Particles, dimension

Figure 10.13 shows such plots of z versus D/X, where D is r for random coils, R for spheres and disks, and L for rods. More detailed theories permit these curves to be extended to larger values of than is justified by consideration of Eq. (10.97) alone. In the following example we illustrate an application of this simple method for estimating particle dimensions. 

Because of the diversity of filler particle shapes, it is difficult to clearly express particle size values in terms of a particle dimension such as length or diameter. Therefore, the particle size of fillers is usually expressed as a theoretical dimension, the equivalent spherical diameter (esd), ie, the diameter of a sphere having the same volume as the particle. An estimate of regularity may be made by comparing the surface area of the equivalent sphere to the actual measured surface area of the particle. The greater the deviation, the more irregular the particle. 

Third, a complicated question on the role of the dispersion of particles dimensions of particles dimensions is of independent value it is known that the viscosity of equi-concentrated dispersions of even spherical particles depends on the fact if spheres of one dimension or mixtures of different fractions were used in the experiments and here in all the cases the transition from monodisperse particles to wide distributions leads to a considerable decrease in viscosity [21] (which, certainly, is of theoretical and enormous practical interest as well). 

The presence of small amounts of dissolved polymer can alter sizably the aerosol particle dimensions when the solutions are sprayed. This antimisting property has received special attention in an effort to develop additives for jet fuel to prevent accidental ignition following crash landing. As in drag reduction, the polymer... 

In general, for decreasing interface reactions, the rate coefficients ft, and the exponent, n, are dependent on particle dimensions and shape... 

The superscript appearing above and in related symbols below will serve as a reminder that the particle dimensions have been assumed small compared to the wavelength of the light. Owing to failure to meet this condition it is often necessary to apply a correction (see Sec. 2d) to the observed intensity ie in order to obtain the intensity applicable in this equation and subsequent relationships. 

Table 2. Influence of PVA amount on the gold particle dimension.

Table 4. Influence of pH on particle dimension and sol stability using PVA as a protecting agent.

Table 6. Influence of different amounts of NaBH4 on particle dimension.

Batch Carbon Amount (g) Gold particle dimension (nm) Surface Au/C (XPS) Total gold, Au% (ICP)... 

Stabilizer Stabilizer/Au Particle (wt/wt) dimension (sol) Support Particle dimension (supported)... 

As it is shown, different support differently influences the transferring of the metal particles. In the case of THPC, the particle dimension in the sol is maintained only when a high THPC/Au ratio is used, especially in the case of carbon as the support. A more bulky stabilizer as PVA provided in contrast a good stability of dimension during the immobilization step. 

From a catalytic point of view, the particle dimension represents for sure an important factor but not the only one. In fact the nature of the support, the possible presence of residual stabilizing agent, metallic dispersion and accessibility of active phase by the reactant are also important. 

After supporting these sols on activated carbon, however, the obtained particle size depends on the capability of the protective agent to maintain the particle dimension. The obtained three catalysts, having different characteristics, are summarized in Table 3. As it is shown, mean size of gold nanoparticle obtained by TEM measurement did not always match with X-ray powder diffraction (XRPD) data. This result is not surprising as TEM measurements represent particle sizes, whereas from X-ray diffraction (XRD) it is possible to obtain crystallite dimensions that do not necessarily coincide with the size of... 

Stanton, M.F., Layard, M., Tegeris, A., Miller, E., May, M., Morgan, E. and Smith, A. (1981). Relation of particle dimension to carcinogenicity in amphibole asbestoses and other fibrous minerals. J. Natl Cancer Inst. 67, 965-975. 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

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