Techniques to measure the surface tension

Before we can discuss the experimental techniques used to measure the surface tension, we need to introduce the so called contact angle 0. When we put a drop of liquid on a solid surface the edge usually forms a defined angle which depends only on the material properties of the liquid and the solid (Fig. 2.8). This is the contact angle. Here we only need to know what it is. In Chapter 8, contact angle phenomena are discussed in more detail. For a wetting surface we have 0 = 0. 

There are several techniques used to measure the surface tension of liquids. The most common technique is to measure optically the contour of a sessile or pendant drop. The measured contour is then fitted with a contour calculated using the Young-Laplace Eq. (2.5). 

From this fit the surface tension is obtained. The same method is applied with a pendant or sessile bubble. Using a bubble ensures that the vapor pressure is 100%, a requirement for doing experiments in thermodynamic equilibrium. Often problems caused by contamination are reduced. 

In the Maximum-bubble-pressure method the surface tension is determined from the value of the pressure which is necessary to push a bubble out of a capillary against the Laplace pressure. Therefore a capillary tube, with inner radius rc, is immersed into the liquid (Fig. 2.9). A gas is pressed through the tube, so that a bubble is formed at its end. If the pressure in the bubble increases, the bubble is pushed out of the capillary more and more. In that way, the curvature of the gas-liquid interface increases according to the Young-Laplace equation. The maximum pressure is reached when the bubble forms a half-sphere with a radius r/s V(j. This maximum pressure is related to the surface tension by 7 = rcAP/2. If the volume of the bubble is further increased, the radius of the bubble would also have to become larger. A larger radius corresponds to a smaller pressure. The bubble would thus become unstable and detach from the capillary tube. 

Drop-weight method. Here, the liquid is allowed to flow out from the bottom of a capillary tube. Drops are formed which detach when they reach a critical dimension. The weight of a drop falling out of a capillary is measured. To get a precise measure, this is done for a number of drops and the total weight is divided by this number. 

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In terms of understanding the mercury/electrolyte interface, it is clear from the above discussion that the measurement of the surface free energy (in terms of the surface tension), is central. If the clectrocapillarity technique could be applied to solid electrodes, then it is capable of supplying information extremely difficult to obtain by any other technique. Sato has indeed developed a technique to measure the surface tension of a metal electrode which he terms piezoelectric surface stress measurement and is based upon the previous work of Gokhshtein (1970). 

Important techniques to measure the surface tension of liquids are the sessile drop method, the pendant or sessile bubble method, the Du-Notiy ring tensiometer, and the Wilhelmy-plate method. 

III. EXPERIMENTAL TECHNIQUES TO MEASURE THE SURFACE TENSION AND THE SURFACE STRESS... 

A somewhat related technique to measure the surface tension between a solid and its melt is described by Still and Skapski 1031. A thin wedge is tilled with the liquid substance and then allowed to solidify. Slowly the temperature is raised. The solid substance starts to melt from the thin part of the wedge, even below its melting temperature (Fig. 6). As in solubility changes, this is caused by the Laplace pressure, which increases the chemical potential in the solid phase. The reduction in melting temperature is given by... 

Techniques to measure the surface tension of solids are notoriously difficult and known for their inaccuracies. Reliable surface tension data requires not only a reliable measurement technique but careful control over parameters such as sample purity and the gaseous atmosphere in which the experiments are conducted. TTie zero creep technique is considered one of the most accurate and reliable of these techniques since it requires only a simple length measurement(8). Samples can be either wires or thin foils. Hondros(9) has postulated that the use of thin foils increases the sensitivity of the technique and thus allows more accurate measurements. The thinner the foil, the more it approximates a surface. Wire gauges are limited due to the loads required to strain the sample. Table I lists some of the results obtained using the zero creep foil technique. It should be pointed out that the terms surface tension and surface free energy are often used interchangeably, though they are not equivalent(9,10). 

Other techniques are of interest but will not be covered here. For example, emphasis is put on the pros and cons of the pendant drop technique by Ambwani and Fort [63]. The pendant drop method has been very laborious traditionally. A fas standard instrumentation using computer image analysis has been described by Hansen and Rodsrud [64]. The characterization of monolayers can be carried out by this technique. For example, Li et al. described the required equipment and the application of the pendant drop technique to measure the surface tension of a insoluble monolayer covered onto a water drop surface [65]. 

Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water-1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water-nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of —0.225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41]. 

The technique used to measure the surface tension of foils in this work couples two well Imown technologies the zero creep technique for foils, and the technique of laser interferometry. The theory behind each of these techniques will be discussed briefly in order to develop the expressions necessary to generate the desired surface tension data which will be used to calculate the surface free energy. 

Droplet deformation in electric fields allows the interfacial tension to be determined, but obviously suffers from the problem of how to keep the object in position. The modem way of achieving this is by levitation, a technique which has, for instance, been applied to measure the surface tension of molten metals ... 

Two methods can be used for the assessment of y and its components contact angle measurements and inverse gas chromatography (IGC) [31]. Chibowski and Perea-Carpio [32] reviewed the problems encountered when attempting to determine the surface free energy of powered solids, like silica particles, using the contact angle technique. Wu reviewed the different techniques that can be employed to measure the surface tension of polymer melts [30]. These techniques are based on the pendant and sessile drop techniques that require density data or contact angle measurements. 

Overall, wettability measurement of small particles is a difficult problem that is further aggravated in the case of heterogeneous surfaces. Some of these problems can result from the presence of patches of different composition in the same particle. It is considered that if these patches are below a critical size of 0.1 mm, the surface is homogeneous regarding its wettability. Several indirect techniques have been developed to measure the surface tension, and thus the wettability of small particles. In these techniques, the surface tensions of the particles are derived from thermodynamic models and include the advancing solidification front or freezing front, sedimentation volume, and particle adhesion techniques [44, 45]. 

A widely used technique for measuring the surface tension is known as the method of maximal pressure of a bubble. Few people are aware that one of its pioneers was a young physicist named Erwin Schrodinger, back in 1915. The principle is quite simple. A capillary tube is partially immersed in a liquid bath down to a depth h much larger than its radius. Air is blown into the tube while the pressure is being measured when the bubble is forming. 

As an extension of this technique, we can introduce into the system a vapor (from a substance other than the solid) prone to getting adsorbed on the surface of the solid, allowing us to measure the surface tension sv of the solid/vapor interface. 

The Wilhelmy Method This is a technique that can be used for both surface/interfacial tension and contact angle measurements (Fig. 7b). To measure the surface tension, a plate with known perimeter P is attached to a balance. 

The advantages of this method include the following (i) it is relatively easy and inexpensive to set up (and commercial systems are available), thanks to the advent of inexpensive electronic pressure transducers (ii) it can be used in extreme environments, such as to measure the surface tension of molten metals, where it would be difficult to image the bubble interface, needed for use in the shape methods and where it would also be difficult to obtain a plate, ring or capillary tube made of suitable materials (iii) the results do not depend on a difficult-to-measure contact angle (iv) a relatively small amount of material is needed (v) in theory, this technique can be applied to liquid/liquid interfaces. The main disadvantage to this technique is that it is not truly a static measurement, as discussed above in Section 1. 

Przyborowski etal. [79] applied the levitation technique for the first time to measure the surface tension of molten silicon and reported a high level of surface tension at the melting temperature and a steep temperature dependence as a = 783.5-0.65(T-1410) mN/m. The rather large absolute value of temperature... 

The automated pendant drop technique has been used as a film balance to study the surface tension of insoluble monolayers [75] (see Chapter IV). A motor-driven syringe allows changes in drop volume to study surface tension as a function of surface areas as in conventional film balance measurements. This approach is useful for materials available in limited quantities and it can be extended to study monolayers at liquid-liquid interfaces [76],... 

There are a number of techniques available to measure the surface or interfacial tension of liquid systems, which together cover a wide range of time. In many cases, several methods are required in order to receive the complete surface tension time dependence of a surfactant system. One of the important points in this respect is that the data obtained from different experimental techniques have to be recalculated such that a common time scale results, i.e. one has to calculate the effective surface age from the experimental time, which is typically determined by the condition of the methods. For example, the maximum bubble pressure... 

The ring technique, and its many variations, is widely used in industrial laboratories. Several kinds of commerical apparatus incorporating a torsion balance are available under the name du Noiiy tensometer. The method is simple and rapid, and is capable of measuring the surface tension of a pure liquid to a precision of 0.3% or better. 

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