Contact Angle Wilhelmy plate method

Three methods are usually used to calculate contact angle—Wilhelmy plate method, sessile drop method [33], and captive bubble method [34]. Sessile drop method is the most commonly used method for biomedical polymers. In this method, about 3 pi of a liquid droplet is placed on the polymer surface and images of the drop are acquired about 30 s of equilibration of the drop. Interface energy between the solid sample snrface and hqnid can also be calculated using the Young s eqnation ... 

Table 1. Air/water/surface contact angles measured using the Wilhelmy plate method on surfaces incubated with deionised water for 10 minutes.

For a plate of rectangular cross section having length f and thickness t, P = 2(f + t) these dimensions can be accurately measured. By suspending the plate from a sensitive balance, we can also measure w with considerable accuracy. The apparatus is called a Wilhelmy balance, and the technique the Wilhelmy plate method. Thus, if the contact angle is known from an independent determination by, say, the tilted-plate method, then 7 can be evaluated by Equation (2). 

Wilhelmy-plate method. What is the force on a plate of 1 cm width having a contact angle of 45° in water ... 

A widely used technique is the Wilhelmy plate method introduced in Section 2.4. If the contact angle is larger than zero, the force, with which the plate is pulled into the liquid, is 27pi cos 0. Here, l is the width of the plate. 

Contact angles are commonly measured by the sessile drop, the captive bubble, and the Wilhelmy plate method. To characterize the wetting properties of powders the capillary rise method is used. 

Some of the commonly used techniques for measuring contact angle [215, 216, 217] are the sessile drop method, captive bubble method and Wilhelmy plate method. These techniques have been extensively used and well documented for characterisation of modified PE surfaces [218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230] for various applications. Whitesides et al. [231 ] studied the wetting of flame-treated polyethylene film having ionisable organic acids and bases at the polymer-water interface. The effect of the size of substituted alkyl groups in amide and ester moieties on the surface hydrophilicity was also studied [232]. The biocompatibility of the polyethylene film surface modified with various water-soluble polymers was evaluated using the same technique [233]. The surface properties of hy-perbranched polymers have been very recently reported [234]. 

For the Wilhelmy plate method, a thin plate with a perimeter of about 4 cm is lowered to the surface of a liquid and the downward force directed on the plate is measured. Surface tension is the force divided by the perimeter of the plate. For this method to be valid, the liquid should completely wet the plate before the measurement, which means that the contact angle between the plate and the liquid is zero. Furthermore, the position of the plate should be correct, which means that the lower end of the plate is exactly on the same level as the surface of the liquid. Otherwise the buoyancy effect must be calculated separately. 

The contact angle of an electrolyte on a solid electrode changes when changing the potential. This effect was used by Morcos and Fischer, who measured the potential-dependent capillary rise of an electrolyte meniscus at the surface of a partially immersed metal plate 11551. The interfaeial energy at a solid elec-trode/solution interface can also be measured by the Wilhelmy plate method 1156,157],... 

From this review it follows that for practical purposes a variety of Wilhelmy plate methods are available. Which one to choose is often a matter of practicality the choice may also depend on the problem at hand. As a trend the rapid methods are less precise, but for many purposes high precision is not needed. The choice also depends on the chemistry of the liquid. For instance, if a solution, containing slowly diffusing solute is studied, the stationary plate mode is recommended, because then one can measure the force as a function of time. Alternatively, when non-zero contact angles pose a problem, the plate can be made intentionally hydrophobic and the downward force measured. 

For some reason the method has lost most of its popularity, probably because sessile droplet methods can nowadays be carried out routinely, providing both the interfacial tension and contact angle. Simultaneously obtaining these two quantities is also feasible with a combination of the Wilhelmy plate method and that of the capillary rise at a stationary vertical plate (see sec. 5.4g). The former gives w = 2y( cos or if b and the latter gives = 2y(l - sin a] / App. see [ 1.3.16]. So we have two equations with two unknowns between which y can be eliminated and a obtained using sin a + cos a = 1. For details, especially in the presence of surfactants, see refs. 

There are two modifications to the Wilhelmy plate method. In the first modification, the cup carrying the liquid is mobile and is lowered until the previously immersed plate becomes detached from the liquid surface, and the maximum vertical pull, / max on the balance is noted, similarly to the ring method. Then the capillary force, for the zero contact angle, can be given as... 

Figure 6.5 Liquid surface tension determination by the Wilhelmy plate method. A rectangular plate of length, /, width, w, and thickness, d, of material having a density of ps, is immersed to a depth of h in a liquid of density pL 6 is the contact angle forming between the liquid and the plate.

Later, Neumann developed the static Wilhelmy plate method which depends on capillary rise on a vertical wall, to measure 6 precisely. A Wilhelmy plate whose surface is coated with the solid substrate is partially immersed in the testing liquid, and the height of the meniscus due to the capillary rise at the wall of the vertical plate is measured precisely by means of a traveling microscope or cathetometer. If the surface tension or the capillary constant of the testing liquid is known, then the contact angle is calculated from the equation, which is derived from the Young-Laplace equation... 

In the measurement of dynamic contact angles utilizing the Wilhelmy plate method with water as the probe liquid, the force on the film is given by the Wilhelmy equation ... 

The essential difference between the two studies is that Elliott and Riddiford, Schwartz et al. (and many others) used optical methods to determine 0 whereas Johnson et al. used the Wilhelmy plate method. The Wilhelmy balance derives the contact angle from a force measurement. 

Figure 4. Determination of contact angles by the Wilhelmy plate method...

Surface Tension, Capillarity, and Contact Angle, Fig. 7 Surface tension measurement, (a) Du Nouy ring method, (b) Wilhelmy plate method... 

Contact angles obtained with the Wilhelmy plate method and near surface energies, Yj and y, obtained with nonlinear programming methods were varied with chain length surface concentrations for 72-alkyldimethyl monochlorosilanes (i.e., 72 = 1, 4, 8, and 18) in various solvents. 

The interesting difference in nanoscale surface phase separation for U-P[AB] is reflected in contrasting wetting behavior. For evaluation of surface wetting properties, DCA analysis by the Wilhelmy plate method was used [44,45]. MDI/BD(36)/ PTMO(2.0) was examined as a reference adv of 93° and 0 of 49°. From previous work [4, 46], 6, 6, and contact angle hysteresis [0 = - 6 = 44°] are... 

This expression makes it possible to obtain solid surface information by making independent contact angle measurements using liquids with known dispersive and polar contributions to O. The surface tension of the solid-vapor interface can be calculated from the slope and the ordinate intercept in plots following Equation 5.12. Alternative approaches based on the Wilhelmy plate method (Wilhelmy, 1863) and variations thereof have been reported recently. 

Ram6, E. 1997. The interpretation of dynamic contact angles measured by the Wilhelmy plate method. Journal of Colloid and Interface Science 185 245-251. 

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