1、Designation: D4641 17Standard Practice forCalculation of Pore Size Distributions of Catalysts andCatalyst Carriers from Nitrogen Desorption Isotherms1This standard is issued under the fixed designation D4641; the number immediately following the designation indicates the year oforiginal adoption or,
2、 in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the calculation of pore size distri-butions for catalysts a
3、nd catalyst carriers from nitrogen des-orption isotherms. The computational procedure is particularlyuseful for determining how the pore volume is distributed incatalyst samples containing pores whose sizes range fromapproximately 1.5 to 100 nm (15 to 1000 ) in radius. It shouldbe used with caution
4、when applied to isotherms for samplescontaining pores both within this size range and pores largerthan 100 nm (1000 ) in radius. In such instances theisotherms rise steeply near P/Po= 1 and the total pore volumecannot be well defined. The calculations should begin at a pointon the isotherm near satu
5、ration preferably in a region near P/Po= 0.99, establishing an upper limit on the pore size distributionrange to be studied. Simplifications are necessary regardingpore shape. A cylindrical pore model is assumed, and themethod treats the pores as non-intersecting, open-ended capil-laries which are a
6、ssumed to function independently of eachother during the adsorption or desorption of nitrogen.NOTE 1This practice is designed primarily for manual computationand a few simplifications have been made for this purpose. For computercomputation, the simplified expressions may be replaced by exact expres
7、-sions.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establi
8、sh appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D3766 Terminology Relating to Catalysts and CatalysisD4222 Test Method for Determination of Nitrogen Adsorp-tion and Desorption Isotherms of
9、Catalysts and CatalystCarriers by Static Volumetric Measurements3. Terminology3.1 DefinitionsConsult Terminology D3766.3.2 Symbols:i = numerical index representing each successivedata point, with i =1,2 n.P4(i) = pressure after equilibration during desorption,torr.P0(i) = liquid nitrogen vapor press
10、ure, torr.Vde= Quantity of gas desorbed (cm3 STP/g); see12.4.10 and 12.5 in Test Method D4222.rk(i) = radius of inner core calculated from Kelvinequation, .T = boiling point of nitrogen, K.VL= liquid nitrogen molar volume at T,cm3/mole. = liquid nitrogen surface tension at T, mN/m.t(i) = average thi
11、ckness of the nitrogen film adsorbedon the pore walls, .rp(i) = radius of cylindrical pore given by rk(i)+t(i), .Q = volume correction factor defined as (rp/rk)2.VT(i) = decrease in the amount of nitrogen adsorbedcaused by a lowering in relative pressure, mm3/g.Vf(i) = volume of liquid nitrogen deso
12、rbed from porewalls during thinning of the film, mm3/g.Vk(i) = liquid volume of the inner core in which capillarycondensation of the nitrogen occurs, mm3/g.1This practice is under the jurisdiction of ASTM Committee D32 on Catalystsand is the direct responsibility of Subcommittee D32.01 on Physical-C
13、hemicalProperties.Current edition approved Feb. 1, 2017. Published February 2017. Originallyapproved in 1987. Last previous edition approved in 2012 as D464112. DOI:10.1520/D4641-17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.o
14、rg. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with inter
15、nationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1Vp(i) = liquid volume contained in a group of po
16、reshaving mean radius rp,mm3/g.vp= cumulative pore volume, mm3/g.Sp( i ) = area of the pore walls of a cylinder having volume Vp,m2/g.4. Summary of Practice4.1 The pore size distribution is determined by analyzingthe desorption data of the nitrogen isotherm. The nitrogenuptake is caused by the multi
17、layer adsorption of a film ofnitrogen on the pore walls and by capillary condensation of thenitrogen in the “inner core” regions of the pores. The relativepressure at which filling of the core occurs for a given pore sizeby capillary condensation is predicted from the Kelvin equa-tion (1).3During de
18、sorption, thinning of the multilayer filmadsorbed on the pore walls occurs in pores which havepreviously lost their capillary condensate. Corrections for filmthinning are determined by a procedure involving the surfacearea and radius of the film which becomes exposed asdesorption proceeds. In princi
19、ple, the computational procedurecan be applied to either the adsorption branch or desorptionbranch of the nitrogen isotherm. Unless the presence ofink-bottle shaped pores is suggested by an abrupt closure of thedesorption branch on the adsorption branch, the distributioncurve derived from the desorp
20、tion data is preferred, and isdescribed in this procedure. The computational method isessentially the procedure developed by Barrett, Joyner, andHalenda (2), except for the incorporation of a few simplifica-tions.NOTE 2In cases where it has been established that the adsorptionbranch of the nitrogen
21、isotherm is to be analyzed, the procedure proposedby Cranston and Inkley (3) can be employed.NOTE 3Thanks to major advances in adsorption science and technol-ogy over the past two decades, it is now widely recognized (see recentIUPAC recommendations (4) that modern statistical mechanics methodsbased
22、 on Density Functional Theory or Monte Carlo simulations providesignificantly more accurate pore size distributions than classical proce-dures based on the Kelvin equation, such as the BarrettJoynerHalenda(BJH) or Cranston-Inkley methods (2, 3). Moreover, the choice ofdesorption (equilibrium) vs. ad
23、sorption (metastable) branches for reliablepore size analysis must take into consideration the potential influence ofpore connectivity, tensile strength and cavitation effects. In addition,although nitrogen sorption at 77 K is widely used, its quadrupoleinteractions with polar surfaces can influence
24、 isotherm shapes and theirinterpretation; therefore, argon adsorption at 87 K is considered to be morereliable and is now recommended, particularly for samples containingmicropores (4). In spite of these advances, the traditional Kelvin-basedapproaches described in this Standard Practice are still d
25、eemed to beuseful for routine work (such as industrial process control).5. Significance and Use5.1 Pore volume distribution curves obtained from nitrogensorption isotherms provide one of the best means of character-izing the pore structure in porous catalysts, provided that thelimitations of the met
26、hod are kept in mind. Used in conjunctionwith the BET treatment for surface area determination (5),these methods provide an indispensable means for studying thestructure associated with pores usually important in catalysts.This practice is particularly useful in studying changes in aseries of closel
27、y related samples caused by treatments, such asheat, compression, or extrusion often used in catalyst manu-facturing. Pore volume distribution curves can often providevaluable information during mechanistic studies dealing withcatalyst deactivation.6. Computational Procedure6.1 This procedure requir
28、es the use of a series of experi-mentally measured relative pressures P4(i)/P0(i) and thecorresponding quantities of nitrogen gas adsorbed Vde ex-pressed in units of cm3STP/g. The experimental data requiredin the use of this procedure can be measured by following thesteps outlined in Test Method D42
29、22. Inspect the nitrogensorption isotherm in the region above P/Po= 0.95. If the solidcontains no pores larger than 100 nm (1000 ) radius, theisotherm remains nearly horizontal over a range of P/Poapproaching unity and it is a simple matter to select a startingrelative pressure within this region, e
30、stablishing an upper limiton the pore size range to be studied. If pores larger than 100 nm(1000 ) are present, however, the isotherm rises rapidly nearP/PO= 1 and the total pore volume cannot be well defined.This limiting adsorption can then be identified reliably only ifthe temperature is very car
31、efully controlled and there are no“cold spots” in the apparatus (which lead to bulk condensationof the gas and a false measure of the adsorption in thevolumetric method). Selecting the starting relative pressure forthe computational procedure is then made more difficult. Inmost cases a starting rela
32、tive pressure of 0.99 will be suitable,which corresponds to an upper limit on pore size of 100 nm(1000 ) in radius. If necessary, interpolate the values of Vdetodetermine the quantity of nitrogen gas adsorbed at the chosenstarting relative pressure.6.2 The procedure requires numerous arithmetical st
33、epswhich can best be carried out with the aid of a work sheet. Anexample (5) of a form found useful in the calculations isprovided in Table 1. List in descending order the experimen-tally determined relative pressures P4(i)/P0(I) in Column 1,beginning with the value chosen as the starting relativepr
34、essure. Generally, values below a relative pressure of 0.25will not be required in the calculations. Convert the uptakevalues into a liquid volume (mm3/g) by multiplying the valueof Vdein cm3STP/g with the conversion factor 1.5468 derivedfrom VL= 34.67 cm3/mole. List in Column 9 the correspondingqua
35、ntities of nitrogen adsorbed.6.3 For each relative pressure, calculate a value for theradius of the core, rk, by means of the Kelvin equation,RTlnP4/P0! 522VLrk(1)given in the formrkA! 529.574lnP4/P0!(2)with T = 77.35 K; = 8.88 mN/m; and VL= 34.67 cm3/mole.List the values in Column 2. For each succe
36、ssive decrement inrelative pressure, calculate rk, the mean of the values of rkforthe present and previous pressures, and list these mean valuesin Column 3.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D4641 1726.4 The average thickness, t, of the mult
37、ilayer film ofnitrogen adsorbed on the walls of the pores at each relativepressure is used to calculate the amount of nitrogen desorbedfrom the film in pores which have lost their capillary conden-sate. For each relative pressure, calculate a value for the filmthickness from the expression (6)t A! 5
38、F13.990.034 2 logP4/P0!G12(3)and list the values in Column 4. For each successivedecrement in relative pressure, calculate the differences in thevalues of t, and list these differences as t in Column 5.6.5 Since a cylindrical pore model is assumed, the radius ofthe pore, rp, is given by addition of
39、the core radius, rk, and thefilm thickness value, t. Add the values in Column 2 to thecorresponding values in Column 4 and record the results inColumn 6 as rp. For each successive decrement in relativepressure, calculate rp, the mean of the pore radii, rp, for thepresent and previous pressures, and
40、record these values inColumn 7.6.6 Compute the quantity (rp/rk)2from the values listed inColumns 7 and 3. This quantity will be used later to correct thecore volume to the volume for each group of pores. The corevolume is the region within the pore that fills by capillarycondensation of the nitrogen
41、. List the computed values inColumn 8 as the volume correction factor, Q.NOTE 4For a cylindrical pore rpand rkare related to Q by the exactexpression:Q 5 rp/ rk1t!#2(4)For rk30,t 1%rk. Simplifying Q by eliminating t gives (rp/rk)2.6.7 The amounts of nitrogen desorbed for each successivedecrement in
42、relative pressure are calculated by progressivesubtraction of the values of the amounts of nitrogen adsorbed,Vde, listed in Column 9 from the succeeding one. Computethese differences and list the values in Column 10 as, VT.Each value of VTexcept for the initial one in line 2 containscontributions fr
43、om the amounts of nitrogen given up by loss ofcapillary condensate and by thinning of the nitrogen filmadsorbed on the walls of pores which have previously releasedtheir capillary condensate. The initial value of VTis duesolely to the amount of nitrogen contributed from loss ofcapillary condensate,
44、since it is assumed that at the highestrelative pressure all of the pores are completely filled withnitrogen, and that no thinning of the nitrogen film occurs forthe first decrement in relative pressure.6.8 In completing the calculation to obtain a value for thepore volume, Vp, corresponding to each
45、 mean pore size, rp,TABLE 1 Pore Distribution Computational Work SheetSample Identification _ Date_1P4/P02rk3rk4t5t6rp7rp8Q9Vdemm3/g10 VTmm3/g11Vfmm3/g12Vkmm3/g13 Vpmm3/g14Spm2/g15 Spm2/g16 Vpmm3/g CColumn 2:rk529.574lnsP4/P0dColumn 11:Vf5 0.085toSpspreceding linedColumn 13:Vp5 Vk3QColumn 4:t 5F13.9
46、90.0342 logsP4/P0dG1/2Column 12:Vk5 VT2 VfColumn 14:Sp5 203sVp/rpdD4641 173of a group of pores, it will be necessary to work through thecalculation for each line before proceeding to the next line. Vfin Column 11 is the amount of nitrogen given up duringdesorption from thinning of the nitrogen film
47、adsorbed on porewalls. For line 2, Vfequals zero and the value of VTisassigned to Vk, the volume of the inner core which fills bycapillary condensation of the nitrogen. Multiply the value ofVkby the corresponding volume correction factor, Q, listed inColumn 8 to obtain Vp. List the value in Column 1
48、3 of line 2.6.9 Calculate the surface area of the pore walls contained involume Vpas follows:Sp m2/g! 5 20 3Vprp(5)Using the value of Vpfrom Column 13 and the correspond-ing value of rpfrom Column 7, compute a value for Spand listit in Column 14. A value for the total surface area of the poresthat h
49、ave become exposed is obtained by summation of thevalue for Spwith other Spvalues in all preceding lines ofColumn 14. List the value of total area in Column 15 as Sp.A value for the cumulative pore volume is obtained bysummation of the value Vpwith other Vpvalues in allpreceding lines of Column 13. List the value of the cumulativepore volume
