ASTM D4641-12
(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
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 (4), 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 �) 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 �) 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 be begun 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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Designation: D4641 − 12
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
3.1 Definitions—Consult Terminology D3766.
containing pores both within this size range and pores larger
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
cannot be well defined. The calculations should be begun at a
point on the isotherm near saturation preferably in a region P (i) = pressure after equilibration during desorption,
4
near P/P = 0.99, establishing an upper limit on the pore size torr.
o
P (i) = liquid nitrogen vapor pressure, torr.
distribution range to be studied. Simplifications are necessary
0
V = see 12.4.10 and 12.5 in Test Method D4222.
regardingporeshape.Acylindricalporemodelisassumed,and
de
r (i) = radius of inner core calculated from Kelvin
k
the method treats the pores as non-intersecting, open-ended
equation, Å.
capillaries which are assumed to function independently of
T = boiling point of nitrogen, K.
each other during the adsorption or desorption of nitrogen.
3
V = liquid nitrogen molar volume at T,cm /mole.
L
NOTE 1—This practice is designed primarily for manual computation
γ = liquid nitrogen surface tension at T, mN/m.
and a few simplifications have been made for this purpose. For computer
T(i) = average thickness of the nitrogen film adsorbed
computation, the simplified expressions may be replaced by exact expres-
on the pore walls, Å.
sions.
r (i) = radius of cylindrical pore given by r (i)+ t(i), Å.
p k
2
1.2 The values stated in SI units are to be regarded as
Q = volume correction factor defined as (r¯ /r¯ ) .
p k
standard. No other units of measurement are included in this
∆V (i) = decrease in the amount of nitrogen adsorbed
T
3
standard.
caused by a lowering in relative pressure, mm /g.
∆V(i) = volume of liquid nitrogen desorbed from pore
1.3 This standard does not purport to address all of the
f
3
walls during thinning of the film, mm /g.
safety concerns, if any, associated with its use. It is the
∆V (i) = liquid volume of the inner core in which capillary
responsibility of the user of this standard to establish appro- k
3
condensation of the nitrogen occurs, mm /g.
priate safety and health practices and determine the applica-
∆V (i) = liquid volume contained in a group of pores
p
bility of regulatory limitations prior to use.
3
having mean radius r¯ ,mm /g.
p
3
∑∆v = cumulative pore volume, mm /g.
p
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
CurrenteditionapprovedMay1,2012.PublishedJuly2012.Originallyapproved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 1987. Last previous edition approved in 2006 as D4641–94(2006). DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D4641-12. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
---------------------- Page: 1 ----------------------
D4641 − 12
approaching unity and it is a simple matter to select a starting
∆S (i ) = areaoftheporewallsofacylinderhavingvolume
p
2
relative pressure within this region, establishing an upper limit
∆ V,m /g.
p
ontheporesizerangetobestudied.Ifporeslargerthan100nm
4. Summary of Practice
(1000 Å) are present however, the isotherm rises rapidly near
P/P = 1 and the total pore volume cannot be well defined.
O
4.1 The pore size distribution is determined by analyzing
This limiting adsorption can then be identified reliably on
...
This document is not anASTM standard and is intended only to provide the user of anASTM 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:D4641–94 (Reapproved 2006) Designation:D4641–12
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 at a point on the isotherm near saturation preferably in a region near P/P = 0.99, establishing an
o
upper limit on the pore size distribution range to be studied. Simplifications are necessary regarding pore shape.Acylindrical 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
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 NitrogenAdsorption and Desorption Isotherms of Catalysts and Catalyst Carriers by
Static Volumetric Measurements
3. Terminology
3.1 Definitions—Consult Terminology D3766.
3.2 Symbols:
P (i) = pressure after equilibration during desorption, torr.
4
P (i) = liquid nitrogen vapor pressure, torr.
0
V = 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
g = 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 ofASTM Committee D32 on Catalysts and is the direct responsibility of Subcommittee D32.01 on Physical-Chemical Properties.
´1
Current edition approved Oct. 1, 2006. Published October 2006. Originally approved in 1987. Last previous edition approved in 1999 as D4641–94(1999) . DOI:
10.1520/D4641-94R06.
Current edition approved May 1, 2012. Published July 2012. Originally approved in 1987. Last previous edition approved in 2006 as D4641–94(2006). DOI:
10.1520/D4641-12.
2
For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM 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 ----------------------
D4641–12
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
DV (i) = decrease in the amount of nitrogen adsorbed caused by a lowering in relative pressure, mm /g.
T
3
DV(i) = volume of liquid nitrogen desorbed from pore walls during thinning of the film, mm /g.
f
3
DV (i) = liquid volume of the inner core in which capillary condensation of the nitrogen occurs, mm /g.
k
3
DV (i) = liquid volume contained in a group of pores having mean radius r¯,mm /g.
p p
3
(Dv = cumulative pore volume, mm /g.
p
2
DS
...
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