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**Micropore Size Calculations**

Quantachrome I N S T R U M E N T S Micropore Size Calculations © Quantachrome Instruments

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**Multilayer adsorption**

Types II, IV Types II+I, IV+I Relative Pressure (P/Po) Volume adsorbed After the knee, micropores cease to contribute to the adsorption process. Low slope region in middle of isotherm indicates first few multilayers, on external surface including meso and macropores… before the onset of capillary condensation

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**Estimation of Micropores... the t-plot method**

This method uses a mathematical representation of multi-layer adsorption. The thickness, t, of an adsorbate layer increases with increasing pressure. The t-curve so produced is very similar in appearance to a type II isotherm. isotherm t-plot

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**The t-plot Resembles a type II isotherm Statistical thickness**

A statistical multilayer A statistical monolayer Relative Pressure (P/Po)

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The t-plot method Not Only Multilayer Correction to the Kelvin Equation, But Also Estimation of Micropores... For every value of P/Po, the volume adsorbed is plotted against the corresponding value of “t”. If the model describes the experimental data a straight line is produced on the t-plot...

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**Statistical Thickness, t**

Halsey equation Generalized Halsey deBoer equation Carbon Black STSA

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**t-plot Method (mesoporous only)**

Slope = V/t = A Zero intercept t (Å)

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**t-plot Method (in the presence of micropores)**

Intercept = micropore volume t (Å)

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**Micropore Size Determination by Gas Sorption**

Type I or pseudo-“Langmuir” Relative Pressure (P/Po) Volume adsorbed Steep initial region due to very strong adsorption, for example in micropores. Limiting value (plateau) due to filled pores and essentially zero external area.

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**Gas Sorption Calculation Methods**

Comparisons Gas Sorption Calculation Methods P/Po range Mechanism Calculation model 1x10-7 to 0.02 micropore filling DFT, GCMC, HK, SF, DA, DR 0.01 to 0.1 sub-monolayer formation DR 0.05 to 0.3 monolayer complete BET, Langmuir > multilayer formation t-plot (de-Boer,FHH), > capillary condensation BJH, DH 0.1 to capillary filling DFT, BJH in M41S-type materials

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**DR & DA Dubinin-Radushkevic and Dubinin-Astakov**

Simple log(V) vs log2(Po/P) relationship which linearizes the isotherm based on micropore filling principles. “Best fit” is extrapolated to log2(Po/P) (i.e. where P/Po = 1) to find micropore volume. DA Closely related to DR calculation based on pore filling mechanism. Equation fits calculated data to experimental isotherm by varying two parameters, E and n. E is average adsorption energy that is directly related to average pore diameter, and n is an exponent that controls the width of the resulting pore size distribution. The calculated pore size distribution always has a skewed, monomodal appearance (Weibull distribution).

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**Estimation of Micropores Dubinin-Radushkevich (DR) Theory**

W = volume of the liquid adsorbate W0 = total volume of the micropores B = adsorbent constant = adsorbate constant A linear relationship should be found between log(W) and log2(Po/P)...

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**Estimation of Micropores Dubinin-Radushkevich (DR) Plot**

Log (W) Extrapolation yields Wo Log2(Po/P)

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**HK & SF Horvath-Kawazoe & Saito-Foley**

Direct mathematical relationship between relative pressure (P/Po) and pore size. Relationship calculated from modified Young-Laplace equation, and takes into account parameters such as magnetic susceptibility. Based on slit-shape pore geometry (e.g. activated carbons). Calculation restricted to micropore region ( 2nm width). SF Similar mathematics to HK method, but based on cylindrical pore geometry (e.g. zeolites). Calculation restricted to micropore region ( 2 nm diameter).

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**DFT Density Functional Theory**

Provides a microscopic treatment . Complex mathematical modelling of fluid interactions plus geometrical considerations (pore geometry). Fluid interactions are “calibrated”. “Kernel” consists of up to 100 theoretical, individual pore isotherms.

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**Gas- and Liquid Density Profiles in a Slit Pore by GCMC (Walton and Quirke,1989)**

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**Pore Filling Pressures for Nitrogen in Cylindrical Silica Pores at 77 K (Neimark et al, 1998)**

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**Pore Size Analysis of MCM 41 (Templated Silica) by N2 Sorption at 77 K**

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**Pore Size Analysis of MCM 41: Calculations Compared**

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**Recent Advances in Pore Size Characterization by Physical Adsorption**

Quantachrome I N S T R U M E N T S Recent Advances in Pore Size Characterization by Physical Adsorption Author: Dr. Matthias Thommes Director of Applied Science, Quantachrome Instruments Boynton Beach, Florida, USA Presented by Dr. Martin A. Thomas Director of Business Development and Applied Technology Quantachrome Instruments

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**Adsorption Potentials : Planar Surface, Meso- and Micropores**

Mesopores (2-50 nm) Micropore (<2 nm)

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**IUPAC’s Classification of Sorption Isotherms**

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**Adsorption in Micro- and Mesopores**

Micropores (pore size < 2 nm): Micropore filling (continuous process) at very low relative pressures P/P0 < 0.15 Type I isotherm (IUPAC Classification) Mesopores (pore size nm): Multilayer adsorption, pore condensation and hysteresis (pore condensation reflects as 1st order phase transition, i.e., discontinuous process) in relative pressure (P/P0) range from – 1 Type IV, and V isotherm (IUPAC Classification)

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**Recent Advances in Micropore (< 2 nm) Analysis**

Quantachrome I N S T R U M E N T S Recent Advances in Micropore (< 2 nm) Analysis

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**Commonly Used Adsorptives for Surface Area and Pore size Analysis**

Nitrogen: at K (liquid nitrogen temperature, T/Tc = 0.61) pore size analysis of micro-,meso and macropores surface area analysis Argon: at K (T – Tr = K; Tr : bulk triple point temperature; T/Tc = 0.50) at K (liquid argon temperature, T/Tc = 0.57 ) pore size analysis of micro- , meso- and macropores surface area analysis CO2 : at 195 K (T/Tc = 0.63) at 273 K (T/Tc = 0.89) pore size analysis of micropores of widths < 1.5 nm (particularly for microporous carbons) Krypton : at K (T – Tr = K) measurement of very low surface areas at K (T – Tr = K) pore size analysis of thin micro/mesoporous films (M. Thommes et al, 2005)

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Argon Adsorbate

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**Adsorption of Nitrogen (77.35 K) and Argon (87.27 K) on some Zeolites**

Ar/87.27 K Faujasite: Ar and N2 Adsorption .

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**Adsorption of Nitrogen (77.35 K) and Argon (87.27 K) on some Zeolites**

H-Mord. NaX MCM-58 5A 1 3X Argon/87.27 K

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Argon Adsorption at K Due to weaker attractive fluid-wall interactions (and the lack of a quadrupole moment), argon fills micropores of dimensions 0.4 nm – 0.8 nm at much higher relative pressures, (.i.e., at least 1.5 decades higher in relative pressures) as compared to nitrogen. High resolution adsorption isotherm of high accuracy can be measured over the complete micro-mesopore range, in less time.

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**Carbon Dioxide Adsorbate**

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**CO2 Micropore Analysis of Porous Carbons at 273.15 K**

At elevated temperatures and higher absolute pressure (P0 = Torr) CO2 can access micropores, which are not accessible for nitrogen at 77 K. Fast analysis: due to higher diffusion rate equilibrium is achieved faster as compared to nitrogen adsorption at 77 K dramatic decrease in analysis time i.e., 3-5 h for CO2 versus h N2. No need for high vacuum system with turbomolecular pump; 10-3 torr vacuum is sufficient. No need for a low-pressure transducer; 1000 Torr transducer is sufficient.

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N2 , Ar (at K) vs. CO2 ( K) Adsorption on Activated Carbon Fiber (ACF-10) and NLDFT-PSD Histograms N2/77.35 K Analysis Time: CO2 = 3 h N2 = 40 h N2 CO2, Ar CO2/ K Quantachrome’s Powder Technote 35

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Water Adsorbate

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**Microporous Carbons: the Standard way**

Nitrogen, K Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004)

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**Featureless Isotherms**

Nitrogen, K Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004

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**State of the Art Cryogenic Differentiation**

NLDFT A 15 A 10 A 5 Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004

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**The Special Behavior of Water**

Water, 25 C A15 A10 A5 Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004

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Hydrogen Adsorbate

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**Hydrogen adsorption at 77K and 273 K for Ultramicropore Characterization**

Including H2 isotherms in the PSD analysis allows extending the lower limit of the analysis to pore sizes of about 3 Å. This pore size range may be useful for hydrogen storage applications. J. Jagiello, M. Thommes, Carbon 42 (2004) 1227

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**H2, CO2 and N2 Adsorption and NLDFT Analysis in ACF Activated Carbon Fibers**

H2,77 K N2 CO2 Ar J. Jagiello, M. Thommes, Carbon 42 (2004) 1227

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**H2, CO2 and N2 Adsorption and NLDFT Analysis in ACF Activated Carbon Fibers**

NLDFT-PSD H2,77 K CO2 J. Jagiello, M. Thommes, Carbon 42 (2004) 1227

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**Pore Shape & Size Influence**

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**Pore Size Analysis by Gas Adsorption**

Macroscopic, thermodynamic methods Micropores (< 2 mn): e.g., Dubinin-Radushkevitch or more advanced methods such as Horvath-Kawazoe (HK) and Saito-Foley (SF) , t-method, alpha-s method Meso/Macropores (2-100 nm): e.g., Kelvin equation based methods such as BJH (Barrett,Joyner, Halenda) Modern, microscopic methods, based on statistical mechanics describe configuration of adsorbed molecules on a molecular level : e.g., Density Functional Theory (DFT), Molecular Simulation these methods are applicable for pore size analysis of both the micro- and mesopore size range An accurate pore size analysis over the complete pore size range can be performed by a single method.

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**Pore Filling Pressures for Nitrogen in Cylindrical Micropores at 77 K**

C. Lastoskie and K.E.Gubbins, J. Phys. Chem 77, 9786 (1997)

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Pore Size Analysis of Zeolites with Novel NLDFT Kernels based on argon adsorption at K (M.Thommes et al., presented at the International Zeolite Conference, Cape Town, 2004) X-Zeolite structure Mordenite structure

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**Mesopore Size Calculations**

Quantachrome I N S T R U M E N T S Mesopore Size Calculations © 2004 –2006 Quantachrome Instruments

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**Pore Size Determination**

Requires a recognition and understanding of different basic isotherm types.

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**Types of Isotherms Volume adsorbed Type I or pseudo-“Langmuir”**

Relative Pressure (P/Po) Volume adsorbed Steep initial region due to very strong adsorption, for example in micropores. Limiting value (plateau) due to filled pores and essentially zero external area.

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**Types of Isotherms Type II Volume adsorbed Relative Pressure (P/Po)**

Rounded knee indicates approximate location of monolayer formation. Absence of hysteresis indicates adsorption on and desorption from a non-porous surface.. Low slope region in middle of isotherm indicates first few multilayers

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**Types of Isotherms Type III Volume adsorbed Relative Pressure (P/Po)**

Lack of knee represents extremely weak adsorbate-adsorbent interaction BET is not applicable Example: krypton on polymethylmethacrylate

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**Types of Isotherms Type IV Volume adsorbed Relative Pressure (P/Po)**

Rounded knee indicates approximate location of monolayer formation. Low slope region in middle of isotherm indicates first few multilayers Hysteresis indicates capillary condensation in meso and macropores. Closure at P/Po~0.4 indicates presence of small mesopores (hysteresis would stay open longer but for the tensile-strength-failure of the nitrogen meniscus.

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**Types of Isotherms Type V Volume adsorbed Relative Pressure (P/Po)**

Example: water on carbon black Type V Volume adsorbed Lack of knee represents extremely weak adsorbate-adsorbent interaction BET is not applicable Relative Pressure (P/Po)

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**Gas Sorption Calculation Methods**

Comparisons Gas Sorption Calculation Methods P/Po range Mechanism Calculation model 1x10-7 to 0.02 micropore filling DFT, GCMC, HK, SF, DA, DR 0.01 to 0.1 sub-monolayer formation DR 0.05 to 0.3 monolayer complete BET, Langmuir > multilayer formation t-plot (de-Boer,FHH), > capillary condensation BJH, DH 0.1 to capillary filling DFT, BJH in M41S-type materials

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**Meso/Macropore Size Determination by Gas Sorption**

Type IV Relative Pressure (P/Po) Volume adsorbed Rounded knee indicates approximate location of monolayer formation. Low slope region in middle of isotherm indicates first few multilayers Hysteresis indicates capillary condensation in meso and macropores. Closure at P/Po~0.4 indicates presence of small mesopores (hysteresis would stay open longer but for the tensile-strength-failure of the nitrogen meniscus.

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**Pore Size Distribution**

Hysteresis is indicative of the presence of mesopores and the pore size distribution can be calculated from the sorption isotherm. Whilst it is possible to do so from the adsorption branch, it is more normal to do so from the desorption branch... Mesopore (Greek meso = middle): 2nm - 50 nm diameter Macropore (Greek macro = large): >50 nm diameter Micropore (Greek micro = small): 0 nm - 2 nm diameter

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**Adsorption / Desorption (macroscopic description)**

Adsorption = multilayer formation, then… Desorption = meniscus “control”

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**BJH & DH Barrett, Joyner, Halenda and Dollimore-Heal**

Modified Kelvin equation. Kelvin equation predicts pressure at which adsorptive will spontaneously condense (and evaporate) in a cylindrical pore of a given size. Condensation occurs in pores that already have some multilayers on the walls. Therefore, the pore size is calculated from the Kelvin equation and the selected statistical thickness (t-curve) equation. DH Extremely similar calculation to BJH, which gives very similar results. Essentially differs only in minor mathematical details.

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Kelvin* Equation * Lord Kelvin a.k.a. W.T. Thomson

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**BJH Pore Size rp = actual radius of the pore**

rk = Kelvin radius of the pore t = thickness of the adsorbed film Pore volume requires assumption of liquid density!

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**Statistical Thickness, t**

Halsey equation Generalized Halsey deBoer equation Carbon Black STSA

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**Pore Size Distribution**

Artifact dV/dlogD 40 Pore Diameter (angstrom)

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**Pore Filling Pressures for Nitrogen in Cylindrical Pores at 77 K (Gubbins et al, 1997)**

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**Pore Filling Pressures for Nitrogen in Cylindrical Silica Pores at 77 K (Neimark et al, 1998)**

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**DFT & Phase Transitions**

equilibrium transition 0.05 spinodal evaporation 0.04 0.03 Adsorption, mmol/m2 spinodal condensation 0.02 Experimental (des) 0.01 Experimental (ads) NLDFT in 4.8nm pore 0.2 0.4 0.6 0.8 1 Relative pressure, P/P0 NLDFT adsorption isotherm of argon at 87K in a cylindrical pore of diameter 4.8 nm in comparison with the appropriate experimental sorption isotherm on MCM-41. It can be clearly seen that the experimental desorption branch is associated with the equilibrium gas-liquid phase transition, whereas the condensation step corresponds to the spinodal spontaneous transition. (a)Neimark A.V., Ravikovitch P.I. and Vishnyakov A. (2000) Phys. Rev. E 62, R1493; (b)Neimark A.V. and Ravikovitch P.I. (2001) Microporous and Mesoporous Materials 44-56, 697.

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**Where Does Cavitation Occur?**

Adsorptive Temperature ~p/po Nitrogen 77K 0.42 Argon 87K 0.38 0.23

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**Recent Advances in Mesopore (2 – 50 nm) Analysis**

Quantachrome I N S T R U M E N T S Recent Advances in Mesopore (2 – 50 nm) Analysis

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Mesopore Analysis Significant progress in the pore size analysis of porous materials was recently achieved, mainly because of the following reasons: (i) The discovery of novel ordered mesoporous molecular sieves which were used as model adsorbents to test theories of gas adsorption (ii) The development of microscopic methods, such as the Non-Local-Density Functional Theory (NLDFT) or computer simulation methods (e.g. Monte-Carlo – and Molecular-Dynamic simulations), which allow to describe the configuration of adsorbed molecules in pores on a molecular level; (iii) Carefully performed adsorption experiments

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TEM of MCM-41 Silica

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**Sorption, Pore Condensation and Hysteresis Behavior of a Fluid in a Single Cylindrical Mesopore**

From: M Thommes, “ Physical adsorption characterization of ordered and amorphous mesoporous materials”, Nanoporous Materials- Science and Engineering” (edited by Max Lu, X.S Zhao), Imperial College Press, Chapter 11, (2004)

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**Pore Size Analysis of Mesoporous Solids: The Modified Kelvin Equation**

ln(P/P0) = -2cos /RT(rp – tc) rp: pore radius tc : adsorbed multilayer film prior to condensation : surface tension : densities of the coexistent liquid (l ) and gas (g) ( = l - g) : contact angle of the liquid meniscus against the pore wall

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SEM- of Mesoporous TiO2

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**Nitrogen Sorption at 77 K into Mesoporous TiO2**

6 nm 10 nm 30 nm 100 nm H. Kueppers, B. Hirthe, M.Thommes, G.I.T, 3 (2001) 110

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**Pore Size Analysis of Mesoporous Materials**

(I) Methods based on (modified) Kelvin Equation e.g., - Barett-Joyner-Halenda (BJH) (1951) - Dollimore-Heal (DH) (1964) - Broeckhoff de Boer (BdB) (1967/68) - Kruk-Jaroniec-Sayari (KJS)) (1997) - Bhatia et al (mod. BdB) (1998/2004) - D.D.Do & Ustinov (mod. BdB) (2004/2005)

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** Errors of 25 % and more in pore size analysis!! Solutions: **

Results of Sorption Studies on Ordered Mesoporous Materials in Combination With Advanced Theoretical and Molecular Simulation Approaches : Problem: Conventional, macroscopic, thermodynamic methods (e.g, methods based on the Kelvin equation such as BJH, BdB) assume bulk-fluid like behavior for pore fluid and neglect details of the fluid-wall interactions Errors of 25 % and more in pore size analysis!! Solutions: (1) Correction,and/or proper calibration of classical methods (e.g, KJS method): Disadvantage: only valid over limited pore size range (2) Application of microscopic methods based on statistical mechanics (e.g., NLDFT, GCMC) which describe the configuration of the adsorbed phase on a molecular level Accurate pore size analysis over complete micro/mesopore size range

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**Phase Diagrams of Pure Fluids Confined to Porous Glasses**

CO2/Vycor SF6/CPG H. Fretwell et al, J. Phys. Condens. Matter 7 (1995) L717 M. Thommes and G.H. Findenegg, Langmuir 10 (1994), 4270

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**Effect of Confinement on Sorption and Phase Behavior**

Pore size and temperature are complimentary variables with regard to the occurrence of hysteresis The shape of sorption isotherms is affected by both, the texture of the material but also by the difference in thermodynamic states of pore and bulk fluid phases In contrast to classical, macroscopic approaches modern microcopic theories based on statistical mechanics (e.g Density-Functional Theory and Molecular Simulation) take these phenomena into account

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**(a) Density Functional Theory :**

Pore Size Analysis by Microscopic Methods based on Statistical Mechanics (a) Density Functional Theory : e.g.- Evans and Tarazona (1985/86) - Seaton (1989), - Lastoskie and Gubbins (1993) - Sombathley and Olivier (1994) - Neimark and Ravikovitch (1995 ……) b) Monte Carlo (MC) and Moleculardyn. (MD), e.g. - Gubbins et. al. (1986…. ) - Walton and Quirke (1989…) - Gelb (1999- ….) - Neimark and Ravikovitch (1995….)

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Theoretical Predictions Of The Pore Size Dependence Of The Relative Pressure Of The Equilibrium Condensation/Evaporation Transition N2/77 K in cylindrical silica pores . Neimark AV, Ravikovitch P.I., Grün M., Schüth F., Unger K.K, (1998) J. Coll. Interface Sci. 207,159

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**Nitrogen sorption (77 K) in MCM-41 and Pore Size Analysis by BJH and NLDFT**

NLDFT method: N2/77K cylindrical-silica pore model

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**Nitrogen Adsorption and Pore Size Analysis in CMK 3 Mesoporous Carbon**

BJH (3.5 nm) NLDFT (5.1 nm) NLDFT Methods: N2/77K cylindrical carbon pore model M.Thommes, H. Huwe, M. Froeba et al, to be published (2005)

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**Other Factors The influence of Pore Geometry Connectivity**

Disorder (geometrical and surface heterogeneity ) on Adsorption, Pore Condensation, Hysteresis, and thus the shape of the sorption isotherm remains under investigation

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**Nitrogen Sorption at 77 K into various Mesoporous Silica Materials**

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**IUPAC Classification of Hysteresis**

Cylindr.Pores Cylindr.&Spherical Pores Disordered. lamellar pore structures, slit & wedge, shape pores Micro/Mesoporous adsorbents

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**Origin of Capillary Condensation Hysteresis**

Single Pore Model : Hysteresis occurs in a single pore and reflects a intrinsic property of phase transition in a pore. Hysteresis is due due to metastable pore fluid H1 Hysteresis - Network Model: Pore blocking, percolation effects, on desorption branch H2 Hysteresis Disordered Porous Materials Model: Combination of kinetic and thermodynamic effects; phenomena are spanning the complete disordered pore system H1 and H2 Hysteresis

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Ar (87 K) and N2 (77 K) sorption in MCM 48 and NLDFT-Pore size analysis by using the NLDFT-equilibrium method (kernel) Des(Ar/87 K) Ar(87K): Hysteresis Ar/ 87 K N2(77K): Reversible Ads(Ar/87 K) N2/77K (M. Thommes et al, Applied Surface Science, 196 (2002) )

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**Network Model: Pore blocking and percolation effects in interconnected pore systems**

Type H Hysteresis Problem for Pore Size Analysis: Adsorption Branch: metastable pore fluid delayed pore condensation Desorption Branch: pore blocking,percolation delayed evaporation How to tackle: Application of approaches based on percolation theory Application of novel NLDFT approaches

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**Mesopore-Analysis by NLDFT**

NLDFT-method for Pore Size Distribution Calculation from Adsorption and Desorption Desorption Branch:: Equilibrium liquid-gas phase transition (evaporation) NLDFT-Kernel of Equilibrium Isotherms Adsorption Branch: NLDFT-spinodal- gas-liquid phase transition (condensation) NLDFT- Kernel of (Metastable) Adsorption Isotherms By P. Ravikovitch, A.V. Neimark, Colloids and Surfaces A: Physicochem Eng. Aspects (2001) 11

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**Nitrogen adsorption/desorption at 77**

Nitrogen adsorption/desorption at K in SBA-15 and pore size distributions from adsorption- (NLDFT spinodal condensation kernel ) and desorption (NLDFT equilibrium transition kernel) M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p (2004)

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Nitrogen sorption at 77 K in porous CPG and Vycor Glasses and pore size distributions from adsorption- (NLDFT spinodal condensation kernel) and desorption (NLDFT equilibrium transition kernel) CPG H1 Hysteresis Vycor H2 Hysteresis M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p (2004)

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**Conclusion: H1 Hysteresis**

Mechanism of hysteresis in single meso- pores (e.g. MCM-41, SBA-15) and in materials consisting of ordered pore networks (e.g., MCM-48 , CPG) seems to be similar. In both cases H1 hysteresis is observed. In case of H1 hysteresis methods based on the independent pore model are in principle applicable for pore size analysis

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H2/H3 Hysteresis In case of type H2 hysteresis, pore blocking, percolation, and cavitation effects play an important role. The position of the desorption branch does not reflect the equilibrium liquid-gas transition. Hence, a method for pore size analysis based on the equilibrium phase transition can here not be applied NLDFT-spinodal condensation method can be applied to the adsorption branch (in case of cylindrical-like pores and silica materials – pore size range up to 80 nm!) Application of a calibrated correlation between the position of capillary condensation step and pore size.

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**H2/H3/H4 Hysteresis: Lower Limit of Hysteresis Loop –Tensile Strength Effect ??**

Hysteresis loop for N2 (77.35 K) always closes at relative pressures > 0.42 and for argon at K at relative pressures > 0.38. The lower closure point of hysteresis is believed (in the classical picture) to be determined by the tensile strength of the capillary condensed liquid, i.e., there exists a mechanical stability limit below which a macroscopic meniscus cannot exist anymore and which leads to a spontaneous evaporation of the pore liquid. This forced closure of the hysteresis leads to an artifical step in the desorption isotherm Pore size distribution artifact at ca. 4 nm Adsorption Branch should be selected for Pore-Size Analysis

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**H3 Hysteresis: Lower limit of Hysteresis Loop –Tensile Strength Effect?**

BJH-PSD N2/77K sorption on disordered alumina catalyst Artifact M. Thommes, In Nanoporous Materials Science and Engineering, (Max Lu and X Zhao, eds.), World Scientific, in press (2004)

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**H4 Hysteresis: Nitrogen adsorption at 77**

H4 Hysteresis: Nitrogen adsorption at K in activated carbon -Tensile Strength effect?

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**Pore Condensation/Evaporation in Ink-bottle Pores: Pore Blocking and Cavitation Phenomena.**

M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006)

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**N2 and Ar adsorption on micro-mesoporous silica (SE3030) and pore size analysis by the NLDFT- method**

Pore size distribution from metastable adsorption branch 9.4 nm 1 nm Cumulative pore volume M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006) Mesopore Size N2/77K sorption (NLDFT) : nm Ar/87K sorption (NLDFT) : nm SANS (CLD) : nm TEM : ca. 9.5 nm Micropore Size N2/77K sorption (NLDFT) : ca. 1.1 nm SANS : ca. 1 – 1.2 nm Micropore Volume N2/77K: 0.12 ml/g SANS: 0.1 ml/g Excellent agreement between NLDFT and SANS/SAXS

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**Nitrogen sorption of “KLE silica“ at 77K and NLDFT analysis**

N2 sorption isotherm Pore size distribution 13.9 nm 1.3 nm Pore diameter (Angström) NLDFT analysis (spherical mesopores, cylindrical micropores) Mesopore Size: N2-sorption: 13.9 nm TEM: Ca. 13 nm SAXS: 13.8 nm Excellent agreement between SAXS and new NLDFT approach! M. Thommes, B. Smarsly, M. Groenewolt, P. Ravikovitch, and A. Neimark, Langmuir, 22,756 (2006)

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**Pore Blocking/Percolation and Cavitation**

“Pore size” distribution determined from desorption branch should be independent of the choice of the adsorptive or temperature Cavitation : Artificial “Pore” size distribution determined from desorption branch of hysteresis loop should depend on the choice of the adsorptive and temperature

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**Poreblocking/Percolation As Dominant Evaporation Mechanism: Nitrogen And Argon Sorption In Vycor**

Analysis of N2 and Ar adsorp. branches “Pore Size” Analysis of N2 and Ar desorp. branches “Neck Size” M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006

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Cavitation as dominant mechanism for pore evaporation: N2 and Ar sorption in SE3030 micro/mesoporous silica 9.4 nm NLDFT pore size from adsorption 0.44 0.47 No pore size info from desorption! M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006)

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**Summary : Sorption Hysteresis in Micro/Mesoporous Pore networks**

• Sorption experiments using different adsorptives (e.g. Argon, Nitrogen) allow to identify pore blocking/percolation and cavitation mechanisms : Pore Blocking controlled desorption (e.g. porous Vycor glass): Neck Size from analysis of desorption branch; Pore (Cavity) size from adsorption branch Cavitation controlled desorption: No pore size info from analysis of desorption branch ; pore (cavity) size from adsorption branch • Cavitation controlled desorption is observed in SE3030, KLE and KLE/IL,SLN-326 silica, which consist of of micro/mesoporous networks of ink-bottle like pores. - The rel. pressure where cavitation occurs does not depend on the actual neck size as long as Wneck < W neck,(critical), and Wneck(critical) is found to be larger than 5 nm! - If Wneck > W neck,(critical) then pore blocking can be observed • We confirm the validity of novel N2/silica and Ar/silica NLDFT methods, applicable to the adsorption branch of a hysteretic isotherm. The pore size data obtained with this method for SE3030, KLE-silica are in excellent agreement with independently obtained results from novel SANS/SAXS techniques.

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**Conclusions &Recommendations: Hysteresis and Pore Size Analysis**

• H1 Hysteresis: Independent pore model applies. Pore size can in principle be determined from both desorption branch and adsorption branch if proper methods are available • H2 Hysteresis: caused by pore blocking/percolation or cavitation phenomena in mesoporous and micro/mesoporous pore networks Pore blocking: Pore (cavity) size from adsorption branch; Neck size from desorption branch, Cavitation: Pore (Cavity Size) from adsorption branch; No pore size information from desorption branch • H3/H4 Hysteresis: observed in very disordered micro/mesoporous pore networks and caused by a combination of various phenomena (incl. cavitation, pore blocking) Pore (Cavity Size) from adsorption branch •

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Conclusions The use of different probe molecules allows not only to check for consistency in the pore size and surface area analysis, but allows also to obtain a much more accurate micro- and mesopore analysis. The shape of sorption isotherms is affected by, surface chemistry and the texture of the adsorbent but also by the difference in thermodynamik states of pore and bulk fluid phases. This has to be taken into account in order to obtain a correct and comprehensive pore size analysis. Microscopic methods (e.g, NLDFT, Molecular simulation) allow to obtain an more accurate and comprehenisve pore size analysis compared to macroscopic, thermodynamic methods (e.g., BJH, HK, SF, DR).

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**Some Selected References**

(1) M Thommes, “ Physical adsorption characterization of ordered and amorphous mesoporous materials”, Nanoporous Materials- Science and Engineering” (edited by Max Lu, X.S Zhao), Imperial College Press, Chapter 11, (2004) (2) S. Lowell, J.E. Shields, M.A. Thomas and M. Thommes, Characterization of porous solids and powders: surface area, pore size and density, Kluwer Academic Publisher, 2004 (3) M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006) (4) B. Smarsly, M. Thommes, P.I Ravikovitch, A.V. Neimark, Adsorption 11 (2004), 653, (2005) (5) J. Jagiello, M. Thommes, Carbon 42 (2004) 1227 (6) M. Thommes, R. Koehn and M. Froeba, Applied Surface Science 196 (2002) 239 (7) M. Thommes, R. Koehn and M. Froeba, J. Phys. Chem. B 104, 7932 (2000)

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Ch 23 pages 573-580 Lecture 15 – Molecular interactions.

Ch 23 pages 573-580 Lecture 15 – Molecular interactions.

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