Ideal contact angle

The ACCA and APCA on an ideal solid surface are identical by definition, and are referred to as the "ideal contact angle (ICA)". As will be explained below, it is the value of the ICA that is required for the characterization of the wettability of a solid substrate in terms of its surface tension. Also, all predictions of wetting behavior start with the ICAas their basis. Therefore, even though ideal surfaces are rarely encountered in practice, the concept is of fundamental importance. 

Since Fowkes assumed that 7tsv = 0 for low-energy solid (polymer) surfaces, where (yLv > ysv) for finite contact angles of high-energy liquid drops on them, he then expressed the equilibrium ideal contact angle, 0e as... 

When measured on a real surface, which is microscopically rough, contact angle 0 is related to the idealized contact angle by the roughness factor, r. 

It can be seen from the formula that the contact angle, 0 of the membrane depends on the ideal contact angle, 0 and siuface area, and the specific surface area plays an important role in the contact angle of a material. 

As shown in Table 6.1, the maximum percental of contamination ) of siu ace, S, (in this case PMMA), by vapors from various contact 2ingle liquids is at most only a few percent and in the cases of glycerol and formamide less than 0.1%. Even in the case of the most hydrophilic material known (PEO) the maximum amount of surface occupied by water is less than 4%. Expressed in decrease (Ai ) in contact angle (i as compared to the ideal contact angle (i i), this usually amounts to less than 1°, except in the case of water on PMMA, where it is 1.55°. It should be noted that the precision of contact angle measurement is rarely better than 1°. In virtually all cases the contamination of the surface by gas molecules emanating from the liquid... 

The basic observation is that a thin plate, such as a microscope cover glass or piece of platinum foil, will support a meniscus whose weight both as measured statically or by detachment is given very accurately by the ideal equation (assuming zero contact angle) ... 

Most of the surfaces that require repellent treatments are not smooth but contain capillaries into which a Hquid can migrate, even though the advancing contact angle of the Hquid on the surface is >0°. The law for the movement of Hquids into an idealized capillary is given by the equation ... 

The phenomenon of wetting of a solid by a liquid depends on the surfaces and interfacial energies. When a liquid droplet is in contact with an ideally smooth solid surface, as shown schematically in Fig. 9, according to the Young s equation [72], the contact angle (6) of the liquid is given by... 

Ideally one would like to visualize the molecular-scale details at the edge of a droplet to obtain direct information about the molecular nature of wetting. This is not always possible, particularly when these details have dimensions below 300 A, the resolution limit of SPFM. However, the height and curvature of a droplet can usually be measured accurately. These parameters can then be used to obtain an effective contact angle, as defined in Eq. (10). We present here a few examples of this type of study. 

Equation (2-14) provides a way to calculate the liquid temperature in equilibrium with the ready-to-grow bubble if the saturation pressure or temperature, the value of B, and the cavity radius are known (Shai, 1967). Several modified versions of nucleation criteria have since been advanced. An example is the model proposed by Lorenta et al. (1974), which takes into account both the geometric shape of the cavity and the wettability of the surface (in terms of contact angle < >). Consider an idealized conical cavity with apex angle ip, and a liquid with a flat front penetrating into it (Fig. 2.3a). Assume that once the vapor is trapped in by the liquid front, the interface readjusts to form a cap with radius of curvature rn. Conservation of vapor... 

This same technique should be helpful in understanding wetting properties important in the oil industry since wetting is very dependent on mineral surface energies. The use of contact angle hysteresis information may allow a better understanding of the effects of surface heterogeneities of natural mineral samples. The dynamic Wilhelmy plate technique is ideally suited for such experiments ... 

Central E14-C bonds are longer (about 0.1 A) than the E14-CMe bonds, and the E14-C-E15 angles are greater than the ideal tetrahedral angle of 109.4°, which indicates considerable steric strain due to short nonvalent contacts X---E15. For betaines of the tin series, the E14 E15 distance approaches the sum of van der Waals radii of atoms (Table XI). This regularity is distinctly seen in the experimental X-ray data (see Section 3). 

For practical purposes, if the contact angle is greater than 90° the liquid is said not to wet the solid (if the liquid is water one speaks of a hydrophobic surface) in such a case drops of liquids tend to move about easily and not to enter capillary pores. If 8 = 0, (ideal perfect wettability) Eq. (A.4.3) no longer holds and a spreading coefficient, Sls(V). reflects the imbalance of surface free energies. 

A] bond distances. The restricted bite distances of the xanthate ligands [the S—M—S chelate angles are 73.50(6) and 69.77(4)°, respectively] are most the likely source for the deviations from the ideal octahedral geometries. The distortions are best seen in the twists of the triangular faces, that is, 40.27(7) and 46.43(5)° for the gallium and indium structures, respectively, compared to the ideal octahedral angle of 60°. Enantiomeric pairs associate in their respective crystal lattices via S- -S contacts of 3.598(4) and 3.592(2) A, respectively. 

As for the ideal smooth surface (Section 1.2.3 and Appendix B), the free energy change AF can be calculated as a function of 0M, when a liquid surface initially in a horizontal position (z = 0, 0M = 90°) rises to form a meniscus of height z and a contact angle 0M- The interfacial (AFs l and AFs 2) and potential (AFb) energy contributions need to be modified to take into account the particular geometry of... 

To sum up, the effects on static contact angles of the departures from ideality of solid surfaces are qualitatively well understood and some of these effects are used in practice to improve or reduce wettability. Moreover, for simple geometries, a semi-quantitative agreement is obtained between experimental results and theoretical predictions. For surfaces with random roughness, predictions of wetting hysteresis present a great difficulty because the relevant size of defects is not yet well-established. 

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