Surface drop shape methods

This unit will introduce two fundamental protocols—the Wilhelmy plate method (see Basic Protocol 1 and Alternate Protocol 1) and the du Noiiy ring method (see Alternate Protocol 2)—that can be used to determine static interfacial tension (Dukhin et al., 1995). Since the two methods use the same experimental setup, they will be discussed together. Two advanced protocols that have the capability to determine dynamic interfacial tension—the drop volume technique (see Basic Protocol 2) and the drop shape method (see Alternate Protocol 3)—will also be presented. The basic principles of each of these techniques will be briefly outlined in the Background Information. Critical Parameters as well as Time Considerations for the different tests will be discussed. References and Internet Resources are listed to provide a more in-depth understanding of each of these techniques and allow the reader to contact commercial vendors to obtain information about costs and availability of surface science instrumentation. 

Many different techniques have been developed for the measurement of contact angles 17.8). Of these, the three most useful methods are the Wilhelnty technique, the technique of capillary rise at a vertical plate, and the drop shape methods. These techniques require the solid surface to be flat and smooth. Direct measurement of contact angles on fibers (of uniform thickness) can also be performed using the Wilhelmy technique. For nonflat surfaces or particles, indirect methods such as capillary penetration into columns of powders, sedi-... 

Figure 6.2 Liquid surface tension determination by the drop shape method a. A pendant drop is formed by suspending the liquid from the tip of a thin tube. b. A sessile air (or vapor) bubble is formed in a liquid by injecting the gas from the tip of a needle connected to a syringe.

Future developments will also focus on the combination of different techniques, such as drop pressure and drop shape methods. A more efficient approach would be to combine macroscopic with microscopic or molecular methods, for example drop shape or pressure experiments with ellipsometric or spectroscopic techniques. Another useful possibility involves linking, for example, the inclinded plate or overflowing cylinder technique with scattering experiments, which would allow studies of structure formation under dynamic conditions and at freshly formed surfaces (Howe et al. 1993). 

From rm experimental point of view, studies with protein solutions are very difficult due to their extremely high surface activity. In many experimental techniques the adsorption at the interface, or sometimes even at the surface of the container, tubes and connectors of the dosing system, can lead to a depletion of protein in the bulk. Estimations have shown that the protein mass in the bulk of a drop and in the adsorption layer at the drop surface, are comparable for drops of a radius of 1.5 mm and a bulk concentration of c < 20 mg/1 [234]. The use of the drop shape method however may be considerably extended to small surface pressures, usually n < 2 mN/m and hence to low bulk concentrations when taking into account the protein mass... 

In the last 20 years, large improvements in numerical techniques were obtained by the availability of fast computers. Hence, drop shape methods became more popular due to the direct estimation of the surface tension by profile fitting techniques. Moreover, the utilisation of automatic imaging techniques also provided an easy way to perform measurements in almost real-time conditions. Several set-ups and minimisation procedures have been proposed [21 - 22, 23, 24, 25, 26, 27, 28, 29], in order to increase the measurement accuracy and the sampling rate. Typically, the output of these modem procedures are the best fit values of P and b. 

Today, thanks to the fast development of computer enhanced imaging techniques and numerical fitting procedures, the accuracy and the sampling rate of drop shape methods are substantially increased. Thus, this technique is an important tool for the investigation of adsorption dynamics, and it is particularly suitable for studying processes with characteristic times from a few seconds up to hours and even longer. In fact, there is a large number of experimental studies in which the drop shape technique is used to evaluate the adsorption equilibrium properties, like adsorption isotherms and the dynamic surface tension behaviour. The method is also extensively utilised in the study of surfactants and proteins both in liquid/liquid and liquid/air systems. 

Fig. 12 Dynamic surface tension during the adsorption of C10E5 at water/air interface. From top, the bulk concentrations are 6 10", and lO mol/cm the empty symbols refer to data acquired by the dynamic maximum bubble pressure method, while the filled ones to data acquired by the drop shape method the solid lines are the theoretical prediction by the diffusion controlled adsorption with the two-state isotherm...

An example of such behaviour, studied by the drop shape method described here, is shown in Fig. 1 lb, where the dynamic surface tension during the adsorptive transfer of CioEOg at a fresh water/hexane interface is shown. The diffusion controlled approach can be applied to model the... 

Woodward, R.P., 2010. Surface tension measurement using the drop shape method. Firsttenangstroms. com. First Ten Angstroms. Web. http //www.firsttenangstroms.com/pdfdocs/STPaper.pdf. 

Figure 12.10. Dynamic surface tensions obtained during three subsequent square pulse perturbations of a 5 x 10 mol/cm human serum albumin (HSA) solutions, as measured by the drop shape method (PATl, SINTECH-Berlin, Germany)...

Interfacial tension (7,2) between immiscible liquids can, in principle, be measured by the same methods with which liquid/vapor surface tensions are mea-smed (Adamson, 1990). However, espedally for the measurement of fairly small 7,2 values, a few of these methods are better adapted for this particular purpose, e.g., the pendant drop-shape method (see above), the simpler, but less accurate dropnweight method (Adamson, 1990), and a few other methods using deformed interfaces, sudi as the rotating drop method (Vonnegut,... 

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... 

Sitting or pendent drop. Both methods involve the determination of the shape of the drop in mechanical equilibrium. The shape is determined by the balance between gravitation and surface tensional forces. If gravitation is negligible the shape is always spherical irrespective of the surface tension. 

The sessile drop method, described in Section 3.2.3, can also be used for the determination of contact angle. A sessile drop is created as for surface tension measurement, but instead of measuring drop shape, the contact angle (0) is measured through the liquid phase (Figure 3.16). This can be done using a goniometer. 

The pendant drop technique measures the shape of a liquid drop suspended from the tip of a capillary needle. The drop is optically observed and the surface tension is calculated from the shape of the drop. This method is not as precise as the force measurement method because it depends on the eye of the operator or the sophistication of detection hardware and analysis software. 

The captive bubble method was applied to quantify the wettability of the resist in contact with water, with surfactant solutions of different concentration and with water after contact with the surfactant solution. The wafer piece is mounted with the photoresist layer down in a cuvette filled with the solution of interest. Through a small hole in the wafer an air bubble is placed under the photoresist surface. The shape of the drop is analyzed while its volume is slowly increased and decreased and the contact angle of the bubble is computed. It has to be converted into the water contact angle by subtracting its value from 180°. 

Various experimental methods for dynamic surface tension measurements are available. Their operational timescales cover different time intervals. - Methods with a shorter characteristic operational time are the oscillating jet method, the oscillating bubble method, the fast-formed drop technique,the surface wave techniques, and the maximum bubble pressure method. Methods of longer characteristic operational time are the inclined plate method, the drop-weight/volume techniques, the funnel and overflowing cylinder methods, and the axisym-metric drop shape analysis (ADSA) " see References 54, 55, and 85 for a more detailed review. 

Inside the drop, we require that the velocity and pressure fields be bounded at the origin [which is a singular point for the spherical coordinate system that we will use to solve (7 199)]. Finally, at the drop surface, we must apply the general boundary conditions at a fluid interface from Section L of Chap. 2. However, a complication in using these boundary conditions is that the drop shape is actually unknown (and, thus, so too are the unit normal and tangent vectors n and t and the interface curvature V n). As already noted, we can expect to solve this problem analytically only in circumstances when the shape of the drop is approximately (or exactly) spherical, and, in this case, we can use the method of domain perturbations that was first introduced in Chap. 4. In this procedure, we assume that the shape is nearly spherical, and develop an asymptotic solution that has the solution for a sphere as the first approximation. An obvious question in this case is this When may we expect the shape to actually be approximately spherical ... 

Figure 6.7 Liquid surface tension determination by the spinning drop tensiometer method. A liquid drop (7) is suspended in an immiscible denser liquid (2) in a horizontal transparent tube which can be spun about its longitudinal axis, and the drop (7) elongates from a spherical shape to a prolate ellipsoid with increasing speed of revolution. Later, the drop becomes approximately cylindrical, at very high rotational velocities. A camera with a frame grabber captures the images of the drop inside the transparent tube.

Contact Angle Measurements, were obtained with a Drop Shape Analysis System DSA100 (Kriiss GmbH, Hamburg, Germany) using water and diiodomethane as test liquids. The contact angles were measured by the sessile drop method within two seconds. The surface tension y as well as the dispersive and polar components (yD and yp) were calculated based on the Owens-Wendt method [7],... 

The sessile drop method is similar to the pendant drop one [Sakai, 1965]. The same scheme is used, but in this case the droplet is resting on a plane surface immersed in the second component (see Figure 4.8) — Vj is calculated from analysis of the drop shape at equilibrium (characterized by the relative magnitude of the shape parameters, X and Z, dehned in Figure 4.8), knowing the densities of the polymeric huids at the temperature of measurement. 

This paragraph will briefly present the most frequently used methods for measuring the surface and interfacial tensions as a function of time the maximum bubble pressure, drop volume, growing bubble/drop, bubble/drop shape, and other methods. 

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