Measurement Techniques

Measuring Displacement Volumes (Pore Volume). Mercury volume displacements may be measured by direct visual observation of the mercury level in a glass penetrometer stem (Fig. 14) with graduated markings (Ref 35). However, most (if not all) instruments on the market will measure this volume automatically by one of the following techniques:

• Precision capacitive bridges: measure changes in the capacitance between the column of mercury in a dilatometer stem and a coaxial sheet surrounding the column

• Mechanical transducer: indicate the change in height of the mercury column by moving a contact wire and measuring the displacement of the mercury interface in the stem

• Submerged wires: measure changes in resistivity corresponding to the change in length of the mercury column

From a practical point of view, the sample mass (pore volume) and the stem volume of the penetrometer should be adjusted to use the instrument to its highest resolution. In general, larger samples are preferred because they provide a better representation of the overall sample.

Fig. 14 Quantachrome filling mechanism and low-pressure porosimetry system. Source: Ref 35

Pressure. The corresponding pressure at which mercury is filling the pore system is usually measured with electronic pressure transducer or with Heise-Bourdon manometer, used in older manual setups. A series of those pressure transducers ensures that accurate data are determined over the entire range from 0.1 psi (0.7 * 10-4 MPa) to 60 psi (0.4 MPa).

Looking at the Washburn equation (Eq 11) makes it obvious that two additional parameters play a critical role in the calculation of pore size from the applied pressure: contact angle, 0. and the surface tension, 7Hg.

Contact Angle Determination. Various techniques are available to determine the contact angle:

• A drop of mercury can be placed on the flat surface of the sample, and the resulting contact angle is visually observed. Problems related to "micro" and "macro" contact angles have been reported (Fig. 15) (Ref 36). Brashforth and Adams (Ref 37) published tables that allow calculation of the contact angle as well as the surface tension of liquids from the shape of a drop of mercury on the substrate surface (Fig.

16). A simplified formula can be used when the maximum height of the drop is reached (Ref 35, 37, 38):

• with g, the acceleration of gravity, and P, the density of the liquid.

• A powder compact can be pressed in such a way that a well-defined hole is created in a disk. Mercury is now placed on top of this disk, and the contact angle can be calculated from the necessary pressure to force the mercury through this cylindrical pore.

• The Willhelmy plate method (Fig. 17) can be used to determine the contact angle (Ref 39). Figures 17 and 18 illustrate the critical observation of an advancing and receding mercury interface. Surface roughness (Fig. 18) or the change in surface composition during the contact with mercury can explain the presence of this difference. (Note: there is no thermodynamic reason or explanation for any contact angle hysteresis.) No surface roughness effects are assumed below pore sizes of about 100 nm. This effect also emphasizes the importance of clean samples and clean mercury.

The contact angle between mercury and the sample being tested is frequently assumed to be 130 or 140°. This assumption is probably the largest source of error. Contact angles of different materials may differ significantly, as shown in Table 2 (Ref 40).

Table 2 Contact angle between mercury and select P/M materials


Angle, degrees











Tungsten carbide



Source: Ref 40

Fig. 15 Differences between microscopic and macroscopic measurement of the contact angle (i0) under conditions of (a) wetting and (b) nonwetting

Fig. 16 Change of mercury-drop shape with size
Fig. 17 Wilhelmy plate method showing the effect of contact angle hysteresis for emersion and immersion. Adapted from Ref 39
Fig. 18 Effect of surface roughness on contact angles

The Washburn equation is directly proportional to the cosine of the contact angle; the respective pore size errors for iron (0 = 115°) and glass (0 = 153°), using the values from Table 2 versus a constant value of 130° for 0. would be:

However, published contact angles differ widely between different research groups, even when presumably the same material was studied.

Some materials might react with mercury, for example, zinc, silver, or lead samples. This severely changes the nonwetting behavior of mercury with that sample and may even lead to a contact angle of <90°. In those cases a protective film of stearic acid can be applied to the sample/pore surface and thus prevent the reaction. Though, for several reactive metals, such as copper, their natural oxide layer on the surface is a sufficient protection (Ref 41).

Surface Tension of Mercury. Values for the surface tension of mercury can vary with atmosphere, temperature, and purity of the mercury used. The purity of mercury has a significant effect on surface tension. Reported values vary by up to 0.1 N/m (100 dynes/cm). Mercury is unusually prone to contamination, and this probably accounts for the lack of reproducibility to be found in the values of surface tension in earlier publications. Later work, however, showed very consistent results (Table 3) (Ref 6). The effect of temperature is minimal, because the temperature coefficient of the surface tension of mercury is only 2.1 x 10-4 N/m • °C. Another error is caused by neglecting the change of surface tension for very small radii of surface curvature. The following correction has been suggested by Kloubek (Ref 42):

For AP = 200 MPa, the correction term gives an error of 12% [7corr = (0.485 - 0.053) N/m],

Table 3 Surface tension of mercury in vacuum

Temperature, °C

Surface tension, mN/m

Method used


484 ± 1.5

Sessile drop


484 ± 1.8

Sessile drop


485 ± 1.0

Drop pressure


483.5 ± 1.0

Sessile drop



Sessile drop



Pendant drop


485.4 ± 1.2

Pendant drop


484.6 ± 1.3

Pendant drop


482.5 ± 3.0

Bubble pressure

Source: Ref 6

Source: Ref 6

Compressibility of Mercury. Due to the slight compressibility of mercury, the measured pore volume of a porous material appears larger than its actual volume. Using a well-balanced combination of the compressibility of the glass sample cell, the mercury and the changes of dielectric properties especially of the high-pressure fluid minimizes this blank effect. In general, the larger the sample and pore volume of the sample in comparison to the amount of mercury in the penetrometer, the smaller the errors due to compressibility. Moreover a blank run correction can be used to correct for compressibility effects. However, the total effect is a combination of all components in the system: the mercury, the high-pressure oil, the glass penetrometer, and the sample.

0 0

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