Chapter 1: Introduction BELSORP analysis program Required computer environment... 8

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2 [Table of contents] Chapte 1: Intoduction BELSORP analysis pogam Requied compute envionment... 8 Chapte : Installation of the analysis pogam Installation of the WIBU-KEY pogam Installation of the analysis pogam File configuation of the analysis softwae Specifying a decimal point symbol and a date fomat Chapte 3: Uninstalling the analysis pogam Uninstalling the analysis pogam Uninstalling the WIBU-KEY pogam Chapte 4: Stating and ending the pogam Stat up Quit Chapte 5: Main window Initial menu Data analysis menus (when the data window is a gaph) Menus duing data analysis (when the active data is numeic)... 9 Chapte 6: Reading in analysis data File open Analysis of active data (gaph) Adding data files to the active window (gaph) Display the numeical values of data on the gaph Chapte 7: Setting window Analysis paametes X axis display settings Y axis display settings Plot settings Smoothing settings Chapte 8: Data analysis window Display plot data details Setting the linea egession stat and end points Displaying numeical data fom a gaph Analyze the active data by using anothe analysis method Tansfe the data using the dag and dop function Displaying the sub sceen Chapte 9: Saving and pinting analysis esults Save data analysis Pinting a data analysis Edit data... 53

3 9-4. Help function...54 Chapte 10: Analysis of adsoption/desoption isothems Adsoption isothem Analysis data obtained fom a nitogen adsoption isothem...58 Chapte 11: Adsoption / desoption isothem Desciption Opeation...63 Chapte 1: PCT cuve Desciption Opeaion...65 Chapte 13: BET analysis Desciption Opeaion...7 Chapte 14: Langmui plot Desciption Opeation...76 Chapte 15: t plot Desciption Opeation...79 Chapte 16: α s plot Desciption Opeation...84 Chapte 17: MP method analysis Desciption Opeation...88 Chapte 18: BJH plot Desciption Opeation...94 Chapte 19: CI plot Desciption Opeation...99 Chapte 0: DH plot Desciption Opeation Chapte 1: INNES plot Desciption Opeation Chapte : DA plot Desciption

4 -. Opeation Chapte 3: HK plot Desciption Opeation Chapte 4: SF plot Desciption Opeaion Chapte 5: Isosteic heat of adsoption Desciption Opeation Chapte 6: Diffeence of adsoption isothem Desciption Opeation Chapte 7: Metal dispesion analysis Desciption Opeation Chapte 8: Molecula pobe method Desciption Opeation Chapte 9: NLDFT/GCMC method Desciption Opeation Chapte 30: How to use [Routine analysis] Settings Opeation Chapte 31: Output an analysis epot Opeation Setting change Chapte 3: Sample analysis examples Silica with mesopoes Activated cabon with micopoes Chapte 33: Majo changes fom vesion Chapte 34: Standad isothem Standad isothem Chapte 35: Measuement data file Measuement data BELSORP 8SA, BELSORP 18, and BELSORP HP seies BELSORP-mini, BELSORP-max, and BELSORP-aqua3 seies

5 Pecautions 1. Copyight of this manual and the pogam belongs to BEL JAPAN, INC.. Use o copying of all o any pat of this manual o pogam is pohibited without pio witten appoval fom BEL JAPAN, INC. 3. The contents of this manual and the pogam specifications may be changed without pio notice. 4. Use of this manual and pogam is pohibited fo any pupose othe than the BELSORP analysis, as descibed in the pogam license ageement, without pio witten appoval by BEL JAPAN, INC. 5. BEL JAPAN, INC. is not liable fo any effects that come fom the esults of using this manual o pogam. 6. Stoe the setup disks in safe place. 7. Although ou poducts ae manufactued with the utmost cae, if you have any questions o find any eos o omissions, please contact us. BEL JAPAN, INC Head office: 9-1, 1-CHOME, HARADANAKA, TOYONAKA-CITY, OSAKA JAPAN TEL: FAX: Web: 5

6 Pepaations fo using the BELSORP analysis pogam Pepaations fo using the BELSORP analysis pogam Chapte 1: Intoduction BELSORP analysis pogam Requied compute envionment... 8 Chapte : Installation of the analysis pogam Installation of the WIBU-KEY pogam Installation of the analysis pogam File configuation of the analysis softwae Specifying a decimal point symbol and a date fomat Chapte 3: Uninstalling the analysis pogam Uninstalling the analysis pogam Uninstalling the WIBU-KEY pogam

7 Pepaation fo using the BELSORP analysis pogam Chapte 1: Intoduction This is a data analysis pogam designed to analyze the datameasued by the BELSORP seies of adsoption measuement appaatuses. This pogam eads the data files that wee measued using a BELSORP measuing instuments, and can then display gaphs and numeical data. The analysis data can be pinted and saved BELSORP analysis pogam The following sample infomation about suface aeas and poes can be obtained fom the measued data. Name of analysis Adsoptive Analysis method Pimay data poduced Adsoption / desoption isothem Istothems ae displayed with this analysis. Judging fom the shape of isothem, the chaacteistic of the sample can be seen and appopiate method to analyze the isothem can be chosen. PCT cuve H Change in amount of hydogen stoage capacity Amount of hydogen stoage capacity BET plot N, A, K, etc. Evaluates a specific suface aea fo physical adsoption Monomolecula laye adsoption Langmui plot O, etc. Evaluates the amount of chemical adsoption Monomolecula laye adsoption t plot N Evaluates micopoes α s plot N Evaluates micopoes Total specific suface aea, extenal specific suface aea, and poe volume Total specific suface aea, extenal specific suface aea, and poe volume MP plot N Micopoe distibution cuve Micopoe distibution BJH plot N Mesopoe distibution cuve Mesopoe distibution, volume and aea CI plot N Mesopoe distibution cuve Mesopoe distibution, volume and aea DH plot N Mesopoe distibution cuve Mesopoe distibution, volume and aea INNES plot N Mesopoe distibution cuve Mesopoe distibution, volume and aea DA plot N, CO, C 6H 6, etc. Evaluate the micopoe volume Micopoe volume HK plot N, A Micopoe distibution cuve SF plot N, A Micopoe distibution cuve Micopoe distibution (Poe shape: Slit) Micopoe distibution (Poe shape: Cylinde) Isosteic heat of adsoption H O, etc. Evaluates diffeential heat of adsoption Diffeential heat of adsoption Diffeence of adsoption isothems H O, NH 3, etc. Evaluates the amount of chemical adsoption Diffeence adsoption isothem Metal dispesion H, CO, etc. Evaluates metal dispesion Metal dispesion Molecula pobe CO, C H 6, n-c 4H 10, iso-c 4H 10, etc. Evaluate micopoes Micopoe distibution cuve NLDFT/GCMC N, A, CO Evaluate micopoes and mesopoes poe distibution cuve 7

8 Pepaations fo using the BELSORP analysis pogam 1-. Requied compute envionment This pogam can be used with the following systems and conditions. [Pesonal compute] Requied system envionment Opeating system Micosoft Windows 7 (3 bit / 64 bit) Home Basic o Home Pemium o moe Micosoft Windows Vista Sevice Pack o moe Micosoft Windows XP Home o Pofessional Edition Sevice Pack o moe (Any compute that can un the English vesion of these OS) CPU Intel pocesso Memoy GB o moe 51 MB o moe Display XGA ( dots) o moe Had disk capacity 1 GB o moe space is equied duing opeation. USB pot At least one USB1.1 / USB.0 pot Disk dive CD-ROM dive (Fo setup CD installation) Othes To use the analysis epot setting function, install Micosoft Excel. To execute Office update. Othewise, opeation becomes unstable. To use the HELP function, install Adobe Reade. To apply the opeational NLDFT GCMC method, Coei3 o moe pocessos. Install Micosoft.NET Famewok.0 o moe. 8

9 Pepaation fo using the BELSORP analysis pogam Chapte : Installation of the analysis pogam This chapte descibes the installation of the BELSORP analysis pogam on a pesonal compute. Fist, install the WIBU-KEY softwae. Then install the Analysis softwae. (Fo instuctions about the basic opeating pocedues fo Windows, see the Windows instuction manual. The sceen images may be diffeent fom those shown hee, depending on you envionment. ) -1. Installation of the WIBU-KEY pogam * If the WIBU-KEY pogam is aleady installed, Fist delete the WIBU-KEY pogam fom you PC and then do the following. (See section 3-. Uninstalling the WIBU-KEY pogam on page 16.) 1. Put the Setup CD in the CD-ROM dive.. Run WkRt-Int.exe, which can be found in the WIBU-KEY device dive folde on the Setup CD. Afte eading this pogam fo a moment, you PC displays the sceen shown at ight. 3. Click the [Next] button. 4. Choose English and then click the [Next] button Click the [Next] button again. 5 9

10 Pepaations fo using the BELSORP analysis pogam 6. Afte clicking the [Next] button, you PC will stat installing the WIBU-KEY dive Click the [Next] button again Click the [Finish] button to end the installation When the window on the ight appeas, click the [OK] button. 10. Connect the WIBU-KEY fo the BELSORP analysis pogam to a USB connecto on you PC. That completes the installation of the WIBU-KEY and dive. 9 10

11 Pepaation fo using the BELSORP analysis pogam -. Installation of the analysis pogam * If the BELSORP pogam is aleady installed, Delete the BELSORP pogam fom you PC and then do the following. (See 3-1. Uninstalling the analysis pogam on page 15. ) 1. Put the Setup CD in the CD-ROM dive.. Run SETUP.EXE, which can be found in the Data analysis pogam folde on the Setup CD. 3. The installe will stat and you will see window on the ight. 4. Click the [Next] button Confim the installation destination folde and then click the [Next] button Click the [Next] button and the set up will stat. 6 11

12 Pepaations fo using the BELSORP analysis pogam 7. When the installation is complete, the sceen on the ight will appea. Click the [Finish] button File configuation of the analysis softwae The file configuation ight afte the pogam is installed is as follows. Please note that, if some files ae not in the specified foldes, the analysis softwae may not opeate nomally. Folde configuation Desciption Details BelAnalys Installation folde A diffeent folde name can be used. BELMaste.exe *.dll BELMaste_Doc.pdf ADSORPTIVE_INF.csv DefFmt.xls T-DATA Execution file Expansion file used by the execution file Help file Adsoptive data file Repot output fomat file T-DATA folde Be sue to place this file in the same folde as the execution file. Note: If you delete the expansion file, this softwae cannot nomally opeate. Be sue to place this file in the same folde as the execution file. If this file is deleted, o if the file name is changed, no infomation is displayed even if you click on [How to use this pogam] in the [Help] menu. Be sue to place this file in the same folde as the execution file. If this file is not povided, the system automatically ceates a file. Be sue to place this file in the same folde as the execution file. If this file not is povided, the analysis epot output function is disabled. Be sue to place this holde in the same folde as the execution file. If this folde is not povided, o if the folde name is changed, an eo occus with the T-intepolation use settings fo the t method, αs method, DH method, BJH method, CI method, INNES method and MP method, and the HK method and SF method, and the analysis softwae cannot nomally opeate. *.t Refeence t-cuve data A diffeent folde is also acceptable. *.as Refeence s data A diffeent folde is also acceptable. *.HKS *.SFS HK method paamete SF method paamete Indispensable fo the HK method. T-DATA folde. Indispensable fo the SF method. T-DATA folde. Be sue to place this file in the Be sue to place this file in the *.TTI T-intepolation use data If this file is not povided, the system automatically ceates a file. 1

13 Pepaation fo using the BELSORP analysis pogam -4. Specifying a decimal point symbol and a date fomat If the decimal point is specified as comma, in the Windows settings, the analysis softwae will not opeate nomally. You can check this setting with the following pocedue. Specifying a decimal point 1. In the Contol Panel, select Regional and Language Options.. Look at the Samples section and make sue the numbes show a peiod. fo a decimal point If a comma, is selected as the decimal symbol, click the [Customize ] button. The Customize Regional Options window will open. 4. Select the Numbes tab and change the decimal point symbol to a peiod.. 5. Click the [OK] button to stoe you changes and exit fom these settings. 4 Specifying a date fomat 1. In the Contol Panel, select Regional and Language Options.. Look at the Samples section and make sue the Shot date. 3. If the yyyy/mm/dd fomat is not selected, click the customized botton. The Customize Regional Options window will open. 13

14 Pepaations fo using the BELSORP analysis pogam 4. Select the Date tab. Change the Shot date fomat to yyyy/mm/dd and Date sepaato to /. 5. Click the [OK] button to stoe you changes and exit fom these settings. 4 14

15 Pepaation fo using the BELSORP analysis pogam Chapte 3: Uninstalling the analysis pogam This chapte descibes the steps to uninstall the BELSORP analysis pogam. softwae. Afte that un-install the WIBU- KEY softwae. Fist, uninstall the analysis 3-1. Uninstalling the analysis pogam 1. Open the Windows Contol Panel.. Click on the Uninstall a pogam. 3. Select the BEL analysis pogam fom the list of pogams shown and click on the [Uninstall/Change] button Click the [Yes] button in the EXEpess Uninstalle window Then, you compute may ask you whethe o not you eally want to delete the shaed files. If you ae sue thee will not be any poblem in deleting them, click the [Delete] button. If you ae not sue, click the [Save] button. If you ae sue you want to delete all the files, click the [Delete all] button. If you want to leave all of them, click the [Save all] button. 6. If you compute displays the message Unable to delete the file duing the uninstall pocess, click the [Yes] button and go ahead. When the uninstall window closes, the data analysis pogam has been uninstalled. 15

16 Pepaations fo using the BELSORP analysis pogam 3-. Uninstalling the WIBU-KEY pogam 1. Open the Windows Contol Panel.. Click on the Uninstall a pogam. 3. Select the WIBU-KEY Setup (WIBU-KEY Remove) fom the list of pogams and click on the [Uninstall/Change] button Follow the instuctions in the WIBU-KEY Setup (WIBU-KEY Remove) window and click the [Next] button Click the [Finish] button to end the uninstall pocess of the WIBU-KEY pogam. 5 16

17 Basic Opeation Basic Opeation Chapte 4: Stating and ending the pogam Stat up Quit Chapte 5: Main window Initial menu Data analysis menus (when the data window is a gaph) Menus duing data analysis (when the active data is numeic)... 9 Chapte 6: Reading in analysis data File open Analysis of active data (gaph) Adding data files to the active window (gaph) Display the numeical values of data on the gaph Chapte 7: Setting window Analysis paametes X axis display settings Y axis display settings Plot settings Smoothing settings Chapte 8: Data analysis window Display plot data details Setting the linea egession stat and end points Displaying numeical data fom a gaph Analyze the active data by using anothe analysis method Tansfe the data using the dag and dop function Displaying the sub sceen Chapte 9: Saving and pinting analysis esults Save data analysis Pinting a data analysis Edit data Help function

18 Basic Opeation Chapte 4: Stating and ending the pogam This chapte descibes how to stat and end the BEL analysis pogam. (Fo details about basic Windows opeations, see the Windows instuction manual. Depending on you system s envionment, the sceen images on you PC may be diffeent fom the images shown in this manual. ) 4-1. Stat up 1. Tun on you compute and stat Windows.. Fom the Stat ba select All Pogams, BELSORP and Data analysis pogam in that ode. 3. The BEL analysis pogam will stat and the main window, shown on the ight, will appea. 4-. Quit 1. Select File (F) and then Quit (Q) fom the BEL menu, That will end the BEL analysis pogam. 1. Afte the dialog box appeas as shown on the ight, select Yes (Y). 18

19 Basic Opeation Chapte 5: Main window Depending on the analysis conditions, one of thee menus will be displayed in the Main window. This chapte biefly descibes the contents of these menus and the function of the items in the menus Initial menu (The fist menu displayed afte stating the BEL analysis pogam) 5-. Menu while analyzing data (When the data is being displayed as a gaph) 5-3. Menu while analyzing data (When the data is being displayed as the numeical data) 19

20 Basic Opeation 5-1. Initial menu 1) Menu contents The fist menu displayed afte stating the BEL analysis pogam (no data file is open) File (F) Open (O) Adsoption/desopotion isothem PCT cuve BET plot : : Repot settings (R) Settings (S) Tools (T) Help (H) Quit (Q) Routine analysis setting (R) Adsobent infomation (I) Edit data (E) How to use this pogam (U) Vesion info (V) ) File (F) menu - Open (O) menu Open the data analysis window by selecting File (F). Then select Open (O) and choose an analysis method. The gaphic data analysis sceen will be displayed. Analysis methods on the menu that ae gayed out cannot be selected. [Refeence] Opeation => File open, on page 30 Analysis method => Page 6 This function is used to execute multiple analyses at once. The analyses can be specified on the Routine analysis setting sceen [Refeence] Opeation => Chapte 9 [Routine analysis] => Page 144 0

21 Basic Opeation Choose DH plot, BJH plot, CI plot, o INNES plot fom the Mesopoe distibution analysis sub menu. Choose MP plot, HK plot, o SF plot fom the Micopoes distibution analysis sub menu. - Repot setting The analysis epot setting sceen will appea. [Refeence] Opeation => Chapte 31: Output an analysis epot, on page 145. Note: If Micosoft Excel is not installed on you PC, this function cannot be used. - Quit Select File (F) and then Quit (Q). The analysis pogam will end. 1

22 Basic Opeation 3) Settings (S) menu - Routine analysis settings (R) Specify the analysis methods to execute in a outine analysis. [Refeence] Opeation => Chapte 30: How to use [Routine analysis], on page Adsoptive infomation You can specify the adsoptive infomation (molecula weight, density, coss sectional aea, etc.) to use in the analysis. If adsoptive infomation with an identical adsoption name and adsoption tempeatue is encounteed while eading a measuement data file, the pogam will execute an analysis based on this adsoption infomation. Ente an adsoption name and adsoption tempeatue. Ente a molecula weight, density, and coss section aea. Add the data just enteed to the adsoption infomation. Delete the cuently selected ecod. The default adsoptive infomation data is as follows. Adsoptive name Adsoption tempeatue / k Molecula weight Density / g cm -3 Coss sectional aea /nm A * *4 A * * CO * *6 HO * *6 K *5 0.0 *6 N * *6 «Refeence» *1 ISO * ISO *3 National Institute of Standads and Technology, *4 Chemisty handbook basic 4th edition, Chemical Society of Japan, Mauzen Co., LTD. *5 The popeties of GASES & LIQUIDS, 4th edition, Robet C Reid, John M. Pausnitz, Buce E. Poli *6 Sicence of adsoption nd edition, Seiichi KONDOU, Tatuo ISHIKAWA, Ikuo ABE, Mauzen Co., LTD.

23 Basic Opeation 1) Tools menu - Edit data (E) Select Tools (T) and Edit data (E). Then you can edit the data settings used fo the measuements (sample, adsobent, and measuement conditions). [Refeence] Opeation => Edit data, on page 54. ) Help (H) menu - How to use (U) Select Help (H) and How to use (U). The BELMaste manual can be efe hee. [Refeence] Opeation => How to use the analysis pogam, on page Vesion info (V) Select Help (H) and Vesion info (V). You will find the BELSORP analysis pogam vesion infomation hee. [Refeence] Opeation => See BEL analysis pogam Vesion infomation, on page 55. 3

24 Basic Opeation 5-. Data analysis menus (when the data window is a gaph) 1) Menu stuctue While analyzing data (moe than one data set is open), this menu will appea when the active data analysis window is a gaph. File Open (O) Additional eading Adsoption/desoption isothem PCT cuve BET plot : : Close Delete the selected data (Not displayed duing the molecula pobe analysis) Repot setting Save as (Displays only the diffeence of adsoption isothem analysis) A pinting esult is output to a file Analysis (Not displayed duing the Molecula pobe analysis) Settings (S) Setting menu duing Molecula pobe analysis Analysis setting Edit data Window (W) Pint Quit (Q) Display numeical data Adsoption/desoption isothem PCT cuve BET plot : Analysis paametes (A) X-axis display settings (X) Y-axis display settings (Y) Plot settings (L) Smoothing settings (S) Routine analysis settings (R) Adsoptive infomation (I) Cascade (C) Tile hoizontally (H) Tile vetically (T) Help (H) 1 Data name.dat Data name.dat : (Names of cuently open data files) How to use this pogam (U) Vesion info (I) 4

25 Basic Opeation ) File (F) menu - Open (O) menu Select File (F), Open (O), and then Read additional data. You can display a maximum of five sets of data ovelaid on the cuently active data analysis window. [Refeence] Opeation => Adding data file to active window (gaph), on page 34 Select File (F), Open (O), and then eithe analysis method. You can display a diffeent data analysis (gaph) in a new window. Analysis methods that ae gayed out cannot be selected fom the menu. Select DH plot, BJH plot o CI plot fom the Mesopoes distibution analysis sub window. Select MP plot, HK plot, o SF plot, fom the Micopoes distibution analysis sub menu. [Refeence] Opeation => File Open, on page 30. Analysis method => Page 6- - Save as This function is only available when Diffeence of adsoption isothems analysis is selected. Save the diffeence of adsoption isothems data, shown in the cuently active data analysis window, in an adsoption isothem file. The saved data can be analyzed using othe analysis methods such as a Langmui plot. - Close Select File (F) and Close. This will close the cuently active data analysis window (gaph). - Delete selected data Select File (F) and Delete selected data. The pogam will delete the selected data (data whose check box has been selected) in the cuently active data analysis window. - Repot setting An analysis epot setting sceen will appea. [Refeence] Opeation => Chapte 31: Output an analysis epot, on page 145. Note: If Micosoft Excel is not installed on you PC, this function cannot be used. - A pintting esult is output to a file Select File (F) and A pintting esult is output to a file. You can save the esults in a file. The gaph of the active analysis window of the cuently active data analysis window can be saved in bitmap o meta file fomat. [Refeence] Opeation => 9-1. Saving a data analysis, on page 48. 5

26 Basic Opeation - Pint Select File (F) and Pint. Then you can pint a data analysis gaph of the active analysis window. [Refeence] Opeation => Pint data analysis (gaph), on page 51 - Quit Select File (F) and then Quit (Q) to end the BEL analysis pogam. 3) Analysis (A) menu The Analysis (A) menu is not displayed if the Molecula pobe method analysis window is active. If you select Analysis (A) and then Display numeical data, the pogam will open a new data analysis window and show you the numeical data. It will display numeical data fo the active data (data whose check box has been selected) in the cuently active window. [Refeence] Opeation => Display numeical values of data on the gaph, on page 35. If you select Analysis (A) and then any analysis method, the pogam will open a new data analysis window and display the data fo analysis. It displays data analysis fo the active data (data whose check box has been selected) in the cuently active window. Select DH plot, BJH plot, o CI plot, INNES plot fom the Mesopoes distibution analysis sub window. Select MP plot, HK plot, o SF plot, fom the Mico poes distibution analysis sub menu. [Refeence] Opeation => File open, on page 9. Analysis method => Page 6 4) Settings (S) menu When executing a Molecula pobe method analysis. Select Setting(S) and then any of the items you want to set. A setting window will open and you can specify individual settings. [Refeence] Opeation => Chapte 7 Setting window, on page 37 6

27 Basic Opeation 5) Window (W) menu Select Window (W) and then Cascade (C). Multiple windows ae displayed by ovelapping them. Select Window (W) and then Tile Hoizontally (H). The pogam will display the windows aanged hoizontally. Select Window (W) and then Tile Vetically (T). The pogam will display the windows aanged vetically. 6) Help (H) menu - How to use this pogam (U) Select Help (H) and How to use (U). Then you can ead the BELMaste manual. [Refeence] Opeation => How to use BEL analysis pogam, on page 54. 7

28 Basic Opeation - Vesion info (V) Select Help (H) and Vesion info (V). You will see vesion infomation about the BELSORP analysis pogam. [Refeence] Opeation => Vesion infomation about the BEL analysis pogam, on page 54. 7) Right click menu If you click the ight mouse button on any point on the cuently active gaph, a menu of available analysis methods and settings will appea. 8

29 Basic Opeation 5-3. Menus duing data analysis (when the active data is numeic) 1) File (F) menu - Pint Select File (F) and then Pint. You can pint the numeical data fom the active analysis window. [Refeence] Opeation => Pint the data analysis (of numeical data), on page Save Select File (F) and then Save. You can save the numeical data fom the cuently active data analysis window. [Refeence] Opeation => Save data analysis (numeical data), on page Close Select File (F) and Close. The cuently active data analysis window (numeical data) will close. 9

30 Basic Opeation Chapte 6: Reading in analysis data This chapte descibes how to ead in data that wee measued by BELSORP seies appaatuses, and how to display the gaphis and numeical File open 1. The following methods can be used to select a data analysis file. Reading data into a new data analysis window - Select fom the analysis pogam menu... Read additional data into the active data analysis window. - Select Additional Data fom the analysis pogam menu Select Additional Data fom the menu displayed by ight clicking the mouse on a gaph To open a file in a new data analysis window, select File (F) and then Open (O). Then pick a file (and an analysis method). 3 Initial menu Menu while analyzing data 3. To add data to the active data analysis window, select File (F), Open (O) and then Read additional data. 30

31 Basic Opeation 4. Move the cuso on the gaph and click the ight mouse button. Select Read additional data fom the menu that pops up to add data to the active data analysis window Afte step, 3 o 4, the File open window shown below will appea Select the data file you want to analyze, and click the [OPEN] button. The pogam will ead in the specified file. Open multiple data files by holding down the [Ctl] key and clicking on the vaious files you want. 31

32 Basic Opeation 7. The pogam will analyze the data using the specifie d analysis method and display a data analysis gaph. The figue on the ight is an example of an adso -ption/desoption isothem. 8. To change the ode in which data is listed, click on the name of an item on the top line, such as File name o comment name. The pogam will sot the list accoding to the selected item. An up aow on the left of the item name means that the data ae displayed in ascending ode. A down aow on the left means that the data ae displayed in descending ode. 6-. Analysis of active data (gaph) 1. Two pocedues can be used to analyze the cuently gaphed data using anothe analysis method. - Select fom the BEL analysis pogam menu Click the ight mouse button on the gaph and select fom the menu that pops up Select the data you want to analyze. If moe than two data cuves ae dawn in a window, check the box fo data you want to analyze. 3

33 Basic Opeation 3. Select Analysis (A) and then an analysis method fom the Analysis method menu Move the cuso onto the gaph and click the ight mouse button. The analysis methods menu will appea. Select a method fom this menu A new data analysis window will be opened, and a gaph of the specified analysis will be displayed. The figue on the ight is an example of a BET plot. 33

34 Basic Opeation 6-3. Adding data files to the active window (gaph) 1. You can add anothe data analysis cuve to the cuent analysis gaph window. The cuves will be ovelapped. The following thee methods can be used fo eading in additional data. - Select fom the BEL analysis pogam menu Click the ight mouse button on the gaph and select fom the menu that pops up Dag and dop... 5 to 8 The maximum numbe of data sets that can be ead in one window is as follows. - Diffeence of adsoption isothems and an iisosteic heat of adsoption:... Two data set pe window - Molecula pobe method... One data sets pe window - Adsoption/desoption isothem and analysis methods othe than those above:... Five data set pe window. Click on the data analysis window you want to add to, to make it active. 3. Select File (F), Open (O) and then Read additional data on the analysis pogam menu. The File open window will appea. Select a file. [Refeence] How to select a file => File open, on page O, move the cuso on the gaph and click the ight mouse button. You can select Read additional data fom the pop-up menu. The File open window will appea. Select the data file fom it. 4 [Refeence] How to select a file => File open, on page

35 Basic Opeation 5. You can add data fom anothe data analysis window to the cuent gaph by dagging and dopping Select the data you want to add to anothe analysis gaph Click the left mouse button on the gaph. The icon will change to. This means that dagging and dopping is 8 possible with the selected gaph. 8. Keep the left mouse button pessed and move the mouse to the gaph you want to add to. Then, elease the left mouse button. 9. Afte analyzing data using a specified analysis method, the pogam displays this data ovelapped on the gaph Display the numeical values of data on the gaph 1. Two pocedues can be used to display the numeical values of data on the cuent gaph. - Select the data set fom the BEL analysis pogam menu Select the data fom the menu that pops up when you click the ight mouse button Select the data set you want to display as numbes. If moe than two data sets ae dawn on a window, check the box fo the data you want to display. 3. Select Analysis (A) and then Display numeical data fom the BEL analysis pogam menu. 3 35

36 Basic Opeation 4. Move the cuso on the gaph and click the ight mouse button. Select Display numeical data fom the pop-up menu A new data analysis window will open and display the numeical data fom the specified data analysis. 36

37 Basic Opeation Chapte 7: Setting window This chapte descibes vaious paamete settings used fo the analysis, gaphic display and pinting. Two methods can be used to display the Settings window. - Select Settings fom the measuement softwae menu. - Put the cuso on the gaph, ight click and select the Settings fom the popup menu. When though setting the items, click the [OK] button and the settings will become effective. If you click [Set as the default value], the cuent settings will be stoed as the default settings. Default settings ae ceated fo each type of analysis Analysis paametes Specify the vaious paametes used fo the calculations pefomed by each analysis in the Analysis paametes window. Below we descibe how to set Intepolate cuve, Pessue unit, and the Data setting. Fo details, see the opeation desciption fom each analysis type. Analysis setting window fo the BET plot. 1) Settings to Intepolate cuve Thee methods can be used to daw an intepolated cuve on a gaph: Linea, 3 dimensional spline cuve and Bezie cuve. Linea Click off Intepolate cuve. 3 dimensional spline cuve Click on Intepolate cuve, and then click on 3dimensional spline cuve. Bezie cuve Click the Intepolate cuve, and then click the Bezie cuve. ) Pessue unit fo numeic data The pessue unit selection section will be seen on the analysis setting sceen fo analyses othe than the adsoption/desoption isothem analysis. This setting allows you to choose kpa o To as the pessue unit when displaying numeical data. 37

38 Basic Opeation Note: In the adsoption/desoption isothem analysis, you can choose the pessue unit to use fo numeical data on the X axis display settings window. 3) Data setting The density and adsoption molecula weight, as well as the sample molecula weight must be enteed, depending on the analysis method. You can ente these paametes in this window. Adsoptive molecula weight Ente the molecula weight of the adsoptive Coss sectional aea Ente the Coss sectional aea [nm ] Adsoptive density Ente the density [g cm -3 ] of the adsoptive If the adsoptive name does not exist and the adsoption tempeatue is not in the adsoptive infomation ecod, click this button. The adsoptive molecula weight, coss sectional aea, and density that ae cuently [Add to adsoptive list] button enteed can be added to the list. To change o delete adsoptive infomation that has aleady been ecoded, select Settings and then Adsoptive info. [Refeence] => Setting menu, on page. Adsobent molecula weight Ente the molecula weight of the samples. Sample density Ente the density of the sample (g cm -3 ). Sample specific suface aea Ente the specific aea of the sample (m g -1 ). [Wite in file] button Save the sample molecula weight, sample density, and sample specific aea cuently enteed in the measued data file. 7-. X axis display settings You can change the maximum value, minimum value, and scale esolution on the X-axis display settings window. You can also change the units and notation. Click on the [Set as the default values] button, and the cuently set values will become the default fo that analysis. X-axis display settings window fo adsoption isothem. 38

39 Basic Opeation Automatic Setting input box Unit Display logaithmic scale Display gid line Specify notation Switch between auto/manual fo the maximum and minimum values and the scale esolution of an axis. When you want to ente the maximum, minimum, and scale esolution manually, change [Autmatic check box] by clicking off it. Then ente the values as numbes. Select the units fo the X axis. The units that can be selected vay with the analysis type. Select whethe o not to display a logaithmic scale. When this is selected, you cannot ente 0 as the maximum o minimum values. Select whethe o not to display gid lines on the gaph. By clicking this check box, you can select the notation used fo the scales. Choose between the numeical value and the exponent (If this box is not checked, the display will be set automatically.). Then numbe of digits below decimal can be enteed hee Y axis display settings You can change the maximum value, the minimum value and the scale esolution on the Y-axis display settings window. You can also change the units and notation. Click on the [Set as the default values] button, and the cuently set values will become the default fo that analysis. Y-axis display settings window fo adsoption isothem. Automatic Setting input box Unit Display logaithmic scale Display gid line Specify notation Switch between auto/manual fo the maximum and minimum values and the scale esolution of an axis. When you want to ente the maximum, minimum, and scale esolution manually, change [Autmatic check box] by clicking off it. Then ente the values as numbes. Select the units fo the Y axis. The units that can be selected vay with the analysis type. Select whethe o not to display a logaithmic scale. When this is selected, you cannot ente 0 as the maximum o minimum values. Select whethe o not to display gid lines on the gaph. By clicking this check box, you can select the notation used fo the scales. Choose between the numeical value and the exponent (If this box is not checked, the display will be set automatically.). Then numbe of digits below decimal can be enteed hee. 39

40 Basic Opeation 7-4. Plot settings The line types and makes fo gaph display can be specified on the Plot settings sceen. Click the [Set as the default value] button to save the cuent settings as the default. Note: You cannot specify the Plot settings with the Molecula pobe method. can do so in the Analysis settings. Howeve, you Plot setting window Line setting Select the line type fo data No. 1 to 10. Line width fo pinting Select the line thickness to use when pinting. Adsoption banch Select the data point make fo the adsoption side. Desoption banch Select the data point make fo the desoption side. Size (make size) Set the make size. Gaphic make colo setting Select the colos used fo makes and lines. 40

41 Basic Opeation 7-5. Smoothing settings The selected data analysis esults can be smoothed with these settings. Smoothing settings window fo the adsoption/desoption isothem Smoothing settings window fo othe analyses. Active Data o All data Select a data, Active Data o All data, fo the smoothing. Active Data Select a banch fo the smoothing pocess on the adsoption/desoption gaph. Stating Point Specify a smoothing stating point in the data. End Point Specify a smoothing end point in the data. Pocessing Mak Point Specify the numbe of pocessing points to smooth. [Aveage Spline Execute] button [RETURN] button [CANCEL] button Smooth the data. Retun the data to thei condition befoe smoothing. End the pocess and close the window. 41

42 Basic Opeation Chapte 8: Data analysis window A gaphic window and a numeical value data window ae available to display the data analysis. This chapte descibes the opeations common to the gaphic window. Fo details about opeations specific to each analysis method, see Chaptes 11 to Display plot data details You can display coodinates of the plot data on a gaph using the pocedues below. 1. Select the plot data to display. When moe than two data cuves ae displayed on the same gaph, click the check box of each data set whose coodinates you want to display.. Move the pointe to the plot data set whose coodinate values you want to display, and click the left mouse button while pessing the [Alt] key. 3. The coodinates of the position you clicked on ae shown on the left of the status ba (bottom ba on the sceen). 4. The data numbe of the data neaest to the position you clicked on, and its coodinates, ae displayed on the ight side of the status ba

43 Basic Opeation 8-. Setting the linea egession stat and end points. 1. When analyses use the linea egession function (e.g. BET plot, Langmui plot, t plot, s plot, DA plot, and metal distibution atio), boxes will appea on the ight of the gaph to let you ente stat and end points.. By changing these values, you can change the objective linea egession ange. The numbes can be changed by enteing a new value o by pessing the buttons on the ight of the boxes. 3. If you want to delete a line, ente the same value fo both the stat and end points. The line will be deleted. 43

44 Basic Opeation 8-3. Displaying numeical data fom a gaph This function displays the numeical data fo the gaph data cuently being analyzed. 1. Click the active data check box on the data analysis window fo the data you want to display. Select the data to be made active.. Select Analysis (A) and Display numeical data fom the BEL analysis pogam menu, o move the cuso on the gaph and click the ight mouse button. Then select Display numeical data fom the pop up menu. 3. A new data analysis window will open and a list of the active data and heade infomation will be displayed. Analysis esults Heade infomation List of gaphed data 44

45 Basic Opeation 8-4. Analyze the active data by using anothe analysis method The data fo used in analysis methods othe than the molecula pobe method ae based on a common fomat. Theefoe, the data aleady opened can be analyzed with othe analysis methods. 1. Move the cuso on the gaph of the data analysis window and click the ight mouse button. O, select Analysis (A) fom the BEL analysis pogam menu. The analysis menu will appea. 1. Afte selecting an analysis method, a new data analysis window will open. The pogam stats analysis of the data specified in the oiginal gaph. The figue below shows the esults of executing a BET analysis fom an Adsoption / desoption isothem. 45

46 Basic Opeation 8-5. Tansfe the data using the dag and dop function When a data analysis window is aleady open, you can tansfe the data by dagging and dopping the gaph data. 1. Confim that data you want to tansfe has been selected.. Move the cuso on the gaph while holding down the left mouse button (The icon will change.). 3. Move the cuso to the data analysis window you want to tansfe data to while holding down the left mouse button. Then, elease the left mouse button. 4. The data and gaph will be added to that window. 46

47 Basic Opeation 8-6. Displaying the sub sceen 1. The file name fo the cuently analyzed gaph data is displayed on the sub sceen.. Even afte gaph data is deleted fom the main sceen, the analysis method and file name will be etained. (If you execute Delete, the analysis method and file name on the sub sceen will be deleted. ) 3. To e-display a gaph afte it is closed on the main sceen, activate the analysis method fo the data to be e-displayed on the sub sceen (it will be displayed in blue), and click the mouse ight button to show the window indicated as 3. If you select Re-display, the elevant gaph will be e-displayed To destoy data, activate the analysis method fo the data to be destoyed on the sub sceen (it will be displayed in blue), and click the mouse ight button to show the window indicated as 4. If you select Destoy, the elevant gaph will be deleted. 4 47

48 Basic Opeation Chapte 9: Saving and pinting analysis esults Gaphs and numeical data analyses can be saved in a file and pinted on pape. This chapte descibes how to save and pint the analysis esults. It also descibes how to edit measued data (the measuement conditions fo a sample weight) and it coves the help function Save data analysis 1) Save data analysis (gaph) A data analysis gaph can be saved as a bitmap file o a meta file. The saved image coesponds to the gaphs output by selecting File and Pint. 1. Make the analysis window of the gaph you want to save active.. Select File (F) and then Output the gaph in a file fom the BEL analysis pogam menu The Save As window shown on the ight will appea. 4. Select a file type (Bitmap File / Meta File) Specify a folde to save the file in and ente a file name. 6. Click the [Save] button. The pogam will save the gaph of the cuently active data analysis window in a chiced file

49 Basic Opeation 7. The figue on the ight is an example of a gaph that has been saved. It can be used with othe pogams. ) Save a data analysis (numeical data) Numeical data fom a data analysis can be saved in a file. 1. Display the numeical data you want to save. [Refeence] Display numeical data => Display the numeical data in a gaph, on page Select the analysis window that is displaying the numeical data to save. 3. Select File (F) and Save fom the BEL analysis pogam menu. 4. The Save As window shown on the ight will appea. 5. Specify a folde to save the file in and ente a file name. 6. Click the [Save] button. The pogam will save the numeical data fom the cuently active data analysis window to a file

50 Basic Opeation 7. The numeical data ae stoed in CSV fomat, so that they can be used with othe pogams. The figue on the ight is an example of a numeical data file opened with Excel. 50

51 Basic Opeation 9-. Pinting a data analysis 1) Pint a data analysis (gaph) A gaph of a data analysis can be pinted on pape. 1. Select the analysis window containing the gaph you want to pint.. Select File (F) and Pint fom the BEL analysis pogam menu. 3. The Pint settings window shown on the ight will appea. Specify a pinte type and pint diection. Then click the [Pint] button. The pogam will pint the specified gaph The data analysis (figue) ae pinted using the fomat shown on the ight. 51

52 Basic Opeation ) Pint data analysis (numeical data) Numeical data fom a data analysis can be pinted. 1. Display the numeical data you want to pint. [Refeence] Display numeical data => Display the numeical data fom a gaph, on page 35.. Select the analysis window that is displaying the numeical data you want to pint. 3. Select File (F) and Pint fom the BEL analysis pogam menu The Pint settings window shown on the ight will appea. Specify a pinte type and pint diection. Then click the [Pont] button. The pogam will pint the specified numeical data Numeical data ae pinted using the fomat shown on the ight. 5

53 Basic Opeation 9-3. Edit data The data items that wee set when taking measuements can be edited and saved (sample, adsoptive, and measuement conditions). 1. Data editing is only possible when the initial menu window is displayed. If a data analysis window (gaph o numeical data) is open, you cannot edit the data. Close any open data analysis windows and ty editing the data again.. Select Tool (T) and Edit data (E) fom the analysis pogam initial menu. 3. The Edit data window shown on the ight will appea. 4. Select the file you want to edit fom the list of data files The data items specified when measuements wee taken will be displayed. Edit any item you want to change. 6. If you want to ovewite the existing file, click the [SAVE] button. An ovewite message window will appea. Select [Yes] and the pogam will ovewite the items that you changed. 7. To save it as a diffeent file, click the [SAVE] button The Save As window shown on the ight will appea. Specify a location to save the file in and ente a file name Click the [Save] button. The pogam will save the data using the file name you enteed. 9 53

54 Basic Opeation 9-4. Help function 1) How to use this pogam You can find instuctions about vaious opeation methods of the analysis pogam using the help function. 1. Select Help (H) and How to use (U) fom the BEL analysis pogam menu. 1. The BEL analysis softwae HELP window appeas. Hee you can find desciptions of the opeations and othe details of the analysis pogam. ) Vesion info. of the analysis softwae 1. You can see the vesion infomation of the analysis pogam.. Select Help (H) and Vesion info (V) fom the BEL analysis softwae menu. 3. The vesion infomation display sceen shown on the ight will appea. 54

55 Analysis of measued data Chapte 10: Analysis of adsoption/desoption isothems Chapte 11: Adsoption / desoption isothem... 6 Chapte 1: PCT cuve Chapte 13: BET analysis Chapte 14: Langmui plot Chapte 15: t plot Chapte 16: α s plot... 8 Chapte 17: MP method analysis Chapte 18: BJH plot Chapte 19: CI plot Chapte 0: DH plot Chapte 1: INNES plot Chapte : DA plot Chapte 3: HK plot Chapte 4: SF plot Chapte 5: Isosteic heat of adsoption Chapte 6: Diffeence of adsoption isothem Chapte 7: Metal dispesion analysis Chapte 8: Molecula plobe method Chapte 9: NLDFT/GCMC method Chapte 30: How to use [Routine analysis] Chapte 31: Output an analysis epot

56 Chapte 10: Analysis of adsoption/desoption isothems The BELSORP seies employs the volumetic theoy to measue adsoption isothems. It can poduce eliable pecision measuement data by setting appopiate measuement conditions. The adsoption amount elative to the pessue can be obtained as measued data. The elationship between them is efeed to as an adsoption isothem. This chapte biefly sums up the featues of the adsoption isothem and its analysis. Chapte 11 and late descibe the opeation methods while showing desciptions and sample examples fo each analysis method Adsoption isothem In physical adsoption, adsoption isothems can be classified as one of 6 types, as shown in the table below. Table 1 shows the types and featues, as well an adsobent example. Analysis of adsoption/desoption isothems Figue 1: IUPAC classification of adsoption isothems 56

57 Table 1: Featues of adsoption isothems Featues Type Inteaction between sample suface and adsobate Poosity Sample Adsoptive example I Relatively stong Micopoes Activated cabon - Nitogen II Relatively stong Nonpoous Oxide - Nitogen III Weak Nonpoous Cabon Wate vapo IV Relatively stong Mesopoe Silica Nitogen V VI Weak Relatively stong Sample suface has an even distibution of enegy Mesopoe Micopoe Nonpoous Activated cabon Wate vapo Gaphite - Kypton Size of poes is classified as shown in table below. Table : IUPAC classification of poes Poe diamete / nm Micopoe Up to Mesopoe to 50 Macopoe 50 o up Adsoption isothems ae classified as shown in table based on the stength of the inteaction between the sample suface and adsoptive, and the existence o absence of poes. Howeve, some actual samples do not fit into adsoption isothem types I to IV. These may be measued as mixed types of adsoption isothems. Fo example, nitogen adsoption fo a poous sample with lage extenal suface aea may geneate a compound isothem esembling types I and II, o types I and IV. To analyze an adsoption isothem, you have to assume cetain sample featues, such as the poes fom the shape of the isothem. Then you can analyze them using an appopiate analysis method. «Refeence» Adsoption Suface Aea and Poosity, nd Ed., S. J. Gegg & K. S. W. Sing, Academic Pess INC., London (198). Adsoption by Powdes and Poous Solids, F. Rouqueol, J Rouqueol & K. S. W. Sing, Academic Pess INC., London (1999). Analysis of adsoption/desoption isothems 57

58 10-. Analysis data obtained fom a nitogen adsoption isothem By measuing nitogen adsoption isothems, a type I, II, o IV adsoption isothem can be measued mainly and sample infomation concening a specific suface aea and poous stuctue will be obtained. Table 3 biefly sums up what analysis data can be obtained fom a nitogen adsoption isothem. Table 3: Analysis data obtained fom a nitogen adsoption isothem Type of adsoption isothem Sample infomation Analysis method Majo analyzed data Remak Total specific suface aea BET plot a s,bet [m g -1 ] Needs caeful evaluation of the Total specific suface aea t plot, s plot a 1 [m g -1 ] analysis esults. Extenal specific suface aea t plot, s plot a [m g -1 ] Analysis of adsoption/desoption isothems Type I Type II Micopoe aea t plot, s plot a 1-a [m g -1 ] Micopoe volume t plot, s plot V [cm 3 g -1 ] Micopoe width t plot t [nm] Micopoe distibution cuve MP plot Micopoe ange Poe shape: Slit Poe dia.: 0.7 to 1.0 nm Micopoe distibution peak MP plot d p peak o p peak [nm] Micopoe volume DA plot V p [cm 3 g -1 ] Micopoe distibution cuve Micopoe distibution peak HK plot HK plot Micopoe ange d p peak o p peak [nm] Poe shape: Slit Poe dia.: 1.0 nm o less Micopoe distibution cuve Micopoe distibution peak SF plot SF plot Micopoe ange d p peak o p peak [nm] Poe shape: Cylinde Poe dia.: 1.0 nm o less Total specific suface aea BET plot a s,bet [m g -1 ] Total specific suface aea t plot, s plot a 1 [m g -1 ] Total specific suface aea BET plot a s,bet [m g -1 ] Total specific suface aea t plot, s plot a 1 [m g -1 ] Mesopoe distibution cuve BJH plot, DH plot, CI plot Mesopoe ange Type IV Mesopoe distibution peak BJH plot, DH plot, CI plot,innes plot d p peak o p peak [nm] Mesopoe volume BJH plot, DH plot, CI plot,innes plot V p [cm 3 g -1 ] Mesopoe aea BJH plot, DH plot, CI plot,innes plot a p [m g -1 ] 58

59 Table 4 sums up symbols used in section 11 o late. Table 4: Using symbols in the BELMaste manual Method Symbol Unit Mean p/p 0 - Relative pessue (p 0 is satuation pessue of the adsoptive at measuement tempeatue. ) Adsoption / desoption isothem PCT cuve BET analysis Langmui plot T plot p kpa, To Absolute pessue RH % Relative humidity V a cm 3 (STP) g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of adsobent m a mg g -1 Specific mass adsobed on 1 g of adsobent molec nm - Numbes of molecules adsobed on a unit suface aea of adsobent n a mol mol -1 Amount adsobed on 1 mol of adsobent expessed in mol n a mol g -1 Amount adsobed on 1 g of adsobent expessed in mol wt % Amount adsobed on 1 g of adsobed expessed in pecentage s A value obtained by dividing an adsoption amount at abitay - equilibium pessue by adsoption amount Va (p/p 0 = 0.4). - Amount (mol) of hydogen occluded by 1 mol of sample (metal). wt % Amount (%) of hydogen occluded by 1 g of sample (metal). V a cm 3 (STP) g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of sample (metal). p kpa, MPa, ba Absolute pessue Relative pessue p/p 0 - (p 0 is satuation pessue of the adsoptive at measuement tempeatue. ) V m cm 3 (STP) g -1 Monolaye volume a sbet m g -1 BET specific suface aea C - Enegy constant (the fist laye) nm Coss section aea of an adsoptive aea M g - Molecula weight of adosoptive L - Avogado numbe a g cm -3 Dencity of adosoptive s g cm -3 Dencity of sample V p cm 3 g -1 Total poe volume d p nm Mean poe diamete l nm Mean paticle size P kpa, To Absolute pessue V m cm 3 (STP) g -1 Monolaye volume a slang m g -1 Langmui specific suface aea B - Ratio of ate constant (adsoption / desoption) nm Coss section aea of an adsoptive aea t nm Thickness of adsoption laye a 1 m g -1 Total specific suface aea a m g -1 Extenal suface aea V 1 cm 3 g -1 Poe volume V cm 3 g -1 Poe volume t nm Poe diamete V a cm 3 (STP) g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of sample Analysis of adsoption/desoption isothems 59

60 Method Symbol Unit Mean Analysis of adsoption/desoption isothems s plot MP plot BJH / CI / DH plot INNES plot DA plot HK plot s - Nomalized adsoption n/ n 0.4 V a cm 3 (STP) g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of sample A 1 m g -1 Total specific suface aea A m g -1 Extenal suface aea V 1 cm 3 g -1 Poe volume V cm 3 g -1 Poe volume p nm Micopoe adius d p nm Micopoe diamete dv p / d p cm 3 g -1 nm -1 Aea distibution dv p / dlog p - Volume distibution dv p / dd p cm 3 g -1 nm -1 Aea distibution dv p / dlogd p - Volume distibution V p cm 3 g -1 Integal cuve a 1 m g -1 Total specific suface aea a m g -1 Extenal suface aea V 1 cm 3 g -1 Poe volume V cm 3 g -1 Poe volume p nm Micopoe adius (cylindical shape) d p nm Micopoe diamete (cylindical shape) dv p / d p cm 3 g -1 nm -1 Aea distibution dv p / dlog p - Volume distibution dv p / dd p cm 3 g -1 nm -1 Aea distibution dv p / dlogd p - Volume distibution V p cm 3 g -1 Integal cuve A p m g -1 Poe specific suface aea V p cm 3 g -1 Poe Volume d x nm Slit poe adius (slit shape) dvp / ddx cm 3 g -1 nm -1 Aea distibution dvp / dlogdx - Volume distibution V p cm 3 g -1 Integal cuve a p m g -1 The poe specific suface aea V p cm 3 g -1 Poe volume V p cm 3 g -1 Poe Volume E 0 kj mol -1 Adsoption potential enegy W nm Slit poe adius (slit shape) dv p / dw cm 3 g -1 nm -1 Aea distibution dv p / dlogw - Volume distibution V p cm 3 g -1 Integal cuve d a nm Adsoptive molecula diamete d s nm Adsobent atom diamete N a m - Numbe of adsoptive molecules adsobed pe unit suface aea N s m - Numbe of adsobent atoms pe unit suface aea X a cm 3 Magnetic susceptibility of the adsoptive molecula X s cm 3 Magnetic susceptibility of the adsobent atom a cm 3 Polaizability of the adsoptive molecula s cm 3 Polaizability of the adsobent atom 60

61 Method Symbol Unit Mean p nm Micopoe adius (cylindical shape) d p nm Micopoe diamete (cylindical shape) dv p / d p cm 3 g -1 nm -1 Aea distibution dv p / dlog p - Volume distibution dv p / dd p cm 3 g -1 nm -1 Aea distibution dv p / dlogd p - Volume distibution V p cm 3 g -1 Integal cuve SFplot d a nm Adsoptive molecula diamete d s nm Adsobent atom diamete Isosteic heat of adsoption Metal dispesion ation analysis Molecula pobe method NLDFT/GCMC N a m - Numbe of adsoptive molecules adsobed pe unit suface aea N s m - Numbe of adsobent atoms pe unit suface aea X a cm 3 Magnetic susceptibility of the adsoptive molecula X s cm 3 Magnetic susceptibility of the adsobent atom a cm 3 Polaizability of the adsoptive molecula s cm 3 Polaizability of the adsobent atom Q st kj mol -1 Isosteic heat of adsoption V a cm 3 (STP)g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of adsobent. P kpa,to Absolute pessue V a cm 3 (STP)g -1 Specific amount adsobed expessed in the gas volume at the standad state (STP: T=73.15 K, kpa) on 1 g of adsobent. N g mol g -1 Numbe of molesof the gas that adsobed on suppoted metal catalyst 1 g N s mol g -1 Numbe of metal atoms on the metal catalyst 1 g N T mol g -1 Numbe of moles of metal atom pe catalyst 1 g C % Metal loading k sf - Stoichiomety facto D m % Metal dispesion atio a m nm atm -1 Coss section aea that a suppoted metal atom occupies (suppoted metal coss section aea) a s (sample) m g -1 Suppoted metal suface aea pe suppoted metal 1 g a s (Metal) m g -1 Suppoted metal suface aea pe suppoted metal 1 g l m nm Metal paticle size p nm Micopoe adius d p nm Micopoe diamete Vp cm 3 g -1 Poe volume W 0 cm 3 g -1 Poe volume D S D L nm Mino axis length of smallest pojection coss section aea (adsoptive) nm Majo axis length of smallest pojection coss section aea (adsoptive) d m nm Adsoptive molecula d p nm Poe diamete (cylindical shape) W nm Poe width (slit shape) d s nm Adsobent atom diamete Vp cm 3 g -1 Poe volume dvp cm 3 g -1 Change of Poe volume V p cm 3 g -1 Integal cuve dv p / d p cm 3 g -1 nm -1 Aea distibution dv p / dlog p - Volume distibution dv p / dd p cm 3 g -1 nm -1 Aea distibution dv p / dlogd p - Volume distibution dsp m g -1 Change of Poe suface aea Sp m g -1 Integal cuve of suface aea Analysis of adsoption/desoption isothems 61

62 Chapte 11: Adsoption / desoption isothem Desciption Adsoption/desoption isothem The adsoption / desoption isothem shows the elationship between the amount of adsobed/desobed gas (y-axis) and the pessue of adsoptive (x-axis) at the constant tempeatue. In ou softwae, use can select the desied x-axis unit among fou. In measuement data, p(i), the pessue of ith measuement point is expessed in kpa. X-coodinate value can be calculated as follows. In case p/p0 is selected: x ( i ) p ( i ) / p 0( i ) (Whee p0(i) / kpa is satuation pessue of the adsoptive at measuement tempeatue. ) In case p / kpa is selected: x ( i) p( i) In case p / To *1 is selected: x ( i) p( i) / In case RH / % is selected: x ( i ) p ( i )/ p 0 ( i ) 100 And also use can select the desied y-axis units among five listed below. In case Va /cm 3 (STP) g -1 * is selected: y ( i) v( i) In case ma / mg g -1 *3 is selected: y( i) v( i) / 414 (Whee Mg is molecule weight of adsoptive.) M g In case Γ/ molec nm - *4 is selected: 3 18 y i) v( i) / / a 10 (Whee as/m g -1 is the specific suface aea of adsobent.) ( s In case na / mol mol -1 *5 is selected: y( i) v( i) / 414 (Whee Ms is molecule weight of sample.) M s In case na / mol g -1 *6 is selected: y ( i) v( i) / 414 In case wt / % *7 is selected: y i) v( i) / 414 M ( g In case s *8 is selected: y i) v( i)/ v( p / p 0.4) (Whee v (p/p0=0.4) is the adosoption volume of the p/p0=0.4.) ( *1: Though To is not included in ISO system of units, it is commonly used even today. Uses can choose it in ou softwae. Pay attention when you use To in official documents. *: Va / ml(stp) g -1 is the specific amount adsobed expessed in the gas volume at the standad state(stp : T=73.15 K and P=101.3 kpa). *3: ma / mg g -1 is the specific mass adsobed. *4: Γ/ molec nm - is the numbe of molecules adsobed on a unit suface aea of adsobent. *5: na / mol mol -1 is the amount adsobed on 1mol of adsobent expessed in mol. *6: na / mol g -1 is the specific amount adsobed expessed in mol. *7: wt/% is pecentage of weight of adsoption pe gam of sample. *8: A value obtained by dividing an adsoption amount at abitay equilibium pessue by adsoption amount Va (p/p0 = 0.4) 6

63 11-. Opeation 1. On the BEL analysis softwae menu, select adsoption/desoption isothem. The pogam will display the following adsoption/desoption isothem. Fo details about how to ead the data, see Chapte 6: Reading analysis data, on page 30.. ADS next to a data name means that it is data fom an adsoption pocess and DES next to a data name means that it is desoption data. 3. Select Analysis paametes on the Settings menu and the Analysis paametes window shown below will appea. Change the settings as needed. When ma/mg g -1 is selected as the Y axis unit in Y axis display settings, this value must be enteed. Adsoption / desoption isothe When na/mol mol -1 is selected as the Y axis unit in Y axis display settings, this value must be enteed. When /molec mn - is selected as the Y axis unit in Y axis display settings, this value must be enteed. 63

64 Chapte 1: PCT cuve 1-1. Desciption PCT cuve (Pessue-Composition-Isothem) is a gaph that shows elationship between the amount of hydogen occluded by hydogen occlusion alloy at a constant tempeatue (x-coodinate) and the hydogen pessue (y-coodinate). When the amount of hydogen occluded at the i-th point in measuement data is indicated as v(i) cm 3 (STP) g -1, the x-coodinate (x (i)) can be obtained with the equation below. When H/M *1 is selected: x( i) v( i) M metal / 414 (Mmetal: Molecula weight of metal) When wt% * is selected: x i) v( i) / 414 M 100 (Whee Mg is molecule weight of adsoptive.) ( g PCT cuve When cm 3 (STP) g -1 *3 is selected: x ( i) v( i) When pessue at the i-th point in measuement data is indicated as P(i) kpa, y coodinate (y (i)) can be obtained with the equation below. When p / kpa is selected: y ( i) p( i) When MPa / kpa is selected: y ( i) p( i) /1000 When p / ba is selected: y ( i) p( i) /100 *1: Amount (mol) of hydogen occluded by 1 mol of sample (metal). *: Amount (%) of hydogen occluded by 1 g of sample (metal). *3: Volume of gas at 0 C and kpa, conveted fom amount of adsoption by 1 g of sample (metal). 64

65 1-. Opeaion 1. If you select PCT cuve fom the menu of the analysis softwae, a PCT cuve is displayed as shown below. Fo the data loading pocedue, efe to page 30.. If you select Analysis setting fom the Setting menu, the Analysis paametes window appeas as shown below. Change the paamete settings as equied. PCT cuve This paamete is equied when wt% is selected fo the unit of the X axis in X-axis display settings. This paamete is equied when H/M is selected fo the unit of the X axis in X-axis display settings. 65

66 Chapte 13: BET analysis Desciption BET Theoy In 1938, Bunaue, Emmett and Telle epoted the multilaye adsoption theoy (BET theoy). They extended the Langmui s monolaye theoy to multilaye adsoption. The deived equation is named the BET equation afte the fist lette of each of thei names. The BET equation has been utilized in detemining the monolaye volume of adsobed gas, fom which we can calculate the suface aea of adsobent. The BET equation was deived on the following hypotheses: 1) Suface is enegetically homogeneous; i.e., all adsoption sites on bae solid suface have the same adsoption enegy(e1). ) Thee is no lateal inteaction between adsobed molecules. 3) The adsoption enegies in the second and all highe layes (E, E3 ) ae equal to condensation enegy of adsoptive (EL) ; i.e., E=E3=...=Ei=EL. The BET adsoption model is shown below, whee N0,N1,N,N3...Ni,... epesent the adsoption sites that ae coveed by 0, 1,, 3,, i, layes of adsobed molecules. At adsoption equilibium, N0,N1,N,N3...Ni,... must emain constant. BET analysis Fist, we conside the case of i=0. N0 deceases when adsoption occus on the bae suface and the adsoption ate is popotional to N0. N0 inceases when desoption occus fom the fist laye and the desoption ate is popotional to N1. Because N0=constant at adsoption equilibium, the adsoption ate is equal to the desoption ate; theefoe, Equation (13.1) is obtained. a pn b N E1 RT exp (13.1) Next, we conside the case of i=1, whee the fou pocesses ae included; namely, (a) the adsoption of gas molecules to the bae solid suface, (b) the desoption of adsobed molecules fom the second adsobed laye, (c) the adsoption of gas molecules to the fist adsobed laye, and (d) the desoption of adsobed molecules fom the fist adsobed laye. At adsoption equilibium, the ate of fomation of the fist adsobed laye, which is the ate of (a) and (b), is equal to the ate of disappeaance of the fist adsobed laye, which is the ate of (c) and (d). Theefoe, the following equation is obtained: E E1 a pn0 b N a pn1 b1 N1 RT RT 1 exp (13.) 66

67 Equation (13.3) is obtained by substituting equation (13.1) into equation (13.), a pn b N E RT 1 exp (13.3) Extending the same agument to the i th laye (Ni = constant), equation (13.4) can be deived. a i pn b N exp Ei RT i 1 i i (13.4) Equation (13.4) is tanfomed into equation (13.5). N i a b i i pn exp Ei RT i 1 (13.5) Equation (13.6) may be obtained if the adsoption behavio of gas is same fo highe than the second laye, g b a b a 3 3 b a i i (13.6) Fom both of equation (13.6) and hypothesis 3), Equation (13.5) can be tansfomed into equation (13.7) and equation (13.8) when i : N i p N g Hee, we define x as follows: x p g exp EL RT i 1 (13.7) EL RT exp (13.8) By inseting equations (1.8) into Equation (13.7), equation (13.9) is obtained: N xn 1( i i i ) (13.9) The next step is to obtain the elationship between Ni and N0. Fom equation (13.9), Ni can be expessed by N1 and x as follows: N i 1 i xni 1 x( xni ) x ( xni 3) x N1 (13.10) Equation (1.1) is tansfomed as follows: a1 E1 N pn0 b RT 1 exp (13.11) 1 Then, equation (13.11) is inseted into Equation (13.10): N i x i 1 a b 1 1 i E1 x E1 pn0 exp pn0 exp (13.1) RT x RT In ode to intoduce EL into equation (13.1), equation (13.8) is used: whee N c a1 E E g exp x N cx N 1 L i i i 0 0 (13.13) b1 RT a1 E1 E g exp b RT 1 E E RT L 1 L exp (13.14) [Note: Equation (13.14) shows that c-constant is always positive.] The total numbe of adsoption sites on the solid suface is expessed as Ns, and the total numbe of adsobed molecules is given as Na; thus, the following equations can be deived: N s N i 0 i N0 N i 1 i (13.15) N a in i 0 i in i 1 i (13.16) BET analyaia 67

68 BET analysis The next step is to change Ns and Na into Vm and Va, the gas volume at the monolaye coveage and the total gas volume adsobed at the standad state (T=73.15 K and P=101.3 kpa), espectively. N N a s V V a m (13.17) Inseting Equations (13.15) and (13.16) into equation (13.17), we equation (13.18) can be obtained. V V in a i 1 i (13.18) m N0 N i 1 i By using equation (13.13), equation (13.18) can be tansfomed into Equation (13.19): i V cn0 ix a i 1 (13.19) V i m N0 cn0 x i 1 Equations (13.0) and (13.1) can be deived when x<1. i 1 x i ix x 1 x d x dx x i i i 1 i 1 dx 1 x (1 x) x d x x (13.0) (13.1) If equations (13.0) and (13.1) ae inseted into equation (13.19), equation (13.) is obtained: V V a m 1 cx x 1 x cx (13.) whee c and vm ae constant. Now, conside the physical meaning of x. The expeimental fact shows that in the adsoption isothem, the adsobed amount, v, becomes infinite at satuation pessue; namely, v = at p = p0. On the othe hand, in equation (13.), v becomes infinite when x is equal to 1. Accodingly, it is concluded that x = 1at p = p0. Inseting these conditions into Equation (13.8), Equation (13.3) is deived: p 0 exp g EL RT 1 (13.3) Fom equation (13.8) and equation (13.3), the physical meaning of x becomes evident; x is the elative pessue of adsoptive. p x (13.4) p 0 If we ewite equation (13.) using the elative pessue, equation (13.5) is obtained: V p V m cp a (13.5) 0 p 1 c 1 p p 0 Equation (13.5) is called the BET equation, o the BET adsoption isothem. The cuves in the above figue show the BET adsoption isothem at the diffeent c constant. When c is lage (i.e., lage adsoption heat), the isothem is of Type II, wheeas when c is small (i.e., small adsoption heat), the adsoption isothem is of Type III. When c is lage and p«p0, Equation (13.5) is changed into equation (13.6), which is equivalent to the Langmui equation. 68

69 6 5 4 v/v m 3 C= C=100 1 C=10 C= p/p 0 V V 1 m c c p p 0 a (13.6) p p 0 In ode to examine the eliability of the BET equation using the expeimental data, equation (13.5) is put into the following fom: p v p 0 p 1 v c m c v m 1 c It is evident fom Equation (13.7) that a plot of (p/va(p0 p p 0 (13.7) p)) against (p/p0), which is called the BET plot, should give a staight line, and that the intecept(i) and the slope(s) of the BET plot give (1 /Vmc) and (c- 1)/Vmc, espectively. The two constants (Vm and c) of the BET equation can be calculated using Equations (13.8) and (13.9): 1 v m s s 1 i i (13.8) c (13.9) In many adsobents, the BET plot gives the good linea line in elative pessue ange 0.05~0.35, but it deviates fom the linea line in low o high pessue ange. Usually, Vm and c ae evaluated fom the BET plots in the pessue ange of (p/p0) = 0.05 to 0.35, but the stating point and the ending point of the BET plot should be caefully selected accoding to the chaacte of adsobent. Fo example, in the case of gaphitized cabon black (Vulcan 3-G (700)), the BET plots in the ange of to is ecommended in evaluating vm. In ou softwae, the stating point and the ending point of the BET plot ae abitaily selected accoding to the chaacte of adsobent. Vm can be used in calculation of the specific suface aea of adsobent (as) as descibed below. BET analyaia Hee, some comments ae given in the BET equation with thee paametes. As mentioned above, the BET plot deviates fom the linea line below (p/p0) = 0.05 and above (p/p0) = Bunaue et al. poposed the thee paamete equation (Equation (13.30) ) in ode to cove the wide ange of the adsoption isothem, whee n is the numbe of laye. It is possible to cove the wide ange of the adsoption isothem by selecting an appopiate numeical value of n, but the thee paamete equation is not fequently used because of complexity. 69

70 V cx (1 x) 1 1 ( n ( c 1) x 1) x nx cx n n 1 m V a (13.30) n 1 Equation (13.30) is educed to Lamgmui equation (Equation (13.6)) when n = 1. [Note] Thee is a citicism that it is inappopiate to apply the BET theoy to Type I isothem. In this case, the maximum value of elative pessue p/p0 (efeed to as BET ange limit) is defined as the BET plot end point when elative pessue p/p0 is plotted on the X axis and Va (p0-p) is plotted on the Y axis so that C is not a negative value. To detemine the stating point, use caution about the following thee points: [1] Constant C is not a negative value. [] Excellent lineaity, and [3] Selection of linea ange at low elative pessue. This method is pescibed in ISO977 appendix. Regadless of the analysis method being used, it must be undestood that the taget is a gas adsoption suface aea, which is diffeent fom geometical suface aea. When C>>1, the BET plot intecept is 1/VmC, which is so small that it can be egaded as zeo. Thus, the equation (13.7) is expessed as follows: p = C-1 p (13.31) V a (p 0 -p) V m C p 0 The following equation is deived by simplifying the equation (8): V m = (1- p p 0 ) (13.3) BET analysis Monomolecula adsoption Vm can be obtained by measuing an adsoption amount Va at abitay equilibium pessue p. Thus, Vm can be detemined based on measuement of one point at abitay equilibium pessue p (geneally, in a elative pessue ange of 0. to 0.3). (BET1 plot method) With this analysis softwae, pepae BET-plot fist, and then select one point (end point). By plotting a line between two points (oigin (0) and the selected point), the softwae calculates inclination s of the line, and detemines an amount of monomolecula adsoption Vm, and calculates a suface aea fom the amount of monomolecula adsoption. It is possible to calculate the total poe volume and mean poe diamete in the analysis, BET plot. To caluculatte the total poe volume, fist the amount adsobed at the elative pessue which can be set in Analysis paamete settings is calculated by linea intepolation. Then intepoated value, Vp[cm 3 g -1 ] is conveted to the volume liquid state as Equation (13.33). (In case that the elative pessue of last adsoption point is smalle than the set value, the total poe volume is to calculate fom amount adsobed of last adsoption point. ) V V 414 / / (13.33) p M g a whee Mg is molecula weight and ρa is density of adsoptive. Mean poe diamete can be obtained as follows by using Vp and as,bet, the BET specific suface aea. 4 V p 3 d p 10 (13.34) as, BET Mean paticle size is calculated as follows. 3 l 10 (13.35) S a S, BET whee ρs is density of adsobent. 6 «Refeence» Adsoption of Gases in Multimolecula Layes, Stephen Bunaue, P. H. Emmett and Edwad Telle, J. Ame. Chem. Soc., 60, 309(1938). ISO977 70

71 Detemination of suface aea fom monolaye volume Specific suface aea of adsobent (as) can be calculated by equation (13.36). a s Vm 414 L (13.36) whee Vm is monolaye volume, L the Avogado constant, and σ the coss-sectional aea of an adsobate molecule. σ is defined as the aveage aea that one adsobed molecule occupies on the solid suface, and it is calculated unde the assumption that adsobed molecules make the closest packing on solid suface. It is obvious fom the model shown below that σ coesponds to the hexagonal aea, which is evaluated fom the molecula weight of adsobate M and the liquid density of adsobate ρ. 3 4 M L 3 (13.37) In case of the nitogen adsoption at liquid nitogen tempeatue, σ(n) = 0.16 nm (M = 8.0, ρ= g cm -3 ) can be calculated fom equation (13.35). The coss-sectional aea of a nitogen molecule, which is calculated by a simple model, was checked by the independent methods such as the absolute method of Hakins and Jua. σ(n) = 0.16 nm is intenationally accepted fo detemination of suface aea of many adsobents. Howeve, it should be mentioned that, when the adsobed nitogen molecules have the specific oientation on the unique solid suface, the diffeent value of σ(n) must be used. BET analyaia In cases of the K o A adsoption at liquid nitogen tempeatue, σ(k, 77 K) = 0.0 nm o σ(a, 77 K) = nm ae estimated fom equation (13.35), using the supe-cooled liquid density of K o A. The coss-sectional aeas of vaious molecules such as alcohols and hydocabons ae calculated based on σ(n) = 0.16 nm [ef. A. L. McClellan, and H. F. Hansbege, J. Colloid Inteface Sci., 3, 577(1967).] Themodynamics of gas adsoption It is well-known that the gas adsoption pocess is essentially exothemic. The themodynamic elation of the gas adsoption is given by equation (13.36). G ad H ad T Sad (13.38) whee ΔGad, ΔHad, ΔSad ae the Gibbs fee enegy change of adsoption, the enthalpy change of adsoption, and the entopy change of adsoption, espectively. ΔGad becomes negative, because the gas adsoption poceeds spontaneously. Futhemoe, ΔSad becomes negative, because the molecules moving at andom in gas phase ae fixed on the solid suface by adsoption. Accodingly, it is concluded fom equation (13.36) that ΔHad must be negative; namely, the gas adsoption is essentially exothemic. 71

72 Opeaion 1. On the Analysis menu, select BET plot. The following BET-plot will be displayed on the sceen. The pogam will execute a BET plot fom adsoption data of an isothem. 3. The pogam automatically daws an staight line. As a default, two points ae selected that ae neaest to the pessue ange specified on the Analysis paametes. 3. Select the stating and end points in ode to poduce a good staight line within a elative pessue ange of 0.05 to BET analysis 4. The figue on the ight is a BET plot of nitogen adsoption measuements on silica with micopoes. The monomolecula adsoption volume (Vm/cm 3 g -1 ) and C value can be obtained fom the slope of the appoximate cuve and intecept. In addition, the coelation coefficient of this appoximate cuve is shown. 5. You can obtain a specific suface aea (as,bet/m g -1 ) fom the monolaye volume (Vm/cm 3 g -1 ) fo the adsoption of nitogen, agon, and kypton. In nitogen adsoption when C is 100 to 00, it is believed that a eliable specific suface aea can be obtained. The specific suface aea obtained fom the BET plot of micopoe silica is 70.0 m g -1 and this value matches well the value of 70.1 obtained fom a t-plot (page 77). 6. The figue on the ight is a BET plot fo activated cabon. Regading nitogen adsoption on a sample with micopoes, C is a negative value (indicated in ed) in a elative pessue ange of 0.05 to 0.03, which cannot povide a BET-plot with excellent lineaity. In this case, an accuate specific suface aea cannot be detemined. Howeve, if Type I (ISO977) is selected in [Analysis paametes], BET specific suface aea can be obtained. The specific suface aea obtained fom the BET-plot of this activated BET-plot of active cabon (p/p0= ) BET-plot of active cabon (TypeI, ISO977) 7

73 cabon is 1370 m g -1. The specific suface aea obtained fom t-plot is 1519 m g -1 (p. 80). Since the amount of adsoption on a micopoe suface is lage than that on non-poous suface, the specific suface aea obtained fom t-plot is consideed to be lage than the actual aea. Theefoe, the specific suface aea of this activated cabon is estimated at 1400 to As descibed above, it is difficult to detemine the specific suface aea of micopoes exactly. Howeve, we can obtain a pope value by using both methods of BET-plot and t-plot. 7. Select Analysis paametes fom the Settings menu. The Analysis paametes window shown below will appea. Change the settings as needed. Select whethe o not to calculate the mean poe diamete and mean paticle size. Chapte 14: You must ente a value hee when you want to calculate the mean paticle size. Even when you click on the mean paticle size, the pogam cannot calculate the mean paticle size unless a sample density is enteed. Specify default linea ange. If you don t click on Use pessue ange setting, the analysis stat point and end point will be the default linea ange. Ente a elative pessue to calculate the total poe volume. If the elative pessue at the adsoption end point is lowe than the elative pessue enteed hee, the pogam will calculate the total poe volume fom the adsoption volume at the adsoption end point. Setting ange: to You must ente this value when you want to calculate the total poe volume and mean poe diamete. Even if you don t click on Calculate mean poe diamete, the pogam will not calculate the total poe volume and mean poe diamete unless an adsobent density is enteed. Select this item to execute the 1-point analysis method. Ente elative pessue used fo 1-point analysis method. BET analyaia Select this item fo Type I adsoption isothem (fo a sample with micopoes). 73

74 Chapte 14: Langmui plot Desciption In 1918, Langmui poposed the monolaye adsoption theoy. adsoption isothem on the following assumption. He deived the equation fo the 1. Adsoption sites on adsobent suface have the same adsoption enegy.. One adsoption site is occupied by one adsobed molecule. 3. Thee is no lateal inteaction between adsobed molecules. 4. Adsoption is complete when mono-molecula laye (monolaye) is fomed. N A1 N A N A=N A1+NA Langmui plot N S The Langmui equation is deived accoding to the monolaye adsoption model given below. In the model, the whole adsoption sites, the occupied adsoption sites, and the unoccupied adsoption sites on the adsobent suface ae shown as NS, NA, and (NS NA), espectively. The suface coveage fo the occupied adsoption sites is defined as follows: N N A S The adsoption ate, va is popotional to p (pessue of adsoptive) and v k p(1 ) (14.1) (bae suface); a a (14.) On the othe hand, the desoption ate, vd is popotional to (occupied suface); v d k d (14.3) ka and kd in Equations (14.) and (14.3) ae the popotional constants. Unde the adsoption equilibium, the adsoption ate is equal to that of desoption; k a p( 1 ) k d (14.4) Equation (14.4) is changed into equation (14.5), Bp 1 Bp (14.5) Whee ka kd is shown as B. Futhemoe, equation (14.5) is expessed using the monolaye volume, Vm. The amount of adsobed gas at an abitay pessue is expessed as follows; V a V m (14.6) By putting equation (14.6) into Equation (14.5), we obtain equation (14.7), the Langmui equation. V a VmBp 1 Bp (14.7) If the condition of 1»Bp (low pessue ange) is satisfied, equation (14.7) is tansfomed to equation (14.8); 74

75 V Vm Bp (14.8) Equation (14.8) is called Heny equation, whee the amount of adsobed gas is popotional to the adsoptive pessue. Equation (13.7) can be conveted to equation (14.9). p / Va 1/ BVm p / Vm (14.9) Equation (14.9) is used to analyze the expeimental data. If the adsoption data matches the Langmui model, the Langmui plot (p/va vs. p) gives a linea line with the slope of 1/Vm and the intecept of 1/BVm, fom which the monolaye volume, Vm and the constant, B can be estimated. In ou softwae, the Langmui plot is automatically displayed on the compute sceen. Next, if use selects the stating point and the end point, the monolaye volume (Vm), the Langmui constant (B), and the suface aea (as,lang) can be calculated by means of the least-squae method, and ae displayed. [Notice]: The Langmui equation (14.7), which is deived fom the adsoption model on the nonpoous suface (cf. adsoption model given above), gives the Type I isothem. In the physical adsoption, howeve, the Type I isothem is obtained fo the micopoous adsobents such as active cabons o zeolites. In such micopoous adsobents, the Type I isothem can be explained by filling of the adsobate molecules into micopoes; that is, the initial shap ise of the isothem coesponds to the filling pocess of adsobate into micopoes, and the flat egion of the isothem appeas when the micopoes ae completely filled by adsobate. It is easonable to conclude that the monolaye volume (Vm) of micopoous adsobent obtained fom the Langmui plot coesponds to the micopoe volume. The suface aea of micopoous adsobent estimated fom Vm occasionally gives the abnomally high value. The suface aea of some micopoous active cabon, if it is calculated fom Vm of the Langmui plot, eaches 3,000 m g -1. This value is lage than the maximum suface aea,,630 m g -1, whose value is estimated by assuming that both sides of the gaphite laye in active cabon ae coveed by monolaye of adsobate. Langmui plot «Refeence» I. Langmui, J. Ame. Chem. Soc. 38, 19(1916); 40, 1368(1918). 75

76 14-. Opeation 1. Select Langmui plot fom the Analysis (A) menu and the sceen will show the following Langmui-plot window. The pogam will execute a Langmui plot fom adsoption data of an isothem adsoption.. The pogam automatically daws an staight line. The default selection is the stat point as the minimum data point and the end point as the maximum data point. The pogam obtains the monolaye volume (Vm/c m 3 g -1 ) and the B value fom the slope of the appoximate cuve and intecept. The pogam will also display the coelation coefficient of the appoximate cuve. 3. Select the stating and end points to obtain good lineaity. Langmui plot 4. In a chemical adsoption volume measuement, the chemical adsoption can be obtained fom the monolaye volume (Vm/cm 3 g -1 ). 5. The nitogen adsoption isothem on a sample with micopoes is shown as type I, and gives good lineaity in a Langmui-plot. Howeve, as descibed in the [Desciption], thee is a tendency that the specific aea obtained may be lage than the actual value. The figue above shows a Langmui-plot of micopoous activated cabon. The specific suface aea obtained will be 1,706 mm g -1 and this is lage than the actual value (1,400 to 1,500 m g -1, on page 7). 6. Select Analysis paametes on the Setting menu. The Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1 Analysis paametes, on page 37. Ente a default linea ange. If you do not click on Use pessue ange setting, the analysis stat point and end point will be the default linea ange. The pessue unit can be set to eithe kpa o Too. 76

77 Chapte 15: t plot Desciption Adsoption amount depends on gas pessue, adsoption tempeatue, and popeties of adsoptive gas and adsobent solid. In a nitogen adsoption isothem measuement, tempeatue is constant and gas is limited, thus the isothem changes accoding to the popety of solid. Howeve, in case of non-poous solid, although thee is diffeence in adsoption amount, thee is almost no diffeence in the shape of isothem. In this case, plual isothems can be expessed in one isothem by standadizing adsoption amount. This is the concept of standad isothem. Thee ae many ways of standadization, but the one that was suggested by Shull et al. is fequently used. In this method, adsoption amount is expessed by the thickness of adsoption laye t, and the equation is as follows: Va t 0.354[nm] (15.1) V m nm is the thickness of monomolecula laye. This value is obtained with a hypothesis that nitogen molecules make hexagonal closest packing on adsobent suface; theefoe, it is smalle than the diamete of nitogen molecule. Standad t-cuve can be calculated fom (15.1) conveting adsoption isothem of vetical axis (adsoption amount) to thickness of adsoption laye. t plot The t-plot method, which was invented by Lippens and de Boe, compaes the above-mentioned standad isothem and abitay isothem. Standad isothem shows the elationship between elative pessue and thickness of adsoption laye. Using standad isothem, x-axis of isothem that you wish to analyze can be changed fom elative pessue to thickness of adsoption laye. Obtained t-plot can be divided into 3 types in boad tem (Above diagam). (3 diffeent types of t-plot fom (I) to (III) ae shown above, but this categoization is just fo the matte of convenience, and thee is no type defined by IUPAC like in adsoption isothem.) If t-plot is a linea cuve that passes the oiginal point like (I), it means that adsoption amount inceased at the same ate as standad isothem, and thus the adsobent is consideed to be non-poous mateial. Hee, the inceased adsoption amount when adsoption laye inceases by one laye (t=0.354nm) is equal to 77

78 t plot mono-molecula adsoption amount. Theefoe, specific suface aea as[m g -1 ] can be calculated fom the following equation with the slope of t-plot, s. s a s L s (15.) Hee, L is Avogado constant and σ is coss sectional aea of adsoptive. If t-plot has diffeent slopes like (II) that one of them is a shap slope passing the oiginal point and the othe is moe gadual slope, it means that the adsobent has homogenious sized micopoes. In the ealy stage of adsoption, adsoption amount inceases dastically due to adsoption into micopoes (micopoe filling) but the thickness of adsoption does not incease so much, as the esult, the slope of t-plot becomes shap. When adsoption into micopoes is completed, adsoption happens only on the suface. As a esult, the slope of the cuve becomes gadual. At this point, whole suface aea (a1) can be calculated by applying the slope of the linea cuve L1 to equation (15.1). In the same manne, extenal suface aea (a) can be calculated by applying the slope of the othe cuve L to the equation. Poe suface aea can be calculated by subtacting a fom a1. Poe volume can be obtained by conveting the value of Y intecept of L to a volume unde liquid condition. Futhemoe, adsoption condition is consideed to be like in the figue above at intesecting point of L1 and L. Thus, doubled value of t (value t) is egaded as the aveage poe diamete. Howeve, value t gives wong analysis esults when poe size is only laye o less. When t value is smalle than 0.7nm, as it is micopoe filing you can have ough idea whethe the poes ae big o small but thee is no cedibility in tems of numeical value. If t-plot daws a shap staight line which begins fom the oiginal point but becomes smoothe cuve fom some point like (III), the adsobent is consideed to have mesopoes. The deviation fom the linea cuve is due to capillay condensation. Even in t-plot of this type, whole suface aea can be measued fom linea that passes the oiginal point like in case of (I). Standad isothem was invented oiginally with a pupose to expess all the type II isothems by one convesion isothem. Howeve, as eseach pogessed it was found that one standad isothem was not enough. Theefoe, BEL Japan softwae contains 6 standad isothems (4 of them ae calculated fom adsoption isothem on non-poous mateial, and of them ae fom the liteatue). It is ideally best to poduce standad isothem with non-poous mateial which suface chemical popety is same as the sample to be analyzed. But it is difficult to poduce such standad isothem in a pactical sense. Fo this eason, Bunaue et al. divided the statistical t-cuves into categoies by C-constant of BET method, and suggested that it is bette to select one that has simila C-constant to the isothem of the analyzed sample. C-constant is cetainly a facto that indicates inteaction between adsoptive and adsobent, and it depends on not only by chemical popety but also by poous stuctue. When micopoes exist, C-constant becomes vey lage and standad isothem cannot be selected with this value. BEL Japan ecommends choosing standad isothem of a mateial that has simila to you sample in tems of bulk popety. «Refeence» Studies on Poe Systems in Catalysts V. The t Method, B. C. Lippens and J. H. de Boe, J. Catalysis, 4, 319 (1965). 78

79 15-. Opeation 1. Select t-plot on the Analysis (A) menu and the sceen will show the following t-plot windows. The pogam will execute t -plot calculations fom the adsoption data of a nitogen isothem.. Select Analysis paametes on the Setting menu. The Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. 3) 4) 1) 5) ) 6) t plot 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics to the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a set of standad t-cuve data file and click on [Open]. ) Select which data will be used fo calculation, the adsoption banch o desoption banch. 3) Select an intepolation method fo the file data. - You can set the intepolation method to Linea, Spline o Bezie. 4) If intepolation method is not selected, the pogam will calculate a t-plot at the default setting point. When any method is selected, the pogam will calculate the t-value specified in the table below. 79

80 4) t-data setting. - This table can be edited when you click on Use definition. 5) Edit t-data settings. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten with the value displayed in the box. - Click on the [Add] button the data displayed in the box will be added. - The data that is applied o added ae automatically soted fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. In a t-plot, the pogam will automatically daw two staight lines. The default stating and end points of the 1st line ae the minimum data point (zeo position) and the minimum data +1. The stating and end points of the nd line ae the maximum data point -1 and the maximum data point. 4. The figue on the ight is a t-plot of a nitogen isothem fo macopoous silica. silica-bet.t is used as a standad isothem. When selecting a standad isothem whose chemical chaacteistics ae simila to the sample suface, a good linea t-plot can be obtained that passes though the zeo position. 3 t plot 5. Select a stat point (nomally the zeo position) and an end point fo the fist staight line. Fom the slope of this line, a specific suface aea (a1) 70.1 m g -1 is calculated. This value is a good match fo the 70.0 m g -1 obtained fom the BET plot (page 7). The nd staight line is not needed. Set the the stating and end points as the same point and delete the line. 6. The figue on the ight is a t-plot of a nitogen isothem fo micopoous activated cabon. NGCB-BET.t was specified as the standad isothem Select a stating point (nomally the zeo position) and end point of the fist staight line. The pogam will calculate the specific suface aea (a1) 1,53 m g -1 fom the slope of this staight line. Select the stating and end points of the nd line. Using the slope of this staight line, the extenal suface aea (a) 45 m g -1 can be obtained. The volume (V) of micopoes cm 3 g -1 can be calculated fom the intecept. A micopoe aea of 1,474 m g -1 is obtained fom a1 and a (a1- a). Also, if thee is an appaent deflection by completed filling adsobate into micopoes, the poe diamete (t/nm) can be obtained fom the cossing point of the two staight lines. The poe diamete of activated cabon is 0.75 mm and this value is a good match fo the peak value (0.8 nm 80

81 on page 90) of the poe width obtained fom the MP-plot. 8. The figue on the ight is a t-plot of a nitogen isothem fo mesopoous silica. silica-bet.t is used as a standad isothem. The Use definition was clicked on and the calculation ange was widened to 3 nm Select a stating point (nomally the zeo position) and an end point of the 1st staight line. The pogam will calculate the specific aea (a1) as 189 m g -1 fom the slope of this line. 10. If the adsoption volume is satuated (figue on the ight) in an adsoption/desoption isothem, it may be assumed that the adsobate (nitogen) filling all of the poes is completed. In this case, select stating and end points fo the nd staight line. The extenal suface aea (a) 9 cm 3 g -1 can be obtained fom the slope of this line and the mesopoe volume (V) cm 3 g -1 is calculated fom the intecept. The mesopoe aea can be obtained as 180 m g -1, fom a1-a. 10 t plot 81

82 Chapte 16: s plot Desciption Like t analysis, s method calculates specific suface aea of sample by compaing isothem of standad sample and isothem of the sample. t value, which is calculated fom standad isothem and is used in t method analysis, indicates the thickness of adsoption laye, but the eliability of the numeical value will be lost when t is below 0.7. Va t 0.354[nm] (16.1) V m t value was oiginally invented to calculate the thickness of adsoption laye on the poe wall when poe size distibution is dawn fom IV type isothem. When only compaison with the isothem of standad sample is intended, values of adsoption laye thickness and monolaye capacity Vm ae not necessay. Also, when single molecula laye is not fomed o when BET-plot does not come into effect, monolaye capacity cannot be calculated and it is impossible to use t analysis. In ode to solve the poblem of t method analysis, Sing et al. (1968) suggested αs method, which analysis is caied out by standadization with n0.4 (adsoption amount at elative pessue, p/p0=0.4, of N adsoption isothem at 77K of standad sample) athe than by standadization with t value. 1)) s plot n a s (16.) n 0.4 na indicates adsoption amount at abitay equilibium pessue. The eason that elative pessue fo standadization was set to 0.4 is due to the following easons: 1. Inteaction behavio between adsobent and adsobate appeas on isothem below this elative pessue.. It is theoetically poved that hysteesis closes at p/p0=0.4. The actual analysis pocedue is that s value of standad sample is calculated fom (16.), and thenαs cuve is dawn (=αs against p/p0). The p/p0 value of an isothem can be conveted to αs value by using αs-cuve and αs-plot can be dawn α s -plot Analysis pocess is basically same fo s-plot and t-plot. Like in t-plot, thee ae 3 diffeent types of αs-plot and specific suface aea can be calculated fom the linea cuve slope. The slope of s-plot of standad sample is calculated, which is bα(standad). Also, the slope of the fist linea cuve is calculated fom s-plot of analysis sample, which is bα(test). The atio between the above mentioned bα(standad) and bα(test) is equal to the atio between two specific suface aeas. Theefoe, if standad sample specific suface aea is expessed by as(standad) and sample specific suface aea is expessed by as(test), V a /cm 3 (STP) g -1 α s 8

83 thus b ( test) b ( standad) n 0.4 n0.4( test) ( standad) as ( test) a ( standad) s (16.3) b (test) a s ( test) as (standad) (16.4) b (standad) bα(standad) and as(standad) ae aleady known in this case, thus k as (standad) b (standad) (16.5) a s ( test) b (test) k (16.6) Whole specific suface aea a1 [m g -1 ] of the sample can be calculated with (16.6). Extenal suface aea a [m g -1 ] and poe volume Vp[cm 3 g -1 ] can be calculated fom the slope of the second linea cuve and the intecept espectively. Moeove, intenal suface aea of poe can be calculated by subtacting extenal suface aea a fom Whole specific suface aea a1 (Refe to Chapte 15 t-method analysis). Unlike t method analysis, in αs-analysis, the aveage poe adius cannot be woked out fom the intesecting point of the linea cuves that ae obtained fom the plot. Howeve, it is possible to calculate poe adius by hypothesizing the shape of poe as slit shape o cylinde-shape. e.g.: in case of cylinde-shaped poe (poe adius=, poe length=l) Inside volume of poe(vp)=poe volume Vp=π L [1] Intenal suface aea of poe(ai)=whole suface aea - extenal suface aea ai =a1 a=πl [] Fom [1] and [], poe adius is calculated as follows. V a i p a V 1 p a [3] s plot In t method analysis, it is impossible to evaluate poe size below 3.5nm because thee would be no physical meaning when t value is below 0.35nm. Howeve, thee is no dimension in s-value, thus it is possible to compae adsoption inteaction at low elative pessue. In s-plot, the fist linea cuve can be dawn easily because plot can be obtained even when s-value is small. Also, the fist linea cuve has to pass the oiginal point in t method analysis, but in s-analysis it is possible to select the ange without the fixed oiginal point so that linea cuve can be dawn easily. It is suggested that non-poous mateial that has simila suface to the sample analyzed should be chosen fo the standad isothem (sample fo compaison). BEL Japan analysis softwae contains standad isothems that ae made fom N adsoption on non-poous mateial of SiO, AlO3 and Cabon (Gaphitized Cabon and non Gaphitized Cabon). Select a most suitable standad isothem to you sample. Futhemoe in s-method, thee is an advantage that it can be used with othe adsobate othe than nitogen because it does not need the values of monomolecula laye adsoption amount o adsoption coss-section aea of adsoptive. «Refeence» 1) D.Atkinson, A.I.McLeod, K.S.W.Sing, J.Chim.Phys., 81,791(1984) ) K.S.W.Sing, Cabon, 7,5(1989) 83

84 16-. Opeation 1. Select s plot, on the Analysis (A) menu and the sceen will show the following s plot windows. The pogam will execute an s plot fom adsoption data of an isothem.. Select Analysis paametes on the Setting menu. The Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. ) 3) 1) 4) s plot 5) 1) Select a standad s -cuve. - Select a standad isothem that has simila chemical chaacteistics to the sample suface. - Click on the [Alte] button. The following selection window will appea. Select a standad s -cuve file and click on the [Open] button. ) Select a method fo intepolating the file data. - You can select Linea, Spline o Bezie. 3) If Use defintion is not clicked, the pogam will calculate an s -plot at the default setting point. When you click on Use definition, the pogam will calculate the s value specified in the table below. 4) s setting - When Use definition is selected, this table can be edited. 5) Edit the s setting. - Click on the [Apply] button. The selected cell (yellow) data will be ovewitten by the value displayed in the 84

85 box. - Click on the [Add] button. The data displayed in the box will be added. - The modified and added data ae soted automatically in top to bottom ode. - Click on the [Delete] button and the selected data will be deleted. 3. In an s -plot, the pogam automatically daws two staight lines. As a default, the stating and end points of the 1st line ae the zeo position and the fist point, and the stating and end points of the nd line ae the maximum data point -1 and the maximum data point. 4. The figue on the ight is an s -plot of a nitogen adsoption isothem fo macopoous silica. SiO.as is used as a standad isothem. When selecting a standad isothem whose chemical chaacteistics ae simila to the sample suface, good lineaity can be obtained as the s -plot passes though the zeo position Select a stating point (nomally the zeo position) and end point of the fist staight line. The specific aea (a1) 7.3 m g -1 is calculated fom the slope of this line. The nd staight line is not needed. Use the same point as both the stating and end points and delete the staight line. 6. The figue on the ight is an s -plot of a nitogen adsoption isothem fo micopoous activated cabon. NGCB-BEL.as is specified as the standad isothem. Select a stating point (nomally the zeo position) and end point of fist the staight line. Fom the slope of this staight line, the pogam will calculate the specific aea (a1) 1,564 m g -1. Select the stating and end points of the nd line. The extenal suface aea (a) 41 m g -1 can be obtained using the slope of this staight line. The volume (V) of the micopoes 0.56 cm 3 g -1 can be calculated fom the intecept. The poe aea of the micopoes is obtained as 1,53 m g -1, fom (a1 - a). 7. The figue on the ight is an s -plot of nitogen adsoption isothem fo mesopoous silica. silica-bel.as is used as a standad isothem. Select a stating point (nomally the zeo position) and an end point fo the 1st staight line. The pogam will calculate the specific aea (a1) 191 m g -1 fom the slope of this line. 7 6 s plot 85

86 8. In an adsoption/desoption isothem, if the adsoption volume is satuated (figue on the ight), it may be assumed that the adsobent (nitogen) has filled all the poes. 9. Select the stating and end points of the nd staight line. Fom the slope of this line, the extenal suface aea (a) 8. m g -1 can be obtained. The mesopoe volume (V) 0.96 cm 3 g -1 is calculated fom the intecept. The aea of the mesopoes can be obtained as 18 m g -1, fom (a1 - a). 8 s plot 86

87 Chapte 17: MP method analysis Desciption In case of samples with micopoes, the slope of t-plot deceases at a cetain point (efe to Chapte 15 t- method analysis). If the size of micopoes is homogenous, the plot will be on eithe of the two lines. In othe wods, the staight line fom the oigin should be bent shaply at the point when filling into micopoes is complete. Howeve, plots have cuvatue. This means that thee is distibution in poe size. In shot, MP method measues distibution fom the cuvatue of t-plot. In ode to pefom MP method analysis, t-plot has to be poduced fist. The slope (s) of the linea cuve (L), which connects the 1st point and the nd point, is smalle than the slope (s1) of the linea cuve (L1), which connects oiginal point and the 1st point. This is because poes ae filled with adsobate. The suface aea of poe can be expessed by the diffeence between a1 and a, which ae both calculated by multiplying each slope by Poe volume V1 [ml g-1] can be calculated by multiplying a1 by thickness of adsoption laye. Thickness of adsoption laye used in this method is the aveage value of the thickness of 1st and nd laye (t1 and t espectively), so the following equation can be made. 3 V 1 ( a1 a ) ( t1 t) / 10 (17.1) Distibution cuve can be obtained by caying out the same calculation until the end point of t-plot and then plotting the obtained poe volume against the thickness of adsoption laye (aveage value). a1 in MP method is the suface aea that is calculated fom linea cuve that passes the oiginal point, and a is the one that is calculated fom the othe linea cuve. Vp is an integated value of poe volume, which can be obtained in (17.1). Although dpeak is the peak position it is not suitable fo MP method analysis when dpeak is below 0.7 nm, due to the same eason fo the fact that aveage poe diamete is not accuate unless o moe adsoption layes ae fomed in poes. MP plot «Refeence» Investigations of a Complete Poe Stuctue Analysis I. Analysis of Micostuctue, R. Sh. Mikhail, Stephen Bunaue, and E. E. Bodo, J. Colloid Inteface Sci., 6, 45 (1968). 87

88 17-. Opeation 1. Select MP plot on the Analysis (A) menu. The sceen will show the following MP plot windows. The pogam will execute an MP plot fom adsoption data of a nitogen isothem.. Select Analysis paametes in the Setting menu. The Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. ) 3) 1) 4) 5) MP plot 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics to the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a standad t-cuve data file and click on the [Open] button. ) Select an intepolation method fo the file data. - You can select Linea, Spline o Bezie. 3) If Poe diamete ange of the use setting is not selected, the pogam will calculate using the default ange. When Poe diamete ange of the use setting is selected, the pogam will calculate the poe diamete ange specified in the table below. 4) If Use definition is not selected, the pogam will calculate a t-plot using the default setting point. When Use definition is selected, the pogam will calculate the t value specified in the table below. t value settings - When the Use definition is selected, this table can be edited. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten by the value displayed in the box. 88

89 - Click on the [Add] button and the data displayed in the box will be added. - The modified and added data ae automatically soted in ode fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. The figue on the ight is an MP-plot of a nitogen adsoption measuement on micopoous activated cabon. NGCB-BEL.t is used as a standad isothem. 4. When you want to smooth the lines, select Smoothing settings on the Settings menu. The Smoothing settings window shown on the ight will appea. 5. The figue on the ight shows the esult of clicking on the [Aveage Spline Execute] button to pefom one ound of smoothing. It can be seen fom the figue that this activated cabon sample has micopoes of 0.4 to 1.1 nm diamete (dp), and has a distibution peak (dp,peak/nm) at 0.8 nm. Fom the slope of the 1st staight line that passes the t-plot zeo position, the pogam will calculate the total specific suface aea (a1/m g -1 ). Fom the slope of the last staight line, the pogam will calculate the extenal specific suface aea (a/m g -1 ). Futhe, by multiplying the poduct of the suface aea at each point by the thickness of the adsoption laye, the poe volume (Vp/cm 3 g -1 ) can be obtained. Since the MP-plot is an analysis method deived fom a t-plot, the esults of the MP-plot closely esemble those fom a t-plot (page 80). MP plot 6. The MP-plot is geatly influenced by the diffeence in chemical chaacteistics between a sample suface and a standad mateial, and by the micopoe filling effect, so it will not poduce a smooth cuve. Howeve, the MP-plot is useful fo detemining the existence o absence of micopoes and thei ange of size. Please note that even when thee ae no micopoes, the MP-plot will analyze a sample as though thee is a peak micopoe aea. 89

90 Chapte 18: BJH plot Desciption In type IV adsoption isothems, hysteesis occus in adsoption and desoption pocesses. The hysteesis shape depends on the shape of mesopoe. Wheneve hysteesis exists, equilibium adsoption amount at desoption is lage than the one at adsoption. This is because capillay condensation of nitogen gas happens in mesopoe and thee is diffeence in meniscus between in adsoption pocess and in desoption pocess. Thee is an equation which epesents the elationship between mesopoe size and citical condensation pessue, Kelvin equation, and some analysis using Kelvin equation to calculate poe size distibution have been epoted. Some of these methods ae based on the assumption that the mesopoes have cylinde shape (Dollimoe & Heal method, Canston & Inkley method and etc. ). Poe size distibution is calculatied fom desoption isothem. In 1951, Baett, Joyne and Halenda poposed a method to evaluate poe size distibution. Poe cuve is expessed as pecentage change of poe volume(δvp/ Δp) against micopoe adius(p). BJH plot In the aea whee capillay condensation is in pesence, adius of cyinde shaped poe is sum of the thickness of adsoption laye at the abitay pessue (t) and coe adius ( k ) of meniscus pat. t (18.1) p k Thickness of adsoption laye can be calculated fom t cuve of standad sample, and coe adius can be calculated by Kelvin equation (18.). ln p p VL 1 0 RT m (18.) Hee, m is meniscus adius, γ is suface tension, VL is mola volume of liquid adsoptive, R is gas constant and T is absolute tempeatue. In mesopoe with cyinde shape, suppose menisucus adius at desoption is equal to coe adius (k), and if γ and VL of nitogen at liquid nitogen tempeatue (77 K) ae applied, the following equation can be obtained. m 0.953/ ln( p0 / p) (18.3) In vey fine poes, having widths of the ode of a few molecula diametes, the Kelvin equation could no longe emain sticty valid. Analytical methods based on the equation give a substantial magin of eo when it is applied to calculation fo poes below nm. 90

91 BJH plot Conside a system of open ended cylindical poes. Assume that the elative pessue (p/p0)1, slightly lowe than satuation vapo pessue and at the pessue all poes ae filled with liquid. As the pessue deceases, desoption occues. When the pessue is educed fom (p/p0)1 to (p/p0), a cetain amount of gas, ΔV1 is desobed. The eduction in elative pessue esult not only in emptying the lagest poe of its capillay condensate, but also in a eduction in thickness of the physically adsobed laye by the amout t1. ΔV1 and Vp1, the volume of poes which has the lagest poe adius p1 ae expessed as follows: V1 ( k t1) L 1 1 (18.4) V p 1 p1l1 (18.5) whee L1 is the total length of fist poe (poe adius : p1). Thus Vp1 can be expessed as follows: V p R (18.6) whee R 1 V p /( t1) 1 k1. When the pessue (p/p0) is loweed to (p/p0)3, ΔV of gas is desobed. ΔV is not only that which comes fom the second poe (poe adius: p) but also includes that fom a second thinning of the physically adsobed laye left behind in the fist laye. If the volume which is eleased by this thinning is designated as V t then: V R V V ) (18.7) whee R p ( t p /( t ) k V. Inspection of the figue above shows that L1 ( t1 t ) L1 ( t1) k1 k 1 t (18.8) 91

92 n p c n-1 Δ Analysis of measued data BJH plot Equation (18.8) is simple but in case that a geate numbe of poes ae involved, such a calculation would become impactical. An altenative expession fo VΔt is: V t t Ac1 (18.9) whee Ac1 is aveage aea fom which the physically adsobed gas is desobed. Equation (18.9) can be genealized to expess VΔtn when the pessue is loweed to (p/p0)n as follows: n 1 V t tn A n c (18.10) j j 1 Genealizing equation (18.7) and substituting (18.10) fo VΔtn yields: n 1 V P Rn Vn Rn t n n Ac (18.11) j j 1 (18.11) is complicated to cay out poe size distibution because Ac vaies stepwise with each successive decease in p/p0. On the othe hand Ap, the aea of each poe, is a constant which can be calculated fom its volume by the elationship Ap=Vp/p. It is obvious that using Ap fo calculation is moe pactical. Figue left epesents Δtn, change in thickness of the physically adsopbed laye of a peviously emptied poe of adius p duing the nth desoption step. In a desoption step, capialy adius changes fom n-1 to n. The aveage value of n-1 and n is c. Although Ac in equation (18.11) vaies actually befoe and afte a desoption step, it can be epesented using Ac Ap ( c / p ) as follows: (18.1) Also c can be descibed as follows: c p t (18.13) whee t is the thickness of physically adsobed laye at the coesponding value of (p/p0). Equation (18.11) can be ewitten as: n 1 V p Rn Vn Rn t n n c j Ap j (18.14) j 1 whee c / R n ( p t ) p (18.15) p /( k t ) n n 1 n (18.16) c is a atio of lateal aea of two cylindes, one of which has a adius of c and anothe has a adius of Even in the same poe, c value vaies accoding to thickness of the physically adsobed laye, i.e. c depends on the pessue. But in the oiginal pape, they insisted that thee was no big deal of eo if c was teated as a constant. Then they deived equation (18.17) fom equation (18.14). n 1 V pn Rn Vn Rn tnc Apj (18.17) j 1 They ecommended using 0.75, 0.8, 0.85, 0.9 as c value to make calculation simple in thei oiginal pape. And they also ecommended that c value should be selected accoding to a peak position of poe size distibution cuve. Nowadays computes have developed and we can use equation (18.14) fo poe size calculation without detemining c value, which makes the calculation moe accuate. Poe adius can be obtained fom equation (18.1), poe volume can be calculated fom equation (18.14) o (18.17). Poe size distibution cuve can be yieleded by plotting ΔV/Δ against poe adius. By summing poe volume vaiation c p. 9

93 and plotting them against poe adius, cumulative poe volume cuve can be obtained. «Refeence» The Detemination of Poe Volume and Aea Distibutions in Poous Substances. I. Computations fom Nitogen Isothems, Elliott P. Baett, Leslie G. Joyne and Paul P. Halenda, J. Ame. Chem. Soc., 73, 373 (1951). BJH plot 93

94 18-. Opeation 1. Select BJH plot on the Analysis (A) menu and the sceen will show the following BJH plot window. The pogam will execute a BJH plot fom adsoption o desoption data of a nitogen adsoption isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. 4) 5) 1) 6) ) 3) BJH plot 7) 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics to the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a standad t-cuve data file and click on the [Open] button. ) Select which data will be used fo calculation, the adsoption banch o desoption banch. - Most poous samples have a poe size distibution. It is believed that distibution of poe size in these samples can be obtained fom the adsoption pocess, and the distibution of the bottle neck can be obtained fom the desoption pocess. 3) Select a calculation method fo the C value. - Nomally, select Auto Calculation. Any fixed value can be selected fom 0.7, 0.75, 0.8, 0.85, o

95 4) Select a method fo intepolating the file data. - You can select Linea, Spline o Bezie. - If you want to execute an intepolation with the same intepolation method in an adsoption/desoption isothem, you can check whethe the intepolation method is appopiate. 5) If Poe diamete ange of the use setting is not selected, the pogam will calculate using the default ange. When Poe diamete ange of the use setting is selected, the pogam will calculate the poe diamete ange specified in the table below. 6) If Use definition is not selected, the pogam will calculate the plots with the elative pessue data below. When Use definition is selected, the pogam will stat calculating based on the default settings of elative pessue. 7) Relative pessue settings - When the Use definition is selected, this table can be edited. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten by the value displayed in the box. - Click on the [Add] button and the data displayed in the box will be added. - The modified and added data ae automatically soted in ode fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. The figue on the ight is a BJH-plot (diffeential cuve) of a nitogen adsoption isothem fo mesopoous silica. silica-bel.t is used as a standad isothem. BJH plot 4. When you want to smooth the data, select Smoothing settings on the Setting menu. The Smoothing settings window shown on the ight will appea. 5. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of to 15 nm adius, and it has a distibution peak at 8.0 nm. The integated poe volume (Vp) will be cm 3 g

96 6. Fo this silica, select the desoption pocess on the Analysis paametes window. The figue on the ight shows a esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of 3 to 9 nm adius at its neck, and has a distibution peak at 5.3 nm. 7. In a BJH plot, the Y axis units can be set to dvp/dp, dvp/dlog p, o Vp in Y axis display settings on the Settings (S) menu. Integated gaphs (integal cuve) ae shown fom a lage poe size. - dvp/dp ---is the aea distibution. - dvp/dlog p --- is the volume distibution. Distibution of lage diamete ae bolded. - Vp --- is an integal cuve. BJH plot 8. The figue on the ight is a BJH plot (integal cuve) of the silica descibed befoe calculated fom adsoption banch of its isothem. 96

97 Chapte 19: CI plot Desciption CI method is the way to calculate poe size distibution using Kelvin equation like BJH method. Canston and Inkley poposed this method in They insisted that thei method was supeio to BJH method in some aspects below: 1) CI method is moe exact than BJH method. ) CI method can be applied eithe adsoption o desoption banch. 3) Compaing suface aea fom CI method and fom BET method povides a measue of the validity of physical assumptions. It is assumed that poes ae cylindical in shape with one end closed. Although the adsoption banch is adopted fo deivation as follows, it does not mean that this method cannot be applied to the desoption banch. At a elative pessue p, all poes which adius is smalle than ae filled with adsobate and poes with adii lage than contain adsobed laye and of thickness t. Let Vδ be the volume of poes having adii between and δ, whee δ is vey small campaed with. Conside an adsoption step fom a elative pessue p to p+δ. Due to this pessue incease, capillay condensation occus in the poes with adii fom to +δ. At the same time the thickness of adsobed laye inceases fom t to t+δt in the poes with adii lage than +δ. As a esult adsobed amount inceases by v : v ( t ) V t t V d (19.1) The fist tem of the ight-hand side epesents the volume of nitogen which has gone to fill poes, while the second tem epesents the volume of nitogen which has contibuted to inceasing the thickness of the adsobed laye. In the limiting case, whee δ tends to zeo, equation (19.1) can be ewitten as follows. v d ( t ) V d dt V ( t ) d (19.) CI plot Conside a finite adsoption step fom p1 to p. With the change in pessue, citical adius vaies fom 1 to and the adsobed laye thickness vaies fom t1 to t. v 1, the inceased amount adsobed in this adsoption step, can be expessed as follows: v 1 v d 1 1 ( t ) V d 1 ( t t ) 1 V ( t 1 t ) d (19.3) Assuming V is sensibly constant ove the ange 1 to. This assumption is valid when the diffeence between 1 and is enough small. (19.3) can be conveted into (19.4). v 1 V ( t ) 1 1 d ( t t1) 1 1 V ( t 1 t ) d (19.4) whee V1 is the volume of poes with adii between 1 and. To calculate poe volume, (19.4) is tansfomed as follows: t1 V 1 R1 v1 k V d (19.5) 1 97

98 whee 1 R 1 (19.6) ( t1) / d 1 k 1 4( t t1) (19.7) t t 1 t 1 (19.8) The integal tem in equation (19.5) is eplaced by a summation tem. V 1 R 1 v 1 k 1 max 1 Equation (19.10) can be deived by eplacing poe adius in equation (19.9) to poe diamete. V 1 R 1 v 1 k 1 d max 1 d d t d 1 d V t 1 V d (19.9) (19.10) Canston et al. made a table fo R1 and k1 fom isothems on 15 nonpoous mateials pio to poe size distibution. Also they made a table fo ( d t1 ) / d to simplify the calculation. Recently compute has developed. Calculating ( d t1 ) / d value against each poe size is not so had and the calculation esult is moe accuate. In ou softwae, calcuation is caied out as such. CI plot «Refeence» The Detemination of Poe Stuctues fom Nitogen Adsoption Isothems, R. W. Canston and F. A. Inkley, Advan. Catalysis, 9, 143 (1957). 98

99 19-. Opeation 1. Select CI plot on the Analysis (A) menu and the sceen will show the following CI plot windows. The pogam will execute a CI plot fom adsoption o desoption data of a nitogen adsoption isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. 3) 1) 4) 5) ) 6) 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics to the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a standad t-cuve data file and click on the [Open] button. CI plot ) Select which data will be used fo calculations, the adsoption side o desoption side. - Most mesopoe samples have a distibution of poe sizes. In these samples, it is assumed that poe size distibution can be obtained fom the adsoption pocess, and the distibution of the bottle neck can be obtained fom the desoption pocess. 3) Select a method fo intepolating the file data. - You can select Linea, Spline o Bezie. - In an adsoption/disoption isothem, if you want to execute an intepolation using the same intepolation method, you can check whethe the intepolation method is appopiate. 4) If Poe diamete ange of the use setting is not selected, the pogam will calculate using the default ange. When Poe diamete ange of the use setting is selected, the pogam will calculate the poe diamete ange 99

100 specified in the table below. 5) If Use definition is not selected, the pogam will calculate the plots with the elative pessue data below. When Use definition is selected, the pogam will stat calculating based on the default settings of elative pessue. 6) Relative pessue settings. - When the Use definition is selected, this table can be edited. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten by the value displayed in the box. - Click on the [Add] button and the data displayed in the box will be added. - The modified and added data ae automatically soted in ode fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. The figue on the ight is a CI-plot (diffeential cuve) of a nitogen adsoption isothem fo mesopoous silica. silica-bel.t is used as a standad isothem. CI plot 4. When you want to smooth the data, select Smoothing settings on the Settings menu. The Smoothing settings window shown on the ight will appea. 5. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of to 15 nm adius, and has a distibution peak at 8.0 nm. The integated poe volume (Vp) will be cm 3 g -1 and the integated poe aea (ap) is 33 m g

101 6. Select the desoption pocess to use fo this silica sample on the CI-plot setting window. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of 3 to 9 nm adius, and has a distibution peak at 5.3 nm. 7. In a CI plot, the Y axis units can be set to dvp/dp, dvp/dlog p, o Vp in Y axis display settings on the Setting(S) menu. Integated gaphs (integal cuve) ae shown fom a lage poe size. - dvp/dp ---is the aea distibution. - dvp/dlog p --- is the volume distibution. Distibution of lage diamete ae bolded. - Vp --- is an integal cuve. DH plot 8. The figue on the ight is a CI plot (integal cuve) of the silica descibed befoe calculated fom adsoption banch of its isothem. 101

102 Chapte 0: DH plot 0-1. Desciption DH-method is based on Kelvin equation and used to calculate poe size distibution like BJH and CI method. Dollimoe and Heal poposed this method in Complex assumptions ae not equied and calculations ae simple. Assume that poes ae cyindical in shape with one ends closed. As the pessue is loweed stepwise fom satuation pessue, desoption occus. Let the citical adius when the nth step of desoption occus,. Total volume of poes which ae still filled with adsobate afte the nth step of desoption, V ], pn can be descibed as follows: pn p n p p p [ p n V[ ] L( ) d (0.1) 0 Also the length and the suface aea of poes which ae emptied befoe the nth step of desoption, ] L can be expessed as follows: A [ p and [ ] n p n A [ p ] p L( p ) d n p (0.) p n CI plot L ) [ p ] L( n p dp (0.3) p n whee L ( p ) expesses the length of poes which has adius of p. It is a continuous function of V n, the amount desobed by the nth step of desoption is: V c Vn Vm (0.4) whee V c is the sum of capillay desoption and V m is the total of multilaye desoption. At this time, the volume of adsobate in a poe of adius ) can be epesented as follows: p p ( p n n [ ( t ) ] L( ) ( t t ) L( ) (0.5) p n p p n whee tn is the thickness of multilaye fo the step n. The total multilaye adsoption in all poes o adii fom to can be calculated by integation of (0.5) and the esult can be ewitten by using (0.) and (0.3) pn p p. as follows. V m pn ( p n t n ) L( p ) d p t n n pn t A[ L( p p n ] p ) d t p n L[ t n p n ] pn L( p n ) d p (0.6) By diffeentiating (0.6) with espect to tn, equation (0.7) can be obtained and the volume change on nth desoption step, V, can be calculated fom the eauation. Changing to m dv dt A ] t dt L[ ] (0.7) m n [ pn n n pn tems fo finite steps: V t A ] t t L[ ] (0.8) m n [ pn n n pn 10

103 A [ p ], [ ] n p n L may be put in finite tems also, as the summations of length and aea of poes involved in pevious steps: V t A t t L (0.9) m n Fom equation (19.4) and (19.8), equation (19.10) can be obtained. c n p n p n n n p V V t A t t L (0.10) By using equation (19.10), the change of poe volume whee R V p [ R p n /( V [ /( t)] k c t)] V c n p V p can be calculated fom V c. (0.11) n p k (0.1) Thus equation (19.10) can be ewitten as follows: V p Rn ( Vn tn Ap t n tn Lp ) (0.13) The inceasing suface aea of poes when desoption occues, Ap can be obtained by next equation. A V / (0.14) And p p p L p, the length of the poes can be epesented as follows: L A / (0.15) p p p These two tems ae summed line by line poe size distibution can be obtained by using equation (0.13). «Refeence» D. Dollimoe and G. R. Heal, J. Applied Chem. 14, 109 (1964); J. Colloid Intefasce Sci. 33, 508 (1970). DH plot 103

104 0-. Opeation 1. Select DH plot on the Analysis (A) menu and the sceen will show the following DH plot windows. The pogam will execute a DH plot fom adsoption o desoption data of a nitogen adsoption isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. 3) 1) 4) 5) ) DH plot 6) 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics as the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a standad t-cuve data file and click on the [Open] button. ) Select which data will be used fo calculations, the adsoption side o desoption side. - Most mesopoe samples have a distibution of poe sizes. In these samples, it is assumed that poe size distibution can be obtained fom the adsoption pocess, and the distibution of the bottle neck can be obtained fom the desoption pocess. 3) Select a method fo intepolating the file data. - You can select Linea, Spline o Bezie. - In an adsoption/disoption isothem, if you want to execute an intepolation using the same intepolation 104

105 method, you can check whethe the intepolation method is appopiate. 4) If Poe diamete ange of the use setting is not selected, the pogam will calculate using the default ange. When Poe diamete ange of the use setting is selected, the pogam will calculate the poe diamete ange specified in the table below. 5) If Use definition is not selected, the pogam will calculate the plots with the elative pessue data below. When Use definition is selected, the pogam will stat calculating based on the default settings of elative pessue. 6) Relative pessue settings. - When the Use definition is selected, this table can be edited. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten by the value displayed in the box. - Click on the [Add] button and the data displayed in the box will be added. - The modified and added data ae automatically soted in ode fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. The figue on the ight is a DH-plot (diffeential cuve) of a nitogen adsoption measuement on mesopoous silica. silica-bel.t is used as a standad isothem. DH plot 4. When you want to smooth the data, select Smoothing settings on the Settings menu. The Smoothing settings window shown on the ight will appea. 5. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of to 15 nm adius, and has a distibution peak at 8.0 nm. The integated poe volume (Vp) will be 1.07 cm 3 g -1 and the integated poe aea (Ap) is 340 m g

106 6. Select the desoption pocess fo this silica sample in the DH-plot setting window. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of 3 to 9 nm adius, and has a distibution peak at 5.3 nm. 7. The Y axis units in a DH plot can be set to dvp/dp, dvp/dlog p o Vp on Y axis display settings in the Setting (S) menu. The integated gaphs (integal cuve) ae shown fom a lage poe size. - dvp/dp ---is the aea distibution. - dvp/dlog p --- is the volume distibution. Distibution of lage diamete ae bolded. - Vp --- is an integal cuve. DH plot 8. The figue on the ight is a DH plot (integal cuve) of the silica descibed befoe calculated fom adsoption banch of its isothem. 106

107 Chapte 1: INNES plot 1-1. Desciption To calculate poe distibution fo mesopoes (poe width: to 50 nm) by using nitogen adsoption isothems, you must select the poe shape. At fist, geneally classify the shape of mesopoes into slit shape and othe shapes (such as cylindical, ink bottle-shaped). Fo analysis of slit-shaped mesopoes, capillay condensation will not occu in adsoption banches of adsoption isothems. When t-plotting is executed fo an adsoption banch, a staight line passing though the oigin is obtained in a ange of t = 0 to 1.0 nm. adsoption pocess dx t no capillay condensation desoption pocess t dx dx-t INNES plot On the othe hand, fo analysis of mesopoes of othe than slit shape (cylindical mesopoes, ink-bottle mesopoes, etc.), capillay condensation occus in adsoption banches of adsoption isothems. When t-plotting is executed fo an adsoption banch, a staight line passing though the oigin is obtained in a ange of t = 0 to 0.5 nm. Howeve, uppe deviation attibutable to capillay condensation is obseved in a ange of t = 0.5 nm o moe. Theefoe, t-plotting is effective in diffeentiation of mesopoe shapes. When the width of slit-shaped mesopoes is indicated as dx, and the thickness of adsoption laye is indicated as t, the meniscus geneated in slit-shaped mesopoes is hemicylindical shape. Kelvin equation fo hemicylindical meniscus is given as (1): ln p γvl 1 - p0 RT (dx - t) (1-1) Now, we will compae the Kelvin equation fo slit-shaped mesopoes with that fo cylindical mesopoes. Shape of meniscus geneated in cylindical mesopoes is hemispheical. Kelvin equation fo hemispheical meniscus is given as (): ln p p γv 1 - (1-) L RT 0 K In compaison between equations (1-1) and (1-), we can see that K (Kelvin adius) fo cylindical mesopoes coesponds to ( dx - t) in the equation fo slit-shaped mesopoes. Befoe calculation of mesopoe distibution, substitute the following values into equation (1-1). 107

108 Substitute γ = 8.85 x 10-3 N m -1, V L = cm 3 mol -1, T = K and R = J mol -1 K -1 into equation (1-1). Then, equation (1-3) is obtained ( dx - t) nm (1-3) log 10 (p/p0 ) Regading the slit-shaped mesopoe as a paallel plate mode, the following equation is established. X V At (1-4) X = Amount (cm 3 g -1 ) of nitogen (adsoptive) adsobed in liquid state V =Volume (cm 3 g -1 ) of nitogen in liquid state when slit-shaped mesopoe is fully filled A = Suface aea (m g -1 ) of slip-shaped mesopoe when the poe is not fully filled INNES plot In consideation of the change in amount of adsoption (X) and mesopoe volume (V), the amount of change can be expessed with the following equation, by using an aveage value (Aave) of suface aea (A) and an aveage value (tave) of adsoptive thickness (t). X ( i) V( i) A( i) t ave ( i) t( i) ave A( i) (1-5) V can be expessed with the following equation, by using an aveage value (dave) of the slit diamete. ( i) d ( i) ave A ( i) V (1-6) Substitute equation (1-6) into equation (1-5). Then, the following equation is established. ( i) ave X ( i) V( i) A( i) t ave ( i) V( i) (1-7) d ( i) ave Tansfom equation (7) to make equation (8). t d ( i ) ave V ( X A t ) (1-8) ( i ) ( i ) ( i ) ave ( i ) d t ( i ) ave ( i ) ave It is consideed that the adsoptive is satuated in slit-shaped mesopoes aound high elative pessue. Theefoe, equations V(0) = X(0) and A = 0, and the equation (1-9) ae established. Thus, ΔV can be obtained in each step: A ave A A (1-9) ( i 1) ( i) ( i 1) Fom the above equation, ΔA can be appoximately expessed with the equation below. ( i) d X ( i) ( i) ave V X ( i 1) A (1-10) Ceate a poe distibution cuve by using dx obtained with equation (1-3), and ΔV obtained with equation (1-8). ( i 1) «Refeence» F. Rouqueol, J. Rouqueol & K. Sing Adsoption by powdes & poous solids (Academic Pess, 1999), 440 W. B. INNES Analytical Chemisty, 9, 1069 (1957). 108

109 1-. Opeation 1. Select INNES method on the Analysis (A) menu and the sceen will show the followimg INNES-plot windows. The pogam will execute a INNES plot fom adsoption o desoption of a nitogen adsoption isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed hee, see section 7-1 Analysis paametes on page 37. 3) 1) 4) 5) ) 6) 1) Select a standad t-cuve. - Select a standad isothem that has simila chemical chaacteistics as the sample suface. - Click on the [Alte] button and the following selection window will appea. Select a standad t-cuve data file and click on the [Open] button. INNES plot ) Select which data will be used fo calculations, the adsoption side o desoption side. - To calculate poe distibution fo slit-shaped mesopoes, use desoption isothem. Fo poe distibution calculation, do not use adsoption isothem, because capillay condensation is not obseved in adsoption isothem. 3) Select a method fo intepolating the file data. - You can select Linea, Spline o Bezie. - In an adsoption/disoption isothem, if you want to execute an intepolation using the same intepolation 109

110 method, you can check whethe the intepolation method is appopiate. 4) If Poe diamete ange of the use setting is not selected, the pogam will calculate using the default ange. When Poe diamete ange of the use setting is selected, the pogam will calculate the poe diamete ange specified in the table below. 5) If Use definition is not selected, the pogam will calculate the plots with the elative pessue data below. When Use definition is selected, the pogam will stat calculating based on the default settings of elative pessue. 6) Relative pessue settings. - When the Use definition is selected, this table can be edited. - Click on the [Apply] button and the selected cell (yellow ) data will be ovewitten by the value displayed in the box. - Click on the [Add] button and the data displayed in the box will be added. - The modified and added data ae automatically soted in ode fom top to bottom. - Click on the [Delete] button and the selected data will be deleted. 3. The figue on the ight shows an INNES-plot cuve (diffeential cuve) obtained with measuement (desoption pocess) of nitogen adsoption into a clay mineal with slit-shaped poes. alumina-bel.t is specified as a standad isothem. INNES plot 4. When you want to smooth the data, select Smoothing settings on the Settings menu. The Smoothing settings shown on the ight will appea. 5. Select the desoption pocess fo this clay mineal sample in the INNES-plot setting window. The figue on the ight shows the esult of clicking the [Aveage Spline Execute] button to pefom one ound of smoothing. Fom the figue, it can be seen that this silica sample has mesopoes of to 15 nm adius, and has a distibution peak at.5 nm. The integated poe volume (Vp) is cm 3 g -1, and the integated poe aea (Ap) is 33. m g

111 6. The Y axis units in an INNES plot can be set to dvp/dp, dvp/dlog p o Vp on Y axis display settings in the Setting (S) menu. The integated gaphs (integal cuve) ae shown fom a lage poe size. - dvp/dp ---is the aea distibution. - dvp/dlog p --- is the volume distibution. Distibution of lage diamete ae bolded. - Vp --- is an integal cuve INNES plot 111

112 Chapte : DA plot -1. Desciption In 1960, Dubinin and Radushkevich intoduced DA equation that they deived fom adsoption potential theoy of Polanyi. Polanyi hypothesized that pessue of adsoptive when it is adsobed is equal to the satuated vapo pessue p0 of its gas. Expessing pessue of adsoptive(adsoption molecule that is not adsobed) as p, wok of tansfeing 1 mol of gas fom gas phase to adsoption laye ε can be expessed as the following. RT ln p 0 / p (.1) Polanyi defined ε as adsoption potential. ε can be eplaced by Gibbs fee enegy change ΔG at adsoption. G (.) Dubinin thought that adsoption into poes pogesses by volume filling but not building up adsoption laye one by one. Then he defines the filling facto by the following equation. V / V p (.3) DA plot Vp indicates whole micopoe volume, V means poe volume at elative pessue p/p0. function of elative pessue thus the function of ε fom (.1). f / (.4) is also the β is a specific constant numbe fo adsobate and is called affinity coefficient. With a hypothesis that poe makes Gaussian distibution, the following equation is obtained. exp k (.5) k is a constant numbe that depends on poe stuctue. The following equation is obtained fom (.3), (.4) and (.5). k V V p exp RT ln p 0 / p (.6) o, V V p T exp B log10 p0 / p (.7) whee b is a constant epesented by equation (.8). B.303R / k (.8) (.7) can be coveted to log10 V log10 V p C log10 ( p0 / p) (.9) whee T C B (.10) (.6), (.7) and (.9) ae called DR equation. If you convet adsoption amount to V using adsobate density at its liquid condition, and then plot log 10V against log10 ( p 0 / p) (DR-plot), you wil get a linea cuve with the intecept log and the slope C. Vp is whole micopoe volume. 10Vp In 1971, Dubinin and Astakov extended the concept of DR equation and made it moe common fom. 11

113 The deived equation is called DA equation expessed as follows. n RT n exp ln p / p (.11) 0 o, n log V log V C'log ( p / p ) p (.1) whee C can be given by equation (.13). n n 1 RT C'.303 (.13) In the same manne as DR-plot, Vp is calculated fom the linea slope value that is obtained by plotting n log against log ( p / p). n is a small integal numbe (nomally 1~3). Kawazoe et al. categoized 10 0 V 10 adsobate molecule diametes expessing adsobate molecule diamete as d and poe size as D like the following table. Applying m= to DA equation, it becomes DR equation. Adsoption site Ratio n Suface D/d > 5 1 Micopoe 5 > D/d > 3 Ultamicopoe 3 > D/d 3 DA method is often used fo calculation of poe volume. If plots make linea cuve, it means it matches the theoy. Depending on the index numbe n the plot becomes convex o concave cuve. Index numbe that makes best lineaity should be selected. Thee is a method that select positive numbe so that lineaity becomes good since thee is an idea that Index numbe n of DA method does not have to be limited to integal numbe in theoy. DA plot «Refeence» Theoy of Volume Filling fo Vapo Adsoption, B. P. Being, M. M. Dubinin, and V. V. Sepinsky, J. Colloid Inteface Sci., 1, 378 (1966). 113

114 -. Opeation 1. On the Analysis (A) menu, select DA plot and the sceen will show the following DA plot windows. The pogam will execute a DA plot fom the adsotption data of an isothem.. If no adsobate molecula weight has been enteed, the window shown on the ight will appea. Click on the [OK] button and the analysis paamete window will open. Ente an adsobate molecula weight ( 6.). 3. A egession line is dawn between the 1st point and the last point. If the Index numbe is not appopiate, the lineaity will decease. Open the Analysis paamete window by selecting Settings and then the Analysis paametes menu. Then, ente an appopiate Index numbe. DA plot 4. Select the stating and end points of a staight line. The pogam will calculate poe volume (Vp/cm 3 g -1 ) and adsoption potential (E0/kJ mol -1 )using the slope and intecept of this staight line. The ma of y axsis (log (ma)) as shown ight figue is specific mass adsobed on 1 g adsobent. Vp/cm 3 g -1 expessed as follows. V m a a V p i 10 a whee a is anadsobate density, i is the slope of staight line. 5. The figue on the ight shows a DA-plot of cabon dioxide adsoption isothem fo micopoous activated cabon. Afte enteing an index numbe of., good lineaity was obtained. The poe volume cm 3 g -1 and adsoption potential 1.3 kj mol -1 wee obtained fom the slope and intecept. 6. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Fo details about items not descibed, see 7-1. Analysis paametes on page 37. Ente a molecula weight of the adsoptive. Ente an adsobate density (g cm -3 ). Ente an index numbe (eal numbe 0 to 10) 114

115 Chapte 3: HK plot 3-1. Desciption Thee ae a numbe of analysis methods suggested fo dawing poe size distibution cuve fom adsoption isothem, and most of them include a pocess to seek the elationship between pessue and poe size. Fo example, in BJH method, CI method and DH method, a elative pessue and filled poe size at the elative pessue ae calculated by Kelvin equation. HK method intoduced by Hovath and Kawazoe in 1983 calculates these values fom aveage potential inside poes. Suppose the distance between molecules is, epulsive foce occus when the distance is substantially shot and attacting foce occus when it is a pope distance, and it can be ignoed when the distance is lage. The following equation is called Lennad-Jones potential, which egads potential enegy U as a function of. U C m m C n n (3.1) Cm and Cn ae constant numbes, and the fist tem of the ight side of the equation indicates epulsive foce and the second tem indicates attacting foce. The distance between one side of the poe suface and the othe side is expessed by l as shown in the left diagam. The potential that the molecule at distance away fom the suface eceives can be expessed as follows using 10:4 potential (m=10, n=4). HK plot N s A s N a Aa 4 l l 10 (3.) Ns indicates the numbe of atom pe adsobent unit suface aea, and Na indicates the numbe of molecule pe unit suface aea of adsobate (aleady adsobed). As and Aa ae constant numbes that ae detemined by combination of adsoptive and adsobent. Theefoe, when the slit-shaped poe which has the distance l between the sufaces is filled the aveage potential enegy can be expessed as follows. follows. N A s s 4 l d / d / N A a a l d 4 10 l 4 l 10 d (3.3) On the othe hand, fom the themodynamic point of view, enegy equied fo 1 mol gas adsoption is as RT ln p 0 / p (3.4) L Avogado constant, fom equation (3.3) and (3.4), 115

116 RT ln( p / p ) 0 N s A L l d / d / s 4 N a A l d 4 a 10 l 4 l 10 d (3.5) Afte integation, the following equation, which shows the elation between l and p, can be deived. RT ln( p / p 0 ) N s As L 4 ( l N a A d) a (3.6) 3( l d / ) 3 9( l d / ) 9 3( d / ) 3 9( d / ) 9 HK method was invented in ode to calculate poe size distibution of active cabon fom nitogen adsoption isothem. ln( p / p 0 ) Enteing physicality values, it comes out as follows l ( l 0.3) ( l 0.3) (3.7) HK plot In BELSORP analysis softwae, poe size is detemined at fist, and then coesponding elative pessue is calculated. Then, adsoption amount at the elative pessue is woked out fom linea intepolation of adsoption data, and integal cuve can be obtained by plotting the adsoption amount against poe size. Poe size distibution cuve can be dawn by diffeentiating integal cuve. As mentioned above, poe size distibution of active cabon is obtained fom nitogen adsoption isothem, but in case of zeolite, this theoy cannot be fomed because inteaction between cation inside poes and quadupole momentum of nitogen molecule is too stong. Emig et al. intoduced coefficient fo poe size distibution analysis of zeolite using agon adsoption isothem, and it became common fo zeolite analysis. HK method is not suitable fo analysis of poes that can cause capillay condensation because this method is based on adsoption potential theoy. It is ecommended to use low pessue ange (elative pessue ange below 0.05) fo analysis. «Refeence» Method fo the Caluculation of Effective Poe Size Distibution in Molecula Sieve Cabon, Géza Hováth and Kunitao Kawazoe, J.Chem.Eng.Japan, 16, 470 (1983). Physical quantity Table1 Physical Paametes fo Micopoe Size Calculation (ISO ) Adsobent paametes Adsoptive paametes Cabon Zeolite Nitogen Agon Cabon dioxide Diamete (nm) ) Polaizability (cm 3 ) 1.0 x x x 10-4 Magnetic susceptibilityχ (cm 3 ) Density N (molecules m - ) 13.5 x x x x x x x x x x 10-4 ) 3.49 x 10-9 ) 4.63 x ) 1) K. Kutics, G. Hovath, Detemination of Poe size distibution in MSC fom Cabon-dioxide Adsopton Isotems, 86. ) HANDBOOK OF CHEMISTRY AND PHSICS, 69th Edition, CRCPess, Inc. 3) Sicence of adsoption nd edition, Seiichi KONDOU, Tatuo ISHIKAWA, Ikuo ABE, Mauzen Co., LTD. 116

117 Opeation 1. Select HK plot on the Analysis (A) menu and the sceen will show the following HK plot window. The pogam will execute a HK plot fom adsoption data of an isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Paametes saved as A-O(87K) HKS, CO-C(98K).HKS, N-C(77K).HKS cannot be changed. Change the name of the file displayed and then you can change the settings. Click on the [OK] button. The file will be stoed as a new settings file. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. Selectable an intepolation method to use fo intepolating the analysis data. Ente a molecula weight and a density fo the adsobate. If the paametes ae aleady stoed, select them fom hee. HK plot The cuently selected paamete filename is displayed. Ente paametes such as the molecula size and magnetic susceptibility. Fo details about each paamete, see the table below o the espective desciption. Paamete Unit da Adsobate molecula diamete nm ds Adsobent atom diamete nm Na Numbe of adsobate molecules adsobed pe unit suface aea molecules m - Ns Numbe of adsobent atoms pe unit suface aea molecules m - Xa Magnetic susceptibility of the adsobate molecula cm 3 Xs Magnetic susceptibility of the adsobent atom cm 3 αa Polaizability of the adsobate molecules cm 3 αs Polaizability of the adsobent atoms cm 3 117

118 3. The pogam will execute an HK plot using the specified conditions and will display the HK plot esults. The figue on the ight is an HK-plot measuing nitogen adsoption by micopoous activated cabon. It can be seen that this activated cabon has a lage numbe of micopoes 0.4 to 0.7 nm in width (dp) and a distibution peak of 0.56 nm. 4. Fom the t plot of activated cabon shown on the ight, the 1st staight line cannot be obtained and theefoe the poe width cannot be given. This means that HK method is effective fo activated cabon with poes 0.7 nm o less in width. HK plot 118

119 Chapte 4: SF plot 4-1. Desciption As mentioned in Chapte 3 HK method analysis, fo cabonaceous slit-shaped micopoous mateials such as active cabon, Hovath and Kawazoe made it possible to calculate micopoe distibution by deiving the equation (3.7) of Chapte 3 fom Hill s view 1) of the aveage potential of N molecule in micopoe. Saito and Foley applied this idea of aveage potential to cylinde-shaped micopoe using Eveett and Powl s view of potential ), and succeeded to calculate micopoe distibution of zeolite, AlPO4 and etc 3)4). Thee ae diffeent ideas fo taking the potential inside cylinde-shaped micopoe. One is line aveage model and the othe is aea aveage model. In line aveage model, molecules have only one degee of feedom, which is along the diamete of micopoe. On the othe hand in aea aveage model, the molecules have two degee of feedom to move acoss the micopoe. It is poved fom some actual analysis that aea aveage model coesponds to cystallogaphic view. BEL Japan analysis softwae also uses aea aveage model. p σ σaσa If the above mentioned aea aveage model is used, the following fomula is deived, which is coesponding to the fomula (3.6) of Chapte 3. ln P P0 3 L 4 RT N s A s 4 N a A a SF plot k 0 1 k 1 1 p k 1 3 k p 10 k p 4 αk andβk ae indicated Γ function and calculated fom the following fomulas. 0.5 k 0.5 k ( ( ( 4.5) 4.5 k) ( k ( 1.5) 1.5 k) ( k 1) 1) (4.1) Please efe to HK method analysis (Chapte ) fo Ns, As, Na and Aa that ae used in the fomulas. 119

120 In case of zeolite o AlPO4, suface atoms ae consideed to be oxygen atoms. In case of N adsoption in this type of system, it is difficult to make accuate adsoption isothems because quadupole momentum of N molecule and solid suface atom cause specific inteaction. Theefoe, in case of oxide micopoous mateial, A, which is mono-atomic molecule, is geneally used as the adsoption molecule. A has boiling point of 87 K and the molecula size of nm (molecula diamete), and it can be handled almost in the same manne as fo N. Theefoe, the paametes necessay fo the calculation of Ns, As, Na and Aa of (4.1) ae as indicated in the table below. Table Physical Paametes fo Micopoe Size Calculation (ISO ) Physical quantity Adsobent Oxide Ion Adsobate Agon Diamete (nm) Polaizability (cm 3 ).50 x x 10-4 Magnetic susceptibilityχ (cm 3 ) a) 1.30 x 10-9 b) 1.9 x ) 3.5 x 10-9 Density N (molecules cm - ) 1.31 x ) A. Saito, H. C. Foley, Micopoous Mateials, 3 (1995) 531. The following equation is deived fom the calculation of each paamete of (4.1) based on Table 1. ln p p 0 k 0 1 k p k 1 3 k p 10 k p 4 (4.) SF plot whee and k k 4.5 k 1.5 k k k k 1 k 1 ε*, magnetic susceptibility value of oxygen, vaies accoding to the choice between a) and b). It is when a) is used, and when b) is used. In pactice, a) is used fo ZSM-5 o Y type zeolite, and b) is used fo AlPO4. In micopoe calculation, poe size is detemined fist, then elative pessue espect to the poe size is calculated using the equation (4.). Integal cuve can be obtained by calculating the adsoption amount against elative pessue that is obtained fom (4.) by intepolation equation using the adsoption data of the adsoption isothem, and then plotting adsoption amount vesus poe size. Poe size distibution cuve can be obtained by diffeentiating this integal cuve. «Refeence» 1) T.L.Hill,J.Chem.Phys., 17, 590 (1949). ) D.H.Eveett, J.C.Powl, J.Chem.Soc., Faaday Tans. 1,7,619 (1976). 3) A.Saito, H.Foley, AIChE J., 37, 49 (1991). 4) A.Saito, H.Foley Micopoous Mateial, 3, 531 (1995). 10

121 4-. Opeaion 1. On the Analysis (A) menu, select SF plot and the sceen will show the following SF plot windows. The pogam will execute an SF plot fom adsoption data of an isothem.. Select Analysis paametes on the Setting menu and the Analysis paametes window shown below will appea. Change the settings as needed. Paametes saved as A-O(87K) SFS and A-O(Zeo)87K.SFS cannot be changed. Change the name of the file being displayed and then you can change the settings. Click on the [OK] button. The file will be saved as a new settings file. Fo details about items not descibed hee, see section 7-1. Analysis paametes, on page 37. Selectable an intepolation method to use fo intepolating analysis data. Ente the molecula weight and density of the adsobate. If the paametes ae aleady stoed, select them fom hee. SF plot The paamete filename cuently selected is displayed. Ente paametes such as the molecula size and magnetic susceptibility. Fo details about each paamete, see the table below o the espective desciption. Unit da Adsobate molecula diamete nm ds Adsobent atom diamete nm Na Numbe of adsobate molecules adsobed pe unit suface aea molecules m - Ns Numbe of adsobent atoms pe unit suface aea molecules m - Xa Magnetic susceptibility of the adsobate molecules cm 3 Xs Magnetic susceptibility of the adsobent atoms cm 3 αa Polaizability of the adsobate molecules cm 3 αs Polaizability of the adsobent atoms cm 3 11

122 3. The pogam will execute an SF plot using the specified conditions and will display the SF plot esults. The figue on the ight is an SF-plot of an agon isothem fo micopoous zeolite. It can be seen that this zeolite has a lage numbe of micopoes 0.5 to 0.9 nm in width (dp), and a distibution peak at 0.74 nm. SF plot 1

123 Chapte 5: Isosteic heat of adsoption 5-1. Desciption Adsoption involves heat geneation. It is impotant to measue this heat quantity fo studying suface aea chaacteistics. When gas adsoption happens unde constant tempeatue, heat of dq is ceated. expessed by the following equation is called diffeential heat of adsoption. qdiff which is q diff dq dn a (5.1) Heat quantity poduced at adsoption is so small, and it is difficult to measue. Theefoe, isosteic heat of adsoption is calculated with the following theoy. The following elation comes in effect at adsoption equilibium. G a G g (5.) G indicates fee enegy of Gibbs, and a and g indicate adsobate (adsoption molecules that ae adsobed) and adsoptive (adsoption molecules in gaseous phase) espectively. Suppose thee is no change in adsoption amount na and only adsoption tempeatue changes. Change of fee enegy can be expessed as the following: na is constant, thus d G S dt V dp (5.3) g g g d G S dt V dp (5.4) a a a d G a dg g (5.5) Isosteic heat of adsoption The following equation can be deived fom (5.), (5.3) and (5.4) P T n a S V g g S V a a (5.6) Applying Vg=RT/P (Vg»Va) fom the state equation of ideal gas, the above equation becomes as follows. ln P T ( S g S a ) RT S ads / RT n a (5.7) Suppose Sg-Sa=ΔSads. At equilibium state, enthalpy change caused by adsoption ΔHads has the following elation with absolute tempeatue and entopy. H ads T S ads (5.8) Following equation can be obtained fom (5.6). ln P T H ads qst (5.9) n a RT RT 13

124 -ΔHads is diffeential enthalpies of adsoption qst. The elation between qst and qdiff is as follows. q q RT st diff (5.10) The pocess to calculate adsoption heat fom Clausius-Clapeyon equation is as follows. At least diffeent adsoption isothems that wee measued at diffeent tempeatues T1 and T ae needed fo the analysis. The BEL Maste softwae enables analysis with two o thee adsoption isothems. qst at an adsoption amount can be calculated fom the equation below with the diffeence between the diffeent pessues at the same adsoption amount (Refe to the gaph below). RT T (ln p ln p1) T T 1 q st (5.11) 1 Heat of adsoption is close to heat of condensation whee adsoption amount is lage. Heat of adsoption at low adsoption amount is impotant fo the suface chaacteistic study. Howeve, in the method that uses Clausius-Clapeyon equation, the diffeence in pessues is so small at low adsoption that eo becomes lage. Also, this equation can be fomed only fo evesible eaction, thus it is impossible to calculate heat of chemical adsoption etc. Isosteic heat of adsoption

125 5-. Opeation 1. The pogam will execute an isosteic heat of adsoption analysis fom adsoption data of the isothem. This analysis eads two data files measued at diffeent adsoption tempeatues. Select Isosteic heat of adsoption on the Analysis (A) menu and ead the fist set of data. The sceen will display Read the second data.. On the BEL analysis pogam menu, o the menu displayed by clicking the mouse ight button, select Read additional data and then ead the nd set of data. 3. Obtain the isosteic heat of adsoption fom these two sets of data. The figue on the ight is the esult of adsoption of wate vapo on non-poous silica. To execute analysis with thee isothems, select [Read additional data] in the analysis softwae menu, o in the sub window ight-click menu, and ead data on the thid isothem. Also, selecting [Analysis with thee adsoption isothems] in [Analysis paametes] enables analysis with thee isothems. Isosteic heat of adsoption 15