Particle-size distribution standard deviation

Information derived from (1) and (2) would indicate if the particle sizes are uniform or not. A small 5A (or more accurately 5A/A) and small 5R (or 5R/r) in general imply a narrower size distribution or more uniform particle sizes. The standard deviation 5AF (or 6AF/AF) is an index of the "goodness" of particle dispersion or the spatial distribution of particles. 

Figure 4 average particle size and standard deviation obtained by reduction of PS(610)-b-PEO(80) loaded with 0.1 mole LiAuCU per mole EO units at different times after solution preparation (A), and particle size distributions (B)... 

A significant modification to the simple mixing of solutions is the slow and controlled release of one of the reactants. For example, Ohtaki et al. prepared CdS nanoparticles in nonaqueous solvents, where one of the reactants (S ) was made available slowly and uniformly via the controlled hydrolysis of P2S5 (114). The CdS particles were, on average, 6 nm in diameter, had a size distribution standard deviation of 1.2 nm, and formed stable suspensions under the protection of polymers (Figure 14). A similar strategy was used by Meisel and coworkers (115) and, more recently, by Yin et al. (116) in the preparation of CdS nanoparticles, where the slow release of S was achieved through the use of pulse radiolysis. 

Ni particles produced. The expansion was at a constant pressure of about 3000 psia through a fused-silica capillary nozzle with an inner diameter of 77 jtm. These Ni nanoparticles had an average particle size of 5.8 nm and a size distribution standard deviation of 0.54 nm, according to the TEM image (Figure 32). The particles were largely amorphous, exhibiting an extfemely diffuse x-ray... 

The average particle size in diameter (Z>, nm) and the size distribution standard deviation (a, nm) were determined via TEM analyses. 

The Ag nanoparticles prepared via RESOLV with the microemulsion having a Wo value of 12 had an average particle size of 10.4 nm and a size distribution standard deviation of 3.8 nm (263). 

The complete mathematical definition of a particle size distribution is often cumbersome and it is more convenient to use one or two single numbers representing say the mean and spread of the distribution. The mean particle size thus enables a distribution to be represented by a single dimension while its standard deviation indicates its spread about the mean. There are two classes of means ... 

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

Theoretical calculations of unattached fractions of radon or thoron progeny involve four important parameters, namely, 1) the count median diameter of the aerosol, 2) the geometric standard deviation of the particle size distribution, 3) the aerosol concentration, and 4) the age of the air. All of these parameters have a significant effect on the theoretical calculation of the unattached fraction and should be reported with theoretical or experimental values of the unattached fraction. 

Particle size distributions of both hydrosols determined using a statistical image analysis of transmission electron microscopy (Jeol TEM 120 CX) micrographs are presented in Fig. 13.7. These hydrosols were prepared at different neutralization levels (pH = 2 and 2.8). Both particle size distributions are centered around 18 to 19 A and are extremely sharp as shown by the low values of the standard deviation a. 

Figures 13.23a and b show the PdO particle size distribution of PdO-supported catalysts prepared from an acidic hydrosol (neutralization of palladium nitrate solution by addition of soda) and a basic one (neutralization of soda by addition of palladium nitrate). Comparisons with the corresponding histograms of the initial suspensions (Figs. 7b and 9b), show that the distributions are not significantly modified. Only a very slight increase of the standard deviation of the dispersion values is observed...

A total of 254 particle size distributions were measured throughout 1979. The average normalized volume distribution is plotted in Figure 2. The error bars are standard deviations. 

Figure 2.1.6 shows the results of such a continuous synthesis process. It shows the variation of the mean particle size during the experiment. The error bars indicate the standard deviation of the particle size distribution of each sample based on the transmission electron micrographs (number distribution). The experiment was performed under the following conditions (A) ammonia, water, and TEOS concentrations were 0.8, 8.0, and 0.2 mol dm-3 7", = 273 K, T2 = 313 K total flow rate was 2.8 cm3 min-1 100 m reaction tube of 3 mm diameter residence time 4 h and (B) ammonia, water, and TEOS concentrations were 1.5,8.0, and 0.2 mol dm- 3 Tx = 273 K, T2 = 313 K total flow rate was 8 cm3 min-1 50 m reaction tube of 6 mm diameter, residence time 3 h. Further details and other examples are described elsewhere (38). Unger et al. (50) also described a slightly modified continuous reaction setup in another publication. 

Plot these results on log-probability coordinates and estimate the mean and standard deviation for each distribution (see Appendix C). What kind of averages are these quantities How do the weekend and weekday particle size distributions compare with respect to the location and width of the maximum The weekend results are attributed to automobile exhaust, whereas the weekday results are assumed to be diluted by aerosols from outside the tunnel. 

Figure 1 shows, as a typical plot, the particle size distributions of the size fractions from a Johnie Boy sample. Only the first fraction, containing the largest particles, deviates significantly from lognormality. The standard deviations are almost the same for the first nine fractions as is apparent from the parallelism of the cumulative frequency curves. When the particle size decreases further, the standard deviations of the size distributions in the fractions increase. 

Carefully prepared Au catalysts have a relatively narrow particle size distribution, giving mean diameters in the range 2-10 nm with a standard deviation of about 30%. A major reason why Au particles remain as NPs even after calcination 573 K is the epitaxial contact of Au NPs with the metal oxide supports. Gold particles always expose its most densely packed plane, the (111) plane, in contact with a-Fe2O3(110), Co304(lll), anatase Ti02(112), and rutile TiO2(110). 

For example, the drug s content uniformity in the final tablet may yield a relative standard deviation greater than 6%, even though the uniformity of the powder blend is much tighter. It may become necessary to control not only the powder blend s uniformity but also its particle size distribution, thus in order to meet the necessary criteria for the latter test, it may be necessary to control the blend process by setting tighter specification limits for the former test. 

As stated above (see Chapter II.B), LII signals also contain information about the size distribution. To compare the influence of different plasma powers on primary particle diameters, different ways of size evaluation have been accomplished. It could be shown by assuming a monodisperse distribution that the mean primary particle diameter is 31 nm for 30 kW and 33 nm for 70 kW. In contrast, under the assumption of a log-normal distribution and by applying the two-decay time evaluation, the determination yields a different result which can be seen in Figure 15. Size distributions with median sizes of 17nm and 28 nm and standard deviations of 0.39 and 0.18 for 30 kW and 70 kW were observed, respectively. This indicates that in practical production systems, the evaluation of a mondisperse distribution is not sufficient. Unfortunately, the reconstruction of particle size distributions is relatively sensitive on... 

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