QUANTACHROME INSTRUMENTS MVP-6DC User manual

1
MULTIPYCNOMETER
Instrument Models:
MVP-6DC
MVP-D160E
OPERATING MANUAL
P/N 05034 Rev F
© Quantachrome Instruments, 2012-2014

2
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3
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TABLE OF CONTENTS
I. INTRODUCTION 7
II. INSTALLATION AND COMPONENTS 9
Location 9
Mains Power 9
Gas Tank Connections 10
Sample Cells and Sample Cell Holder 10
Toggle Valves 11
Needle Valves 11
Selector Valve 11
Pressure Display and Transducer 11
Pressure Relief Valve 12
Calibration Status 12
RS232 Port 12
III. SAMPLE PREPARATION 13
Purging Method 13
Vacuum Method 13
IV. SAMPLE ANALYSIS 14
Stepwise measurement instructions 14
Density Worksheet 15
V. CALIBRATION 16
Recalibration 16
Calibration Spheres 19
VI. SOURCES OF ERROR 20
Non-ideal gas behavior 20
Diffusion/Absorption 20
Impure gases 20
Insufficiently prepared samples 20
The size of the gas molecule 20

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MULTIPYCNOMETER
CALIBRATION VALUES
LARGE CALIBRATION SPHERE Vcal large = 56.5592 cm3
MICRO CALIBRATION SPHERES (2) 1.0725 cm3each Vcal micro = 2.145 cm3
LARGE SAMPLE CELL VOLUME Vc large = __________cm3
LARGE REFERENCE VOLUME VRef large = __________cm3
SMALL SAMPLE CELL VOLUME Vcsmall = __________cm3
SMALL REFERENCE VOLUME VRef small = __________cm3
MICRO CELL VOLUME Vcmicro = __________cm3
MICRO REFERENCE VOLUME VRef micro = ___________cm3
Model Number ______________ Serial Number ______________

7
I. INTRODUCTION
“Pycnometer” is derived from the Greek word pyknos which has long been identified with volume
measurements. The MULTIPYCNOMETER is an instrument specifically designed to measure the
true volume of a variety of solid materials by employing Archimedes’ principle of fluid
displacement and Boyle’s Law of gas expansion. The displaced fluid is a gas which can penetrate the
finest pores to assure maximum accuracy. For this reason helium is recommended since its small
atomic dimension assures penetration into crevices and pores approaching two Ångströms (2 x 10-
10m). Its behavior as an ideal gas is also desirable. Other gases such as nitrogen can also be used,
often with no measurable difference.
It is used to determine the true volume of solid or powder samples by measuring the pressure
difference when a known quantity of gas under pressure is allowed to expand from a precisely
known reference volume into a sample cell holder, also of known volume, containing the sample cell
with sample.
Figure 1 is a flow diagram of the MULTIPYCNOMETER. The shaded area represents the known
reference volume(s) VR. After the system is purged with analysis gas, the valve that admits gas in to
the system is closed, the selector valve between VRand the cell holder VCis turned to connect them,
and the vent valves are opened. The system is now at ambient pressure Paand the state of the sample
cell with sample is defined by
(
)
RT
n
=
V V
Pa
aSC
a
−
(1)
where nais the number of moles of gas occupying the calibrated cell volume (VC) with sample
present of volume (Vs), R is the gas constant and Tais ambient temperature in kelvin.
When the reference volume alone is pressurized above ambient (after isolating it from the sample
cell holder), the state of the reference volume (VR) can be expressed as
RT
n
=
V
Pa
1R
1(2)
where P1represents a pressure above ambient (17 psig, ~120kPa, for example) and n1is the total
number of moles of gas in the reference volume (VR).
When the selector valve is turned again to connect the reference volume to the sample cell holder,
the pressure will fall to a lower pressure P2, given by
(
)
RT
n
+
RT
n
=
V
+
V V
Pa
1
a
aRSC
2
−
(3)

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Substituting into equation (3) Pa(VC– VS)and P1VRfor naRTaand n1RTa, respectively, gives
()
(
)
V
P
+
V V
P
=
V
+
V V
PR
1
SC
a
RSC
2
−
−
(4)
or
()
(
)
(
)
V
P P
=
V V
P P
R
21
SC
a2
−
−
−(5)
Then
V
P PP
P
=
V VR
a2
21
SC −
−
−(6)
Since Pais made to read zero on the digital meter, that is, all pressure measurements are relative
to Pa, equation (6) becomes
V
PP
P
=
V VR
2
21
SC
−
−(7)
or
(
)
[
]
-
P
/
P
V
-
V
=
V21
RCS 1(8)
Equation (8) is the working equation employed with the MULTIPYCNOMETER.

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II. INSTALLATION AND COMPONENTS
Location
Place the MULTIPYCNOMETER on a level surface away from sources of heat and cold such as
radiators, air conditioning vents, direct sunlight, etc.
Mains Power
Ensure that the voltage selector at the rear of the unit matches your local mains supply. The
MULTIPYCNOMETER is designed for operation on 100V, 120V, 220V or 240V, 50/60 Hz. It was
shipped from the factory set for the voltage according to the purchase order which should match the
voltage on the serial number plate at the rear of the unit. If the selector needs to be changed refer to
the diagram below and carefully follow these steps:
1. Make sure the unit is switched OFF and unplug the power cord from its socket on the unit.
2. Pry open the plastic cover by inserting a screwdriver behind the tab on the side away from the
socket.
3. Using long-nosed pliers, gently pull out the wheel located behind the plastic cover.
4. The 4 voltages are printed on the wheel. Re-insert the wheel with the voltage required facing out,
towards you. Then close the plastic cover. Ensure that the voltage visible in the opening in the
plastic cover matches your local mains supply before reconnecting the power cord.

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Gas Tank Connections Tools required: 7/16” wrench (not supplied).
Attach a dual stage gas regulator to a cylinder of analysis gas, usually ultra-high purity helium or
nitrogen. Connect the output of the regulator to the compression fitting on the right side of the
cabinet using the 1/8” copper tubing and nut & ferrule set supplied.
Do not use plastic tubing. If you need to extend the gas supply line always use clean copper (or
stainless steel) tubing with appropriate metal compression fittings.
It will be necessary to obtain an adapter to connect the tubing to the regulator if it does not have a
1/8” Swagelok® brand fitting. A suitable regulator assembly (P/N 01207) complete with shut-off
valve, CGA580 cylinder connector and 1/8” Swagelok® brand outlet fitting is available from
Quantachrome.
Adjust the pressure regulator to slightly above 20 psig (140 kPa). Pressures above 25 psig could
potentially damage the MULTIPYCNOMETER’s pressure transducer.
Check all connections for leaks using soap solution.
Sample Cells and Sample Cell Holder
Three sample cells (stainless steel cups) and two adapter sleeves are supplied with the
MULTIPYCNOMETER. Sample cells are placed in the chamber with the screw cap - the sample
cell holder. To open the sample cell holder, rotate the cap’s outer ring counter-clockwise until it can
be lifted off. To remove the sample cell insert the lift out tool into one of the holes near the top of the
cell and lift it out of the holder.
Sample cells should be removed from the unit before being filled with sample or adding calibration
spheres. Use the largest amount of sample available for best accuracy. If you do not have enough
sample material to fill the large cell (135 cm3) to at least 50% of its volume, use the small cell (20
cm3) and the micro cell (4.5 cm3) for even smaller quantities. The small and micro cells are always
used with the appropriate adapter sleeve.
When calibrating a cell, especially the large cell, do not simply drop the large sphere into the cell but
turn the cell sideways and roll the sphere into it to prevent deforming the cell.
When using the large sample cell, ensure that the horizontal slit(s) near the top of the cell line up
with the vertical groove(s) machined into the cell holder. This ensures that the gas has a free path
into and out of the cell.
Before replacing the cell holder cap make sure that its O-ring1is undamaged, clean, lightly greased2
and is secured in the groove inside the cap. Align the fiduciary mark on the cap with the line on the
cabinet ring; a locating pin on the bottom side of the cap slots into a hole in the top edge of the
sample cell holder. Then rotate the outer ring of the cap clockwise (on the threads of the cell holder)
until metal to metal contact is made.
1 Spare O-rings are sold in packs of two, p/n 51000-032.
2 Use Vacuum Grease P/N 91000-.25 to lubricate O-ring, never petrolatum.

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Toggle Valves
Toggle valves are used to start and stop gas flow in and out of the unit (see Sections III and IV) and
to select the appropriate reference volume according to the size of sample cell being used (see
Section IV).
They are closed when their handles are parallel to the cabinet face and open when perpendicular to
the cabinet face. Closing the toggle valves can sometimes cause a slight pressure increase in the
sample cell which can be observed on the pressure display. To relieve this slight pressure, press the
toggle valve’s handle down against the cabinet. This will slightly open the valve seat and relieve the
pressure without building up new pressure when it is released.
Needle Valves
Needle valves are used to control the rate at which gas flows in and out of the unit.
The "GAS FLOW IN” RATE needle valve is used to control the flow rate into the MULTI-
PYCNOMETER. It determines both the rate at which pressure builds in the Reference volume
during a measurement (see Section IV) and – in combination with the VENT needle valve - the rate
at which the sample is purged of contaminants (see Section III). This valve should not be used to
stop flow. Flow of gas in to the unit is stopped using the "GAS FLOW IN" ON/OFF toggle valve.
The "VENT" needle valve controls the rate at which pressure is released when venting the sample
cell (and reference volume) or when vacuum is required to decontaminate the sample (see Section
III). To prevent elutriation of a powder sample as the pressure is released, open the Vent toggle
valve and needle valve carefully to release pressure slowly. This valve should not be used to stop
flow. Flow of gas out of the unit is stopped using the "VENT" OPEN/CLOSE toggle valve.
Selector Valve
This valve is used to expand gas from the reference volume, VR, into the sample cell holder, VC. It
rotates 90degrees between “2 o’clock” (right) and “10 o’clock” (left); when pointing to the right
only the reference volume (VR) is in the gas path and when pointing to the left the sample cell holder
is also included in the gas path (VC+ VR).
Pressure Display and Transducer
Pressures within VRand VR+ VCare displayed on the LCD in psig. (Note, since pycnometric
measurements use pressure ratios, the units are in fact unimportant for calculating volume and
density (but can be useful for setting the gas supply regulator and for troubleshooting). The
display is zeroed using the zero knob to the right of the display when VRis open to ambient (Gas
flow toggle valve is OFF and vent toggle valve and needle valve are open).

12
When not used for prolonged times, the pressure transducer can exhibit some drift during the
initial start up operation. To avoid this problem, it is recommended that after switching the unit
on, the transducer undergo several pressurization/depressurization cycles prior to making an
actual density measurement (or calibration).
Pressure Relief Valve (Internal)
A 25 psig (~172 kPa) pressure relief valve is located inside the unit immediately after the gas
input fitting (See Figure 1). It is designed to prevent damage to the pressure transducer due to
overpressurization. Gas cylinder regulator output pressures over 25 psig (~172 kPa) will activate
the valve to vent excess gas pressure, in which case a hissing sound may be heard, and will
prematurely empty your cylinder. Therefore the cylinder regulator should be set at only slightly
more than 20 psig (138 kPa).
Calibration Status
The MULTIPYCNOMETER was calibrated at the factory and should only require recalibration
after a sample cell or adapter sleeve has been replaced (for example if lost or damaged), after
service or component replacement, if its new environmental temperature is outside the range 21-
25°C, when required by your local regulations, and is recommended when the environmental
temperature has changed by more than 4°C since the last calibration.
RS232 Port
Models with the D160E designation have an RS232 connection port on the left side of the unit,
and are supplied with an RS232 cable and a software program (“PycData”) on a CD which also
contains an electronic copy of its own User Manual. PycData reads the pressure display and can
perform all required calculations.

13
III. SAMPLE PREPARATION
Switch on the power to the unit using the mains on/off switch. Allow at least 15 minutes for the
pressure transducer to warm up and stabilize, during which time you can prepare your first sample.
Purging Method
To purge contaminating vapors and atmospheric gases from the sample (and the system) attach a
length of flexible plastic tubing to the hose barb connector on the right side of the
MULTIPYCNOMETER and immerse the other end of the tubing into a beaker of water. Then
perform the following steps.
1. Weigh accurately the clean, dry sample cell (cup). Record its (tare) weight, W1.
2. Fill the sample cell (cup) to just below the slot/hole with dry sample. If the sample has been
heated, ensure it has been cooled to room temperature (preferably in a desiccator) before
proceeding. Record the total weight of cell plus sample, W2.
3. Insert the cell with sample into the cell holder and replace the cover.
4. Close the “GAS FLOW IN” ON/OFF toggle valve and open the "VENT" toggle valve. Turn
the selector valve to "CELL".
5. Open the "VENT” RATE needle valve fully counter-clockwise.
6. Turn the "GAS FLOW IN” RATE needle valve fully clockwise. Do not over tighten it. Open
the “GAS FLOW IN” ON/OFF toggle valve.
7. Adjust the "GAS FLOW IN” RATE needle valve to give a slow rate of bubbling (1-2
bubbles per second) in the beaker of water then remove the tubing from the water.
8. After 5-10 minutes of flow, close the “GAS FLOW IN” ON/OFF toggle valve.
9. See Section IV for analyzing the sample (volume measurement).
Vacuum Method
If you prefer to decontaminate your sample with vacuum, use the following procedure.
1. Close the “GAS FLOW IN” ON/OFF toggle valve and open the "VENT" toggle valve. Turn
the Selector Valve to "CELL". Gently close the "VENT RATE" fully clockwise; do not over
tighten it.
2. Attach vacuum tubing between the hose-barb connection on the right side and a vacuum
pump. Switch on the pump.
3. Very slowly open the "VENT” RATE needle valve. If it is opened too rapidly, powder can
be pulled out of the cell holder. Wait at least 10 minutes for the system to be evacuated.
4. To repressurize the system, close the "VENT” toggle valve, switch off the pump and remove
the vacuum tubing. Open the “GAS FLOW IN” toggle valve, then slowly open the "GAS
FLOW IN" RATE needle valve to admit analysis gas until the system is returned to ambient
pressure.

IV. SAMPLE ANALYSIS
Stepwise measurement instructions
1. Ensure that the unit has been switched on for at least 15 minutes for the pressure transducer
to warm up and stabilize.
2. Select the appropriate REFERENCE VOLUME for the size of sample cell by using the
toggle valves “I” and “II” according to the table printed on the unit (below the zero knob).
3. Open the "VENT" toggle and "VENT” RATE needle valves. Wait for a stable near-zero
reading.
4. Close the "VENT" toggle valve and set the display to zero.1
5. Turn the Selector valve to “VR” (REF).
6. Open the “GAS FLOW IN” toggle valve, and pressurize to approximately 17 (psig) using the
"GAS FLOW IN” RATE needle valve to control the rate of pressurization. Stop the flow by
closing the “GAS FLOW IN” toggle valve.
7. Record the display reading after it has stabilized. This value is "P1" in Equation (8).
8. Turn the selector valve to VC+ VR(CELL).
9. Record the display reading after it has stabilized. This value is "P2" in Equation (8).
10. Vent the pressure slowly to prevent blowing powder out of the cell, by opening the "VENT"
toggle valve with the "VENT” RATE needle valve slightly open.
11. Use equation (8) to calculate the true sample volume and density (see Worksheet).
12. Repeat steps 4 – 11 to obtain at least three replicate measurements. Average the results.
NOTE: The pressure transducer used in this pycnometer dissipates a very slight amount of heat. Because of its extreme
sensitivity it can track the slight pressure increases associated with the heating of the gas. Accordingly, it is necessary to
take the first reading observed after the digital display stabilizes. A change of approximately 0.001 on the digital display
every 10-20 seconds is indicative of pressure increases due to heat dissipation and is normal. By taking the first reading
after the display stabilizes and then rotating the selector valve and again immediately obtaining the first stable reading,
the most accurate and rapid results will be achieved.
1 If unable to zero the display please email [email protected] for assistance.

MULTIPYCNOMETER WORKSHEET
TRUE DENSITY REPORT
SAMPLE I.D. ____________________________________ DATE ____________________
COMMENTS _____________________________________ OPERATOR _______________
PREPARATION CONDITIONS __________________________________________________
TOTAL WEIGHT (W2) ____________ g REFERENCE VOLUME (VR) ____________cm3
TARE WEIGHT (W1) _____________ g CELL HOLDERVOLUME (VC) __________cm3
SAMPLE WEIGHT (W2-W1) ____________ g
CALCULATE SAMPLE VOLUME:
(
)
(
)
-
P
/
P
V
-
V
=
V21
RCS 1
VS= Volume of sample (cm3)
VC= Volume of Sample cell holder (cm3)
VR= Reference Volume (cm3)
P1= Pressure reading after pressurizing just the Reference Volume
P2= Pressure reading after expanding gas into the Sample cell holder
CALCULATE SAMPLE DENSITY:
Density = (W2-W1) / VS
DATA
RUN 1 RUN 2 RUN 3
P1______________ ______________ ______________
P2______________ ______________ ______________ Average
VS______________ ______________ ______________ ______________
DENSITY ______________ ______________ ______________ ______________

V. CALIBRATION
Page 6 of this manual contains calibration information for reference during calibration and analysis
calculations. Print that page and enter the values as indicated on the Calibration Tag or Printout
provided with your instrument. This includes the sample cell volumes (VC), the reference volumes
(VR), the volume of the large calibration sphere (Vcallarge) and the volume of the micro calibration
spheres (Vcalmicro) provided with the MULTIPYCNOMETER. If, for any reason it is suspected that
the value of VCor VRhas been altered then recalibration should be performed. Powder blowing out
of the sample cell into the tubing or operation at temperatures substantially different that room
temperature will require recalibration.
Recalibration
To calibrate the MULTIPYCNOMETER the following steps should be followed in order:
1. Place the large calibration sphere into the large cell. Insert the large cell into the cell holder,
replace and secure the cap.
2. Open toggle valves I and II.
3. Turn the selector valve to "CELL".
4. Open the "VENT" toggle and "RATE" valves.
5. Open the “GAS FLOW IN” toggle valve and adjust its "RATE" valve until the display
shows about 1 (psig).
6. Purge the MULTIPYCNOMETER" in this mode for about 5 minutes.
7. Close the “GAS FLOW IN” toggle valve.
8. When the display shows a stable reading, set it to 0 using the zero knob and turn the selector
valve to "REF".
9. Close the "VENT" toggle valve.
10. Open the “GAS FLOW IN” toggle valve until the pressure is approximately 17 (psi), then
close the “GAS FLOW IN” toggle valve.
11. When the display is stable, note the pressure reading (P1).
12. Turn the selector valve to "CELL".
13. When the display is again stable, note the new pressure reading (P2).
14. Vent the reference volume and sample cell holder (VR+ VC) by opening the "VENT" toggle
valve.
15. Remove the calibration sphere from the large cell and repeat steps 1-14 noting the pressures
P1′, P2′with the selector valve in "REF" and "CELL" positions respectively.

16. Calculate the volume of the large Reference Volume (VRlarge) using equation (9).
()
[]
()
[] 1/1/ 21
'
2
'
1−−−
=largePlargePlargePlargeP largeV largeV cal
R(9)
Where:
V
callarge = volume of the large calibration sphere
P′1large = pressure in VRlarge with no sphere in the cell.
P′2large = pressure in VRlarge + VClarge with no sphere in the cell.
P
1large = pressure in VRlarge with the calibration sphere in the cell.
P
2large = pressure in VRlarge + VClarge with the sphere in the cell.
17. After solving equation (9) for VRlarge use this value in equation (10) to calculate VClarge
for the large sample cell.
(
)
(
)
1-large
P
large/
P
large
V
+large
V
=large
V21
RcalC (10)
18. Close toggle valve I and repeat steps 8-14.
19. Calculate the small reference volume using equation (11).
()
[]
1'' *
21 −
=smallPsmallP earglV smallV C
R(11)
Where:
P
1′small = pressure in VRsmall with no sphere in the cell.
P
2′*small = pressure in VRsmall + VClarge with no sphere in the cell.
20. Remove the large sample cell and insert the small adapter sleeve and small sample cell.

21. Repeat steps 3-14 and calculate the small cell volume using equation (12).
(
)
[
] 1'' 21
−
smallPsmallPsmall
V
=small
VRC (12)
Where:
P
1′small = pressure in VRsmall with no sphere in the cell.
P
2′small = pressure in VRsmall + VCsmall with no sphere in the cell.
22. Remove the small sample cell and adapter and insert the micro adapter sleeve, micro sample
cell and both micro calibration spheres.
23. Close toggle valves I and II.
24. Open the “GAS FLOW IN” toggle valve until the pressure is approximately 17 (psi). Then
close the “GAS FLOW IN” toggle valve.
25. When the display is stable, note the pressure reading.
26. Turn the selector valve to "CELL".
27. When the display is again stable, note the new pressure reading.
28. Vent both the reference volume and cell holder by opening the "VENT" toggle valve.
29. Remove both calibration spheres from the micro cell and repeat steps 24-28 noting the
pressures with the selector valve in "REF" and "CELL" positions.
30. Calculate the volume of the micro reference volume (VRmicro) using equation (13).
()
[]
() []
1/1/ 21
'
2
'
1−−−
=microPmicroPmicroPmicroP
microV
microV cal
R(13)
Where:
V
cal micro= combined volume of both micro calibration spheres
P′1micro = pressure in VRmicro with no spheres in the cell
P
′2micro = pressure in VRmicro + VCmicro with no spheres in the cell.
P
1micro = pressure in VRmicro with the calibration spheres in the cell.
P
2micro = pressure in VRmicro + VCmicro with the spheres in the cell.

31. After solving equation (13) for VRmicro use this value in equation (14) to calculate Vcmicro
for the micro sample cell.
(
)
(
)
-micro
P
micro/
P
micro
V
+micro
V
=micro
V21
RcalC 114)
NOTE: If only the large sample cell is to be used, it is not necessary to recalibrate the small and
micro cells. Similarly, if only the small cell is to be used, it is not necessary to calibrate the micro
cell.
If the sample is analyzed at a temperature different by more than 4°C from that used to calibrate the
instrument, the MULTIPYCNOMETER should be recalibrated at the new temperature.
Calibration Spheres
The table below shows the various spheres that are available for calibrating the instrument.
PART NUMBER SIZE DIAMETER (mm) VOLUME (cm3)
01500-MICRO1 Micro212.7 1.0772
01500-SMALL Small 23.812 7.0699
01500-MEDIUM Medium 38.1 28.958
01500-LARGE Large247.625 56.5592
NOTE: The large and small calibration spheres are available with NIST measured diameters.
Contact [email protected] for more details.
____________________________________________________________________________
1. Sold in pairs.
2. Provided with the Multipycnometer.

20
VI. SOURCES OF ERROR
Non-ideal gas behavior
Equation (8) was derived using the equation of state for an ideal gas; therefore dry helium is
recommended for use in the MULTIPYCNOMETER. However, dry nitrogen can also be used at
room temperature often with no adverse effect. The use of gases which do not behave in a near ideal
fashion at room temperature should be avoided.
Diffusion/Absorption
When analyzing vegetable matter, materials containing cellulose or low density polymers (including
foams) it is preferred that nitrogen (or sulfur hexafluoride, SF6) be used instead of helium because
helium can diffuse into the solid matter and across cell walls.
Impure gases
If air or other gases which contain adsorbable impurities are used, the pressure readings will be
affected due to adsorption on the sample surface. The extent of the resulting error depends upon the
amount and nature of the impurities as well as the solid's surface area. Always use high purity gases
and clean, metal gas lines – never plastic gas tubing.
Insufficiently prepared samples
Many samples contain impurities, usually adsorbed moisture, on their surface and within pores that
should be removed prior to analysis. The presence of these impurities can affect the results in several
ways:
1. The actual weight of the sample is less that the weight measured.
2. Contaminants fill pores causing a larger sample volume to be determined.
3. Volatile impurities will cause erroneous readings.
Successive volume determinations yielding results trending in one direction are usually an indication
that contaminants are being removed after each cycle. Measurements should be repeated until two or
three successive determinations are obtained to within 0.2%.
Another indication of the presence of volatile contaminants is a gradual pressure increase when the
sample is included in the flow path (selector valve in the CELL position, VR+ VC) after purging
with dry gas. This occurs as the contaminants leave the surface and establish their own partial
pressure.
The size of the gas molecule
An additional source of error in high surface area powders can be the annulus volume created
between the powder surface and the center of mass of the gas phase molecules at the interface.
Assuming that the closest approach of the center of mass of the gas molecules to the powder surface
is 0.5Å (5 x 10-11 meter) and that the powder surface is in the order of 1000 square meters per gram,
there will exist an annulus volume of 5 x 10-8 cubic meters (5 x 10-2 cm3) per gram of powder. Thus,
with samples of about 1 gram of high specific surface area, volume errors of 0.05 cm3can occur.
Corrections for this error can be made with knowledge of the effective diameter (i.e., Van der Waals
diameter) of the gas molecules and the powder's specific surface area.