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© 2004-2006 Quantachrome Instruments Micropore Size Calculations Quantachrome I N S T R U M E N T S © 2004-2006 Quantachrome Instruments.

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Presentation on theme: "© 2004-2006 Quantachrome Instruments Micropore Size Calculations Quantachrome I N S T R U M E N T S © 2004-2006 Quantachrome Instruments."— Presentation transcript:

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

2 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

3 © Quantachrome Instruments t-plot 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

4 © Quantachrome Instruments The t-plot Resembles a type II isotherm Relative Pressure (P/Po) Statistical thickness A statistical monolayer A statistical multilayer

5 © Quantachrome Instruments 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... The t-plot method

6 © Quantachrome Instruments Statistical Thickness, t Halsey equation Generalized Halsey deBoer equation Carbon Black STSA

7 © Quantachrome Instruments t-plot Method (mesoporous only) Slope = V/t = A Zero intercept t (Å)

8 © Quantachrome Instruments t-plot Method (in the presence of micropores) Intercept = micropore volume t (Å)

9 © Quantachrome Instruments 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.

10 © Quantachrome Instruments Comparisons Gas Sorption Calculation Methods P/Po rangeMechanismCalculation model 1x10-7 to 0.02micropore fillingDFT, GCMC, HK, SF, DA, DR 0.01 to 0.1sub-monolayer formationDR 0.05 to 0.3monolayer completeBET, Langmuir > 0.1 multilayer formationt-plot (de-Boer,FHH), > 0.35 capillary condensationBJH, DH 0.1 to 0.5 capillary filling DFT, BJH in M41S-type materials

11 © Quantachrome Instruments DR & DA Dubinin-Radushkevic and Dubinin-Astakov DR Simple log(V) vs log 2 (Po/P) relationship which linearizes the isotherm based on micropore filling principles. “Best fit” is extrapolated to log 2 (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).

12 © Quantachrome Instruments Estimation of Micropores Dubinin-Radushkevich (DR) Theory W = volume of the liquid adsorbate W 0 = total volume of the micropores B = adsorbent constant  = adsorbate constant A linear relationship should be found between log(W) and log 2 (Po/P)...

13 © Quantachrome Instruments Log 2 (Po/P) Log (W) Extrapolation yields Wo Estimation of Micropores Dubinin-Radushkevich (DR) Plot 0

14 © Quantachrome Instruments HK & SF Horvath-Kawazoe & Saito-Foley HK 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).

15 © Quantachrome Instruments DFT Density Functional Theory a) Provides a microscopic treatment. b) Complex mathematical modelling of fluid interactions plus geometrical considerations (pore geometry). c) Fluid interactions are “ calibrated ”. d) “ Kernel ” consists of up to 100 theoretical, individual pore isotherms.

16 © Quantachrome Instruments Gas- and Liquid Density Profiles in a Slit Pore by GCMC (Walton and Quirke,1989)

17 © Quantachrome Instruments Pore Filling Pressures for Nitrogen in Cylindrical Silica Pores at 77 K (Neimark et al, 1998)

18 © Quantachrome Instruments Pore Size Analysis of MCM 41 (Templated Silica) by N 2 Sorption at 77 K

19 © Quantachrome Instruments Pore Size Analysis of MCM 41: Calculations Compared

20 © Quantachrome Instruments 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 Boynton Beach, Florida, USA Quantachrome I N S T R U M E N T S

21 © Quantachrome Instruments Adsorption Potentials : Planar Surface, Meso- and Micropores Planar Surface Mesopores (2-50 nm) Micropore (<2 nm)

22 © Quantachrome Instruments IUPAC’s Classification of Sorption Isotherms

23 © Quantachrome Instruments Adsorption in Micro- and Mesopores Micropores (pore size < 2 nm):  Micropore filling (continuous process) at very low relative pressures P/P 0 < 0.15 Type I isotherm (IUPAC Classification) Mesopores (pore size nm):  Multilayer adsorption, pore condensation and hysteresis (pore condensation reflects as 1 st order phase transition, i.e., discontinuous process) in relative pressure (P/P 0 ) range from 0.15 – 1 Type IV, and V isotherm (IUPAC Classification)

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

25 © Quantachrome Instruments Commonly Used Adsorptives for Surface Area and Pore size Analysis Nitrogen: at K (liquid nitrogen temperature, T/T c = 0.61)  pore size analysis of micro-,meso and macropores  surface area analysis Argon: at K (T – T r = K; T r : bulk triple point temperature; T/T c = 0.50) at K (liquid argon temperature, T/T c = 0.57 )  pore size analysis of micro-, meso- and macropores  surface area analysis CO 2 : at 195 K (T/T c = 0.63) at 273 K (T/T c = 0.89)  pore size analysis of micropores of widths < 1.5 nm (particularly for microporous carbons) Krypton : at K (T – T r = K)  measurement of very low surface areas at K (T – T r = K)  pore size analysis of thin micro/mesoporous films (M. Thommes et al, 2005)

26 © Quantachrome Instruments Argon Adsorbate

27 © Quantachrome Instruments Adsorption of Nitrogen (77.35 K) and Argon (87.27 K) on some Zeolites N 2 /77.35 K Ar/87.27 K Faujasite: Ar and N 2 Adsorption.

28 © Quantachrome Instruments 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

29 © Quantachrome Instruments 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.

30 © Quantachrome Instruments Carbon Dioxide Adsorbate

31 © Quantachrome Instruments CO 2 Micropore Analysis of Porous Carbons at K  At elevated temperatures and higher absolute pressure (P 0 = Torr) CO 2 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 CO 2 versus h N 2.  No need for high vacuum system with turbomolecular pump; torr vacuum is sufficient.  No need for a low-pressure transducer; 1000 Torr transducer is sufficient.

32 © Quantachrome Instruments N 2, Ar (at K) vs. CO 2 ( K) Adsorption on Activated Carbon Fiber (ACF-10) and NLDFT-PSD Histograms N 2 /77.35 K CO 2 / K Analysis Time: CO 2 = 3 h N 2 = 40 h CO 2, N2 N2 Ar Quantachrome’s Powder Technote 35

33 © Quantachrome Instruments Water Adsorbate

34 © Quantachrome Instruments Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004) Nitrogen, K Microporous Carbons: the Standard way

35 © Quantachrome Instruments Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004 Nitrogen, K Featureless Isotherms

36 © Quantachrome Instruments A 15 A 5 A 10 NLDFT Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004 State of the Art Cryogenic Differentiation

37 © Quantachrome Instruments A15 A10 A5 Water, 25 C Nitrogen (77.35 K and Water Sorption (298.4K) in Activated Carbon Fibers (ACF), (M. Thommes, et al., FOA 8, 2004 The Special Behavior of Water

38 © Quantachrome Instruments Hydrogen Adsorbate

39 © Quantachrome Instruments Hydrogen adsorption at 77K and 273 K for Ultramicropore Characterization Including H 2 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

40 © Quantachrome Instruments H 2, CO 2 and N 2 Adsorption and NLDFT Analysis in ACF Activated Carbon Fibers CO 2 N2N2 Ar H 2,77 K J. Jagiello, M. Thommes, Carbon 42 (2004) 1227

41 © Quantachrome Instruments H 2, CO 2 and N 2 Adsorption and NLDFT Analysis in ACF Activated Carbon Fibers H2H2 N2N2 CO 2 N2N2 Ar H 2,77 K J. Jagiello, M. Thommes, Carbon 42 (2004) 1227 NLDFT-PSD

42 © Quantachrome Instruments Pore Shape & Size Influence

43 © Quantachrome Instruments 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.

44 © Quantachrome Instruments Pore Filling Pressures for Nitrogen in Cylindrical Micropores at 77 K C. Lastoskie and K.E.Gubbins, J. Phys. Chem 77, 9786 (1997)

45 © Quantachrome Instruments 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) Mordenite structure X-Zeolite structure

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

47 © Quantachrome Instruments Pore Size Determination Requires a recognition and understanding of different basic isotherm types.

48 © Quantachrome Instruments 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. Types of Isotherms

49 © Quantachrome Instruments Types of Isotherms Type II Relative Pressure (P/Po) Volume adsorbed 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

50 © Quantachrome Instruments Types of Isotherms Type III Relative Pressure (P/Po) Volume adsorbed Lack of knee represents extremely weak adsorbate-adsorbent interaction BET is not applicable Example: krypton on polymethylmethacrylate

51 © Quantachrome Instruments Types of Isotherms 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.

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

53 © Quantachrome Instruments Comparisons Gas Sorption Calculation Methods P/Po rangeMechanismCalculation model 1x10-7 to 0.02micropore fillingDFT, GCMC, HK, SF, DA, DR 0.01 to 0.1sub-monolayer formationDR 0.05 to 0.3monolayer completeBET, Langmuir > 0.1 multilayer formationt-plot (de-Boer,FHH), > 0.35 capillary condensationBJH, DH 0.1 to 0.5 capillary filling DFT, BJH in M41S-type materials

54 © Quantachrome Instruments 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.

55 © Quantachrome Instruments 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

56 © Quantachrome Instruments Adsorption / Desorption (macroscopic description) Adsorption = multilayer formation, then… Desorption = meniscus “control”

57 © Quantachrome Instruments BJH & DH Barrett, Joyner, Halenda and Dollimore-Heal BJH 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.

58 © Quantachrome Instruments Kelvin* Equation * Lord Kelvin a.k.a. W.T. Thomson

59 © Quantachrome Instruments BJH Pore Size r p = actual radius of the pore r k = Kelvin radius of the pore t = thickness of the adsorbed film Pore volume requires assumption of liquid density!

60 © Quantachrome Instruments Statistical Thickness, t Halsey equation Generalized Halsey deBoer equation Carbon Black STSA

61 © Quantachrome Instruments Pore Size Distribution 40Pore Diameter (angstrom) dV/dlogD Artifact

62 © Quantachrome Instruments Pore Filling Pressures for Nitrogen in Cylindrical Pores at 77 K (Gubbins et al, 1997)

63 © Quantachrome Instruments Pore Filling Pressures for Nitrogen in Cylindrical Silica Pores at 77 K (Neimark et al, 1998)

64 © Quantachrome Instruments DFT & Phase Transitions spinodal condensation spinodal evaporation equilibrium transition Experimental (des) Experimental (ads) NLDFT in 4.8nm pore Adsorption, mmol/m 2 Relative pressure, P/P 0 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.

65 © Quantachrome Instruments Where Does Cavitation Occur? AdsorptiveTemperature~p/p o Nitrogen77K0.42 Argon87K0.38 Argon77K0.23

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

67 © Quantachrome Instruments 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

68 © Quantachrome Instruments TEM of MCM-41 Silica

69 © Quantachrome Instruments 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)

70 © Quantachrome Instruments Pore Size Analysis of Mesoporous Solids: The Modified Kelvin Equation ln(P/P 0 ) = -2  cos  /RT  (r p – t c ) r p : pore radius t c : 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

71 © Quantachrome Instruments SEM- of Mesoporous TiO 2

72 © Quantachrome Instruments Nitrogen Sorption at 77 K into Mesoporous TiO 2 6 nm 10 nm 30 nm 100 nm H. Kueppers, B. Hirthe, M.Thommes, G.I.T, 3 (2001) 110

73 © Quantachrome Instruments 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)

74 © Quantachrome Instruments 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 Results of Sorption Studies on Ordered Mesoporous Materials in Combination With Advanced Theoretical and Molecular Simulation Approaches :

75 © Quantachrome Instruments Phase Diagrams of Pure Fluids Confined to Porous Glasses M. Thommes and G.H. Findenegg, Langmuir 10 (1994), 4270 SF 6 /CPG H. Fretwell et al, J. Phys. Condens. Matter 7 (1995) L717 CO 2 /Vycor

76 © Quantachrome Instruments 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

77 © Quantachrome Instruments 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….)

78 © Quantachrome Instruments Theoretical Predictions Of The Pore Size Dependence Of The Relative Pressure Of The Equilibrium Condensation/Evaporation Transition. Neimark AV, Ravikovitch P.I., Grün M., Schüth F., Unger K.K, (1998) J. Coll. Interface Sci. 207,159 N 2 /77 K in cylindrical silica pores

79 © Quantachrome Instruments Nitrogen sorption (77 K) in MCM-41 and Pore Size Analysis by BJH and NLDFT BJH NLDFT NLDFT method: N2/77K cylindrical-silica pore model

80 © Quantachrome Instruments Nitrogen Adsorption and Pore Size Analysis in CMK 3 Mesoporous Carbon NLDFT Methods: N 2 /77K cylindrical carbon pore model M.Thommes, H. Huwe, M. Froeba et al, to be published (2005) NLDFT (5.1 nm) BJH (3.5 nm)

81 © Quantachrome Instruments 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

82 © Quantachrome Instruments Nitrogen Sorption at 77 K into various Mesoporous Silica Materials

83 © Quantachrome Instruments IUPAC Classification of Hysteresis Cylindr.Pores Cylindr.&Spherical Pores Disordered. lamellar pore structures, slit & wedge, shape pores Micro/Mesoporous adsorbents

84 © Quantachrome Instruments 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

85 © Quantachrome Instruments Ar (87 K) and N 2 (77 K) sorption in MCM 48 and NLDFT-Pore size analysis by using the NLDFT-equilibrium method (kernel) Ads(Ar/87 K) Ar/ 87 K N2/77K Des(Ar/87 K) Ar(87K): Hysteresis N 2 (77K): Reversible (M. Thommes et al, Applied Surface Science, 196 (2002) )

86 © Quantachrome Instruments Network Model: Pore blocking and percolation effects in interconnected pore systems 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 Type H2 Hysteresis

87 © Quantachrome Instruments 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

88 © Quantachrome Instruments 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)

89 © Quantachrome Instruments 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) H1 Hysteresis H2 Hysteresis CPG Vycor M. Thommes, in Nanoporous Materials- Science and Engineering” (edited by Max Lu), Imperial College Press, Chapter 11 p (2004)

90 © Quantachrome Instruments 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

91 © Quantachrome Instruments 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.

92 © Quantachrome Instruments H2/H3/H4 Hysteresis: Lower Limit of Hysteresis Loop –Tensile Strength Effect ??  Hysteresis loop for N 2 (77.35 K) always closes at relative pressures > 0.42 and for argon at K at relative pressures >  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

93 © Quantachrome Instruments H3 Hysteresis: Lower limit of Hysteresis Loop –Tensile Strength Effect? BJH-PSD Artifact N2/77K sorption on disordered alumina catalyst M. Thommes, In Nanoporous Materials Science and Engineering, (Max Lu and X Zhao, eds.), World Scientific, in press (2004)

94 © Quantachrome Instruments H4 Hysteresis: Nitrogen adsorption at 77.4 K in activated carbon -Tensile Strength effect?

95 © Quantachrome Instruments 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)

96 © Quantachrome Instruments N 2 and Ar adsorption on micro-mesoporous silica (SE3030) and pore size analysis by the NLDFT- method 1 nm 9.4 nm Mesopore Size N 2 /77K sorption (NLDFT) : 9.4 nm Ar/87K sorption (NLDFT) : 9.1 nm SANS (CLD) : 9.5 nm TEM : ca. 9.5 nm Micropore Size N 2 /77K sorption (NLDFT) : ca. 1.1 nm SANS : ca. 1 – 1.2 nm M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006) Micropore Volume N 2 /77K: 0.12 ml/g SANS: 0.1 ml/g Excellent agreement between NLDFT and SANS/SAXS Pore size distribution from metastable adsorption branch Cumulative pore volume

97 © Quantachrome Instruments Nitrogen sorption of “KLE silica“ at 77K and NLDFT analysis 13.9 nm 1.3 nm Mesopore Size: N 2 -sorption: 13.9 nm TEM: Ca. 13 nm SAXS: 13.8 nm N 2 sorption isotherm NLDFT analysis (spherical mesopores, cylindrical micropores) Pore size distribution Pore diameter (Angström) Excellent agreement between SAXS and new NLDFT approach! M. Thommes, B. Smarsly, M. Groenewolt, P. Ravikovitch, and A. Neimark, Langmuir, 22,756 (2006)

98 © Quantachrome Instruments Pore Blocking/Percolation and Cavitation Pore Blocking/Percolation: “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

99 © Quantachrome Instruments Poreblocking/Percolation As Dominant Evaporation Mechanism: Nitrogen And Argon Sorption In Vycor Analysis of N 2 and Ar adsorp. branches  “Pore Size” Analysis of N 2 and Ar desorp. branches  “Neck Size ” M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006

100 © Quantachrome Instruments Cavitation as dominant mechanism for pore evaporation: N 2 and Ar sorption in SE3030 micro/mesoporous silica NLDFT pore size from adsorption 9.4 nm No pore size info from desorption! M. Thommes, B. Smarsly, P.I. Ravokovitch, A.V. Neimark et al.. Langmuir, 22, 765 (2006)

101 © Quantachrome Instruments 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 N 2 /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.

102 © Quantachrome Instruments 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

103 © Quantachrome Instruments 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).

104 © Quantachrome Instruments 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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