Growing drop methods

The difference in the design of the other growing drop set-ups consists most of all in the use of a direct pressure transducer instead of a differential one. In all cases the data acquisition is made by an on-line coupled computer. In the instrument of Nagarajan Wasan (1993) the syringe is also controlled by the computer allowing different types of volume, and consequently drop surface area changes to be measured. The instruments of MacLeod Radke 

Data acquisition and interpretation is comparatively fast, and processes from time scales of tens of milliseconds up to 100 seconds and more can be studied. The accuracy of the method depends directly on the pressure transducer. It amounts to 0.1 mN/m for example for the setup described by Nagarajan Wasan (1993). By applying definite volume changes, linear or step-type ones, this set-up can be used simultaneously for relaxation studies. Such experiments are described in the next chapter. 

As discussed by MacLeod Radke (1993) the growing drop instrument in the design shown in Fig. S.19 provides three experimental techniques a maximum drop pressure, a continuously 

Under certain conditions, the hydrodynamics of growing drops can cause flow pattern inside and outside the drop, dependent on the liquid flow rate. Such situations were described above in connection with the drop volume method. 

According to Liggieri et al. (1990), the process of bubble of drop growth is stable when a stability number BSN, defined by 

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A growing-drop method has been reported [53] for measuring interfacial liquid-liquid reactions, in which mass transport to the growing drop was considered to be well-defined and calculable. This approach was applied to study the kinetics of the solvent extraction of cupric ions by complexing ligands. 

Growing drop methods constitute a more recent group of techniques, not discussed so far. They have in common that a drop is formed at the tip of a narrow capillary, inside which the pressure is measured by a very sensitive transducer. A variety of sophisticated designs to carry out the measurement can be found in the recent literature. ... 

In the first case, either the theoretical model has to allow for the evaporation process or evaporation has to be avoided by the establishment of special experimental conditions. MacLeod Radke (1994) report on the adsorption kinetics of 1-decanol at the aqueous solution interface using the growing drop method. They distinguish between three cases decanol in the aqueous phase only, decanol in the air phase only, decanol in both phases. The adsorption kinetics shows different behaviour and is fastest for the case of decanol in both phases (Fig. 5.34). The application of a proper theory (for example Miller 1980, MacLeod Radke 1994) in all three cases is a diffusion-controlled mechanism of the decanol adsorption kinetics. 

In the applications of the capillary pressure tensiometry deseribed, an equivalent to Eq. (4.119) is used in the two particular cases in which either the surface tension (pressure derivative method) or the drop curvature (expanded drop method) are constant. In other applications, like the expanding or growing drop methods developed respectively by Nagarajan and Wasan and McLeod and Radke, respectively [25, 154], the capillary pressure is monitored while the surface area is increasing continuously. In these methods APcap changes due to the variation of the drop radius and of the interfacial tension caused by the dilation of the surface which put the system in a state out of the adsorption equilibrium. The problem is that area change, flow in the bulk phases, and the adsorption kinetics of the present surface active compounds have to be considered in a model simultaneously. 

Figure 12.13. Schematic set-up for the growing drop method (according to Liggieri and Ravera (3))...

In LSV usually a single-sweep procedure, the so-called impulse method, is applied with the result illustrated in Fig. 3.30. In the multi-sweep procedure, formerly called Kipp method, Fig. 3.31 is obtained, which shows the saw-tooth character of the sweep and a series of peak curves of increasing height caused by the growing drop surface. Exceptionally, use is made of a triangular sweep in the impulse method this variant of cyclovoltammetry is depicted in Fig. 3.32... 

Figure 3.2 Growing crystals by the hanging-drop method. The droplet hanging under the cover slip contains buffer, precipitant, protein, and, if all goes well, growing protein crystals.

FIGURE 2.8. Some methods for growing crystals from solution, (a) Slow solvent evaporation, primarily used for small molecules, (b) Vapor diffusion, (c) The hanging drop method, primarily used for macromolecules, (d) A crystallization plate used for hanging drops there are slightly different crystallization conditions in each well, varied systematically with respect to, for example, pH and ionic strength. 

The following so-called dynamic capillary method was developed by Van Hunsel Joos (1987b) and complements the area of application with respect to other methods. This method allows measurements from 50 ms up about 1 s, similar to the inclined plate and growing drop techniques described above, and can be used at liquid/liquid and liquid/gas interfaces without modification. The principle of the experiment is schematically given in Fig. 5.23. Two fluids are contained in a tube of diameter R. The interface (or surface in case of studies at the water/air interface) is located in such a way that its interfacial tension can be measured by the capillary rise of the lower liquid in a narrow capillary c, which connects the both fluids. The height of the capillary rise h is determined via a cathetometer Cat. 

Fig. S.26 Schematic relations between specific experimental time scales and the effective surface age (adsorption time) for several methods drop volume (1), maximum bubble pressure (2), growing drop (3)...

As discussed in detail in the book [193] there is a group of methods based on static or growing drops and bubble which give access to interfacial tensions at short adsorption times, i.e. parts of a second, up to several minutes and even hours. These methods are based on the measurement of the capillary pressure, however, the entire process of the drop or bubble formation is used to study the adsoiption processes at the respeetive interface. 

All the methods are based on the Laplace equation (4.126). While the eapillary pressure method works with drops or bubbles of constant size, the pressure derivative method [194] has been conceived for measuring the interfacial tension of pure liquids. To study dynamic aspects of adsorption the growing drop or bubble [25, 154] and the expanded drop [195, 196] methods have been developed. 

Deuteiiiim. This is very cheap, readity available, and can be measured by the falling drop method very simply. It is possible to grow quite large organisms on heavy water (D O). Studies of the results of such substitutions have been very informative about numerous molecular processes. 

In the flame fusion method (Verneuil), the powder falls onto an O2-H2 flame and the melt drops on a seed crystal, which is slowly lowered as the crystal grows. The method has been applied to grow high-melting-point oxides (ruby and sapphire). The starting powder is usually placed on a gently hopped mesh to get a continuous flow of solid particles of the same size. 

All drop and bubble methods are based on the Laplace equation of capillarity. In order to study dynamic aspects of adsorption, the growing drop or bubble and the expanded drop methods are suitable (3). In Figure 12.13, the schematic of a static or growing drop instrument is shown. In applications of capillary pressure tensiometry, an equation which is equivalent... 

The dripping radius, r, has to be equal to the capillary radius or be known. The method is not very precise and demands a careful manipulative skill. Semiautomatic [377] and automatic drop volume methods [378] have been developed. The calculation of interfacial tensions corrected for transport processes inside the growing drop is simplified by interfacing the tensiometer with a computer. 

The Metrohm method may have the advantage that the residual current (iF effect) remains constant during the sampling steps, but the drop still grows (ic effect) both are miniscule effects. The PARC method can be combined with the PARC SMDE technique (see p. 136), which excludes ic alterations due to drop growth during sampling. 

Convective diffusion to a growing sphere. In the polarographic method (see Section 5.5) a dropping mercury electrode is most often used. Transport to this electrode has the character of convective diffusion, which, however, does not proceed under steady-state conditions. Convection results from growth of the electrode, producing radial motion of the solution towards the electrode surface. It will be assumed that the thickness of the diffusion layer formed around the spherical surface is much smaller than the radius of the sphere (the drop is approximated as an ideal spherical surface). The spherical surface can then be replaced by a planar surface... 

Now consider the gradient-pH case, with pHD 3 and pHa 7.4. In Fig. 3.5b, the dashed curve (donor concentration) corresponding to pH 3 decreases more steeply after the retention period than that of the previous iso-pH example. Furthermore, there is not the large initial drop due to the disappearance of the sample into the membrane in the gradient-pH case, retention drops from 56% to 9%. Thus, more of the compound is available for sample concentration determination. The solid curve (acceptor concentration) corresponding to pH 3 also grows more rapidly than in the iso-pH example. The dashed and solid curves cross at 7 h, with C(t)/CD(0) close to the 0.5 value. Note also, that about 70% of the compound ends up in the acceptor well at the end of 16 h - much higher than is possible with the iso-pH method. 

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