Contact Angle

The importance of hydrophobic–hydrophilic balance at interfaces has prompted numer-ous investigators to develop techniques to measure this property at solid surfaces. Contact angle methods have been prominent in this regard [10]. Contact angle analysis is inexpen-sive, rapid, and fairly sensitive. However, contact angle data can be difficult to interpret, and the technique is subject to artifacts due to macroscopic, energetic heterogeneities in the surface; hysteresis; and drop-volume effects among others. Still, useful conclusions regarding biological interactions with surfaces have been based on the results of contact angle analysis in numerous areas relevant to food technology [11].

When a liquid phase contacts both a second fluid phase and a solid surface there occurs a net, characteristic orientation of the liquid–fluid interface with respect to the solid surface. This orientation is reflected in the so-called contact angle [1,2,4]. Under controlled equilibrium conditions, the contact angle can be considered to be an intensive property, dependent only on the natures of the three component phases and independent of the geometry and quantities present. Placing a drop of liquid on a solid surface is a conve-nient way to create this kind of three-phase system. The contact angle, θ, is identified in Figure 2.3 for this solid–liquid case. Theoretically, the contact angle identified in this way would be the same characteristic angle defining a meeting of the same three phases in any geometry.

All of the interfacial “tensions,” γ, shown in Figure 2.3, are acting to minimize the overall interfacial energy (i.e., reduce interfacial area), such that

γs = γsl +γlcosθ (2.6)

Equation 2.6 is Young’s equation, essentially a force balance on the drop at rest. An energy balance defines the work of adhesion between the solid and liquid (also see Figure 2.2 and Equation 2.2), such that

Wa = γs +γl −γsl (2.7)

S θ γ_SL γ_S

γ_L

L

Figure 2.3 The contact angle, θ, between a liquid (l) and a solid (s). Contributions of the tension forces, γ, between the phases are indicated by arrows.

Equation 2.7 is sometimes called the Dupré equation. Young and Dupré equations are not very useful by themselves, as γs and γsl are difficult, if not practically impossible, to measure. They can be combined, however, to yield a very useful equation for calculating the work of adhesion,

= γ + θ

Wa L(1 cos ) (2.8)

Equations 2.6 through 2.8 are valid only at equilibrium: the liquid should be satu-rated with the solid, the vapor and solid must be at adsorption equilibrium, and the solid surface must be energetically homogeneous and smooth (effects of surface roughness are discussed below). Although that is not always the case, and θ for a given three-phase sys-tem, in practice, can depend somewhat on judgment, Equations 2.6 through 2.8 are fully functional, and form the basis for evaluation of surface energetics. We summarize three different but widely used approaches to this end in the next section.

2.2.3.1 Critical Surface Tension

The most common interpretation of contact angle data to gain a measure of surface energy is completely empirical. Given an uncharacterized solid surface one determines θ for each of a series of homologous liquids contacted with the surface. The cosine of each angle is plotted against the surface tension of the corresponding liquid. The result, a (typically) rectangular band of data, is called a Zisman plot [11]. The intercept of a line drawn through the data at the cos θ = 1 axis is termed the critical surface tension of the solid, γc.

Figure 2.4 shows a Zisman plot constructed for an acetal surface, and one constructed for a polyethylene surface [11]. The data indicate that γc,acetal = 23.7 and γc,polyethylene = 21.8 mN/m.

That implies that a liquid with γl = 23.7 mN/m would completely spread on acetal, whereas a liquid of γl > 23.7 mN/m would yield a nonzero value of θ. In general, for any combina-tion of solid and liquid, the higher the value of θ, the higher the interfacial energy between them (γsl). Put another way, the lower the value of γc, the higher the interfacial energy between that surface and water.

Although data derived in this manner are widely considered to be a function of the solid surface alone, and therefore related to the “true” surface energy of the solid, a Zisman plot can yield highly misleading results [12]. In particular, it can be difficult to determine the best value of the slope and therefore, cos θ = 1 intercept, which represent the material surface properties. A major advantage of the method is, however, that it is very simple.

2.2.3.2 Polar and Dispersive Contributions to Surface Energy

Approaches to interpretation of contact angle data were much improved by Fowkes [13].

With a focus on liquid–liquid and liquid–vapor interfaces, he proposed resolving liquid surface tension into two components:

γl γld γ

lp

= + (2.9)

where γld refers to surface tension contributions arising only from the London–van der Waals dispersion forces, and γlp refers to those contributions arising from electrostatic forces, dipole–dipole, dipole–induced dipole, so-called donor–acceptor interactions, and

suRFACe PRoPeRties

so on. Superscripts “d” and “p” stand for dispersive and polar contributions, respectively.

The following development is based on two truisms:

• At the interface between any two liquids where the intermolecular attraction of any one of them is entirely due to London dispersion forces, the only appreciable interfacial interactions present will be due to London dispersion forces.

• If we think of the interface as comprising two interfacial regions, the interfacial energy is the sum of the energies in each region.

When the intermolecular attraction of any one of two phases is entirely due to disper-sion forces, it can be shown [13] that the geometric mean of the disperdisper-sion force attractions is an adequate representation of the magnitude of the interaction between the two phases.

That is, when liquid 1 contacts liquid 2, the energy in “interfacial region 1” is γ1 γ γ12 22

− and the energy in “interfacial region 2” is γ2 γ γ12

22

− . Thus, the interfacial energy where the two phases 1 and 2 meet is

γ12 γ1 γ2 γ γ12 22

= + −2 (2.10)

1.0 Acetal

Polyethylene

0.8

0.6

0.4

cos θ

0.2

0.020 30 40 50

γ_L (mN/m) 60 70 80

Figure 2.4 A Zisman plot constructed with contact angle data recorded for an acetal and a polyeth-ylene surface. (Reproduced with permission from J McGuire, V Krisdhasima. In H Schwartzberg, R Hartel, Eds. Physical Chemistry of Foods. New York: Marcel Dekker, 1992, pp. 223–262.)

Note that with reference to Equation 2.2, Wa = 2 12 22

γ γ . Since only dispersive interac-tion is possible in the present case, we can write

Wad = 2 12 22

γ γ (2.11)

where Wad is the dispersive component of the total work of adhesion, Wa. Of course, if only dispersive forces interact at the interface, then Wa =Wad. In any event, the same rationale for splitting γ into γ ^d and γ ^p components allows us to write Wa Wad W

ap

= + .

Kaelble [14] applied these concepts to solid–liquid interfaces, stating that γs γsp γ

sd

= + . That is appropriate, but the analogy was made complete by stating, as above, that the geometric mean of the polar force attractions is an adequate represen-tation of the magnitude of the total polar interaction between two phases, leading to Wap = 2 γ γ1 2p p. While mathematically convenient, there is no theoretical justification for this and in fact, although two surfaces may be characterized as “polar,” there may well be no polar attraction between them [15]. Fowkes [15] argued that all “polar” interac-tions are of the “acid–base” type. “Acids,” here, are electron acceptors, while “bases”

are electron donors (i.e., Lewis acids and bases). A pure liquid exhibiting only acidic or basic character, while certainly polar, for example, will be miscible with an organic solvent. In summary, two polar bodies interact only when one is acidic and the other is basic. It is worth noting that researchers never try to estimate Wap for two liquids in contact according to 2 γ γlp_{1 2}

lp but literally hundreds of researchers have estimated Wap

= + . For a solid–liquid contact system, Equation 2.3 can be expanded with Equation 2.11, such that Waab, the functional relationship is not known, and calculation of γs (and therefore γsab) is not possible using contact angle methods. Nevertheless, Waab is a very useful property, in and of itself. We know that in addition to capacity to take part in dispersive attractions, solid surfaces can take part in acid–base attractions; they can be acidic, basic, or harbor both types of sites, and Waab for a given solid surface necessarily depends on acid–base properties of the liquid contacting it. With reference to food science and technology, we would be most concerned with processes where solid surfaces are contacting fluids with some biological relevance, that is, aqueous solutions and suspensions. Water acts as an acid as well as a base, and often, surface hydrophobicity is of most interest. The acid–base component of the work required to remove water from a surface, Wa waterab

, , is clearly related to its hydrophobicity: a high work of adhesion would correspond to a hydrophilic surface, while a low value would correspond to a hydrophobic surface. As summarized in Section

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2.3, measurement of θ, γl, γld, and γsd is straightforward. Thus Waab is readily determined, according to Equation 2.12 when rearranged as follows:

Waab

l ld

sd

= γ (1+cos )θ −2 γ γ (2.13)

Measurement of θ for a drop of water on the surface of a material of interest yields Wa waterab

, directly. Alternatively, Wa waterab

, can be evaluated using a series of test liquids. In this case, Waab of the test liquid is calculated according to Equation 2.13 for each solid–liquid contact, and then plotted against γl −γld (which equals γlab) of each corresponding liquid.

A reasonably straight line is usually observed, with a better coefficient of determination than found in the Zisman plot [16]. From the straight line fit, one can calculate surface hydrophobicity according to

Wa waterab k b

l waterab

, = (γ , )+ (2.14)

where k is the slope of the line, and b its ordinate intercept.

In other cases, it may be a material’s capacity for acid–base attraction that is of interest, rather than its hydrophobicity. This capacity is evaluated by contacting the surface with liquids of only basic character, and then with liquids of only acidic character [15]. Waab is cal-culated for each solid–liquid contact, to determine the dominant character of the surface.

This information provides direction for selecting the kinds of polymers to place adjacent to another in layered packaging materials, the kinds of adhesives to use in a given situation, and so on. Unfortunately, only very few such “monopolar” diagnostic liquids exist. But for solid–fluid contact in food processing, Equation 2.13 can be quite useful, since proteins and other “solutes” in fluid foods can take part in acid–base interactions with acidic and basic sites, as can water. This analysis can be used to explain some observations, in spite of the fact that the relative numbers of acidic and basic sites on a solid are often unknown.

To this point, we have discussed ways to measure properties relevant to solid surface energy (e.g., γc, Wa waterab

, ), without seriously exploring calculation of γs directly. Below we discuss the existence of an equation of state relationship among solid–liquid, solid–vapor, and liquid–vapor interfacial energies, allowing direct calculation of γsl and γs.

2.2.3.3 An Equation of State Relationship among Interfacial Energies

Ward and Neumann [17] stated that an equation of state relationship must exist among γsl, γs, and γl in a two-component, three-phase system, such as that illustrated in Figure 2.3. That is,

γsl = ( ,f γ γs l) (2.15)

If the functional relationship of Equation 2.15 were known, its combination with Young’s equation (Equation 2.6) would yield two equations and the two unknowns γsl and γs (since θ and γl are readily measurable). Neumann et al. [18], using contact angle data recorded on low-energy surfaces, obtained an explicit empirical formulation of Equation 2.15:

γ γ γ

They then combined Equation 2.16 with Young’s Equation 2.6, to arrive at

With Equation 2.17, one can measure θ for any liquid of known γl, and thus determine γs directly. However, it is very important to note that Equation 15.17 was developed using very low-energy solids, for which γs ≪ γwater. Such solids would be most accurately charac-terized as “hydrophobic,” with values of Wa waterab

, close to zero.

2.2.4 Effects of Adsorbed Layer Composition and Structure