Size distribution function graphing

From such measurements, surface areas (normalized cumulative and relative), pore radii (choice of three measuring units), pore volumes (raw, normalized, cumulative and relative) and pore-size distribution functions of samples can calculated. Figure 8 presents the graphs of mercury-penetrated volume versus pressure in pores of Na- and La-montmorillonite samples. Figure 9 shows pore-size distribution functions from porosimetry data. 

Figure 21 presents the graphs of mercury-penetrated volume versus pressure in the pores of Na- and La-montmorimllonitamples. Figure 22 shows the pore-size distribution functions calculated from the porosimetry data. 

These few examples do not exhaust a long list of difficulties in calculation of exact values of potential from electrophoretic or electroacoustic data, and most results reported in literature appear to be rough estimates rather than exact values, except for some results obtained with nearly spherical particles having very narrow size distributions, e.g. Stober silica. Many publications tend to overestimate the accuracy of ( potentials presented therein. For example in a recent publication a graph was presented showing the variations of the measured potential as a function of time, and all data points showed in that graph ranged from 6 to 7 mV. 

If the particle size distribution is normal or log normal, then the data can be linearized by plotting the particle frequency as a function of particle rize on arithmetic or logarithmic probability graph p r respectively. The 50% value of sudi plots yields the geometric median diameter and the geometric standard deviation is the ratio of the 84.1% m the 50% values. 

Fig. 2 (a) Typical variation of difference in the band gap compared to the bulk band gap as a function of size for the case of ZnO nanocrystals. The inset shows the absorption spectra for various sizes of ZnO QDs. (b) Bar graph depicting the size distribution obtained from TEM as well as the absorption spectrum for a typical nanocrystal. The inset shows the fit to the experimental absorption spectrum using convolution bulk shifted absorption edge for various sizes. 

The particles in a latex are not necessarily uniform in size (or monodisperse), although they can be made that way (46, 316, 362). There is usually a distribution of particle diameters found within a single latex sample. The breadth of the distribution varies for different latexes, and is determined by the length of the nucleation period relative to the entire reaction. Bimodal particle size distributions (385, 407) and multimodal (287) are the result of secondary nucleation. Particle size distributions are usually graphed as number or weight percents as a function of particle diameter, as in Figure 4. 

More realistically. Equation (2.35) is geared to the physical nature of X molecular weight, density, temperature, and so on (x) = 0 at x = 0. In all cases, however, the distribution function increases, or at least stays constant, as y increases. The maximum size of F (x) is clearly 1, the sum of all the normalized probability values. In picture terms, a graph of Fx(x) versus x suggests a curve whose height increases, or stays flat in certain portions, as the x values progress left to right. In some cases, Fx(x) has the appearance of a titration curve. 

Consider the two density functions in Fig.21.8 from a different point of view. The first is the density function of the sample average when the sample size is 1. The second when the sample size is 2. As the sample size increases, the graph becomes more like the bell-shaped curve for the normal distribution. This is the content of the Central Limit Theorem in the next section. As the sample size increases, the... 

If, however, no analytical function is fitted and the particle size distribution is in the form of a graph or a table, evaluation of mean diameters can best be done graphically. 

Owing to the gradual increase in the avaUabUity and capacity of computers, it is becoming more and more convenient and feasible to fit an analytical function to the experimental particle size distribution data and then handle this function mathematically in further treatment It is for example very much easier to evaluate mean sizes from analytical functions than from experimental data. Apart from the many curve-fitting techniques available, use can also be made of special graph papers which exist for many of the common... 

Although experimental values of E can be obtained from the test data via the grade efficiency curve (from which X50 is determined—see chapter 3, Efficiency of Separation ), industrialists prefer to measure the fraction of solids unsedimented (1 — Ei) and plot this against the ratio of the measured flow rate and the calculated E value (which can be varied by changing the speed of rotation). This curve, which often comes out as a straight line on log-probability paper, is naturally a function of the size distribution of the feed but can be used to find the ratio of Q/IL for acceptable efficiency with the given feed material. Extrapolation of the data over the linear parts of the graph can be made with caution. 

The following graph in Figure 6.12 illustrates the size distribution of dry citric acid nanoparticles generated with the constant output atomizer as a function of precursor concentration. By increasing the citric acid... 

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