Adhesion

The work of adhesion is defined as the reversible thermodynamic work that is needed to separate the interface from the equilibrium state of two phases to a separation distance of infinity. Equation (3.10) shows the work of adhesion for a liquidesolid combination. This definition is attributed to the French scientist A. Dupre.

Wa ¼ gL þ gS � gSL (3.10) gL is the surface energy (tension) of the liquid phase, gS is the surface energy of the solid phase, gSL is the interfacial surface tension, and Wa is the work of adhesion. A rise in the interfacial attraction results in an increase in the work of adhesion. Equation (3.10) can be rewritten to determine the work of cohesion (Wc) when the two phases are identical and no interface is present, as shown in Eqn (3.11) for a solid phase.

Wc ¼2 gS (3.11)

3.5 Contact Angle (Young’s Equation)

Most liquids wet solid surfaces to some extent and exhibit a contact angle. A contact angle in a static system can be measured at equilibrium. Figure 3.3 illustrates the contact angle in an ideal system where the solid surface is homogeneous, smooth, planar, and rigid. The interfacial tensions designated as g repre- sent equilibrium values at the point where three pha- ses intersect. The subscripts L, S, and V denote liquid, solid, and vapor phases, respectively. go is used to indicate that the solid surface must be in equilibrium with the liquid’s saturated vapor; that is, a film of the liquid is absorbed on the solid surface. Young12

described Eqn (3.12) without presenting a proof. It has since been proven by different researchers.13e15

24 HANDBOOK OF ADHESIVES AND SURFACE PREPARATION

gLV cos u ¼ goSV � gSL (3.12)

One route to prove Young’s equation is by using the Gibbs free energy of the wetting, proposed by Poynting and Thompson.16 After the liquid droplet forms the meniscus and reaches equilibrium, the variation in Gibbs free energy is zero. An assumption in Eqn (3.13) is the neglect of the gravitational force.

dG ¼ 0 (3.13)

dG ¼ gLV dALV þ goSV dASV þ gSL dASL ¼ 0 (3.14)

In Eqn (3.14), dA represents small incremental increases/decreases in the surface or interface area. Changes in the interfacial areas are given by Eqns (3.15) and (3.16), because any increase in the solid- eliquid interface is countered by a decrease in the solidevapor interface. Substitution from these two equations in Eqn (3.14) will yield Young’s equation (Eqn (3.12)).

dASL ¼ �dASV (3.15)

dALV ¼ cos u dASL gLVðcos u dASLÞ þ goSVð�dASLÞ þ gSL dASL ¼ 0

(3.16)

gLV cos u ¼ goSV � gSL (3.12)

The difference between the equilibrium surface energy of solidevapor and solideliquid is sometimes called adhesion.17 It must be noted that the work of adhesion and adhesion tension involves the solidevapor equilibrium instead of the solideliquid equilibrium.

ASLV ¼ goSV � gSL ¼ gLV cos u

Most surfaces have heterogeneous composition and

are not perfectly smooth. Wetting of such a surface may reach equilibrium or remain in a metastable state. In the case of an ideal surface, the addition or removal of a small volume of liquid from the drop will result in the advancement or recession of the drop. The contact

angle will return to its equilibrium value. In the case of a real surface, which may contain roughness and heterogeneity, there is a delay in the movement of the liquid drop in response to the addition or removal of liquid. This phenomenon is called hysteresis, which requires a revision of the definition of contact angle.

The contact angle formed as a result of the addition of liquid to the drop is dubbed the advancing angle. The angle formed because of the removal of liquid is called the receding angle. The contact angle of a liquid on a real surface is measured in both contacting and advancing modes. Typically, after the addition or removal of the liquid there is a delay followed by a sudden motion in the drop of the liquid. The maximum angle for the advancing mode and the minimum angle for the receding mode are defined, respectively, as advancing and receding contact angles.

Harkins and Livingston18 proposed a correction to Young’s equation, concerning the surface of the solid carrying a film of the liquid’s vapor. The surface energy of a solid surface that contains an adsorbed vapor layer (gSA) is less than that of a “clean” solid surface. This concept has practical significance because clean surfaces tend to adsorb the ambient vapors and oils and must therefore be protected prior to the application of adhesive. Hankins’ and Livingston’s correction, known as spreading coeffi- cient (pE), is shown in Eqn (3.17); thus, resulting in Eqn (3.18) after substitution in Eqn (3.12).

goSV ¼ gSA � pE gLV cos u ¼ gSA � pE � gSL

(3.17)

gSA ¼ gLV cos u þ gSL þ pE (3.18)

The spreading coefficient can be measured by a technique developed by Padday. In this method, it has been shown19 that such a sessile drop, when successively increased in volume, reaches some constant maximum height (h) for a given solid- eliquid system, provided the system is aged to reach equilibrium. It has also been shown that this maximum height is related to the spreading coeffi- cient by Eqn (3.19). In this equation, r is the density of the liquid and g is the gravitational acceleration.

pE ¼ � rgh2

2 (3.19)

3: SURFACE TENSION AND ITS MEASUREMENT 25

Finally, by substituting for the interfacial tension from the modified Young’s equation (Eqn (3.12)) into the work of adhesion (Eqn (3.20)) for a solideliquid system, the equation for the work of adhesion can be simplified to Eqn (3.21), also known as Younge Dupre’s equation.

Wa ¼ gLV þ goSV � gSL (3.20)

Wa ¼ gLVð1 þ cos uÞ (3.21)

This means that the work of adhesion can be calculated by measuring the contact angle and the surface tension of the liquid.

3.6 Laplace’s Equation

This equation is the governing relationship for the shapes of all bubbles and drops of liquids. It is also the basis for measuring the static surface/interface tensions of fluids. Laplace’s equation states that the pressure drop across a curved surface is proportional to the capillary forces as shown in Eqn (3.22).12

DP ¼ Pa � Pb Pa � Pb ¼ g

� 1

R1 þ 1 R2

� (3.22)

Pa and Pb are pressures in the two phases and R1 and R2 are the main radii of curvature. Dimensionless forms of Laplace equation that are more convenient to apply have been derived.20 For a spherical surface R1 ¼ R2; simplify Eqn (3.22) to the following form:

DP ¼ Pa � Pb ¼ 2g

R (3.23)

3.7 Effect of Temperature on Surface Tension

An important variable of surface tension is temperature, which has practical value during the adhesion bonding of plastics. Surface tension of both adhesive and polymer is affected by temperature. Guggenheim’s equation (Eqn (3.24)) is applicable to liquids that have small molecules.21 It has also been found to be applicable to polymers. In this equation, g0 is surface tension at T ¼ 0 K and Tc is the critical temperature (K) of the liquid. The values of g0 and Tc

can be determined by fitting a line to the surface tension data as a function of temperature. According to the Guggenheim equation, surface tension decreases with an increase in temperature.

22 The rate of surface tension decrease as a function of temperature is 0.1 dynes/�C cm for liquids with small molecules.21,23

g ¼ g0 � 1 � T

Tc

� 11=9

(3.24)

3.8 Surface Tension Measurement

Surface tension measurement techniques are clas- sified into methods for solids and liquids. There are two modes for measuring surface tension of liquids: static and dynamic. Values reported in the literature are often for static surface tensions of liquids. Tables 3.1 through 3.3 present a brief description of the common techniques for surface tension measurement of liquid and solid materials. Some of these methods have been described in further detail.

Several standards have been written to define methods for measuring contact angle for different applications (Table 3.4). The objective of these methods is to provide procedures for the comparison of surface energy of industrial materials.

3.8.1 Measurement for Liquids: Du Nouy Ring and Wilhelmy Plate Methods

The du Nouy ring and Wilhelmy plate methods (Fig. 3.4) are two most frequently used techniques of measuring surface tension at the liquideair interface or interfacial tension at a liquideliquid interface. Only the du Nouy method can be applied to measure interfacial tension. Both of these techniques are based on pulling an object with a well-defined geometry off the surface of liquids and measuring the pull force. These techniques are also known as pull-force methods. In the Wilhelmy method, a plate is the pull object, whereas in the du Nouy technique a ring is used. These techniques are ascribed to two scientists who conducted some of the earliest research in the area of surface tension measurement. In 1863, Wilhelmy24 described measurement of capillary constants in a paper, without a detailed calculation of surface tension. Lecomte du Nouy illustrated the

Table 3.1 Static Surface Tension Measurement Methods for Liquids

Technique Brief Description

du Nouy Ring Traditional method for the measurement of surface and interfacial tension. Maximum pulling force on a ring by the surface is measured. Wetting properties of liquids have no influence on this technique.

Wilhelmy Plate This technique is broadly applicable to liquids, especially when surface tension must be measured over a long time period. A vertical plate with known perimeter is attached to a balance and submerged in the liquid. The force due to wetting is measured by the balance.

Spinning Drop Suitable for low interfacial tensions. The diameter of a drop within a heavy phase is measured when both are being rotated.

Pendent Drop Surface and interfacial tensions are measured by this method.

Table 3.2 Dynamic Surface Tension Measurement Methods for Liquids

Technique Brief Description

Bubble Pressure This method is used for determining surface tension at short surface ages. The actual measured variable is the maximum pressure of each bubble.

Drop Volume A method employed for determining interfacial tension as a function of time (interface age). The time between two consecutive drops is measured when liquid of one density is pumped into a second liquid of a different density.

Table 3.3 Surface Tension Measurement Methods for Solids

Technique Brief Description

Sessile Drop This method involves measurement of the contact angle optically and is used to estimate wetting properties of a localized region on a solid surface. The angle between the baseline of the drop and the tangent at the drop boundary are determined. This technique is ideal for curved samples or when one side of the sample surface has different properties than the other side.

Dynamic Wilhelmy This method requires uniform geometry for calculating average advancing and receding contact angles on solids. Both sides of the solid must have the same properties. Wetting force on the solid material is measured as the solid is submerged in, or withdrawn from, a liquid of given surface tension.

Single Fiber Wilhelmy This is a dynamic Wilhelmy method, applied to single fibers to measure advancing and receding contact angles.

Powder Contact Angle This procedure allows the measurement of average contact angle and adsorption speeds of powders and other porous species. The change in the weight as a function of time is measured.

Liquid Homolog Method (Zissman) Called critical surface tension, it is based on measuring the contact angle of several liquids and plotting the cosine of the angle versus surface tension of the liquids. The surface tension at which cosine of the contact angle is equal to one, obtained by extrapolation, is the critical surface tension of the solid.

26 HANDBOOK OF ADHESIVES AND SURFACE PREPARATION

Table 3.4 Standard Contact Angle Measurement Methods for Various Materials

Technique TitledScope

ASTM D724-99 Standard Test Method for Surface Wettability of Paper. Method covers the quantitative determination of the resistance of paper surfaces to wetting by measuring the behavior of a drop of liquid applied directly to the paper surface.

ASTM D5725-99 Standard Test Method for Surface Wettability and Absorbency of Sheeted Materials using an Automated Contact Angle Tester. Method measures the contact angle of a test liquid on a flat sample of a film or a paper substrate under specified conditions.

ASTM C813-90 (1994)e1 Standard Test Method for Hydrophobic Contamination on Glass by Contact Angle Measurement. Method covers the detection of hydrophobic contamination on glass surfaces by means of contact angle measurement.

ASTM D5946-96 Standard Test Method for Corona-treated Polymer Films using Water Contact Angle Measurement. Method covers the measurement of contact angle of water droplets on corona-treated polymer film surfaces; the results are used to estimate the film’s wetting tension.

TAPPI T458* Surface Wettability of Paper. In this method, the contact angle between air and liquid on a paper surface is taken as a measure of the resistance of the paper surface to wetting by the liquid. The initial angle of contact or initial wettability is considered to be a measure of the ruling quality of the paper. The rate of change in the wettability is considered to be a measure of the writing quality.

*See TAPPI (Technical Association of the Pulp and Paper Industry) Web site: www.tappi.org.

3: SURFACE TENSION AND ITS MEASUREMENT 27

shortcomings of the past surface tension determina- tion methods in a paper published in 1919.25

Equation (3.25) shows the relationship for the calculation of surface tension by the du Nouy ring method.Inthisequation,PTisthetotalforceonthering which is measured, PR is the weight of the ring, R is the radius of the ring, and gideal is the ideal surface tension. In practice, a meniscus correction factor is required because the size and shape of the surface inside and outside the ring are not the same. Surface tension must, therefore, be corrected for the shape of the ring by a factor ( f), as shown in Eqn (3.26). The correction factors have been determined and tabulated.23,26,27

PT ¼ PR þ 4pRgideal (3.25)

(a) (b)

Figure 3.4 Schematic of (a) du Nouy Ring and (b) Wilhelmy Plate.

g ¼ fgideal (3.26)

The Wilhelmy method does not require a correction factor for meniscus shape. Though it does require correction if the plate is partially or completely submerged in the liquid. In Equation (3.27), PT is the total force on the plate that is measured, PP is the weight of the plate, p is the perimeter of the plate, and gideal is the ideal surface tension. A buoyant force term must be added or subtracted to/from the second part of the equation, depending on whether the plate is above or below the level of the free liquid. In Eqn (3.28), h is the height above or below the free liquid level, A is the cross-sectional area of the plate, and g is the surface tension.

PT ¼ PP þ pgideal (3.27)

PT ¼ PP þ pg þ rghA (3.28)

The total force (PT), acting on the ring (du Noy) or the plate (Wilhelmy), can be measured by a balance connected to either device. Substituting for the total

Table 3.5 Surface Free Energy of Select Plastics

Plastic Material Surface Free Energy, dynes/cm

Polytetrafluoroethylene 18e19

Polytrifluoroethylene 22

Polyvinylidene Fluoride 25

Polyvinyl Fluoride 28

Polypropylene 29

Polyethylene 30e31

Ionomer (low) Polystyrene

33

Ionomer (high) Polystyrene

37

Polymethylmethacrylate 38

Polyvinyl Chloride 39

Cellulosics 42

Polyester 43

Nylon 46

28 HANDBOOK OF ADHESIVES AND SURFACE PREPARATION

force and other parameters in Eqn (3.28) allows the value of surface tension (g) to be calculated.

3.8.2 Measurement for Solids: Liquid Homolog Series

Surface tension of solid plastics cannot be measured directly and is thus determined indirectly, usually by contact angle methods. The problem with the direct measurement of surface tension arises from the difficulty in the reversible formation of a solid surface. Table 3.3 shows a list of methods that can be applied to measure the surface energy of solids.

An alternative method uses a concept called critical surface tension, proposed by Fox and Zissman10,28,29

to characterize the surface energy of solids. A plot cosine of the contact angle (cos u), and liquidevapor surface tension (glv), yields a straight line for a homologous series of liquids (Fig. 3.5). Nonho- mologous liquids yield a curved line that may not be easily extrapolated. The intercept of the line at cos (u) equal to one is defined as the critical surface tension of the polymer (gc). Values of 18 dynes/cm for

Figure 3.5 Zissman plot for polytetrafluoroethylene using n-alkanes as the testing liquids.4,23

Figure 3.6 Zissman plot for polytethylene using n-alkanes as the testing liquids.4,23

polytetrafluoroethylene and 30 dynes/cm for poly- ethylene are obtained according to this procedure (Figs 3.5 and 3.6). Tables 3.5 and 3.6 present surface free energies of solids and surface tension of liquids.

One can obtain a relationship (Eqn (3.29)) between the critical surface tension and the solidevapor surface tension by setting the contact angle to zero in Young’s equation (Eqn (3.12)). Critical surface tension is therefore smaller than solidevapor surface

Table 3.6 Surface Tension of Select Liquids

Liquid Surface Free Energy, dynes/cm

n-Hexane 18

Alcohols 22

Cyclohexane 25

Toluene, Xylene 29

Phenol 41

Aniline 43

Glycol 47

Formamide 58

Glycerol 63

Water 72

Figure 3.7 Effect of temperature on critical surface tension of two plastics.24

3: SURFACE TENSION AND ITS MEASUREMENT 29

tension. Figure 3.7 shows the effect of temperature on critical surface tensions of two plastics.30 Surface energy of plastics decreases with temperature.

gc ¼ lim u/0

ðgLV cos uÞ ¼ gSV � gSL (3.29)

In summary, the experimental and analytical methods described in this chapter enable the reader to both measure and calculate surface energy of liquids and solids. Surface preparation techniques are partly aimed at changing surface energy of materials, which can be determined using the methods provided in this chapter.

References

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(b) Padday JF. Proc. 2nd Int. Conf of Surface Activity, Vol. III. London: Butterworths Scientific Publications; 1958. p. 136.

20. Bashforth S, Adams JC. An Attempt to Test the Theory of Capillary Action. London: Cambridge University Press and Deighton, Pub. By Bell and Co; 1892.

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30 HANDBOOK OF ADHESIVES AND SURFACE PREPARATION

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