1、Designation: D 4641 94 (Reapproved 2006)Standard Practice forCalculation of Pore Size Distributions of Catalysts fromNitrogen Desorption Isotherms1This standard is issued under the fixed designation D 4641; the number immediately following the designation indicates the year oforiginal adoption or, i
2、n the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 an
3、d 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 w
4、hen 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 be begun at apoint on the isotherm near sa
5、turation preferably in a regionnear P/Po= 0.99, establishing an upper limit on the pore sizedistribution range to be studied. Simplifications are necessaryregarding pore shape.Acylindrical pore model is assumed, andthe method treats the pores as non-intersecting, open-endedcapillaries which are assu
6、med to function independently ofeach other 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-si
7、ons.1.2 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 establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenc
8、ed Documents2.1 ASTM Standards:2D 3766 Terminology Relating to Catalysts and CatalysisD 4222 Test Method for Determination of NitrogenAdsorp-tion and Desorption Isotherms of Catalysts and CatalystCarriers by Static Volumetric Measurements3. Terminology3.1 DefinitionsConsult Terminology D 3766.3.2 Sy
9、mbols:P4(i) = pressure after equilibration during desorption,torr.P0(i) = liquid nitrogen vapor pressure, torr.Vde= see 12.4.10 and 12.5 in Test Method D 4222.rk(i) = radius of inner core calculated from Kelvinequation, .T = boiling point of nitrogen, K.VL= liquid nitrogen molar volume at T,cm3/mole
10、.g = liquid nitrogen surface tension at T, mN/m.T(i) = average thickness 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.DVT(i) = decrease in the amount of nitrogen adsorbedcaused by a loweri
11、ng in relative pressure,mm3/g.DVf(i) = volume of liquid nitrogen desorbed from porewalls during thinning of the film, mm3/g.DVk(i) = liquid volume of the inner core in which capil-lary condensation of the nitrogen occurs, mm3/g.DVp(i) = liquid volume contained in a group of poreshaving mean radius r
12、p,mm3/g.(Dvp= cumulative pore volume, mm3/g.DSp(i ) = area of the pore walls of a cylinder havingvolume DVp,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 multilayer adsorption of a
13、 film ofnitrogen on the pore walls and by capillary condensation of thenitrogen in the “inner core” regions of the pores. The relative1This practice is under the jurisdiction of ASTM Committee D32 on Catalystsand is the direct responsibility of Subcommittee D32.01 on Physical-ChemicalProperties.Curr
14、ent edition approved Oct. 1, 2006. Published October 2006. Originallyapproved in 1987. Last previous edition approved in 1999 as D 464194(1999)e1.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards
15、 volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.pressure at which filling of the core occurs for a given pore sizeby capillary condensation is predi
16、cted from the Kelvin equa-tion (1).3During desorption, 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 bec
17、omes exposed asdesorption proceeds. In principle, 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,
18、the distributioncurve derived from the desorption 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 establishe
19、d that the adsorptionbranch of the nitrogen isotherm is to be analyzed, the procedure proposedby Cranston and Inkley (3) is recommended.5. Significance and Use5.1 Pore volume distribution curves obtained from nitrogensorption isotherms provide one of the best means of character-izing the pore struct
20、ure in porous catalysts, provided that thelimitations of the method are kept in mind. Used in conjunctionwith the BET treatment for surface area determination (4),these methods provide an indispensable means for studying thestructure associated with pores usually important in catalysts.This practice
21、 is particularly useful in studying changes in aseries of closely 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
22、deactivation.6. Computational Procedure6.1 This procedure requires 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 c
23、an be measured by following thesteps outlined in Test Method D 4222. 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 m
24、atter to select a startingrelative pressure within this region, establishing 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 ca
25、n then be identified reliably only ifthe temperature is very carefully 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 pro
26、cedure is then made more difficult. Inmost cases a starting relative 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 Vdeto determine the quantity of nitrogen gas adsorbed at thechosen starting rela
27、tive pressure.6.2 The procedure requires numerous arithmetical stepswhich can best be carried out with the aid of a work sheet. Anexample (4) 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 C
28、olumn 1,beginning with the value chosen as the starting relativepressure. 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 der
29、ivedfrom VL= 34.67 cm3/mole. List in Column 9 the correspond-ing quantities of nitrogen adsorbed.6.3 For each relative pressure, calculate a value for theradius of the core, rk, by means of the Kelvin equation,RT ln P4/P0! 522gVLrk(1)given in the formrkA! 529.574ln P4/P0!(2)with T = 77.35 K; g = 8.8
30、8 mN/m; and VL= 34.67 cm3/mole. List the values in Column 2. For each successivedecrement in relative pressure, calculate rk, the mean of thevalues of rkfor the present and previous pressures, and listthese mean values in Column 3.6.4 The average thickness, t, of the multilayer film ofnitrogen adsor
31、bed 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 (5)t A! 5F13.990.034 2 log P4/P0!G12(
32、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 Dt in Column 5.6.5 Since a cylindrical pore model is assumed, the radius ofthe pore, rp, is given by addition of the core radius, rk, and t
33、hefilm 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 record these values inColu
34、mn 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. List the computed valu
35、es inColumn 8 as the volume correction factor, Q.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D 4641 94 (2006)2NOTE 3For a cylindrical pore rpand rkare related to Q by the exactexpression:Q 5 rp/ rk1Dt!#2(4)For rk30,Dt 1%rk. Simplifying Q by eliminati
36、ng Dt gives ( rp/rk)2.6.7 The amounts of nitrogen desorbed for each successivedecrement in 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 Col
37、umn 10 as, DVT.Each value of DVTexcept for the initial one in line 2 containscontributions from 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 val
38、ue of DVTis duesolely to the amount of nitrogen contributed from loss ofcapillary condensate, 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
39、 In completing the calculation to obtain a value for thepore volume, D Vp, corresponding to each mean pore size, rp,of a group of pores, it will be necessary to work through thecalculation for each line before proceeding to the next line. DVf in Column 11 is the amount of nitrogen given up duringdes
40、orption from thinning of the nitrogen film adsorbed on porewalls. For line 2, DVfequals zero and the value of DVTisassigned to DVk, the volume of the inner core which fills bycapillary condensation of the nitrogen. Multiply the value ofDVkby the corresponding volume correction factor, Q, listed inCo
41、lumn 8 to obtain D Vp. List the value in Column 13 of line2.6.9 Calculate the surface area of the pore walls contained involume DVpas follows:DSp m2/g! 5 20 3DVprp(5)Using the value of DVpfrom Column 13 and the correspond-ing value of rpfrom Column 7, compute a value for DSpandlist it in Column 14.
42、A value for the total surface area of thepores that have become exposed is obtained by summation ofthe value for D Spwith other DSpvalues in all preceding linesof Column 14. List the value of total area in Column 15 as(DSp. A value for the cumulative pore volume is obtained bysummation of the value
43、DVpwith other DVpvalues in allpreceding lines of Column 13. List the value of the cumulativepore volume in Column 16 as (DVp.NOTE 4The expression relating the surface area of the pore wallscontained in volume DVpis as follows:DSpm2/g! 5 2 3DVprp3 104(6)with DVpin cubic centimetres and rpin angstroms
44、. Converting cubicTABLE 1 Pore Distribution Computational Work SheetSample Identification _ Date_1P4/P02rk3rk4t5Dt6rp7rp8Q9Vdemm3/g10DVTmm3/g11DVfmm3/g12DVkmm3/g13DVpmm3/g14DSpm2/g15(DSpm2/g16(DVpmm3/g xcirc Column 2: rk529.574lnP4/P0!Column 11: DVf5 0.085 Dt (DSppreceding line! Column 13: DVp5DVk3
45、QColumn 4: t 5F13.990.034 2 log P4/P0!G1/2Column 12: DVk5DVT2DVfColumn 14: DSp5 20 3 DVp/ rp!D 4641 94 (2006)3centimetres to cubic millimetres gives rise to the conversion factor of 20in the preceding equation.6.10 An essential feature of this test method is that thevolume of nitrogen lost from the
46、adsorbed multilayer film canbe calculated from the total area of the pores exposed, (DSp,and the decrease in the thickness of the film, Dt. Using thevalue (DSpfrom the preceding line, compute D Vffrom theexpressionDVf5 0.085 3Dt 3 (DSppreceding line! (7)and record the value in Column 11. Subtract th
47、e value of DVffrom DVTto obtain the value of DVkof Column 12. Multiplythe value of DVkwith the corresponding value of Q in Column8 to obtain the value of DVpof Column 13. Compute DSpand(DSpfollowing the procedure in 6.9. Determine a value for(DVp.NOTE 5 See Appendix X1 for a more detailed discussion
48、 on thecalculation of values for DVfand the source of the coefficient.6.11 Repeat the calculations in 6.10 for each line down to arelative pressure lying between 0.25 and 0.30. If at anintermediate relative pressure, the value of D Vkshould becomeequal to zero or negative, discontinue the calculatio
49、n, and in allsubsequent calculations use the data from the preceding lineand above.NOTE 6It is generally agreed that the value of the pore size to whichthe Kelvin equation will no longer apply at the lower end of the pore sizerange varies from one adsorption system to another.As a result, difficultiesarise in knowing precisely where to end the pore volume calculation fora particular nitrogen sorption isother
copyright@ 2008-2019 麦多课文库（www.mydoc123.com）网站版权所有
备案/许可证编号：苏ICP备17064731号-1