Wilhelmy method

It is important to note that a number of different techniques are based on the Wilhelmy method. Here, we will describe only the capillary rise method (based on the Wilhelmy gravimetric plate technique) presented by Lim and Wang [101] and Wang [192]. For more detail on the other Wilhelmy methods, please refer to Mathias et al. [9]. 

The synthesis and purification of C12BMG by the reaction of N-methyl-benzylamine with sodium chloroacetate followed by the quaternization of the resulting tertiary ammonioacetate with 1-bromododecane is described elsewhere (12). Purification of aqueous solutions of the surfactant for surface tension measurements and determination of the surface tension of the solutions by the Wilhelmy method using a sandblasted platinum blade were by techniques previously described (13). The concentration of C12BMG in aqueous solution was determined by measuring its absorbance at 263 nm (e = 350.5). 

All the techniques described here are easily conducted, so that both 0a and 0, may be observed. When the tilted plate method is used to evaluate the contact angle, 6r values are obtained if the plate has been pulled out (emersion) from the liquid 0a results if the plate is pushed into the liquid (immersion). Likewise, both values of 0 may be obtained from the Wilhelmy method, depending on whether the liquid is making an initial contact (0a) with the plate or is draining from it (6r). 

The Wilhelmy method. In the top picture a plate of the solid surface is lowered into a submerging liquid. The liquid pushes up on the solid sample with force due to the buoyancy and the surface tension, and these forces are measured by instruments attached to the arm above the sample and depend on the length d, surface tension n, and wetted length / (the perimeter of the sample along the line of contact of the air, liquid, and solid). In the bottom picture the sample is being raised and the liquid exerts a downward force. 

While the Wilhelmy method at first sight seems to be an ideal method, it has several drawbacks that are not immediately obvious and that can restrict the usefulness of the method. The high sensitivity of the electrobalance employed in the Wilhelmy method can be exploited only if the perimeter is constant. 

In this method, the solid surface is also aligned vertically and brought into contact with the liquid. Instead of the capillary pull as in the Wilhelmy method, the capillary rise h at the vertical surface is measured (see Fig. 3). This method has been found particularly effective for measuring contact angles as a function of the rate of advance and retreat and for determining the temperature coefficient of 0. 

Figure 26.20 A correlation between the average of dynamic advancing and receding contact angles from the Wilhelmy method and static advancing contact angles from the sessile droplet method for untreated, TMS and TMS + O2 treated pol5rmers follows the relationship given by cos 6s = (cos 0u, .,i + cos 0D,a,i)/2.

It has been observed the formation of continuous liquids on high-energy solid surfaces, such as mica, quartz, and silica, when those surfaces are subjected to immersion and emersion in water [13,14]. A continuous film of water on a hydrophilic (i.e., high energy) plasma polymer-coated glass slide moments after it was immersed to a depth of 3 cm in a beaker of DDI water is shown in Figure 26.21A. The water film remained continuous as it receded to the bottom of the plate. After about 2 min the water film front receded to approximately 1 cm from the bottom of the plate, as shown in Figure 26.21B. The presence and stability of a continuous water film can be detected and quantified by the Wilhelmy method [15]. 

The mathematical analysis of the detachment of the circular (pin method) and rectangular (Wilhelmy method) rod from the liquid surface was given by Lillebuen (1970). He showed that the surface tension of the liquid is given by the equation... 

Vilanove and Rondelez11 measured the surface osmotic pressure of a polymer as a function of concentration. They used poly-vinyl acetate (PVAc) spread on an air-liquid interface. They determined the osmotic pressure by using the Wilhelmy method (see Section 1.10). 

Figure 18.3 Wilhelmy method for measuring surface tension.

The so-called synthetic fibres, e.g. nylon, show their peculiarities of wetting in the presence of surfactants of various nature. Capillary wetting rates of nylon fibrous assemblies were studied in [172] using conductivity measurements as well as contact angle measurements by the Wilhelmy method. For sodium dodecyl sulphate and dodecyl trimethyl ammonium chloride a minimum wetting rate was observed near pH 4, which coincided with the isoelectric point of the nylon fibre. When the surface charge increased, the wetting rate increased. 

The measurement of surface pressure (jr) was accomplished using the Wilhelmy method in which a glass slide was partially immersed in the water subphase and the effective change in weight of the slide was recorded after a monomolecular film was spread and compressed at the air-water interface. The equation relating ir to change in weight of the slide is ... 

Single fiber This is a dynamic Wilhelmy method which is... 

The Wilhelmy method does not require a correction factor for meniscus shape. It requires correction if the plate is partially or completely submerged in the liquid. In Eq. (2.9), is the total force on the plate which is measured, Pp is the weight of the plate, p is the perimeter of the plate, and is the ideal surface tension. A buoyant force term must be added to or subtracted from the second part of equation, depending on whether the plate is above or below the level of the free liquid. In Eq. (2.10), h is the height above or below the free liquid level, A is the cross-sectional area of the plate, and y is the surface tension. 

For measurement of the work of adhesion to the surface of the fibres the Wilhelmy method is known to be appropiate /15/. Although here the contact angle cannot be measured directly. But the method allows us to measure the wetting force F and the tear-off force F q with an electrical balance. The contact angle can be obtained according to one of the following two equations. 

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