Surface tension method accuracy

The maximum bubble pressure method is good to a few tenths percent accuracy, does not depend on contact angle (except insofar as to whether the inner or outer radius of the tube is to be used), and requires only an approximate knowledge of the density of the liquid (if twin tubes are used), and the measurements can be made rapidly. The method is also amenable to remote operation and can be used to measure surface tensions of not easily accessible liquids such as molten metals [29]. 

It is thus apparent from what has been discussed so far that the measurement of the surface tension of liquids is an important analysis. The method to use in the measurement of y depends on the system and experimental conditions (as well as the accuracy needed). For example, if the liquid is water (at room temperature), then the method used will be different from that if the system is molten metal (at very high temperature, ca. 500°C). These different systems will be explained in the methods described in this section. 

However, the advantage of the former over the latter method consists in that it makes it possible to choose the most convenient form and size of the body (platinum rod, ring, or plate) so as to enable the measurement to be carried out rapidly but without any detriment to its accuracy. The detachment method has found an application in the case of liquids whose surface tensions change with time. 

This is one of the many detachment methods of which the drop weight and the Wilhelmy slide methods are also examples. As with all detachment methods, one supposes that, within an accuracy of a few percent, the detachment force is given by the surface tension multiplied by the periphery of the surface (liquid surface) detached (from a solid surface of a tubing or ring or plate). This assumption is also found to be acceptable for most experimental purposes. Thus, for a ring, as illustrated in Figure 2.12,... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

The many methods available for the measurement of surface and interfacial tensions can be classified as static, detachment and dynamic, the last of these being used to study relatively short time effects. Static methods usually offer a greater potential for accurate measurement than detachment methods (especially when solutions of surface-active agents are involved)43, but detachment methods tend to be the more convenient to operate. With careful experimentation and exclusion of contaminants (especially surfactants), it is usually possible to measure surface tensions to an accuracy of 0.01 to 0.1 mN m-1. It is unwise to use water which has been in contact with ion-exchange resins. 

Harkins and his colleagues1 have extended these measurements of the work of adhesion to water, and also to mercury.2 The measurements of surface tension were made by the drop-weight method, using the corrections necessary for accurate results as three separate measurements of surface tension are required, considerable accuracy is desirable for trustworthy results in the work of adhesion. 

This method might be very useful as a differential method for comparing the surface tensions of two similar liquids, such as water at different temperatures, and water and dilute solutions, for differences of gaseous pressure can be measured with great accuracy. 

For the case where is not very small, Ferguson and Vogel1 have calculated the corrections to (12) and Griinmach2 has constructed an instrument with a series of hyperbolas ruled on the plates the angle is altered until the surface of liquid coincides with one of them, when the surface tension can be calculated from (12). The method is ingenious but not capable of very high accuracy. 

The various dynamic methods give the surface tension of more or less recently formed surfaces, and may yield results different from the static methods, if adsorption occurs, and is incomplete at the moment when the tension is actually measured. One factor in dynamic measurements, which cannot be satisfactorily measured at present, is the time which has elapsed between the formation of the surface from the homogeneous interior liquid, and the actual measurement of the surface tension. If this could be varied, and measured with an accuracy of say 10 4 second, a valuable new weapon would be available for investigating the progress of adsorption. Bohr s work on oscillating jets is probably the best on any dynamic method. 

The applied pressure is related to the desired pore size via the Washburn Equation [1] which implies a cylindrical pore shape assumption. Mercury porosimetry is widely applied for catalyst characterization in both QC and research applications for several reasons including rapid reproducible analysis, a wide pore size range ( 2 nm to >100 / m, depending on the pressure range of the instrument), and the ability to obtain specific surface area and pore size distribution information from the same measurement. Accuracy of the method suffers from several factors including contact angle and surface tension uncertainty, pore shape effects, and sample compression. However, the largest discrepancy between a mercury porosimetry-derived pore size distribution (PSD) and the actual PSD usually... 

Initially there were great hopes that the drop-time method would provide fast and accurate data on the surface tension in general and on its potential dependence in particular. Closer examination, with the use of fast photography, has shown the process of detachment of a drop from the surface to be rather complex. Just before the drop falls off, it becomes elongated. Eventually it breaks off at a small distance from the capillary, not at the capillary itself. Based on these observations, it is clear that Eq. 55H cannot be exactly correct, and one may even wonder why the drop time should depend on surface tension at all. The fact is that a dependence such as shown in Eq. 55H is nevertheless obeyed, to a good approximation. Tlie limited accuracy of the drop-time method is due to this uncertainty, and the results probably can be considered to be accurate to within about 2%. 

A combined apparatus for measuring surface tension by the capillary tube method, viscosity, and density, seems handy for work of moderate accuracy carried out by experimenters in a hurry. In measuring the surface tensions of liquid mixtures or solutions, evaporation must be completely prevented, otherwise the surface tension will depend on time. ... 

Variations to improve accuracy, facilitate handling, or render the method applicable to special systems have been proposed. For instance, Richards and Carver ) developed a capillary with a reflush device (a wider tube, parallel to the vertical capillary) to facilitate rejuvenation of the liquid surface. This apparatus was modified by Young and Gross ). Ramakrishnan and Hartland ) developed a procedure of measuring surface tensions in the annular ring between two concentric cylinders. This approach was duplicated by Agrawal and Menon ). Long ago Sentis ) experimented with an isolated capillary on the lower end of which a... 

Before continuing, it is appropriate to consider the accuracy and reproducibility of the various static methods discussed so far. To that end data for the surface tension of water, y", obtained by different investigators with different materials and conditions will be compared. 

In surface tension measurements using the maximum bubble pressure method several sources of error may occur. As mentioned above, the exact machining of the capillary orifice is very important. A deviation from a circular orifice may cause an error of 0.3%. The determination of the immersion depth with an accuracy of 0.01 mm introduces an error of 0.3%. The accuracy of 1 Pa in the pressure measurement causes an additional error of 0.4%. The sum of all these errors gives an estimated total error of approximately 1%. Using the above-described apparatus, the standard deviations of the experimental data based on the least-squares statistical analysis were in the range 0.5% < sd > 1%. 

In theory, every surface tension measurement method can be used to determine the interfacial tension between two liquids. However, the accuracy of these methods is reduced when applied to liquid-liquid interfaces, or when one or both of the liquids is viscous. In practice, the maximum bubble pressure and pendant drop methods are the most suitable, giving consistent and reliable values for interfacial tensions, although there is sometimes the... 

The maximum bubble pressure method, realised as the set-up discussed above, allows measurements in a time interval from 1 ms up to several seconds and longer. At present, it is the only commercial apparatus which produces adsorption data in the millisecond and even sub-millisecond range (Fainerman Miller 1994b, cf. Appendix G). Otherwise data in this time interval can be obtained only from laboratory set-ups of the oscillating jet, inclined plate or other, even more sophisticated, methods. The accuracy of surface tension measurements in... 

An obvious method is to define the equilibrium state as the condition of constant surface or interfacial tension over an appropriate time interval, taking into account the accuracy of the method used. Difficulties are inherent to such procedures as the time interval and the accuracy of the method chosen are subjective. For example, if a state is called as an equilibrium one after the surface tension has changed less than 0.1 mN/m within a time period of 10 minutes, this state is characterised by the relation. 

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