Diffuse equilibrium in thin films

Speciation is best carried out directly in the aquatic system, without sampling. This has been possible since the development of Diffusive Equilibrium in Thin Films (DET) and Diffusive Gradient in Thin Films (DGT) probes.31 The DET probe consists of a very thin gel layer that is immersed in the aquatic system and allowed to equilibrate with the bulk solution. The concentration of solutes in the gel is similar to that in the bulk solution for all solutes that can diffuse through the pore openings of the gel (some gels have open pores >5 nm and some gels have restricted pores <1 nm). The DGT... 

Leermakers, M., Y. Gao, C. Gabeille, et al. 2005a. Determination of high resolution pore water profiles of trace metals in sediments of the Rupel River (Belgium) using DET (diffusive equilibrium in thin films) and DGT (diffusive gradients in thin films) techniques. Water Air Soil Pollut. 166 265-286. 

A variant of the device, known as diffusive equilibrium in thin films (DET), can be deployed to perform relatively rapid (within a day) response times and has the ability to measure at high spatial resolution. The DET comprises a single relatively thick sheet of gel (typically 0.8 mm) supported in a holder. Solutes in the surroimding water diffuse into the gel until concentrations in gel and water are equal. 

Meylan, S., N. Odzak, R. Behra, and L. Sigg. 2004. Speciation of copper and zinc in natural freshwater Comparison of voltammetric measurements, diffusive gradients in thin films (DGT) and chemical equilibrium models. Anal. Chim. Acta 510 91-100. 

Diffusion Gradient in Thin films (DGT) and equilibrium techniques such as Peepers and DETs... 

Additional deviations from the Nernst law [Eq. (4)] can come from kinetic effects in other words, if the potential scan is too fast to allow the system to reach thermal equilibrium. Two cases should be mentioned (1) ion transport limitation, and (2) electron transfer limitation. In case 1 the redox reaction is limited because the ions do not diffuse across the film fast enough to compensate for the charge at the rate of the electron transfers. This case is characterized by a square-root dependence of the current peak intensity versus scan rate Ik um instead of lk u. Since the time needed to cross the film, tCT, decreases as the square of the film thickness tCT d2, the transport limitation is avoided in thin films (typically, d < 1 xm for u < 100 mV/s). The limitation by the electron transfer kinetics (case 2) is more intrinsic to the polymer properties. It originates from the fact that the redox reaction is not instantaneous in particular, due to the fact that the electron transfer implies a jump over a potential barrier. If the scan... 

It has been well known for several decades that reactive diffusion in thin films usually demonstrates one-by-one (sequential) phase formation. Despite the existence of several stable intermediate phases in the phase equilibrium diagram, only one growing phase layer is usually observed. The next phase appears or at least becomes visible, after one of the terminal materials has been consumed, so that the first phase has no more material for growth, becoming a material for second phase formation itself, and so on. Such sequential growth has at least three possible explanations ... 

Note that the diffusion process within thin films approaches equilibrium in very short times, thereby enabling the correlation between E and m, including the dependence of g on m. For the specific material at hand, additional experimental evidence suggested that Eg and g depended on m alone, thus the effect of moisture could be further isolated. 

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

Diffusion in general, not only in the case of thin films, is a thermodynamically irreversible self-driven process. It is best defined in simple terms, such as the tendency of two gases to mix when separated by a porous partition. It drives toward an equilibrium maximum-entropy state of a system. It does so by eliminating concentration gradients of, for example, impurity atoms or vacancies in a solid or between physically connected thin films. In the case of two gases separated by a porous partition, it leads eventually to perfect mixing of the two. 

The solution diffusion properties of FITC-labelled BSA were measured by FRAP [12], The results showed that the protein diffused freely in solution with a diffusion coefficient of approximately 3xl0 7 cm2/s. This was in reasonable agreement with previously published values [36]. FRAP measurements were also made on thin films stabilized by FITC-BSA. The films were allowed to drain to equilibrium thickness before measurements were initiated. Thin films covering a range of different thicknesses were studied by careful adjustment of solution conditions. BSA stabilized films that had thicknesses up to 40 nm showed no evidence of surface diffusion as there was no return of fluorescence after the bleach pulse in the recovery part of the FRAP curve (Figure 14(c)). In contrast, experiments performed with thin films that were > 80 nm thick showed partial recovery (55%) of the prebleach level of fluorescence (Figure 14(b)). This suggested the presence of two classes of protein in the film one fraction in an environment where it was unable to diffuse laterally, as seen with the films of thicknesses < 45 nm, and a second fraction that was able to diffuse with a calculated diffusion coefficient of lxlO 7 cm2/s. This latter diffusion coefficient was 3 times slower than that... 

We have tested this hypothesis in some recent o/w thin film experiments [45]. It was not practical to reduce the protein load per unit area of interface to that found in the emulsion experiments, since the very low concentrations required would have been very slow to reach equilibrium adsorption. We circumvented this problem in a unique way. Rather than adsorb emulsifier mixtures from aqueous solution, we formed the oil droplets and the thin film in a preformed emulsion. Therefore, the adsorbed layers on the captive droplets formed by adsorption of surfactant from the continuous phase of the emulsion. The results are shown in Figure 23, where surface diffusion data of FITC-/8-lg in o/w and a/w thin films as a function of added Tween 20 are summarised. 

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