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

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

5. 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...

6. Statistical Thickness, t
Halsey equation
Generalized Halsey
deBoer equation
Carbon Black STSA

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

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

9. 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. 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

11. 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).

12. 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)...

13. Estimation of Micropores Dubinin-Radushkevich (DR) Plot
Log (W)
Extrapolation yields Wo
Log2(Po/P)

14. 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).

15. 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.

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

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

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

19. Pore Size Analysis of MCM 41: Calculations Compared

20. 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

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

22. IUPAC’s Classification of Sorption Isotherms

23. 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)

24. 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

25. 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)

26. Argon Adsorbate

27. Adsorption of Nitrogen (77.35 K) and Argon (87.27 K) on some Zeolites
Ar/87.27 K
Faujasite: Ar and N2 Adsorption .

28. 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. 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. Carbon Dioxide Adsorbate

31. 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.

32. 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

33. Water Adsorbate

34. 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)

35. 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

36. 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

37. 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

38. Hydrogen Adsorbate

39. 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

40. 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

41. 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

42. Pore Shape & Size Influence

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

45. 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

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

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

48. 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.

49. 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

50. 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

51. 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.

52. 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)

53. 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

54. 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. 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. Adsorption / Desorption (macroscopic description)
Adsorption = multilayer formation, then…
Desorption = meniscus “control”

57. 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.

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

59. 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!

60. Statistical Thickness, t
Halsey equation
Generalized Halsey
deBoer equation
Carbon Black STSA

61. Pore Size Distribution
Artifact
dV/dlogD 40
Pore Diameter (angstrom)

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

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

64. 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.

65. Where Does Cavitation Occur?
Adsorptive
Temperature
~p/po
Nitrogen
77K
0.42
Argon
87K
0.38
0.23

66. 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

67. 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. TEM of MCM-41 Silica

69. 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. Pore Size Analysis of Mesoporous Solids: The Modified Kelvin Equation
ln(P/P0) = -2cos /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

71. SEM- of Mesoporous TiO2

72. 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

73. 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.  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

75. 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

76. 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. (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….)

78. 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

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

80. 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)

81. 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. Nitrogen Sorption at 77 K into various Mesoporous Silica Materials

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

84. 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. 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) )

86. 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

87. 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. 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)

89. 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)

90. 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. 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. 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

93. 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)

94. H4 Hysteresis: Nitrogen adsorption at 77
H4 Hysteresis: Nitrogen adsorption at K in activated carbon -Tensile Strength effect?

95. 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. 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

97. 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)

98. 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

99. 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

100. 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)

101. 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.

102. 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. 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. 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)