Intrusion curve

To bring the two curves into correspondence it is necessary to choose some reference point on the mercury intrusion curve, not too close to the lower... 

A typical example, from the extensive study by Kamakin on an alumina-silica gel, is shown in Fig. 3.32. When the mercury pressure was reduced to 1 atm at the end of the first cycle, 27 per cent of the intruded mercury was retained by the sample a second intrusion run followed a different path from the first, whereas the second extrusion curve agreed closely with the first. Change in f re structure of the kind described above could perhaps account for the difference between the two intrusion curves, but could not explain the reproducibility of the remainder of the loop. There is no doubt that hysteresis can exist in the absence of structural change. 

Fig. 3.35 Mercury porosimetry intrusion-extrusion plots of alumina gels prepared from solutions of aluminium monohydrate in A, propan-2-ol (2-5w/v%) B, propan-2-ol (4-9w/v%) C, 2-methylpropan-2-ol (4-9 w/v%) D, 2-methylpropan-2-ol (9-5 w/v%) E,butan-2-ol (9-5 w/v%). -------, ascending, intrusion curve -----, descending, extrusion curve.

In a pore system composed of isolated pores of ink-bottle shape, the intrusion curve leads to the size distribution of the necks and the extrusion curve to the size distribution of the bodies of the pores. In the majority of solids, however, the pores are present as a network, and the interpretation of the mercury porosimetry results is complicated by pore blocking effects. 

A plot of the volume of mercury versus pressure is a common way to display the raw data, as shown in Fig. 4. When increasing the pressure, mercury is forced into the pores and an intrusion curve is produced from the increased mercury volume in the sample. When decreasing the pressure, mercury will leave the pores, causing a decrease in volume, and an extrusion curve is observed. The instrusion and extrusion curves will not be the same due to hysteresis, which is caused by mercury being permanently trapped in the pores of the sample... 

The steps displayed in the porosimetry curves are attributed to the pores of the sample. Very low pressures will fill the interparticle spaces when the sample is a powder. Increasing pressures will cause the mercury to penetrate into the pores, with higher pressures corresponding to smaller pores. For each step in the intrusion curve, there will be a corresponding step in the extrusion curve at a lower pressure. 

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. 

For membranes with pore diameters smaller than 3.5 nm, the nitrogen adsorption/desorption method based on the widely used BET theory ean be employed. This measurement technique, however, is good only for pore diameters ranging from 1.5 nm to 100 nm ( = 0.1 micron). Typical data from this method are split into two portions adsorption and desorption. The nitrogen desorption curve is usually used to describe the pore size distribution and corresponds better to the mercury intrusion curve. Given in Figure... 

The extrusion curve shown in Fig. 1.16A cannot retrace the intrusion curve exactly because mercury is not expelled completely because it is entrapped in so-called ink-bottle pores [79, 96] (Fig. 1.17). 

The differences of the intrusion and extrusion mechanisms are the main factors, leading to the different pathways (hysteresis) of the branches in Fig. 1.16A. Furthermore, this effect causes the pore size distribution obtained from the intrusion curve to be incorrectly shifted towards smaller pore sizes. Unlike some inorganic materials of very regular pore structure (e.g. zeolites), permanently porous organic polymers consist of a very complex network of pores of different sizes connected to each other. Correction of these falsifications in the results described above is virtually impossible, since it implies a detailed understanding of the network. 

The specific surface area is calculated as the area of the intrusion curve that results by plotting the cumulative volume versus the pore radius [117]. 

A plot of the intruded (or extruded) volume of mercury versus pressure is sometimes called a porogram. The authors will use the terms intrusion curve to denote the volume change with increasing pressure and extrusion curve to indicate the volume change with decreasing pressure. Figure 11.1 shows a typical porosimetry curve of cumulative volume plotted versus both pressure (bottom abscissa) and radius (top abscissa). The same data plotted on semilog paper is illustrated in Fig. 11.2. 

The authors have found similar stepwise intrusion on other materials. The low pressure (0.5-15 psia) intrusion curve in Fig. 11.5 was obtained using a scanning porosimeter which continuously plots the pressure and corresponding intruded volume on an XY recorder. Only in this continuous manner can the exact position and height of each intrusion step be fully determined. 

All porosimetry curves exhibit hysteresis. That is, the path followed by the extrusion curve is not the same as the intrusion path. At a given pressure the volume indicated on the extrusion curve is greater than that on the intrusion curve and for a given volume the pressure indicated on the intrusion curve is greater than that on the extrusion curve. 

Each step on an intrusion curve has a corresponding step on the extrusion curve at a lower pressure. 

Figure 11.7 is a cumulative pore-volume intrusion curve which shows the summation of volume intruded into the pores and interparticle voids plotted versus the applied pressure. Recognizing that the increase in interfacial area from equation (10.22) is effectively the pore and void surface area S, this equation can be rewritten as... 

By graphical integration, using the cumulative intrusion curve in Fig. 11.7, the surface area of all pores filled by mercury up to 60 000 psia (r = 0.00178 /rm) is calculated as follows ... 

Figure 11.12 (a) Pore surface area distribution versus pressure plot, (b) Pore surface area distribution versus radius plot. Intrusion curve (->) extrusion curve ( ). 

Figure 11.14 (a) Derivative plot dK/dP versus pressure, (b) Derivative plot dK/dP versus radius. Intrusion curve (- ) extrusion curve (+-). 

The total area above the first intrusion curve, A in Fig. 12.1, to the maximum intruded volume indicated by the horizontal dotted line, corresponds to the P-V work of intrusion, IFj. This work term consists of three parts, the first of which is the work of entrapment, W, corresponding to the area between curves A and B. The second contribution to IF. is the work, fV g, associated with the contact angle change from 0, to 0 ... 

Figure 12.3 Intrusion-extrusion curves on an alumina sample coated with various amounts of copper sulfate, (a) Intrusion curve for all samples (b) extrusion curve for untreated alumina (c) extrusion curve for alumina treated with 0.5 % CUSO4 (d) extrusion curve for alumina treated with 2% CUSO4 (e) extrusion curve for alumina treated with 40% CUSO4.

It is evident from Fig. 12.3 that, as the copper sulfate concentration in the sample is increased, the hysteresis increases, that is the difference between P and increases while, at the same time, the extrusion contact angle decreases. Similarly, the work of entrapment, IF, increases as the salt concentration is raised, as evidenced by the quantities of mercury entrapped in the sample. It can be seen in Fig. 12.3 that the intrusion curves for both treated and untreated samples are virtually identical, indicating that impregnation does not significantly alter the radius of the pore opening. However, in all cases the volume of mercury intruded decreased with increasing salt concentration, an indication that precipi-... 

At no time along the intrusion curve does the pressure relax. Therefore, no opportunity is provided for a small quantity of extrusion to occur following intrusion. This is a condition which can produce a data point somewhere in the hysteresis region between the intrusion and extrusion curves. 

The apparent density, that is, the volume of a given mass of sample plus voids divided into the sample mass can be calculated as a function of the void and pore volume from a mercury intrusion curve. The ambient to 60000 psia curve for the silica gel sample is illustrated in Fig. 21.2. Using the volume of mercury intruded at various pressures, the volume of the sample including voids and pores, and thus, the apparent density can be obtained, as shown in Table 21.2. The calculated apparent densities are obtained by subtracting the intruded volume from the initial sample volume and dividing the resulting value into the sample weight. 

The stepped intrusion curves clearly denote different pore size ranges. In the case of experiments EN1 and EN2, this is possibly the reason for the mean pore diameter and activity-coupling yield being the highest. The specific surface areas obtained for all experiments are listed in Table 2. 

Nitrogen adsorption/condensation is used for the determination of specific surface areas (relative pressure < 0.3) and pore size distributions in the pore size range of 1 to 100 nm (relative pressure > 0.3). As with mercury porosimetry, surface area and PSD information are obtained from the same instrument. Typically, the desorption branch of the isotherm is used (which corresponds to the porosimetry intrusion curve). However, if the isotherm does not plateau at high relative pressure, the calculated PSD will be in error. For PSD s, nitrogen condensation suffers from many of the same disadvantages as porosimetry such as network/percolation effects and pore shape effects. In addition, adsorption/condensation analysis can be quite time consuming with analysis times greater than 1 day for PSD s with reasonable resolution. 

The intrusion-extrusion data are presented as pressure vs AV plots, where AV is the volume variation of the system due to water penetration in the porosity. Derivative representations d(AV)/dP of the intrusion curves allow to determine precisely the range of injection pressures. AV values are expressed in mm per gram of bare silica. 

Open symbols intrusion curve, solid symbols extrusion curve. 

Fig. 2 Mercury porosimetry intrusion curve of a mesoporous glass membrane Table 1...

Mercury porosimetry experiments themselves can be criticised from two points of view. Firstly, the sample is pretreated under a primary vacuum of around 10" mbar. As mentioned above, care has to be taken to ensure that this is not already sufficient to degrade the sample, especially in the case of hydrates. Secondly, the pressures that are attained (400 MPa) can be sufficient, in some cases, to crush the samples. This explains the interest to perform intrusion-extrusion-reintrusion curves. This procedure was used in the present study. The extrusion occurs until 0.1 MPa which was enough just to investigate the smaller pores. However, the second reintrusion curve follows the first intrusion curve in both cases (mlO, mVT4) indicating that destruction did not occur for this class of pore. 

The results of simulations demonstrating the effect of various factors on mercury intrusion into porous solids are shown in Figs. 24-26. All the intrusion curves presented have been calculated for the same void radius distribution [Eq. (41) with v = 3000 A and = 0.5]. The mercury intrusion process is seen to start at higher pressures with decreasing Zo (Fig. 24), r (Fig. 25), and o- (Fig. 26). 

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