A generalized analysis for mercury porosimetry

A detailed analysis of mercury-intrusion data has been undertaken without specifying a particular pore shape. An equation, derived from a pore-size distribution function in generalized form, has been used to linearize the compression-corrected mercury-intrusion data of several samples on a log-log plot. Using log-log plots, volume changes due to sample compaction can be straightforwardly identified and then separated from volume changes due to mercury intrusion into pores.Equations have also been derived for calculating surface areas from the slope and intercept parameters of these log-log plots. These surface areas, which are compression-corrected and compaction-corrected, have agreed well with BET surface areas.Methods developed for mercury-intrusion porosimetry, to correct data for compression effects, linearize mercury-intrusion data, and calculate surface areas, have been effectively applied to water-intrusion porosimetry. As the hydrostatic pressure was increased on the water surrounding an untreated sample of macroporous polystyrene, water intruded the pores of this sample with a contact angle near 112°.     

Theory of mercury porosimetry hysteresis

Intrusion—extrusion hysteresis and energy conservation in mercury porosimetry can be explained thermodynamically. In a first intrusion—extrusion cycle, hysteresis is explained and work is shown to be conserved when the processes of mercury entrapment and contact angle changes are considered. In subsequent cycles, when mercury entrapment ceases, it can be shown that work is conserved and hysteresis can be explained by the use of the correct intrusion and extrusion contact angles.     

Pore size distribution in Separon using mercury contact angles in pores and hysteresis in porosimetry

The porous co-polymer Separon HEMA 1000 for HPLC column packing was examined by using a special method of mercury porosimetry evaluation. The advancing and receding contact angles of mercury in pores were determined and the method used is described in detail. The pore distribution curves obtained from mercury porosimetry and from the nitrogen desorption isotherms are in good agreement. The dependence of the hysteresis of the porosimetry curves and mercury retention in the pores on the intrusion volume was investiaged to characterize the porous structure of the sample. The influence of the pore potential on the hysteresis was evaluated.     

Correction factors involved in mercury porosimetry

In order to calculate the true volume intrusion of mercury into the pores of a sample, a correction must be made to the observed intrusion to account for the compression of the sample cell, mercury and sample. A theoretical analysis of this correction is presented which is shown to overcome the inadequacies of the usual corrective measure of running a blank experiment in the absence of a sample or on a non-porous sample. The equations derived involve the mercury fill volume in the sample cell, the compressibilities of the mercury, glass and sample and the solid volume of the sample.     

The applicability of mercury porosimetry to materials wetted by mercury

The pore size distribution of porous electrodes made of lead, zinc, cadmium, silver and copper was measured by the intrusion of mercury to establish the applicability of the method to the field of storage batteries. For lead, zinc and copper reproducible results were obtained either without or with a thin protective coating to prevent mercury from wetting their surface; for cadmium and silver, only qualitative information was obtained.     

The contact angle in mercury intrusion porosimetry

The general theory of the contact angle of mercury on complex, internal surfaces of solids, i.e. within pores that cannot be approximated as circular cylinders, is examined. A model for such pore surfaces, in which the pores are represented as cylinders with surfaces that are very rough and that contain void spaces corresponding to the entrances of branch pores, is developed. This model enables us to conclude that in the Washburn equation, for the pressure required to force mercury into a pore of radius r, the contact angle that should be used is 180°, particularly for macropores and mesopores in most practical solids.     

Empirical correction factors involved in mercury porosimetry

An empirical calculation method has been developed to correct the apparent porosity measured by mercury penetration porosimetry. It was found that the value of the correction depends on the geometry and volume of the sample cell, the volume of mercury in the sample cell, and the pressure applied. The effect of the compressibility of the sample was found to be negligible. Application of this correction enables valid porosity curves to be obtained even at high pressures up to 50,000 psi. Thus, by adopting Rootare and Prenzlow's method for specific surface area, appropriate results can be calculated.     

Wood's metal porosimetry and its relation to mercury porosimetry

Wood's metal porosimetry permits the determination of the frequency distribution α(D, D_e) of the volume of pores having diameters in the range D → D + dD whose penetration by Wood's metal (or mercury) is controlled by pores having diameters in the range D_e → D_e + dD_e. The results obtained in sandstone samples indicate that the volume of the entry pores is very small in comparison with the volume of the much larger (up to four times) pores which are penetrated through the entry pores. The accessibility of pores of a wide diameter range is controlled by pore necks of diameters which are distributed over a narrower range. The accessibility function α(D, D_e) has been the starting point of a great deal of in-depth research of pore structure.     

Pore spectra from continuous scan mercury porosimetry

A method for obtaining pore spectra is described. Continuous pressure—volume data from mercury porosimetry were used to determine the volume distribution as a function of the intrusion and extrusion pressure or the pore radius for a number of porous samples.An explanation is offered for delayed intrusion of mercury into pores. Mercury vapor transfer has been postulated as a thermodynamically allowed mechanism in those few cases where pore size or constrictions prohibit liquid transfer.     

Mercury porosimetry studies II. The application of mercury porosimetry to porous polymer powders

Two experimental methods are outlined for the separation of the inter- and intraparticle intrusion volumes of porous powders. The first of these relies upon the control of interparticle bed packing by mounting the particles upon a transparent adhesive substrate. The pressure at which interparticle penetration occurs (critical pressure) is measured by observing the penetration process directly in a microscope pressure cell. A mercury intrusion experiment is then run on a similarly mounted sample and the value of the critical pressure obtained previously used to define the interparticle volume.In the second method, the critical pressure is determined by running a mercury intrusion experiment on a powder sample whose intraparticle volume has been filled with a wetting liquid—dioctyl phthalate (DOP). This technique depends upon the observation made previously in Part I of this series that bed depacking rather than bed penetration is the initial step of the penetration process.Total intraparticle volumes determined by both of these methods were compared with those obtained by the uptake of a wetting oil (DOP). Although an excellent degree of correlation was observed between the two methods, the DOP uptake values were found to be high by a constant amount. This was demonstrated to be due to oil retained in the interparticle volume. The values of critical pressure determined in this study indicate that the filling of the interparticle voids in a mercury intrusion experiment may not correspond to any feature observed in the penetration curve. Thus it is necessary to determine this quantity separately.     

A new method for the investigation of porous structures using mercury porosimetry

The influence of wetting angle hysteresis on volume hysteresis and retention of mercury in porous solids was considered. Although different explanations are possible (as explained in the paper), the resulting effect for cylindrical pores in the examined sample of active carbon was that the advancing angle θ_A = 162°, and the effective value of the receding angle θ_R = 90°. The rise of the mercury volume (V_m) intruded in the second run after the preceding reduction of pressure (p) to zero corresponds with a formation of spherical caps at the orifice of pores. The dependence of V_m on p in such a case has been called local hysteresis and it has been used to evaluate the true θ_A, the number of pores with a radius corresponding to the pressure of intrusion and their mean length.     

Characterization of hyperporous polyurethane-based gels by non-intrusive mercury porosimetry

Evaporative drying of polyurethane-based gels produces xerogels. Supercritical drying after replacement of interstitial liquid by supercritical CO₂ produces aerogels. SEM micrographs show that both materials are made up of small size particles gathered up in filament-shaped, strongly cross-linked aggregates. Density measurements show that they both have a large pore volume.When submitted to mercury porosimetry, the behavior of these materials is similar to that of inorganic aerogels, as previously observed. Mercury does not penetrate the pore network, but the whole material is densified. The usual Washburn equation cannot be used to analyze the mercury porosimetry. A well-suited equation based on a buckling model of filament-shaped aggregates has been developed in order to determine the pore volume distribution of mineral dried gels. This equation is also valid for analyzing the texture of organic hyperporous materials like polyurethane dried nanoporous gel.     

The effect of elliptical pores on mercury porosimetry results

Heat transfer coefficients were measured between gas-fluidized beds and spherical calorimetric probes of different sizes and to a water-cooled horizontal tube. The bed materials used were alumina and sand of narrow size ranges. Operating temperatures extended up to 980 °C and some estimate of the magnitude of the radiant heat transfer component was obtained by comparing the results for surfaces of oxidized copper (high emissivity) and polished fine gold (low emissivity). Tests with small spherical calorimetric probes immersed in beds of large mean particle diameter showed that there is an effect of relative heat capacity leading to enhanced bed-to-surface heat transfer coefficients if the heat capacity of the ‘heat transfer surface’ is less than an order of magnitude greater than that of the bed particles. Relative bed/surface temperature affects the heat transfer coefficient in two ways: through the temperature influence on gas thermal conductivity affecting the particle convective component of the coefficient, and through the rate of cooling of material directly adjacent to the transfer surface affecting the radiant component of heat transfer. Bed-to-tube coefficients are lower than those to a small calorimetric probe because of the sustained low temperature of a coolant tube and the obstruction that it presents to the circulation of the fluidized solids. The predictive capabilities of the published correlations are poor over the range of operating temperatures tested.     

Density measurement of small porous particles by mercury porosimetry

The concept of density of solid particles is discussed, and the relation between these concepts and the different measurement methods is considered with the emphasis on the porousness (i.e. the property of ‘porous’ or ‘non-porous’) of the solid particles.Mercury porosimetry was used to determine the density of porous small particles. The limitations of this method and the influence of surface roughness and other particle characteristics on the density values obtained are also discussed.     

The application of mercury porosimetry to porous polymer powders

The problem of distinguishing between intraparticle and interparticle volume in mercury intrusion data is sometimes difficult. A method of calculating a theoretical cut-off point between intra- and interparticle voids has been derived for powders of uniform size. The method has been evaluated using three polymer powders with different morphological properties. In addition, the procedure is often useful for detecting structural changes arising from the high intrusion pressures. The theoretical background to the method and some of its limitations are discussed. Scanning electron micrographs of the polymers have been used to provide further structural information to aid the interpretation of the porosimeter results.     

Assessment of permeation quality of concrete through mercury intrusion porosimetry

Permeation quality of laboratory cast concrete beams was determined through initial surface absorption test (ISAT). The pore system characteristics of the same concrete beam specimens were determined through mercury intrusion porosimetry (MIP). Data so obtained on the measured initial surface absorption rate of water by concrete and characteristics of pore system of concrete estimated from porosimetry results were used to develop correlations between them. Through these correlations, potential of MIP in assessing the durability quality of concrete in actual structure is demonstrated.