Properties of very small particles

If a particle is small enough, the surface energy produces measurable effects on the observable properties of a substance. Two examples are the enhanced vapor pressure of small droplets and the increased solubility of fine particles. 

Consider a liquid in equilibrium with vapor, with a plane interface between the two phases. Let the vapor pressure in this circumstance be. The pressure just inside the liquid phase is also p, since the interface is plane, by Eq. (18.9). If, on the other hand, we suspend a small droplet of radius, r, then the pressure inside the droplet is higher than in the gas phase because of the curvature of the surface, also by Eq. (18.9). This increase in pressure increases the chemical potential by an amount dp = dp, where is the molar volume of the liquid. If the vapor is to remain in equilibrium, the chemical potential of the vapor must increase by an equal amount, or 

Using Eq. (18.9) for the pressure jump across the interface, we have 

Another consequence of Eq. (18.14) is that a vapor condenses in a fine capillary at pressures below the saturation pressure if the liquid wets the capillary. In this situation, r is negative the liquid surface is concave. Similarly, if the liquid is to evaporate from the capillary, the pressure must be below the saturation pressure. 

The solubility of solids depends on particle size in a similar way. The solubility equilibrium condition is 

---

In the treatment of thermodynamics, some errors have been corrected, some passages clarified, and a few new topics introduced. The emphasis on the laws of thermodynamics as generalizations from experience is maintained. The chapter on electrochemical cells has been revised and a discussion of electrochemical power sources has been added. The chapter on surface phenomena now includes sections on the BET isotherm and on the properties of very small particles. 

It is usual but not necessarily sensible to regard geometric and electronic structures as quite separate things, whereas in reality they are closely connected. The form adopted by a metallic or bimetallic particle will depend on the bonds formed between the component atoms, that is to say, on its electronic structure and, because of the mobility of surface atoms, the properties of very small particles (dispersion >50%) will be dominated by electronic factors. 

Besides size and geometric properties, it is also possible to study the electronic properties of very small particles through their ionisation potential or electron affinity. These parameters have been evaluated by mass spectrometry in the case of very small aggregates of selenium [38]. 

The metal size clearly increases when the decomposition takes place on the substrate. Nevertheless, the overall shift after complete decomposition is the same both on crystalline and amorphous substrates. This can be explained by the assumption that the increase of the number of the metal atoms in the cluster takes place also on an amorphous substrate, on a scale high enough to shift the core levels but low enough to maintain a constant emitted intensity ratio between the substrate and the metal core levels. The authors concluded therefore that the core-level position is highly size-sensitive in the range of very small particles, e.g. < 100 atoms where the associated electronic properties are primarily atomic. However, on approaching the metallic state for >100 atoms, the corelevel shift is a much poorer criterion of the cluster size. 

Coated particles are of interest for investigations involving catalysis, medicine and pigment production. The coatings which can be used to modify the properties of the underlying Fe oxide, may consist of a continuous, uniform shell around the core particle, or may be made up of very small particles that adhere to the core. 

In the gas black process (Fig. 55), the feed stock is partially vaporized. The residual oil is continuously withdrawn. The oil vapor is transported to the production apparatus by a combustible carrier gas (e.g., hydrogen, coke oven gas, or methane). Air may be added to the oil-gas mixture for the manufacture of very small particle size carbon black. Although this process is not as flexible as the furnace black process, various types of gas black can be made by varying the relative amounts of carrier gas, oil, and air. The carbon black properties are also dependent on the type of burners used. 

Nanoparticle transport in aifeous systems. Nanoparticles are intermediate in size between most clay-sized materials (and colloids) and molecules. Their transport behavior should vary accordingly. Important factors will be nanoparticle size and aggregation state. However, size-dependent surface properties may lead to unanticipated behavior. This could arise, for example, due to modified surface reactivity compared to macroscopic equivalents. Most research on transport of submicron-scale materials has dealt with larger particles or colloidal aggregates. Specific consideration of transport of very small particles may be worthwhile. 

Metals constitute a wide class of catalysts, and because catalysis occurs on the surface, there is an economic incentive, especially for precious metals, to obtain catalysts in the form of small metal particles. This, however, raises two main problems. One is fundamental in nature and addresses the question as to below which particle size the metallic properties are lost. The other is more practical and concerns the preparation and characterization of very small particles and their catalytic activity. 

All the manifestations of the size-dependent physical properties of very small metal particles arise from the self-evident fact that a substantial fraction of the atoms are on the surface, and being there they differ from atoms inside simply because they have fewer neighbours and more unused valencies. This difference was quantified by defining a free-valence dispersion (Section 2.4.1), which depends upon the number of atoms in the particle in a similar way to that predicted by the equation... 

Various types of industrial reactors may occur in different phases as applications and desired properties of the final product, for example, the fixed bed, fluidized bed, slurry bed, and bed phase reactors. In fluidized bed reactors as in slurry bed, the solid (catalyst) is composed of very small particles and moving along the reactor. The fluid flow over these reactors is complex. In these systems, the flow of the fluid phase is not homogeneous and there are large deviations from the ideal behavior of a CSTR or plug flow reactor (PFR), characterizing them in nonideal reactors. 

The stability of colloidal suspensions is frequently examined for a certain variety of suspension properties (e.g. solid content, liquid phase, concentration of ionic, or polymeric additives). That is, for instance, relevant for developing suspension formulas and preparation procedures for particle characterisation or for predicting the particle behaviour in environmental milieus. A typical problem of such parameter studies is that a variation in the concentration of the charge determining additive (e.g. a pH variation as in Fig. 5.10, p. 261) coincides with a significant variation of the total electrolyte content. This problem is most pronounced for dense suspensions (pv 1 vol%) of very small particles (or particles with a high specific surface area). 

INFLUENCE OF THE SIZE OF VERY SMALL PARTICLES AND OF MOLECULAR CLUSTERS ON THEIR ELECTRONIC PROPERTIES. 173... 

Influence of the size of very small particles and of molecular clusters on their electronic properties... 

One of the characteristic properties of colloidal solutions is the more or less energetic movement of the particles. The closer study of this movement has been made possible by the ultramicroscope. The movement of very small particles can be seen with the ordinary microscope, and has been known since 1827. It was discovered by a botanist, Robert Brown, and has been named after him. It has since been thoroughly investigated by a large number of scientists. A short bibliography relative to the earlier experiments will be found in Lehmann s Molekularphysik, 1, 264 (1867). 

---