The Equilibrium Contact Angle

When a drop of liquid placed on a solid surface does not spread, the drop assumes a shape that appears to be constant and exhibits an angle, 6 (Fig. 11.4). The angle 6 is called the contact angle and is considered to be characteristic of the particular liquid-solid interaction. Therefore, the equilibrium contact angle serves as an indication of the wettability of the solid by the liquid. The emphasis here is on equilibrium, because valid conclusions can be drawn from the value of the contact angle only when equilibrium is assured. 

Many years ago, Young [5] proposed that a liquid drop on a plane solid surface (Fig. 11.4) is subject to the following equilibrium forces  

Equation (8) is more useful than Eq. (4), because it includes measurable quantities. Equation (8) relates adhesion to cohesion of the liquid, because yuv = 4 c- Equation (8) also appears to suggest that when the contact angle 6 is 0, adhesion is equal to the cohesion of the liquid, ly v and the spreading coefficient, W5, is equal to zero. Such a conclusion would not be correct, however, because Eq. (8) applies to an equilibrium condition, which spreading is not. It is better to visualize that the wettability of a solid is higher by liquids that exhibit a smaller contact angle when placed on the solid when the contact angle approaches zero, the wettability has its maximum limit. 

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The equilibrium contact angles for PE and triallyl cyanurate (TAC) grafted PE with water and formamide are presented in Table 7. The grafting of TAC onto PE increases the surface energies of modified PEs [32]. 

Table 7 reveals that the grafting of TAC onto PE decreases the equilibrium contact angles of water and formamide from 92° to 65° and from 75° to 53°, respectively. This decrease is a function of the monomer level and the irradiation dose. At a fixed irradiation dose of 15 Mrad, variation of the TAC level from 0.5 to 3 parts causes a reduction in the contact angles of water by 13° (from 88° to 75°) and of formamide by 11° (from 72° to 61°). This is due to the fact that the concentration of... 

Let us consider a circular puddle of liquid, L, on solid, S, in the presence of liquid vapor, V. The puddle is of radius Rq and small initial thickness Bq. We assume that holes nucleate spontaneously in the puddle and grow with radius r(t) as time t passes because the equilibrium contact angle. Go, is nonzero. The liquid is unstable as a wetting film. Equilibrium thickness of a film, < is given by [27,28]... 

The first term on the right-hand side is due to the hydrostatic pressure (or suction) acting over the base of the rod and the second term is due to surface tension forces around the perimeter. (It should be noted that O is not equal to the equilibrium contact angle 0 but is determined by the meniscus shape.)... 

The value of the equilibrium contact angle (9) at the three-phase line (TPL) produced by a liquid droplet placed on a flat, solid substrate is determined by the balance of interfacial energies at each surface. Thomas Young derived an equation describing this situation in 1804 ... 

For nonspreading systems, the final spreading coefficient is related to the equilibrium contact angle by the equation... 

ZISMAN, W.A., Relation of the equilibrium contact angle to liquid and solid constitution , A.C.S. Advances in Chemistry Series, 43, 1—51 (1964)... 

Wetting of a solid by a liquid is normally described in terms of the equilibrium contact angle 6 and the appropriate interfacial tensions as shown in Fig. 3.32. 

It is worth noting that if 0a and 0r are equal to the equilibrium contact angle 0, then the first component becomes zero, whereas the second component reduces to the above Equation 21.6. For more information on the difference between 0a, 0r and equilibrium contact angle given by the Young equation the reader may refer to the original works [46, 47]. 

Wetting can be determined by contact angle measurements. It is governed by the Young equation, which relates the equilibrium contact angle 9 made by the wetting component on the substrate to the appropriate interfacial tensions ... 

Our own investigations have concerned (a) liquid spreading on solids and the laws relating the equilibrium contact angle and the critical surface tension of wetting to solid and liquid constitution (26, 27, 28, 53, 54,62), (b) liquid/liquid displacement from solid surfaces (1,5), (c) the properties of adsorbed monolayers on solids and their relation to the monolayer retraction method (28, 54, 62), (d) the surface electrostatic potentials of adsorbed organic monolayers on metals (9, 10, 11, 58, 59), (e) the effects of surface constitution on adhesion and abhesion (60),... 

The minima of these curves correspond to the equilibrium contact angle of the system. 

Figure 1.10 demonstrates that the equilibrium contact angle depends only on the value of A. Variations in the values of (XLV, p or g (such as might be encountered in spacelab experiments) for a constant value of A will merely displace the AF(0) curve perpendicularly to the 0-axis, without changing the position of the minimum value of 0. 

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