Single-particle properties mean size

If a population of particles is to be represented by a single number, there are many different measures of central tendency or mean sizes. Those include the median, the mode and many different means arithmetic, geometric, quadratic, cubic, bi-quadratic, harmonic (ref. 1) to name just a few. As to which is to be chosen to represent the population, once again this depends on what property is of importance the real system is in effect to be represented by an artificial mono-sized system of particle size equal to the mean. Thus, for example, in precipitation of fine particles due to turbulence or in total recovery predictions in gas cleaning, a simple analysis may be used to show that the most relevant mean size is the arithmetic mean of the mass distribution (this is the same as the bi-quadratic mean of the number distribution). In flow through packed beds (relevant to powder aeration or de-aeration), it is the arithmetic mean of the surface distribution, which is identical to the harmonic mean of the mass distribution. 

In this Chapter, we intend to investigate mechanisms of particle growth. We will, in the next chapter, address the methods used to form (grow) single crystals and how they have been utilized. Certain properties of particles, including measurement of size, wiU be discussed later in this chapter. But first, we need to define exactly what we mean by a particle. 

This chapter deals with the study of structural properties of catalysts and catalytic model surfaces by means of interference effects in scattered radiation. X-ray diffraction is one of the oldest and most frequently applied techniques in catalyst characterization. It is used to identify crystalline phases inside catalysts by means of lattice structural parameters, and to obtain an indication of particle size. Low energy electron diffraction is the surface sensitive analog of XRD, which, however, is only applicable to single crystal surfaces. LEED reveals the structure of surfaces and of ordered adsorbate layers. Both XRD and LEED depend on the constructive interference of radiation that is scattered by relatively large parts of the sample. As a consequence, these techniques require long-range order. 

In this chapter, we have described the colloid chemistiy of ceramic powders in suspension. Colloid stability is manipulated by electrostatic and steric means. The ramifications on processing have been discussed with emphasis on single-phase ceramic suspensions with a distribution of particle sizes and composites and their problems of component segregation due to density and particle size and shape. The next chapter will discuss the rheology of Uie ceramic suspensions and the mechanical behavior of dry ceramic powders to prepare the ground for ceramic green body formation. The rheology of ceramic suspensions depends on their colloidal properties. 

The total mass of particulate matter per unit volume of air is perhaps the simplest integral property, and it is on this quantity that U.S. federal standards for particulate pollution have been based. Until recently there was a single primary (health related) standard of 50 g/m (annual geometric mean) and 150 /rg/m- (maximum 24-hr concentration not to be exceeded more than once per year), with an upper cutoff in panicle size of 10 /ttm (PMio). However, epidemiological studies indicate an association between adverse health effects, including enhanced mortality, and submicron aerosol concentrations in many U.S. cities (Pope cl al.. 1995). This has led to the establishment of an additional mass ba.sed standard for particles smaller than 2.5 /im (PMj.j) (U.S. EPA, 1996). There is also a separate health-based standard for lead, one component of the atmospheric aerosol. 

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