Local composition methods

Local composition is very useful supplementary information that can be obtained in many of the transmission electron microscopes (TEM). The two main methods to measure local composition are electron energy loss spectrometry (EELS), which is a topic of a separate paper in this volume (Mayer 2004) and x-ray emission spectrometry, which is named EDS or EDX after the energy dispersive spectrometer, because this type of x-ray detection became ubiquitous in the TEM. Present paper introduces this latter method, which measures the X-rays produced by the fast electrons of the TEM, bombarding the sample, to determine the local composition. As an independent topic, information content and usage of the popular X-ray powder dififaction database is also introduced here. Combination of information from these two sources results in an efficient phase identification. Identification of known phases is contrasted to solving unknown stmctures, the latter being the topic of the largest fiaction of this school. 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

The local composition model (LCM) is an excess Gibbs energy model for electrolyte systems from which activity coefficients can be derived. Chen and co-workers (17-19) presented the original LCM activity coefficient equations for binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with electrolytes. The LCM activity coefficient equations are explicit functions, and require computational methods. Due to length and complexity, only the salient features of the LCM equations will be reviewed in this paper. The Aspen Plus Electrolyte Manual (1) and Taylor (21) present the final form of the LCM binary and multicomponent equations used in this work. 

It should be noted that distribution coefficients Ki comprise both fugacities in the gas phase and activity coefficients in the liquid phase. These coefficients are determined by the three-parametric Electrolyte-NRTL method. The latter is based on the local composition concept and satisfactorily represents physical interactions of this multicomponent electrolyte system [46]. 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

Absuleme, J. A. Vera, J. H., "A Generalized Solution Method for the Quasi-Chemical Local Composition Equations," Can. J. Chem. Eng., 63, 845 (1985). 

We have seen that the method of preparation and the information provided by transmission electron microscopy may vary considerably depending on the type of study undertaken. At the same time, a considerable range of qualitative and quantitative observations is potentially available. It is thus essential to clearly define in advance the goal of the transmission electron microscopy observation (particle size, variations in local composition, etc.). 

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood—Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol -I- water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state. 

In the present paper, the method which the authors employed previously to derive an expression for the solubility of various proteins in aqueous solutions, has been extended to the solubility of gases in mixtures of water + strong electrolytes. One parameter equation for the solubility of gases has been derived, which was used to represent the solubilities of oxygen, carbon dioxide and methane in water -i- sodium chloride. In additions, the developed theory could be used to examine the local composition of the solvent around a gas molecule. The results revealed that the oxygen, carbon dioxide and methane molecules are preferentially hydrated in water-i-sodium chloride mixtures. A similar result was obtained for the water -i- methane -i- sodium chloride by molecular dynamics simulations [72]. 

There are many other equations, which have been proposed, that do not result from Wohl s method. Two of the most popular equations are the Wilson and the universal quasi-chemical theory (UNIQUAC) by Abrams and Prausnitz.These equations are based on the concept of local composition models, which was proposed by Wilson in his paper. It is presumed in a solution that there are local compositions that differ... 

Since 1980 polymer thermodynamics has been developed considerably and, to date, models are available that are suitable for at least satisfactory calculations of VLE and, qualitatively, also for LLE. Some of these methods are models for the activity coefficient, which are modifications of the FH equation. These modifications use a similar to FH but better combinatorial/free-volume expression and a local-composition-type energetic term such as those found in the UNIQUAC and UNIFAC models. Models like the UNIFAC-FV and the Entropic-FV are discussed in Section 16.4. 

Simple GC methods based on UNIFAC, containing corrections for the FV effects, satisfactorily predict the solvent activities and VLE for binary and ternary polymer solutions. They are less successful for the prediction of LEE if the parameters are based on VLE. They are much more successful if the parameters are based on LEE data. The combination of a simple FV expression such as that employed in the Entropic-FV model and a local composition energetic term such as that of UNIQUAC seems to be a very promising tool for both VLE and LLE in polymer solutions. We expect that such tools may find widespread use in the future for practical applications. 

With an SECM positioned above a surface with deposited nanoparticles of dioxygen reduction electrocatalysts in a solution saturated with dioxygen, significant decreases of tip current are observed. Variations in the nature of catalyst spots, including inhomogeneities, could be localised. Further modes include the potentio-metric mode with an ion selective UME that is used to probe the local composition of the solution. This method is basically equivalent to the scanning ion-sensitive electrode technique SIET (see p. 270, particularly pH microscopy). 

Although a flame is ideally an inert matrix for the study of kinetics at high temperatures and some reactions are indeed known for which the flame is in this sense ideal, in the great majority of the reactions studied in flames is some interaction between the reactants and the flame, and it is therefore necessary to specify the local flame composition before a meaningful study of kinetics can be achieved. Even before these local compositions can be specified, the local temperature and time scale must be established, and, in the present section, the methods whereby these local parameters are established will be briefly considered. 

---