ASTM D4641-17
(Practice)Standard Practice for Calculation of Pore Size Distributions of Catalysts and Catalyst Carriers from Nitrogen Desorption Isotherms
Standard Practice for Calculation of Pore Size Distributions of Catalysts and Catalyst Carriers from Nitrogen Desorption Isotherms
SIGNIFICANCE AND USE
5.1 Pore volume distribution curves obtained from nitrogen sorption isotherms provide one of the best means of characterizing the pore structure in porous catalysts, provided that the limitations of the method are kept in mind. Used in conjunction with the BET treatment for surface area determination (5), these methods provide an indispensable means for studying the structure associated with pores usually important in catalysts. This practice is particularly useful in studying changes in a series of closely related samples caused by treatments, such as heat, compression, or extrusion often used in catalyst manufacturing. Pore volume distribution curves can often provide valuable information during mechanistic studies dealing with catalyst deactivation.
SCOPE
1.1 This practice covers the calculation of pore size distributions for catalysts and catalyst carriers from nitrogen desorption isotherms. The computational procedure is particularly useful for determining how the pore volume is distributed in catalyst samples containing pores whose sizes range from approximately 1.5 to 100 nm (15 to 1000 Å) in radius. It should be used with caution when applied to isotherms for samples containing pores both within this size range and pores larger than 100 nm (1000 Å) in radius. In such instances the isotherms rise steeply near P/Po = 1 and the total pore volume cannot be well defined. The calculations should begin at a point on the isotherm near saturation preferably in a region near P/Po = 0.99, establishing an upper limit on the pore size distribution range to be studied. Simplifications are necessary regarding pore shape. A cylindrical pore model is assumed, and the method treats the pores as non-intersecting, open-ended capillaries which are assumed to function independently of each other during the adsorption or desorption of nitrogen.
Note 1: This practice is designed primarily for manual computation and a few simplifications have been made for this purpose. For computer computation, the simplified expressions may be replaced by exact expressions.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D4641 − 17
Standard Practice for
Calculation of Pore Size Distributions of Catalysts and
1
Catalyst Carriers from Nitrogen Desorption Isotherms
This standard is issued under the fixed designation D4641; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
2
1.1 This practice covers the calculation of pore size distri- 2.1 ASTM Standards:
butions for catalysts and catalyst carriers from nitrogen des- D3766 Terminology Relating to Catalysts and Catalysis
orption isotherms. The computational procedure is particularly D4222 Test Method for Determination of Nitrogen Adsorp-
useful for determining how the pore volume is distributed in tion and Desorption Isotherms of Catalysts and Catalyst
catalyst samples containing pores whose sizes range from Carriers by Static Volumetric Measurements
approximately1.5to100nm(15to1000Å)inradius.Itshould
3. Terminology
be used with caution when applied to isotherms for samples
containing pores both within this size range and pores larger 3.1 Definitions—Consult Terminology D3766.
than 100 nm (1000 Å) in radius. In such instances the
3.2 Symbols:
isotherms rise steeply near P/P = 1 and the total pore volume
o
cannotbewelldefined.Thecalculationsshouldbeginatapoint
ontheisothermnearsaturationpreferablyinaregionnear P/P
i = numerical index representing each successive
o
= 0.99,establishinganupperlimitontheporesizedistribution
data point, with i=1,2… n.
range to be studied. Simplifications are necessary regarding P (i) = pressure after equilibration during desorption,
4
pore shape. A cylindrical pore model is assumed, and the torr.
P (i) = liquid nitrogen vapor pressure, torr.
method treats the pores as non-intersecting, open-ended capil-
0
V = Quantity of gas desorbed (cm3 STP/g); see
laries which are assumed to function independently of each
de
12.4.10 and 12.5 in Test Method D4222.
other during the adsorption or desorption of nitrogen.
r (i) = radius of inner core calculated from Kelvin
k
NOTE 1—This practice is designed primarily for manual computation
equation, Å.
and a few simplifications have been made for this purpose. For computer
T = boiling point of nitrogen, K.
computation, the simplified expressions may be replaced by exact expres-
3
V = liquid nitrogen molar volume at T,cm /mole.
sions. L
γ = liquid nitrogen surface tension at T, mN/m.
1.2 The values stated in SI units are to be regarded as
t(i) = average thickness of the nitrogen film adsorbed
standard. No other units of measurement are included in this
on the pore walls, Å.
standard.
r (i) = radius of cylindrical pore given by r (i)+ t(i), Å.
p k
2
1.3 This standard does not purport to address all of the Q = volume correction factor defined as (r¯ /r¯ ) .
p k
∆V (i) = decrease in the amount of nitrogen adsorbed
safety concerns, if any, associated with its use. It is the
T
3
caused by a lowering in relative pressure, mm /g.
responsibility of the user of this standard to establish appro-
∆V(i) = volume of liquid nitrogen desorbed from pore
priate safety and health practices and determine the applica- f
3
walls during thinning of the film, mm /g.
bility of regulatory limitations prior to use.
∆V (i) = liquid volume of the inner core in which capillary
k
3
condensation of the nitrogen occurs, mm /g.
1
This practice is under the jurisdiction of ASTM Committee D32 on Catalysts
and is the direct responsibility of Subcommittee D32.01 on Physical-Chemical
2
Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Feb. 1, 2017. Published February 2017. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1987. Last previous edition approved in 2012 as D4641–12. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D4641-17. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
---------------------- Page: 1 ----------------------
D4641 − 17
This practice is particularly useful in studying changes in a
∆V (i) = liquid volume contained in a group of pores
p
3
series of closely related samples caused by treatments, such as
having mean radius r¯ ,mm /g.
p
3
heat, compression, or extrusion often used in catalyst manu-
∑∆v = cumulative pore volume, mm /g.
p
∆S ( i ) = areaoftheporewallsofacylinderhavingvolume facturing. P
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D4641 − 12 D4641 − 17
Standard Practice for
Calculation of Pore Size Distributions of Catalysts and
1
Catalyst Carriers from Nitrogen Desorption Isotherms
This standard is issued under the fixed designation D4641; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice covers the calculation of pore size distributions for catalysts and catalyst carriers from nitrogen desorption
isotherms. The computational procedure is particularly useful for determining how the pore volume is distributed in catalyst
samples containing pores whose sizes range from approximately 1.5 to 100 nm (15 to 1000 Å) in radius. It should be used with
caution when applied to isotherms for samples containing pores both within this size range and pores larger than 100 nm (1000
Å) in radius. In such instances the isotherms rise steeply near P/P = 1 and the total pore volume cannot be well defined. The
o
calculations should be begun begin at a point on the isotherm near saturation preferably in a region near P/P = 0.99, establishing
o
an upper limit on the pore size distribution range to be studied. Simplifications are necessary regarding pore shape. A cylindrical
pore model is assumed, and the method treats the pores as non-intersecting, open-ended capillaries which are assumed to function
independently of each other during the adsorption or desorption of nitrogen.
NOTE 1—This practice is designed primarily for manual computation and a few simplifications have been made for this purpose. For computer
computation, the simplified expressions may be replaced by exact expressions.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
D3766 Terminology Relating to Catalysts and Catalysis
D4222 Test Method for Determination of Nitrogen Adsorption and Desorption Isotherms of Catalysts and Catalyst Carriers by
Static Volumetric Measurements
3. Terminology
3.1 Definitions—Consult Terminology D3766.
3.2 Symbols:
i = numerical index representing each successive data point, with i = 1, 2… n.
P (i) = pressure after equilibration during desorption, torr.
4
P (i) = liquid nitrogen vapor pressure, torr.
0
V = Quantity of gas desorbed (cm3 STP/g); see 12.4.10 and 12.5 in Test Method D4222.
de
r (i) = radius of inner core calculated from Kelvin equation, Å.
k
T = boiling point of nitrogen, K.
3
V = liquid nitrogen molar volume at T, cm /mole.
L
γ = liquid nitrogen surface tension at T, mN/m.
T(i) = average thickness of the nitrogen film adsorbed on the pore walls, Å.
1
This practice is under the jurisdiction of ASTM Committee D32 on Catalysts and is the direct responsibility of Subcommittee D32.01 on Physical-Chemical Properties.
Current edition approved May 1, 2012Feb. 1, 2017. Published July 2012February 2017. Originally approved in 1987. Last previous edition approved in 20062012 as
D4641–94(2006).D4641–12. DOI: 10.1520/D4641-12.10.1520/D4641-17.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
---------------------- Page: 1 ----------------------
D4641 − 17
t(i) = average thickness of the nitrogen film adsorbed on the pore walls, Å.
r (i) = radius of cylindrical pore given by r (i) + t(i), Å.
p k
2
Q = volume correction factor defined as (r¯ /r¯ ) .
p k
3
ΔV (i) = decrease in the amount of nitrogen adsorbed caused by a lowering in relative pressure, mm /g.
T
3
ΔV (i) = volume of liquid nitrogen desorbed from pore walls during thinning of the film, mm /g.
f
3
ΔV (i) = liquid volume of the inner core in which capillary condensation of the nitrogen occurs, mm /g.
k
3
ΔV (i) = liquid volume contained in a group of pores having mean radius r¯
...
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