Surface Area Determination

Under the assumption of a specific pore geometry, one can calculate the surface area of a sample from mercury porosimetry measurements. Usually the cylinder pore model is used.

Rootare and Prenzlow (Ref 45) derived the following equation:

0 ftr cos 8

This equation is equivalent to the cylinder pore model.

The later derivation does not contain an assumption about the pore geometry; it does however, assume that the movement of the mercury meniscus is reversible. For an interconnected pore system, this is not the case and the equation will always calculate higher values for the surface area. Surprisingly many publications report a relatively good correlation between surface area values derived from mercury porosimetry measurements and corresponding N2-gas adsorption BET values (Ref 6, 45) (Table 4).

Table 4 Comparison of surface area measurements with N2 gas adsorption and Hg porosimetry

Sample

Surface area, m /g

Hg-porosimetry

N2-adsorption

Tungsten powder

0.11

0.10

Iron powder

0.20

0.30

Zinc dust

0.34

0.32

Copper powder

0.34

0.49

Silver iodide

0.48

0.53

Aluminum dust

1.35

1.14

Fluorspar

2.48

2.12

Iron oxide

14.3

13.3

Anatase

15.1

10.3

Graphitized carbon black

15.7

12.3

Boron nitride

19.6

20.0

Hydroxyapatite

55.2

55.0

Carbon black (Spheron-6)

107.8

110.0

The value of the specific surface area is often used to determine ("adjust") the contact angle of mercury on a specific material by modifying the contact angle until the surface area calculated from mercury porosimetry measurements correlates with the values determined from nitrogen adsorption data. For materials that do not indicate a severe effect of compressibility or pores smaller than about 10 nm, this method might be a valid alternative to determine the contact angle.

Hysteresis and Entrapped Mercury in the Sample. Interpretation of the extrusion data from mercury porosimetry measurements has been mostly neglected because the interpretation was very vague and questionable. Traditionally, three theories are used to explain the hysteresis between the intrusion and extrusion curve in mercury porosimetry measurements (Fig. 21) (Ref 48): contact angle hysteresis, ink-bottle theory, and connectivity model.

Fig. 21 Mercury porosimetry analysis of an ordered packed sphere structure. Source: Ref 48

Contact Angle Hysteresis. Numerous authors have reported different values for advancing and receding contact angles (Fig. 22). The problem, however, is much more complicated because thermodynamic reasoning does not support such a difference. In addition, the observed intrusion and extrusion curves do not fit as perfectly as they should according to the contact angle hysteresis model. Moreover, the model does not provide any explanation for the trapped mercury, which may remain in the sample even after complete depressurization.

Fig. 22 Hysteresis model based on differences in advancing and receding angles

The ink-bottle theory accurately describes the situation in which mercury enters and leaves pores (Fig. 23). It explains why some of the mercury remains trapped in the sample. However, it explains the principal hysteresis only in part. For most samples, the ink-bottle theory would predict a much larger amount of mercury remaining in the sample than actually observed in the measurement. The contradiction has not been resolved.

Fig. 23 The ink-bottle theory of hysteresis when mercury enters and leaves the pores

The connectivity model uses a network of pores. In order for a pore to become filled with mercury, it is essential to be larger than the corresponding pore size at the applied pressure, but it is also necessary that a continuous path of mercury leads to the pore. Large internal voids that are surrounded by smaller pores are not filled unless the pressure is sufficient to fill the smaller pores. During the extrusion process, the reverse process can occur, and certain pores or islands of pores remain filled with mercury.

The connectivity model probably best describes the real situation, but conflicting results have been reported as well. Several new approaches have been studied recently, and further details are given in the corresponding publications (Ref 46, 47, 48, 49). Analysis of the extrusion curve as well as a back-and-forward pressure scanning within the hysteresis is presently studied. This technique can provide a better understanding of the pore and network structure of the sample.

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