Particle size Geometric mean

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

The size of inhaled particles varies markedly. The size distribution approximates a log-normal distribution that can be described by the median or the geometric mean, and by the geometric standard deviation. For fibers, both... 

Ksdm = Geometric mass mean of the particle size distribution... 

In many catalytic systems, nanoscopic metallic particles are dispersed on ceramic supports and exhibit different stmctures and properties from bulk due to size effect and metal support interaction etc. For very small metal particles, particle size may influence both geometric and electronic structures. For example, gold particles may undergo a metal-semiconductor transition at the size of about 3.5 nm and become active in CO oxidation [10]. Lattice contractions have been observed in metals such as Pt and Pd, when the particle size is smaller than 2-3 nm [11, 12]. Metal support interaction may have drastic effects on the chemisorptive properties of the metal phase [13-15]. Therefore the stmctural features such as particles size and shape, surface stmcture and configuration of metal-substrate interface are of great importance since these features influence the electronic stmctures and hence the catalytic activities. Particle shapes and size distributions of supported metal catalysts were extensively studied by TEM [16-19]. Surface stmctures such as facets and steps were observed by high-resolution surface profile imaging [20-23]. Metal support interaction and other behaviours under various environments were discussed at atomic scale based on the relevant stmctural information accessible by means of TEM [24-29]. 

A word of caution is also in order with respect to assigning a particular particle to the fine or coarse particle modes. Since the size distributions can generally be described as log-normal, they do not have sharp cutoffs. A few particles at the top end of the fine mode distribution will have diameters larger than 2.5 [jlm and a few at the bottom end of the coarse mode will have diameters smaller than this. For example, as Lodge (1985) points out, for a coarse particle distribution with a geometric mean diameter of 15 fim and a geometric standard deviation of 3, about 5% of the particles will have diameters below the 2.5-gm fine particle cutoff. This may be responsible for observations that while Si and Ca dominate the coarse particle mode, they are also often found at significant levels in fine particles (e.g., see Katrinak et al., 1995). 

A monodisperse aerosol is one with a narrow size distribution, which, for log-normal-distributed particles, usually means a geometric standard deviation of about 1.2 or smaller. Monodisperse particles are expected to have simple shapes and uniform composition with respect to size. A polydisperse aerosol, on the other hand, is one containing a wide range of particle sizes, but which may otherwise be homogeneous in terms of the basic physical and chemical properties that are not related to size. The term heterodisperse is also used occasionally this describes aerosols varying widely in physical and chemical characteristics, as well as size. 

The size distributions of the fractions were plotted on log-probability paper as particle diameter (in microns) against cumulative percent of particles smaller than the indicated size. Figure 1 shows such a plot for the Johnie Boy size fractions. Such plots were compared for several samples with similar plots on linear-probability paper. Almost always the data could be described better by a lognormal rather than by a normal distribution law, after proper allowance for the presence of a maximum and a minimum size in each fraction. The parameters of the distributions were determined from the graph the geometric mean as the 50% point (median) and the logarithmic standard deviation as the ratio of the diameters at the 84 and 50% points. 

The data were obtained from the samples summarized in Table L The fallout samples were separated into particle-size classes by standard sieves for particles larger than 44p and by the Roller analyzer for particles smaller than 44fi. In the sequel the size classes are characterized by their geometric mean diameters. The larger size classes of the Tewa sample were separated mechanically under the microscope into spherical and irregular fractions. Very few spheres could be found below the 177-/x class. The ratio of active to inactive particles was measured auto-... 

Particle Size. The important physical data for inorganic pigments comprise not only optical constants, but also geometric data mean particle size, particle size distribution, and particle shape [1.8]. The standards used for the terms that are used in this section are listed in Table 1 ( Particle size analysis ). 

To determine the mean primary particle size and particle size distribution, the diameters of 3000-5000 particles are measured on electron micrographs of known magnification. Spherical shape is anticipated for calculations. However, since the primary particles generally build up larger aggregates, the results may be somewhat uncertain. The specific electron microscopic surface area can be calculated from the primary particle size distribution. This value refers only to the outer (geometrical) surface of the particles. For porous carbon blacks the electron microscopic surface area is lower than the specific surface area according to BET (see below). 

The mean primary particle sizes of pigment blacks he in the range 10-100 nm specific surface areas are between 20 and 1000 m2/g. The specific surface area, determined by N2 adsorption and evaluation by the BET method [4.29], is often cited as a measure of the fineness of a black. Blacks with specific surface areas >150 m2/g are generally porous. The BET total specific surface area is larger than the geometric surface area measured in the electron microscope, the difference being due to the pore area resp. the pore volume. 

Referring to Table 4.8, there are differences between the two homogenizers and types of particle size analysis. However, an independent study (Gooch 2002) showed that emulsification with an APV Homogenizer (3,500 psig) produced an emulsion with a mean particle size of 0.688/1.128 pm (number/volume-weight geometric mean). 

Emphasis has also been placed on the particle size distribution and the uniform size distribution of the API rather than on the mean particle size alone by other authors.1416 Rohrs et al.16 give a nomograph for identifying the maximum median particle diameter to pass USP 28 stage I content uniformity criteria with 99% confidence as a function of dose as well as width of particle size distribution (geometrical standard deviation). 

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