Size distribution curve

Fig. 1.13 Gaussian particle size distributions. Curve I represents a more uniform size distribution than does Curve II.

Now the relationship between v and A is given by the size distribution curve the value of A merely represents the lengths of the particles measured in terms of a particular, arbitrary, unit. Thus, if the size distribution curve remains of exactly the same shape during the grinding process, the values of... 

Thus for a fixed size distribution curve we have... 

The significance of the various columns is explained in the notes below the table, which enable the calculations of 6v l6r to be followed through. Only the first few lines are reproduced, by way of illustration the pore size distribution curve resulting from the complete table is given in Fig. 3.18 (Curve A), as a plot of 6i j6r against f. 

The curve for core size distribution—Foster s plot of 6 j6r against r —is also shown, as Curve D, in Fig. 3.18. It differs markedly from the pore size distribution curves, clearly showing that the corrections for the film thinning effect which have become possible since Foster s day, are of first-order importance. 

Everett concludes that in systems where pore blocking can occur, pore size distribution curves derived from the desorption branch of the isotherm are likely to give a misleading picture of the pore structure in particular the size distribution will appear to be much narrower than it actually is. Thus the adsorption branch is to be preferred unless network effects are known to be absent. 

Fig. 3.19 Contrast between the pore size distribution curves based on the adsorption and the desorption branch of the hysteresis loop respectively.

FIG. 20-1 Particle -size distribution curve plotted on linear axes,... 

Crusher Product Sizes Table 20-10 relates product size to the discharge setting of the crusher in terms of the percent smaller than that size in the product. Size-distribution curves differ for various types of materials crushed, and a general set of curves is not vahd. 

The shape of the pore size distribution curve strongly depends on the molecular weight distribution of the linear polymer. The narrowest pore size distributions were obtained with the linear polymers having the lowest polydisper-sity indices. 

Size Distribution Curves for Three Methods of Particle Size Analysis — Tungsten M-10... 

As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

DIVER METHOD- This is a modification of the hydrometer method. Variation in effective density i and hence concn, is measured by totally immersed divers. These are small glass vessels of approximately streamline shape, ballasted to be in stable equilibrium, with the axis vertical, and to have a known density slightly greater than that of the sedimentation liq. As the particles settle, the diver moves downwards in hydrodynamic equilibrium at the appropriate density level. The diver indicates the position of a weight concn equal to the density difference between the diver and the sedimentation liq. Several divers of various densities are required, since each gives only one point on the size distribution curve... 

As it turns out, one vendor s material contains almost no particles (0.5%) in the 261-564 /xm class (bin 15) this means that the %-weight results accurately represent the situation. The other vendor s material, however, contains a sizable fraction (typically 5%, maximally 9%) in this largest size class this implies that 1-5% invisible material is in the size class >564 /xm. Evidently then, the size distribution curve for this second material is accurate only on... 

Inspection of this equation shows that in the course of the snowballing growth the size distribution curves at various times are simply shifted toward the right on the pellet size scale without any change in their shape, as demonstrated by Capes (C2) for sand pellets snowballed in a pan granulator (Fig. 13). 

Figure 4.2. Cumulative droplet size distribution curve based on mass.

A complete theory predicting retention times or volumes as function of molecular size has not yet been formulated for gel permeation chromatography. A specific column or set of columns is calibrated empirically to give such a relationship, by means of which a plot of amount of solute versus retention volume (the chromatogram figure below) can be changed into a molecular-size-distribution curve. Generally commercially available narrow... 

The pore size distributions of the molded monoliths are quite different from those observed for classical macroporous beads. An example of pore size distribution curves is shown in Fig. 3. An extensive study of the types of pores obtained during polymerization both in suspension and in an unstirred mold has revealed that, in contrast to common wisdom, there are some important differences between the suspension polymerization used for the preparation of beads and the bulk-like polymerization process utilized for the preparation of molded monoliths. In the case of polymerization in an unstirred mold the most important differences are the lack of interfacial tension between the aqueous and organic phases, and the absence of dynamic forces that are typical of stirred dispersions [60]. 

The polymerization temperature, through its effects on the kinetics of polymerization, is a particularly effective means of control, allowing the preparation of macroporous polymers with different pore size distributions from a single composition of the polymerization mixture. The effect of the temperature can be readily explained in terms of the nucleation rates, and the shift in pore size distribution induced by changes in the polymerization temperature can be accounted for by the difference in the number of nuclei that result from these changes [61,62]. For example, while the sharp maximum of the pore size distribution profile for monoliths prepared at a temperature of 70 °C is close to 1000 nm, a very broad pore size distribution curve spanning from 10 to 1000 nm with no distinct maximum is typical for monolith prepared from the same mixture at 130°C [63]. 

Figure 1.5. Size distribution curve — cumulative basis...

Modern N2 sorption porosimeters are very sophisticated and generally reliable. Typically they come supplied with customized user-friendly software which enables the experimental data to be readily computed using the above models and mathematical expressions. Usually the raw isotherm data is displayed graphically along with various forms of the derived pore size distribution curve and tabulated data for surface area, pore volume and average pore diameter. 

In the past it was very common to derive the mesopore size distribution from the desorption branch of the isotherm. The above considerations make it clear that this practice is questionable especially for Type H2 hysteresis loops, and can lead to misinterpretations [90]. Indeed a significant downward turn in the desorption branch of a N2 isotherm at p/po 0.4 leads to an apparent sharp maximum in the pore size distribution curve at 2 nm which is totally artefactual. Although no general guidelines exist on whether the adsorption or desorption branch should be used for computation, it should be understood that with Type H2 and H3 hysteresis loops, reliable results are much more Hkely to be obtained if the adsorption branch is used [21]. 

First the particle size and shape should mentioned. As columns packed with nominally 5 or 10 pm particles are used most commonly in HPLC, the particle size distribution has become an important characteristic of the packing because with such small particles it is difficult to obtain a monodisperse product. Size distribution of the particles can be represented in many different ways. Most commonly the cumulative particle size distribution curve obtained with an instrument such as the... 

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