Restrictions and Limitations

Results obtainable by mercury porosimetry are limited a priori in three ways:

• The volume of pore space filled with mercury is limited by the maximum pressure. This aspect is related to the question of what is to be counted as pore space; this is not self-evident for all materials (e.g., cement stone). Mercury cannot penetrate very small pores.

• At the other end of the scale, the penetration of very large pores is limited by the height of the sample, which determines a minimum pressure. Hence, very large pores may go unnoticed. (This was observed, e.g., for porous nickel plaques.)

• The sample size is finite and usually quite small. This boundary condition determines that results are not necessarily representative of an infinite pore space, as large pore openings (at the surface) are more easily accessible in a smaller sample. Empirical support for this has been found by carrying out experiments with jacketed and unjacketed samples.

Geometrical properties of the sample can affect the reproducibility and can cause difficulty in giving an unambiguous interpretation of the result:

• In many cases, a distinction is to be made between the interparticle and intraparticle voids. In a packing of nonporous particles there is only an interparticle pore space. However, in many applications—for example,sorbents--the prime concern is in the intraparticle void space. In such cases, a judgment must be made as to which part of the measured pore volume belongs to the interparticle voids and which part belongs to the intraparticle porosity. If the sample exists as larger particles, the pore size distribution frequently shows a bimodal pore size distribution. The larger pore size fraction can then be attributed to the interparticle porosity. It may also help to use a narrow size fraction of these particles for the porosity analysis. A narrow particle size distribution causes a distinct peak in the pore size distribution at about 20 to 50% of the particle size, which can be clearly attributed to the interparticle voids.

• A special problem is caused by the roughness of the surface of the particles or lumps that are measured. Reich (Ref 44) already pointed out that characterization of samples should be based on those with the same surface roughness. He found a significant difference for pieces of brick broken in different ways. Corrections for the "part of the surface" that belongs to the particle pore space have been made, but it remains difficult to separate pores at the surface from pores in the inside if a cross-sectional area through the surface is different from a cross-sectional area through the interior of the porous medium. Sometimes these differences are very great, and the presence of a characteristic surface layer can actually be observed.

• Pretreatment of the sample may involve comminution. This may change the internal pore space in two ways. First, if closed pores are present, some of these will be broken open. Second, particles tend to break along large pores; hence the relative volume of larger pores decreases.

• Similar problems arise for nonparticulate materials such as paper. Sheetlike material should be packed in a controlled way to eliminate artificial pores between the sheets.

The points mentioned up to now are basically limitations of the technique. If they are overlooked, they can lead to errors of interpretation. The following is a list of factors that can upset the accuracy and the reliability of the results in a more direct way.

• Even if clean mercury is used at the beginning, the surface may soon be contaminated by components that were adsorbed on the surface of the sample. It is known that impurities can change the surface tension of mercury by as much as 30%.

• Before mercury enters the dilatometer, the sample should be outgassed. Evacuation of the sample can change the contact angle of the sample (compared with the contact angle on the sample in its original condition). It has been stated that strong outgassing is necessary if the smallest pores are to be measured. However, the error caused by compression of residual air seems to become significant only if the evacuation does not reach a pressure below 10 torr.

• A serious problem arises when the sample is mechanically destroyed by the applied pressure during the analysis. Fragile porous materials may be subject to a breakdown of pores during pressurization, or solgel materials are frequently compressed reversibly or irreversibly during the mercury porosimetry analysis at high pressure. Knowledge of the compressibility or fracture strength of the material to be analyzed is desirable to properly estimate whether mercury intrusion will occur before deformation or fracture of the porous material occurs. In other cases, a powder compact can be further compacted during the measurement; for example, a powder was compacted at a pressure of 10 MPa; however, mercury does not penetrate the pores before a pressure of 20 MPa is reached. In this case, the sample experiences a second compaction and the results are not related to a compaction pressure of 10 MPa but rather 20 MPa.

• Corrections have to be made for the compressibility of the dilatometer and the mercury, as well as compressibility effects of the sample. Due to the compression of the mercury and oil, the temperature in the dilatometer may rise considerably when a high pressure is applied. It has been estimated that the temperature rise could be as much as 15°. Although it has occasionally been mentioned that a cooling fan is used, this point seems to have gone largely unnoticed. A change in temperature then changes the volume of the mercury and the dilatometer and thus causes an artificial pore volume effect.

• The so-called kinetic hysteresis effect is related to the time that is required for the mercury to flow into pores. If a volume reading is taken before equilibrium has been reached, this will result in a shift of the

Moreover, the rate of advance of mercury interfaces in horizontal, cylindrical capillaries was computed and also verified experimentally. For a given sample size and pore size, the time required for equilibrium to be achieved during injection can be calculated.

For a horizontal, cylindrical capillary, mercury enters the capillary at the threshold pressure, as given by the Laplace equation, but does not continue to advance. A finite rate of advance is dependent on an excess pressure (AP) above the threshold pressure and the distance-to-time relationship for the advancing mercury front is given by the following equation, which can be derived from the Poiseulle equation (see Ref 39, p 286, and Ref 49):

where t is time, / is distance, '/is viscosity, r is radius, and A.P is pressure applied in excess of the injection pressure.

The distance-to-time relationship for mercury in tubes of five different sizes is shown in Fig. 19. A total applied pressure of 110% of the injection pressure—that is AP in the previous equation is equal to 10% of injection pressure given by the Laplace equation—was used. The graph shows that for a tube of 0.5 /'m radius, the time required to travel 3 cm is in excess of 100 s.

0 1 2 S 4 5 6 Injection distance, cm

Fig. 19 Distance-to-time ratio for mercury advancing in tubes of five different radii (r). Source: Ref 49

The measured data are not reliable if they do not refer to an equilibrium situation. In older publications, for example, kinetic hysteresis is stressed and the effect of mechanical vibrations ("tapping") is noted. In practice, those limitations only apply to very large samples or for extremely small pore sizes. An equilibration time of 1 to a maximum of 5 min should be sufficient in all samples.

In general, effects due to different intrusion rates are not very severe. However, an example where pore size as well as pore volume was greatly influenced is shown in Fig. 20. Five samples of an alumina extrudate were analyzed with different equilibration routines. One sample was scanned (equilibration by time for 0 s). Three others were analyzed at different equilibration intervals (2, 10, and 30 s), and a fourth was analyzed at an equilibration rate of 0.001 /'L/g- s. The data from the five experiments are summarized in Fig. 20.

Fig. 20 Effect of equilibration routines on measurement of (a) cummulative intrusion and (b) log differential intrusion with alumina extrudate. Source: Courtesy of D. Smith, Micromeritics and Ref 53
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