A generalized analysis of hysteresis in mercury porosimetry

Powder Technology, 38 (1984) 165 - 173

165

A Generalized Analysis of Hysteresis in Mercury Porosimetry R. W. SMITHWICK and E. L. FULLER, JR.

Union Carbide Corporation - Nuclear Division, P.O. Box Y, Oak Ridge, TN 37830 (U.S.A.) (Received June 14, 1983; in revised form September 23,1983)

SUMMARY

Modifications in hardware, including the addition of a computer, and in operating procedures, were made to a commercial mercury porosimeter to facilitate thermal and mechanical equilibration. These modifications reduce temperature changes in the hydraulic fluid which cause an 'apparent hysteresis' even in the mercury-only blank. These modifications also allow the allocation of additional time for slow processes such as mercury extrusion from the porous samples analyzed in this work. Hysteresis observed between intrusion and' extrusion mercury porosimetry data has been interpreted by a generalized analysis. Without specifying a particular pore shape, detailed features of sample compaction, mercury retention, and contact-angle changes can be identified by this method. The hysteresis in the mercury porosimetry data of the samples analyzed in this work are completely consistent with contact-angle hysteresis. INTRODUCTION

Mercury intrusion porosimetry [1,2] is a technique used to characterize the porosity and surface area of a solid by measuring, at increasing pressures, the volumes of mercury which intrude the accessible pores in the sample. Following intrusion, the volume can also be measured as mercury extrudes from the sample at decreasing pressures. Several researchers [3, 4] have noted that the hysteresis observed between the intrusion data and the extrusion data of mercury porosimetry is consistent with the hysteresis observed between advancing and receding contact angles, respectively. Recently, other authors [5, 6] have proposed this again and have disputed a former interpretation [7] that the hysteresis encountered in mercury porosi0032-5910/84/$3.00

metry is due solely to the presence of 'inkbottle '-shaped pores. Both dynamic and static contact angle hystereses on solid interfaces are the subjects of recent studies [8, 9]. Differences in advancing and receding contact angles have long been observed [10,11] for liquids on rough or heterogeneous surfaces. On smooth, homogeneous surfaces no hysteresis is observed for dynamic contact angles but an intrinsic contact angle hysteresis is observed for liquids in static equilibrium with the surface. This intrinsic hysteresis is presumably due to a 'frozen' layer of liquid immediately adjacent to the solid [8]. In the specific case of liquid mercury, an advancing contact angle of either 130 or 0 140 has traditionally been assumed for samples run by mercury intrusion porosimetry because these angles are typical for mercury on smooth, flat, non-wetting surfaces. However, the contact angle of mercury in microscopic contact with a porous sample is not easily measured directly. The measurement of the contact angle for a porous sample is usually accomplished only after 'smoothing' a surface prior to mercury contact and measurement. For example, a sample of powder is usually compacted so that the mercury contacts a smooth surface during contact angle measurement. Alternatively, Good and Mikhail [12] have 0 proposed a contact angle of 180 for mercury intrusion into macroporous and mesoporous samples which do not have smooth, flat surfaces. The use of a contact angle of 180 0 in recent work [13, 14] has resulted in improved agreement between BET surface areas and surface areas calculated from the compression-corrected mercury intrusion data of macroporous samples. In a previous report [14], the following relationship was derived for mercury intrusion 0

© Elsevier Sequoia/Printed in The Netherlands

166

into a distribution of pores of unspecified shape: log[ WOR(P,,,) -

-

VPOR(P)]

log[VPOR(P,,,)

= - X[log(P)

-

+

VPOR(P,)]

=

- log(P,)]

INTRUSlON

Using this ‘generalized analysis’, data points were found to lie on one of two intersecting lines on a log-log plot of the total pore volume, VPOR (Pm,,), minus the cumulative pore volume at P, VPOR(P), versus the hydraulic pressure P. The line of low slope at low pressure was interpreted to be sample compaction, whereas the line of slope --X, beginning at P, (the breakthrough pressure), was interpreted to be mercury intrusion described by eqn. (1). An expression for surface area in terms of the slope and intercept parameters of the log-log plot were also derived in this previous work (P, is in MPa): SA (small PC. X > 2) =

~ORV’m,,

I-

-

2.083 cos 8

WOW’,)

X X-l

p

(2)

= Pbulk In the present work, the log-log plots of this generalized mercury porosimetry analysis will be used to interpret the intrusion and extrusion data of two samples with respect to sample compaction, mercury retention, and changes in contact angles. EXPERIMENTAL

Macroporous polystyrene was obtained from Aldrich Chemical Company. A beryllium oxide powder, obtained from BrushWellman Company, was compacted to 550 hIPa (80 000 psi) with a die and press_ Intrusion and extrusion data were obtained with a Pore Sizer 9300 mercury porosimeter manufactured by Micromeritics Instrument Corporation. This porosimeter was automated using a Digital Equipment Corporation LSI11/2 microcomputer system. The major features of this Pore Sizer 93OO/LSI-11 combination are shown in Fig. 1. The basic measurement, programmed in FORTRAN language, involves successively: (1) reading pressures from a pm-established table; (2) activating the appropriate relay to raise or lower the pressure of the system until the target pressure is obtained; (3) maintaining

PRESSUREDOWN

(1)

Fig. 1. Schematic of computerized Mercury Porosimeter.

RELAY

Pore Sizer 9300

(and, if necessary, adjusting) this pressure for a minimum of ten 6-second periods; (4) then storing the pressure and capacitance (intrusion) readings. At pressures above 4.48 MPa (6500 psi), the number of waiting periods is increased to P(MPa)/O.45 [of P(psi)/650]. The target pressure is maintained for additional periods if the capacitance is changing by more than 0.0020 pF (0.022 FL) per G-second wait_ The additional precision of this capacitance measurement, compared with 0.01 pF of the Pore Sizer 9300 readout, was obtained by employing a Keithley Model 192 digital multimeter with an IEEE-438 programmable interface. The computer is programmed to back-up the pressure of the porosimeter if, at any time, the target pressure is overshot by more than 0.10 MPa (15 psi). To promote thermal equilibrium, two copper inserts were employed around the bulb of the penetrometer inside the pressure vessel. This copper displaces approximately 40 cm3 of the hydraulic fluid (which heats up as the pressure is increased) with a medium of high thermal conductivity. The basic geometry of these copper inserts are hollow cylinders of 4.1 cm 0-D. One insert, which remains in the pressure vessel, is 2.2 cm tall with a 3.3 cm I.D. The other insert, which is installed in the pressure vessel with the penetrometer, is 3-3 cm tall with a 2.0 cm I.D. and has a spring mounted axially so that the top of the pressure vessel presses, this

167

insert downward_ One additional moditkation to the operation of the Pore Sizer 9300 was the use of forced air directed at the bottom outer wall of the pressure vessel to help maintain a constant temperature with which the sample may equilibrate during the measurements. Although the Pore Sizer 9300 can operate at pressures up to 207 MPa (30 000 psi), the macroporous samples described in this work were run only at pressures up to 138 M?a (20 000 psi) because thermal equilibrium is increasingly harder to obtain at higher pressures. Use of the copper inserts, described above, required replacement of the standard penetrometer enclosing device- For this purpose, a two-piece threaded nylon collar (2.1 cm tall and 3.1 cm 0-D.) was fabricated to hold the metal cap of the penetrometer to the greased, ground glass lip of the penetrometer. Small air spaces within this collar caused the capacitance to increase appreciably at low pressures in the pressure vessel when copper inserts were used. To eliminate this increase in capacitance, the collar around each mercury-filled penetrometer (stem-up) was submerged in hydraulic oil and outgassed with vacuum prior to measurements within the pressure vessel. Another addition to the Pore Sizer 9300 was a sheathed thermocouple which was inserted all the way through the stem of an auxiliary penetrometer and then bonded with epoxy resin to the end of the stem. By installing this stem in parallel with the sample

penetrometer during mercury filling, the temperature (and corresponding density) of the mercury was established without significant modification to the instrumentPRESSURIZATION-DEPRESSURIZATIOX

DATA

A mercury-only blank, shown in Fig. 2, was run at a rate of one data point per minute using a Pore Sizer 9300 in its recommended configuration_ Even though no sample is present in the (5 cm3) penetrometer, a large ‘apparent hysteresis’ is observed between the pressurization data and the depressurization data_ The vertical scale of Fig. 2 is the measured capacitance which changes with the level of mercury within the metalsheathed stem of the penetrometer. One picofarad corresponds to lo-79 t.lL of volume change_ The pressurization and depressurization curves in Fig. 2 are offset from one another due to heating of the sample about. 4 “C above ambient temperature during pressurization and cooling of t.he sample about 4 “C below ambient temperature during depressurization. After the pressure was reduced so that the pressure vessel could be opened to atmospheric pressure, thirteen additional l-minute points xvere taken before the capacitance reading became constant at approximately the original (pressurization) reading. A mercuq blank, shown in Fig. 3, was run on a Pore Sizer 9300 mercury porcsimeter with added computerizafion. Esperimental conditions and programmed criteria

0 PRESSURlZATlON 0 OEPRESSURlZATION CORRESPONDSTO 1

IO1

t27-m

Wi.161

pL INTRUSION

(82.741 PRESSURE.

Fig.

2. Mercury

blank run in a typical fashion.

~110.32) PSIA WPal

(137.90)

(165.47)

( 193.051

168 62.3 0 PRESSURIZATION 62.2 -

62.1

0 EiEPRESSURlZATlON

I

O.

CORRESPONDS TO 1 J.ZLINTRUSION

2

= 62.0 c!3 z D Q 61.9 :

0 0

“0’ T 61-8 k 2 2 a

\ 0

61.7 -

\

* 0

61.6 -

61.5 -

61.4’ 0 (0)

I

I

4.ooo (27.58)

8.00’3 (55161

I 12.000 (82.74)

I 16.000 l110.32)

0 20.000 (137.90)

PRESSURE_ PSIA (NIPa) Fig.

3. Mercury

blank run with hardware changes in order to facilitate thermal equilibrium_

were chosen to facilitate thermal equilibrium. The offset between pressurization and depressurization curves in Fig_ 3 corresponds to about O-4 “C above and below ambient temperature, respectively. Computer data management readily permits a point-by-point subtraction of blank data from sample data for either the corresponding pressurization or depressurization. Although about twothirds of the data for a blank (or a sample) was obtained at pressures below 13.8 MPa (2000 psi), only two data points were plotted in Fig. 3 for this low-pressure region. Plots of log[ VPOR(Z’,,,) - VPOR(P)] vers‘sus log P are show-n in Fig. 4 for the compressioncorrected 1133 intrusion and extrusion data of macroporous polystyrene. The two complete intrusion-extrusion cycles shown in this figure indicate that the two successive intrusions are different due to irreversible mercury retention in the sample, whereas the two extrusions are almost the same- Volume changes in the nearly horizontal lines are due to compaction (or decompaction) of the macroporous polystyrene at pressures below that at which mercury

intrusion (or extrusion) occurs_ The intrusion data above about 11.0 MPa (1600 psi) fall on a straight line having a slope of about -4. Upon depressurization, a parallel extrusion line is established above a volume change of 0.01 which intersects the decompaction line at about l-6 MPa (230 psi). To the extent that the intrusion line and the extrusion line have the same slope (-X), the pore-size distributions ze the same for intrusion and extrusion. By using eqn. (2) and by equating the surface area covered by the second mercury intrusion to the surface area uncovered by the mercury extrusion, the following relationship is obtained: P, (intrusion) PC (extrusion)

= cos 6 (advancing) cos 6 (receding)

(3)

Therefore, in the region in which the intrusion and extrusion lines are parallel, the hysteresis of the mercury porosimetry data is completely consistent with contact angle hysteresis. The region in Fig. 4 below 0.01 in plotted volume is also consistent with contact angle hysteresis where the contact

169

0.1 -

0 f5

0.01

-

1

-SC 5

2

i5

s

-

ORIGINAL

0 SECOND 0.001

CYCLE CYCLE

-

I

0.0001

10

(0.069)

I

IJ

I

100

1

10.689)

.ooo

10.000 i68.951

(6.875) PRESSURE.

PSIA IMPa)

Fig_ 4. Log-log plots of data on macroporous surization-deprwurization cycles.

polystyrene

angle is continuously changing between 0 (advancing) and 0 (receding)_ In previous work 113,143, an advancing contact angle of lS0” was found to result in improved agreement between the surface area calculated by mercury intrusion porosimetry and the BET surface area of this macroporous polystyrene. Using eqn. (3) in the present work, an advancing contact angle of 180” corresponds to a receding contact angle of about 9S”“. Thii value of the receding contact angle is consistent with other determinations 14, 5,15, IS]_ The same intrusion-extrusion data for macroporous polystyrene is shown in Fig. 5 with an additional intrusion (following an extrusion to 2.1 MPa (300 psi)) and with an additional extrusion (following an intrusion to 20.7 MPa (3000 psi)). Although the hysteresis of these additional data is not

for two pres-

simple to describe, the data are consistent with continuously changing contact angles between B (advancing) and 6 (receding) and are also consistent with contact angle hysteresis_ The amount of mercury retained in the sample increased in the case of the estrusion from 20.8 MPa (3000 psi). The total run time for acquisition of all of the data shown in Fig. 5 was IS h. Log-log plots are shown in Fig_ 6 for the compressioncorrected 1133 intrusion and extrusion data of a sample of compacted beryllium oxide powder_ The two intrusions in Fig- 6 are different from one another due to mercury retention and to experimental deviations which are accentuated in the lower decades of the log-log plot. On a traditional plot of cumulative pore volume uerssuspressure, the accuracy of these points would be unquestioned even if the deviations

. ORIGINAL 0 SECOND

CYCLE

0 lNTRUSlON AT

FOLLOWING

2.1 Mi’a

= EXTRUSlON AT

20.7

\

CYCLE 1300 PSIA) FOLLOWING

MPa (3000

.._,,

o.cwo1’

EXTRUSION

10

INTRUSION

PSIA)

l.

i

I

5.

Log-log

plots

with

additional

data

PSIA

on

.

10.000 168.95)

16.8751

PRESSURE. Fig-

,:-

~9Jo

100 IO.6991

to 0691

,

(MPa,

macroporous

were detected_ Unfortunately, the data are too sparse and too scattered in Fig_ 6 between 0.55 MPa (SO psi) and 1.10 MPa (160 psi) to determine whether the extrusion data (having plotted volumes greater than 0.02) lie on a straight line or not. However, the receding contact angle can be estimated by assuming that the same (size and shape) pore empties between 0.55 MPa (80 psi) and 0.76 MPa (110 psi) which fills at 2.38 MPa (345 psi)_ In this fashion, eqn. (3) can also be obtained by equating two Washburn 1171 relationships, each multiplied by the same shapecorrection factor. All of the depressurlzation data are consistent with continuously changing contact angles between 8 (advancing) and 8 (receding). In previous work [13,14], an advancing contact angle of 140” was found to give satisfactory agreement between the surface

polystyrene_

area calculated from mercury porosimetry data and the BET surface area of beryllium oxide powders similar to the powder used in this compacted sample. Using eqn- (3) in the present work, an advancing contact angle of 140” corresponds to a receding contact angle between 100” and 104” (or 102 A 24. This value of the receding contact angle is very similar to that previously discussed in this article for macroporous polystyrene (98”) and is consistent with other determinations [4,5,15, IS]. The same intrusion-extrusion data for this sample of compacted beryllium oxide powder are shown in Fig. 7 with an additional intrusion (following an extrusion to 0.69 MPa (100 psi)) and with an additional extrusion (following an intrusion to 5.5 MPa (800 psi))_ These additional hysteresis scans, although complex, are consistent with contact angle

171 05

0.1

!z x ‘:

0.01

-2 % o8 “> l

ORlGlNAL

0 SECOND

CYCLE CYCLE

0.001

O.oool

_

10 (0.0691

1

I

II,

I

7

*

,.,,,a

100

uJoo

lO.699)

16.695)

PRESSURE.

vi

11

KJ

(6

51

PSIA IMPa)

Fig. 6. Log-log plots of data on compacted pressurization-depressurization cycles.

beryllium

hysteresis for continuously changing angles between 8 (advancing) and 6 (receding)_ The amount of mercury retained in the sample increased in the case of the extrusion from 5-5 MPa (800 psi)_ The total run time for acquisition of all of the data displayed in Fig. 7 was 11 h. From the log-log plots in Figs. 4 - 7, the low pressure at which mercury ceased to extrude can be estimated. In the course of obtaining the extrusion data, the programmed criteria for mechanical and thermal equilibrium are met at one pressure, readings are stored by the computer, and then the pressure is quickly lowered to the next pressure_ The applied pressure drop at some low pressure

oxide powder for two

evidently separates the bulk mercury from the imbibed mercury which becomes retained in the sample- In this fashion, mercury retention in a given sample may depend to some degree on the manner and rate at which the pressure is lowered_ An interesting feature of mercury extrusion from macroporous polystyrene and compacted beryllium oxide relates to the time required to meet the chosen criteria for thermal and mechanical equilibrium_ Whereas 2 or 3 min was a typical time for a mercury intrusion data point, 20 or 30 min (up to 90 minutes) was a typical time for a mercury extrusion data point in the region in which appreciable volumes of mercury extruded.

- ORIGINAL

CYCLE

0 SECOND CYCLE l INTRUSION FOLLOWING AT 0.69 MPa I1 00 PSS1Al 0 EXTRUSION FOLLOWING AT 5.5 MPa 18w PSIA)

EXTRUSION INTRUSION

!o lO.069)

10.669)

16.695)

PRESSURE.

Fig_ 7_ Log-log oxide powder.

plots with additional

(66951

PSIA IMPal

data on compacted

This slow rate of extrusion probably increases the likelihood of retaining mercury in a sample for a given reduction in pressure_ Another interesting phenomenon was observed for mercury extrusion from macroporous polystyrene. After the pressure had been lowered to a value below 2.8 MPa (about 400 psi), the pressure decreased spontaneously as mercury extruded. This phenomenon is believed to be caused by a cooling effect due to mercury extrusion from this high surface area (9 m2/g) material_ Presumably a corresponding heating effect was present but was not observed as a spontaneous pressure increase at high pressures during mercury intrusion. When mechanicalonly P-V work is done on (or by) a system originally at a ce&a.in temperature T, an amount of heat equal to JPAV must be

beryllium

removed (or added) from the system in order to maintain a constant temperatureIn mercury porosimetry, this (heat and) work is proportional to the mercury-covered surface area of the sample [IS] CONCLUSION Use of the log-log plots of the generalized analysis method indicates that the hysteresis observed in mercury porosimetry data of the samples studied in this work is consistent with contact angle hysteresis_ In addition, the present method modeis mercury intrusion and mercury extrusion in greater detail than has been previously achieved- Changes in contact angle, the establishment of the advancing or the receding contact angle, the identification of sample compaction, and the estimation of the pressure and volume

173

at which the mercury ceases to extrude are some of the detailed features which were interpreted. ACKNOWLEDGEMENTS

The Oak Ridge Y-12 Plant is operated by the Union Carbide Corporation’s Nuclear Division for the Department of Energy under U.S. Government Contract W-7405eng-26. The authors are indebted to J. B. Condon, D. L. Dcnsbach and J_ M. Younkin, all of Y-12 Development Division, and to E. R. Kelly and E. R. Rogers, both of the Y-12 Plant Laboratory, all of whom helped with the computer automation of the Pore Sizer 9300. REFERENCES 1

J_ van Brake1 and S. Modry, Powder Technol. 29 (1981) l_ 2 H. M. Rootare, in J. S. Hirshhom and K H. Roll (Eds.), Advanced Experimenta Techniques in Powder MetaZZuurgy, Plenum Prw, New York. 1970. pp_ 225 - 252. 3 R P_ Mayer and R A Stowe. J_ Phys_ Chem_. 70 (1966) 386’7.

M. Teman and 0. M. Fuller, Can_ J. Chem. Eng. 57 (1979) i50_ J_ Kloubek. Powder TechnoZ-, 29 (1981) 63_ S_ Lowell and J_ E_ Shields, J. CoZZoid Inferface Sci. 80 (1981) 192 G. Ferraiolo and A. Peloso. =Inn_ 7 A. Reverberi, Chem.. 56 (1966) 1552. J. CoZloid Interface Sci. 75 8 A M. Schwartz, (1980) 404. and M_ D. Nguyen, J_ CoZZoid 9 N. R. Morrow Interface Sci. 89 (1982) 523. Physical Chemistry of Surfaces. 10 A. Wl Adamson, John Wiley. New York. 3976. pp. 339 - 355. ii Chemistry Series. 11 R. F_ Gould (Ed.). Ad&nces No. 43. Am. Chern. Sot., Washington. D-C., 1964. Powder TechnoL. 12 R. J. Good and R. S. Mikhail, 29 (19Sl) 53. Powder TechnoZ_. 33 (1982) 55. 13 R. W_ Smithwick, 55. Powder TechnoL. 33 (1982) 14 R ?V_ Smithwick, 201. 15 S. Lowell and J_ E_ Shields, I CoZZoid Interface Sk. 83 (1981) 273. 16 S. Lowell and J_ E_ Shields. J. CoZZoid Interfuce sci. 90 (1982) 203_ Proc. -Vat_ Acad_ Sci_ LX&-l. i 1-Z E. W_ Washburn, (1921) 115. and C. F. Prenzlo. J. Phys. Chcm.. 18 H_ M_ Rootare 71 (1967) 2733. 4

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