Intrusion-extrusion curves

During depressurization, pores which commenced filling at point D begin to empty at point F and at lower pressures pores that filled between points B and C begin to empty at G. At point H on the extrusion curve the cycle is terminated. The intrusion-extrusion cycle does not close when the initial pressure is reached indicating that some mercury has been permanently entrapped by the sample. Often, at the completion of an intrusion-extrusion cycle mercury will slowly continue to extrude, sometimes for hours. 

On the other hand some samples possess a wide and continuous range of pore sizes, resulting in the porosimetry curve shown in Fig. 11.4. 

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. 

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A method for calculating the dimensions of the cavities and narrow necks from the intrusion-extrusion curves has been proposed by Reverberi." " The method is essentially as follows the ascending curve (penetration) branch is measured in the usual way, but the descending curve is mapped out from a series of steps each step commences at the same maximum pressure, proceeds to a pre-determined minimum pressure which is different for... 

Figures 11.1 and 11.2 illustrate mercury porosimetry data of a bimodal size distribution. However, other types of less typical curves are often encountered. For example, samples of controlled porous glass exhibit intrusion-extrusion curves illustrated by Fig. 11.3, in which all the pores are essentially of one radius.

All mercury intrusion-extrusion curves have certain characteristics in... 

The value of j8 for most solids lies in the range 10" to 10" dynes" Vcm" or about 10 to 10" psia" This implies that a sample with a volume of about 1 cm will be compressed by one millionth to one ten-millionth of a cubic centimeter for each pound of applied pressure. Therefore, at pressures as high as 60 000 psia the sample will compress by only 0.006 to 0.06 cm. However, some softer plastics and other materials may have greater compressibilities for which corrections should be made. Some materials have occluded pores without access to the surface and can collapse on pressurization. Figure 11.6 illustrates an intrusion-extrusion curve accompanied by compression and decompression curves for a sample of porous material. 

The line from the origin to point A is the compressibility curve. It is from this line and not from the abscissa that intruded volumes are measured. Similarly, the line from point B to the ordinate is the decompression curve from which the extruded volumes are measured. The assumptions made when using this method for correcting intrusion-extrusion curves for compressibilities are ... 

It has been demonstrated that first and subsequent mercury intrusion-extrusion curves can be viewed as consisting of three significant areas when the extrusion contact angles are not corrected, as shown in Fig. 12.1. 

Since IF = 0 and since no work difference exists between and for any element of the intrusion-extrusion curve, it follows that hysteresis on volume-pressure plots results only as a consequence of ignoring the additional energy terms and... 

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.

In those cases where pores are ink-bottle in shape, a method, proposed by Reverberi for calculating the sizes of the narrow and wide portions of the pore from intrusion-extrusion curves can be used. The method involves scanning the hysteresis loop by means of a series of pressurization and partial depressurization cycles in order to determine the volume of the wide inner portion of pores having neck radii in various radius intervals. 

An advantage of isotherms constructed from mercury intrusion-extrusion curves is the capability of extending the isotherm well beyond the limits of vapor adsorption-desorption isotherms. Intruded and extruded volumes can be measured for pores of several hundred micrometers in diameter at pressures below 1 psia. 

Porcheron et al. revealed different intrusion/extrusion characteristics and hysteresis behaviours between Vycor and CPG [52]. The intrusion/extrusion curves in Figure 3.12a reveal a type HI hysteresis loop for the CPG sample and a type H2 hysteresis loop for the Vycor glass. Entrapment was also observed that is mercury remains in... 

When compressional effects occur, one can either try to correct for their contribution or to exploit them to determine the mechanical characteristics of the aerogel under investigation. Pirard compared two intrusion/extrusion curves taken for two different pieces of monolithic precipitated silica taken from the same batch [80] hereby one sample was wrapped into a mercury impermeable membrane. The experimental curves showed that the first flat slope of the intmsion curve can exclusively be related to compression of the sample while the subsequent steep increase of the intmsion volume with increasing pressure applied is actually dominated by intmsion of the pores. Upon extmsion, the volume detected for the unwrapped sample was not fully recovered it could be shown that the missing volume upon extmsion was equivalent to the volume compressed in the first stage of pressurization (intmsion). 

Figure 21.33. Mercury intrusion/extrusion curves for two different TEOS-based silica xerogels. The arrows indicate the pressure at which the behavior crosses over from sample compression to mercury intrusion of the sample. The extrusion curves reveal an irreversible deformation of the samples upon intrusion. Plot reproduced from [79], p. 337.

Transformation of Intrusion/Extrusion Curve into Adsorption/Desorption Isotherm... 

Likewise, Hg letraction can be considered as the equivalent of N2 adsorption both processes are controlled a eat deal by the sizes of sites when a piston-like retraction is assumed. ConsKjuently, all Hg retraction curves that are shown in Fig. 5 are located within a range of similar pressure values. Neverthelras, the three Hg retraction curves differ in the slopes of the boundary intrusion-extrusion curves and in the amount of Hg trapped. 

Many commercially important processes involve the transport of fluids through porous media and the displacement of one fluid, already in the media, by another. The role play by pore stnicture is of fundamental importance, and its size distribution determination necess. in order to obtain an understanding of the processes. The quality of powder compacts is also affected by the void size distribution between the constituent particles. For these reasons mercury porosimetry has long been used as an experimental technique for the characterization of pore and void structure. Although quantitative information is contained in mercury intrusion - extrusion curves it can only be elucidated fiilly by the use of a theoretical model for pore structure. 

Mercury porosimetry intrusion-extrusion curves were obtained using Quantachrortte High (2(X)-50,000 psi) and Low (1-500 psi) Pressure Autoscan Porosimeters. An Analog Devices Macsym 150 computer was used to collea and analyze the data. Typical run times for intmsion and retraction was 7-8 minutes. 480 dyne cm" was used for the surface tension of the mercury with a contact angle of 140 degrees in the calculation pore dimensions. Total pore volume (maximum mercury intmded to 50,000... 

Figures 1 and 2 show typical mercury intrusion-extrusion curves obtained in our study. The step volume increase and hysteresis are seen for all seven of the silica samples. The mercury extrusion volume is small for the data shown in Figure 1, and is much larger for the curve in Figure 2. At least a portion of the volume of mercury remaining in the sample is most likely due to initial compaction of the loosely packed structure and is also seen in varying degrees for all samples.

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