Spreading of size

A second reason why very high resolution can be obtained in chromatography is that very large numbers of theoretical plates are readily achieved. If the column is well packed with particles having a narrow spread of sizes, the plate height is about twice the particle diameter 9, n A typical large-scale GC or LC column will contain of 103-104 plates. 

An increase in the spread of sizes in a batch crystallization could be due to size dependent growth or also growth dispersion. Whatever the cause, the spreading decreases substantially for the high alcohol content crystallizations. There seems to be no current explanation for this effect. In practical terms, this means that batch growth from alcoholic solutions should give a more uniform product than from aqueous solution. 

Without an appreciation for the possible spread of sizes in real particulate systems the values of a in Fig. 11.6 are merely those of an adjustable parameter. We therefore give distribution widths for some natural and artificial aerosols and hydrosols in Table 11.1 we excluded from this list broad distributions, such as raindrops, to which the notion of a width is not really applicable. 

Figure 7. Mean diameter of droplets and spread of size distribution N in isothermal spray. Measurements were made by laser diffraction meter across the spray at various axial locations.

Increase air pressure Decreases spread of size Decreases spread of size... 

Xia Y and Whitesides G M 1994 Use of controiied reactive spreading of iiquid aikanethioi on the surface of goid to modify the size of features produced by microcontact printing J. Am. Chem. Soc. 117 3274-5... 

In the next several sections, the theoretical distributions and tests of significance will be examined beginning with Student s distribution or t test. If the data contained only random (or chance) errors, the cumulative estimates x and 5- would gradually approach the limits p and cr. The distribution of results would be normally distributed with mean p and standard deviation cr. Were the true mean of the infinite population known, it would also have some symmetrical type of distribution centered around p. However, it would be expected that the dispersion or spread of this dispersion about the mean would depend on the sample size. 

Equation (2.28), being statistical in nature, requires a large number of particles to be measured, especially if the spread of particle size is wide. The possibility of error from this source is stressed by Arnell and Henneberry who found that in a particular sample of finely ground quartz, two particles in a total of 335 had a diameter about twenty times the most probable diameter, and that if these were overlooked the calculated value of A would be nearly doubled. 

For a continuous distribution, summation may be replaced by integration and by assuming a Gaussian distribution of size, Stoeckli arrives at a somewhat complicated expression (not given here) which enables the total micropore volume IFo, a structural constant Bq and the spread A of size distribution to be obtained from the isotherm. He suggests that Bq may be related to the radius of gyration of the micropores by the expression... 

Once the primary electron beam is created, it must be demagnified with condenser lenses and then focused onto the sample with objective lenses. These electron lenses are electromagnetic in nature and use electric and magnetic fields to steer the electrons. Such lenses are subject to severe spherical and chromatic aberrations. Therefore, a point primary beam source is blurred into a primary beam disk to an extent dependent on the energy and energy spread of the primary electrons. In addition, these lenses are also subject to astigmatism. AH three of these effects ultimately limit the primary beam spot size and hence, the lateral resolution achievable with sem. 

The complete characterization of a particulate material requires development of a functional relationship between crystal size and population or mass. The functional relationship may assume an analytical form (7), but more frequentiy it is necessary to work with data that do not fit such expressions. As such detail may be cumbersome or unavailable for a crystalline product, the material may be more simply (and less completely) described in terms of a single crystal size and a spread of the distribution about that specified dimension. 

The coefficient of variation (cp) of a distribution is a measure of the spread of the distribution about some characteristic size. It is often used in conjunction with dominant size to characterize crystal populations through the equation... 

Figure 15 shows how the population density function changes with the addition of classified-fines removal. It is apparent from the figure that fines removal increases the dominant crystal size, but it also increases the spread of the distribution. 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Where is the mean pore size and is a constant reflecting the spread of the distribution. The probability that one tip of a single defect will cause failure under applied stress o may now be defined from equations (48) and (49) as ... 

Acetonitrile serves to greatly enlarge the spread of relative volatilities so that reasonably sized distillation equipment can be used to separate butadiene from the other components in the C4 fraction. The polar ACN acts as a very heavy component and is separated from the product without much difficulty.The feed stream is carefully hydrogenated to reduce the acetylene level rerun, and then fed to the single stage extractive distillation unit. Feed enters near the middle of the extractive distillation tower, while (lean) aqueous ACN is added near but not at the top. Butenes and butanes go overhead as distillate, with some being refluxed to the tower and the rest water washed for removal of entrained ACN. 

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 ... 

The eoeffieient of variation is a statistieal measure of the spread of the distribution about the mean. In effeet, it is a seeond term to quantify a distribution in terms of its shape sinee many distributions may have a eommon mean size (in some respeet) but differ eonsiderably in the spread about that mean. 

Mass loss determinations refer to the total change resulting from reactant decomposition and usually include contributions from a mixture of product compounds, some of which would normally be condensed under conditions used for accumulatory pressure measurements. Such information concerned with the overall process is, however, often usefully supplemented by evolved gas analyses (EGA) using appropriate analytical methods. Sestak [130] has made a detailed investigation of the effects of size and shape of reactant container on decomposition kinetics and has recommended that the sample be spread as a thin layer on the surfaces of a multiple plate holder. The catalytic activity of platinum as a reactant support may modify [131] the apparent kinetic behaviour. 

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