Thermodynamic approach to prediction of the effect of size on nanostructure properties
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THERMODYNAMIC APPROACH TO PREDICTION OF THE EFFECT OF SIZE ON NANOSTRUCTURE PROPERTIES
K. I. Patrylak, L. K. Patrylak, and S. V. Konovalov
UDC 544.3:544.77.023.5
Approaches to the prediction of the properties of small particles with diameter down to 1-2 nm are proposed using the Thomson–Kelvin, Clapeyron–Clausius, and Laplace laws as well as the Poynting effect. Particles with minimal dimensions but with a well-formed surface characterized by surface tension were found to be optimal relative to chemical potential.
Key words: small particles, nanostructures, clusters, dimensional effect, thermodynamics, fundamental properties, catalytic activity.
Recently, small particles, usually termed nanostructures or clusters, have been the subject of increasing attention due to their catalytic and other special properties. Since the dimensions of the active phase can be controlled in the preparation of catalysts, it is important to know the dependence of catalytic properties of nanostructures on their size. These investigations have just begun [1-4] and a complex relationship has been found between the activity and selectivity of nanocatalysts on the dimensions of the nanophase. In particular, we should note the work of Stolyarchuk et al. [2] on the catalytic reforming of ethanol vapor on 8-nm particles of manganese ferrite, which display extremely high activity. Even more interesting is the work of Bychko et al. [3], in which the optimal diameter (6.5 nm) was found for different particles in a different reaction. Particles with greater or smaller diameter display lower activity. These authors regard this finding as proof of an irregular dependence of catalytic activity on particle size and relate this irregularity to the particle morphology, i.e., different ratio of faces, edges, and apices in the particles with different activity of these surface elements. However, while not rejecting a relationship of surface morphology to the catalytic properties of small particles, we do not exclude the possibility that an irregular dependence of the activity of particles on their size is primarily due to thermodynamic factors. Unfortunately, concepts of “small particles” or “nanostructures” are rather indefinite relative to the dimensions of these particles, especially in regard to the concept of “nanostructures” since particles with an extremely wide range of sizes fall into this category. In our view, the concept of “cluster,” which includes particles with diameter down to 1-2 nm is more definite and implies a body not fully formed with virtually identical accessibility of all the atoms or molecules comprising such a body for other particles from liquid, vapor, or gaseous media. We prefer to differentiate small particles on the basis of whether or not they have surfaces, i.e., a defined layer with special properties, especially surface tension. We term small particles with a well-formed surface “dispersed particles,” while we term those without a well-formed surface “clusters.” This classification markedly facilitates the discover
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