Porosimeter

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.)...

Considering each juation of Pfeifer [11], Washburn [12] and Rootare-Prenzlow [13], the surface area of porous solid, Srp, measured by porosimeter can be expressed as Eq. (4). 

Here, P is the equilibrium pressure. Therefore, Dj of the anode electrode can be also calculated through the slope of a log-log plot of Eq. (4) by the data from the mercury porosimeter. 

With the advent of mercury intrusion porosimeters, it is advantageous to perform a pore size distribution of investigational batches of a drug [43]. The Washburn equation [44] states that the pressure, P, necessary to intrude a pore is given by... 

Since mercury has a contact angle with most solids of about 140°, it follows that its cosine is negative (i.e., it takes applied pressure to introduce mercury into a pore). In a mercury porosimeter, a solids sample is evacuated in a cell, mercury is then intruded, and the volume, V, is noted (it actually reads out), and the pressure, P, is then increased stepwise. In this fashion it is possible to deduce the pore volume of a particular radius [corresponding to P by Eq. (21)]. A pore size distribution will give the total internal pore area as well, which can be of importance in dissolution. 

The pore size distribution of the dried sample was measured by a Aminco 60,000 psi Mercury-Intrusion Porosimeter. 

Porosimeters fall into two groups depending on the pressure used for the measurements. Low-pressure, or subambient, units operate from 0.5 psi to ambient pressure to measure large pores. High-pressure porosimeters operate from ambient pressure to as high as 60,000 psi [43] to measure much smaller pores. These elevated pressures are achieved in a number of ways, such as pressurizing in a hydraulic pump oil medium. 

Aside from N2 adsorption, Kr or Ar adsorption can be used at low temperatures to determine low (<1 m2/g) surface areas [46], Chemically sensitive probes such as H2, Oz, or CO can also be employed to selectively measure surface areas of specific components of the catalyst (see below). Finally, mercury-based porosimeters, where the volume of the mercury incorporated into the pores is measured as a function of increasing (well above atmospheric) pressures, are sometimes used to determine the size of meso- and macropores [1]. By and large, the limitations of all of the above methods are that they only provide information on average pore volumes, and that they usually lack chemical sensitivity. 

Relation 9.77 is usually called the Washburn equation [55,237], One should consider it as a special case of the fundamental Young-Laplace equation [3,9-11], Washburn was the first to propose the use of mercury for measurements of porosity. Now, it is a common method [3,8,53-55] of psd measurements for a range of sizes from several hundreds of microns to 3 to 6 nm. The lower limit is determined by the maximum pressure, which is applied in a mercury porosimeter the limiting size of rWl = 3 nm is achieved under PHg = 4000 bar. The measurements are carried out after vacuum treatment of a sample and filling the gaps between pieces of solid with mercury. Further, the hydraulic system of a device performs the gradual increase of PHg, and the appropriate intmsion of mercury in pores of the decreasing size occurs. 

Where there is a wide distribution of pore sizes and, possibly, quite separately developed pore systems, a mean size is not a sufficient measure. There are two methods of finding such distributions. In one a porosimeter is used, and in the other the hysteresis branch of an adsorption isotherm is utilised. Both require an understanding of the mechanism of capillary condensation. 

The carbon content of a stationary phase is measured by an elemental analyser, as a weight balance before and after heating at 800 °C. Particle size, pore size, and surface area are measured by specific instruments, such as a particle size analyser, nitrogen adsorption porosimeter, and mercury depression analyser, respectively. The precision of the measurement of carbon content is high however, that of the other measurements is relatively poor. Therefore, it is difficult to relate the surface area of different silica gels to analyte retention factors. 

The commercial mercury porosimeters can usually provide pore diameter distribution data in the range of 3.5 nm to 7.5 microns. It is a useful and commonly used method for characterizing porous particles or bodies. Figure... 

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. 

The experimental method employed in mercury porosimetry, discussed more extensively in Chapter 20, involves the evacuation of all gas from the volume containing the sample. Mercury is then transferred into the sample container while under vacuum. Finally, pressure is applied to force mercury into the interparticle voids and intraparticle pores. A means of monitoring both the applied pressure and the intruded volume are integral parts of all mercury porosimeters. 

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. 

Some newly developed automated porosimeters have associated computer-aided data reduction capabilities which perform the above integration as rapidly as data is acquired. 

Figures 11.9 to 11.14 illustrate some of the previously discussed functions plotted linearly versus pressure (Figs 11.9a to 11.14a) and logarithmically versus radius (Figs 11.9b to 11.14b), such that each decade of pore radius assumes a uniform interval. A mixture of porous glasses was used as the sample and the data was obtained on a Quantachrome Autoscan-60 porosimeter. An associated Autoscan computer was used to reduce the data and produce the plots of the various functions on an X-Y recorder. Each plot contains approximately 750 data points and as a result, appears continuous. The volume versus pressure curve. Fig. 11.9a, is composed of analog data produced directly from the porosimeter.

If the porosimeter can generate 60000 psia of hydraulic pressure, the minimum radius into which intrusion can occur will be about 18 A. Assuming that pores centered about 15 A radius are present and contain a volume of 0.01 cm, an approximation of their surface area can be made by assuming cylindrical geometry. Thus,... 

Although many high-pressure mercury porosimeters have been constructed, they all have several essential components, which are perhaps different in their design but nevertheless are common to each apparatus. These components include the following ... 

A mercury porosimeter capable of producing continuous plots of both the intrusion and extrusion curves has recently been developed. Figure... 

Figure 20.3 Autoscan-60 porosimeter. (Courtesy of Quantachrome Corporation.)...

Unlike conventional incremental porosimeters, which produce a limited number of data points, the presentation of continuous scans eliminates the need to rerun an analysis to obtain information between data points for additional resolution in the regions of interest. 

The dilatometer stem is coaxially enclosed in an open-ended stainless-steel sheath which serves as one plate of a capacitor in a manner similar to the sheath used in the high-pressure porosimeter. When connected to the capacitance bridge of the porosimeter, the filling apparatus, using its own low-pressure transducer, measures the intruded volume and continuously plots the data on an X-Y recorder up to 24 psia. 

Mercury porosimetry provides a convenient method for measuring the density of powders. This technique gives the true density of those powders which do not possess pores or voids smaller than those into which intrusion occurs at the highest pressure attainable in the porosimeter and provides apparent densities for those powders that have pores smaller than those corresponding to the highest pressure. 

As noted above, much of the data manipulation of commercial porosimeters is computerized, so a pore size distribution is produced automatically by these instruments. 

Nitrogen sorption measurements were performed on a Quantachrome Autosorb 6B (Quantachrome Corporation, Boynton Beach, FL, USA). All samples were degassed at 423 K before measurement for at least 12 hours at 1 O 5 Pa. Mercury-porosimetrie has been measured on a Porosimeter 2000 (Carlo Erba Instruments) Scanning electron micrographs were recorded using a Zeiss DSM 962 (Zeiss, Oberkochen, Germany). The samples were deposited on a sample holder with an adhesive carbon foil and sputtered with gold. 

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