Pore distribution curve

Pore distribution curves can be obtained plotting the change in the sum of residuals, which can be calculated by experimental elution volumes of all standards against the mean diameter of the PS standards [119]. 

After coking, the 5-plots are linear on the entire xenon concentration range, the slopes and 5S values increase with coke loading. At the same time, the total micropore volume measured by HR ADS decreases by about 30% but the pore distribution curve, if rp > 0.55nm, is the same than for the uncoked sample. 

It is evident from the above considerations that the use of the physisorption method for the determination of mesopore size distribution is subject to a number of uncertainties arising from the assumptions made and the complexities of most real pore structures. It should be recognized that derived pore size distribution curves may often give a misleading picture of the pore structure. On the other hand, there are certain features of physisorption isotherms (and hence of the derived pore distribution curves) which are highly characteristic of particular types of pore structures and are therefore especially useful in the study of industrial adsorbents and catalysts. Physisorption is one of the few nondestructive methods available for investigating meso-porosity, and it is to be hoped that future work will lead to refinements in the application of the method -especially through the study of model pore systems and the application of modem computer techniques. 

Illston [134] found a good relation between the maximum continuous pore radius, measured with mercury porosimeter and permeability (Fig. 5.61). The maximum continuous pores radius is defined as a pore size at which the maximum on the pore distribution curve occurs (see Fig. 5.27). This maximum radius of continuous pore system decreases with the time of hydration, as a space between cement grains is filled with hydration products. The term continuous pores was firstly used by Winslow and Diamond [135] they attributed it to the maximum on the pores size distribution curve, as it could be derived from the flow of mercuiy through the main, continuous pore chaimels. However below the peak mercuiy is intmding only to the local pore channels [135]. Mehta and Manmohan [136] are considering... 

Figure 4. Pore distribution curves over the 2-ISO A range for samples ACM (curve 1) and OACM (curve 2).

Pore distribution in general is calculated according to the desorption isotherm, which is a desorption process with equilibrium steam pressure descending and adsorption volume reducing. The relationship between the total adsorption quantity and pore radius is shown in Fig. 7.8. The relationship between the differential values of adsorption quantity vs. pore radius is the so-called pore distribution curve, as shown in Fig. 7.9. 

Fig. XVI-2. Comparison of the pore volume distribution curves obtained from porosimeter data assuming contact angles of 140° and 130° with the distribution curve obtained by the isotherm method for a charcoal. (From Ref. 38.)...

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. 

In using the table for pore size calculations, it is necessary to read off the values of the uptake from the experimental isotherm for the values of p/p° corresponding to the different r values given in the table. Unfortunately, these values of relative pressure do not correspond to division marks on the scale of abscissae, so that care is needed if inaccuracy is to be avoided. This difficulty can be circumvented by basing the standard table on even intervals of relative pressure rather than of r but this then leads to uneven spacings of r . Table 3.6 illustrates the application of the standard table to a specific example—the desorption branch of the silica isotherm already referred to. The resultant distribution curve appears as Curve C in Fig. 3.18. 

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.

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. 

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

The shape of the porosimetry curve provides information about the pores. The diagram in Fig. 5a represents a sample that contains essentially one pore size, as indicated by only one increase in volume. As diagrammed in Fig. 5b, two volume increases in the intrusion curve are observed, which is indicative of a bimodal pore distribution. Figure 5c is an example of a curve demonstrating a continuous range of pore sizes. 

An illuminating example is the effect of Ostwald ripening on pore size distribution in a sintered body, resulting from vacancy transfer from the smaller to the larger pores, where the decrease in the number and the increase in average diameter of the pores can be clearly seen. The distribution curve for... 

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]. 

The pore size distribution (PSD) for mesopores and micropores were calculated using DFT (Density Funetional Theory) method and the resulting distribution curves are given in Fig. 21.3. Total mesopore volume (V ) was determined as 0.022 cm g and total mieropore volume (V. ) was determined as 0.709 em g from the eorresponding method. The ACC consists of pores mainly in micro character (<20 A) as seen both from Fig. 21.3. The pH value of ACC used in this study had been previously found to be 7.4 [4]. 

Rgure 2.1. Pore radius distribution curve for a porous Vycor glass heat-treated at 500 C for 5 h (McMillan 1980). 

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. 

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