Particle size estimation

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

TEM investigations support the interpretation of the nitrogen physisorption isotherms (Fig. 19.3). They show particles 5-20 run in diameter, whereas the particle size estimated from the specific surface area, assuming spherical particle morphology, is 7 nm. Indeed, the particle morphology for sample 7 is mostly spherical, but for some crystallites edges are discernible. 

Fig. 3.5,19 Open-circuit voltage (K. ) for CdS formed in 9-layer CdAr films as a function of particle size (estimated from UV/visible absorption spectra). The electrolyte was 1.0 M Na2S03 at pH 7.25, and platinum and standard calomel electrodes were used as the counter and reference electrodes, respectively. (From Ref. 5.)...

Therapeutic group Drug Surfactants/ excipients Propellant system Formulation type Particle size estimate (pm) References... 

Finally an attempt was made to reconcile the various techniques for particle size estimation (Table 4). To do this it was necessary to assume a particle shape, and the results were evaluated both for spherical and hemispherical models, the former showing the greatest consistency. The particle size was defined as the cube root of the volume. The results obtained by the various methods are in quite close agreement (Table 4), and Coenen is justified in concluding that the agreement between the methods is probably better than reported anywhere in the literature, which is the more remarkable when we note that measurements were carried out in ten different laboratories" [27],... 

All the emulsions appeared to have similar particle sizes, estimated to be in the range of 0.1-0.5/. The monomers were all polymerization grade and polymerized without purification since no significant difference in induction period or rate was observed with distilled monomer. 

The average particle sizes estimated from the TEM are consistent with the values obtained from the XRD patterns. The indexed SAED pattern shown in Fig. 7(a) suggests the particles to be crystalline. The pattern could be indexed on the basis of the Fmlm space group. The HREM image of a 6 nm NiO particle, shown as an inset in Fig. 7(b), shows a lattice spacing of 2.09 A, corresponding to the interplannar distance between the (100) planes. 

The most difficult part of particle size estimation is related to the determination methods themselves. Particle size determination is complicated by size distribution, the presence of particle associations, and the shape of particles. If particles are not spherical, more than one parameter is needed to describe them and if the shape of the particle is irregular, numerous parameters are needed to express their dimensions. The method used for particle size determination (sieving, light scattering, microscopy, etc.) determines what dimensional aspects are measured. In addi-... 

The palladium dispersion on the activated charcoal (AC) was somewhat different when compared to that observed on the CNTs catalyst. On the activated charcoal, palladium was present in agglomerate shape instead of individual particles as observed on the CNTs, which led to a less homogeneous dispersion of the metal particles on the support. However, the average particle size estimated fi om TEM was similar to that of the palladium supported on the CNTs, i.e. 5 nm. 

CO adsorption on coat-Pt catalysts was carried out in order to examine whether or not the R metal particles covered with silica layers were contacted with gaseous molecules, for we would use the coat-R as the catalysts. CO molecules were adsorbed on R metal particles in all the coat-R and the adsorbed amounts of CO per all the R atoms in coat-R catalysts were similar to one another in spite of different R loadings, i.e. different thickness of silica layers. R particle size estimated based on the amount of CO adsorbed on coat-... 

Note Error band in CO-H2 methanation particle sizes based on range of values obtained in repeat experiments. Typically 5-6 runs were made on each sample. Error bands in the XRD particle sizes result from particle size estimates made from different x-ray lines. 

The diffraction pattern of Ni/A Os catalyst NiD28 after reaction with AsPha at 443 K (Fig. 5c) shows clear lines at 33.6 and 50.5° attributed to the NiAs phase (nickeline). The width of the (101) and (110) lines at 33.6 and 50.4° (2q) respectively, corresponds to a crystallite size of about 10 nm, using the Schemer equation [12]. Knowing that the volume of an unity cell of Ni and NiAs are respectively 0.04376 and 0.05729 nm and that there are 4 Ni and 2 NiAs per unit cell, for the same number of nickel atoms, the diameter of a NiAs particle is 2.62 times greater than that of a Ni particle. This result is in agreement with the particles size estimated from the width of the diffraction pattern. 

In Table II the percent of silica present as colloid was determined by extrapolating the linear portions of the reaction data curves of Figures 3 and 8 to zero time as demonstrated in Figure 2. The values of were calculated from the slopes of these lines and the particle size estimated from Jk according to Figure 3. 

Hypothetical particle size estimated for the case where the systems would contain pure Pt or Re02 particles. 

All these results are different from those one could expect on the basis of a mechanical mixture. Indeed, in that case a bimodal distribution is expected at least for x > 0.5, based on the different sizes of the separate Pt and Re02 particles. Table 17 also includes the particle sizes estimated for the hypothetical case of a system containing pure Pt and Re02 particles (see Tables 15 and 16). 

We note further from Fig. 13.12 that fully 40% of the small-particle size distribution falls below the critical particle-size estimate of Dc = 0.93 pm, reducing the effective fraction of the particle volume fraction from 0.22 to 0.13. This results in a substantial upper yield stress of 24 MPa, as Fig. 13.11(c) shows. However, once an effective craze network has developed the actual craze-flow stress of this blend drops to 20.5 MPa, in keeping with expectations. 

Figure 3.50 shows typical EPMA and TEM micrographs of the as-prepared precursors and powders calcined at 1000 °C for 2 h, respectively. It can be seen that the precursors have a foamy-like and porous morphology (Fig. 3.50a), veiy similar to the one observed for the previously studied (Gd,Y)203 powders. The TEM micrograph of the precursors, shown in Fig. 3.50b, reveals the shape and size of primary particles. The as-prepared powders are agglomerated and consist of near-spherical crystallites of about 30-nm particle size estimated from TEM images. The TEM micrograph of the powders calcined at 1000 °C for 2 h, shown in Fig. 3.50c,... 

A very similar method as above [376] was used by Que et al. [377] in which CUCI2 was used as the source of the dopant (Cu) instead of MnClj. A hydrothermal treatment was performed at 120 C/15 h the particle size, estimated by XRD, was about 9 nm. The authors used water-rich compositions in the phase field (system [NP-5 -1- NP-9]/petroleum ether/aqueous solution) for microemulsions with high particle yield. Xu et al [378] extended the same work to the rare earth cation Eu as dopant in ZnS. The particle size varied in the range 3-18 nm. A comparison of room temperature photoluminescence shows the obvious superiority of Eu in the intensity of the luminescence. 

Figure 22.1 shows the surface of Carbotron P (J) by scanning electron microscopy (SEM). X-ray powder diffraction (XRD) patterns of these carbons, measured on Rigaku RAD-C diffractometer with roter-flex and Cu-Ka radiation, are shown in Fig.22.2. The interlayer distances and the crystallite size factors (Lc) calculated from XRD(002) reflection using Schener formula" are given in Table 22.1. Figure 22.3 also shows the particle size distributions of these three carbons. The average particle sizes estimated from distributions are shown in Table 22.1.

FIGURE 12.17 Average Pt particle size estimations from uptakes and XRD line broadening. H2 uptakes correspond to the extrapolation to zero pressure of the first isotherm obtained for a fresh sample prelreated imder... 

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