1 http://nano.materials.drexel.edu Physisorption Analysis of Porous Solids Ranjan Kumar Dash Advisor: Prof. Yury Gogotsi March 11, 2004 http://nano.materials.drexel.edu Contents Background Background 1 1 Porosity Measurement Porosity Measurement 3 3 Critical Comments and Conclusion Critical Comments and Conclusion 4 4 Theory of Adsorption Theory of Adsorption 2 2 2 http://nano.materials.drexel.edu Applications of Porous Materials Molecular sieves Energy storage Catalyst Membranes Application Biomedical http://nano.materials.drexel.edu Degree of Porosity Pore size and its distribution Pore volume Surface area Porosity 3 http://nano.materials.drexel.edu Types of Pores Dead end (open) Closed Inter-connected (open) Passing (open) F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999 http://nano.materials.drexel.edu Shapes of Pores Conical Interstices Slits Cylindrical Spherical or Ink Bottle Pore Shapes F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1-25, 1999 4 http://nano.materials.drexel.edu Size of Pores (IUPAC Standard) 2 nm 50 nm Micropores Mesopores Macropores http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques 5 http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Can measure only open pores ? Pore size : 0.4 nm – 50 nm ? Easy ? Established technique http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Similar to gas adsorption ? Can measure only open pores ? Pore size >1.5 nm ? Easy ? Established technique 6 http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Provide information regarding pore connectivity ? Pore size can be measured if the materials contains ordered pores ? Rarely used for pore analysis http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Pore size > 5nm ? Rarely used for pore analysis 7 http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Any pore size ? Open + Close porosity http://nano.materials.drexel.edu Techniques for Porosity Analysis Mercury porosimetry TEM SEM Small angle X-ray scattering Small Angle Neutron scattering Gas adsorption Techniques ? Any pore size ? Open & Close porosity ? Costly 8 http://nano.materials.drexel.edu Theory of Adsorption http://nano.materials.drexel.edu Adsorption Process Adsorption is brought by the forces acting between the solid and the molecules of the gas. These forces are of two kinds: physical (physiosorption) and chemical (chemisorption) Adsorbent - the solid where adsorption takes place Adsorbate - the gas adsorbed on the surface of solids Adsorptive - adsorbate before being adsorbed on the surface 9 http://nano.materials.drexel.edu MONOLAYER ADSORPTION Langmuir Isotherm is used to model adsorption equilibrium. MULTILAYER ADSORPTION BET Isotherm used to model adsorption equilibrium. Surface reactions may take place:- Dissociation, reconstruction, catalysis. No surface reactions. Can be activated, in which case equilibrium can be slow and increasing temperature can favour adsorption. Non activated with equilibrium achieved relatively quickly. Increasing temperature always reduces surface coverage. ?H ads = 50 ….. 500 kJ mol -1 ?H ads = 5 ….. 50 kJ mol-1 SURFACE SPECIFIC E.g. Chemisorption of hydrogen takes place on transition metals but not on gold or mercury. NOT SURFACE SPECIFIC Physisorption takes place between all molecules on any surface providing the temperature is low enough. STRONG, SHORT RANGE BONDING Chemical bonding involved. WEAK, LONG RANGE BONDING Van der Waals interactions CHEMISORPTIONPHYSISORPTION Physisorption vs Chemisorption http://www.soton.ac.uk http://nano.materials.drexel.edu Adsorption Process 1. Diffusion to adsorbent surface 2. Migration into pores of adsorbent 3. Monolayer builds up of adsorbate 1 2 3 ?Gas molecules admitted under increasing pressure to a clean, cold surface. ?Data treatment techniques find the quantity of gas that forms the first layer. 1 2 3 S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 10 http://nano.materials.drexel.edu Adsorption Process Adsorbent Adsorbate adsorptive of pressure saturated adsorbate of pressure where :as written becan equation above theconstant, made are I and T, W,If adsorbent. and adsorbatebetween n interactio re; temperatu adsorbate; theof pressure adsorbent; of weight adsorbed; gas of volume where ),,,( = ? ? ? ? ? ? ? ? = = = = = = = p p p p f I T P W PITWf o o V V V a a a Equation of adsorption isotherm S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 http://nano.materials.drexel.edu Gas Sorption: Isotherm Adsorption isotherm ?Isotherm is a measure of the volume of gas adsorbed at a constant temperature as a function of gas pressure. ?Isotherms can be grouped into six classes. adsorptive of pressure saturated adsorbate of pressure where = ? ? ? ? ? ? ? ? = p p p p f o o V a V a Desorption isotherm p p o 11 http://nano.materials.drexel.edu Gas Sorption: Isotherm V a 1 P/P o Type I or Langmuir S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 ?Concave to the P/P o axis ?Exhibited by microporous solids ( < 2nm ) 1 P/P o Type II ?Exhibited by nonporous or macroporous solids ( > 50nm ) ?Unrestricted monolayer-multilayer adsorption ?Point B indicates the relative pressure at which monolayer coverage is complete B V a http://nano.materials.drexel.edu Gas Sorption: Isotherm V a 1 P/P o Type III ?Convex to the P/P o axis ?Exhibited by nonporous solids V a 1 P/P o Type IV ?Exhibited by mesoporous solids ?Initial part of the type IV follows the same path as the type II S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 12 http://nano.materials.drexel.edu Gas Sorption: Isotherm V a 1 P/P o Type V 1 P/P o Type VI ?Highly uncommon ?Exhibited by mesoporous solids ?Exhibited by nonporous solids with an almost completely uniform surface S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 V a http://nano.materials.drexel.edu Gas Sorption: Hysteresis ?Hysteresis indicates the presence of mesopores. ?Hysteresis gives information regarding pore shapes . ?Types I, II and III isotherms are generally reversible but type I can have a hysteresis. Types IV and V exhibit hysteresis. 1 P/P o Hysteresis V a S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 13 http://nano.materials.drexel.edu Gas Sorption: Hysteresis V a 1 P/P o Type A Cylindrical Slits Type B 1 P/P o 1 P/P o Type C Type D 1 P/P o Type E 1 P/P o Conical Bottle neck http://nano.materials.drexel.edu Adsorption/Desorption Adsorption = multilayer formation Desorption = meniscus development 14 http://nano.materials.drexel.edu Adsorption Theories: Langmuir Adsorbate Adsorbent Assumptions: ? homogeneous surface (all adsorption sites energetically identical) ? monolayer adsorption (no multilayer adsorption) ? no interaction between adsorbed molecules adsorbate. of pressure and constant; empirical monolayer; form torequired gas of volume ; pressureat adsorbed gas of volume where 1 = = = = += P b V PV V P bVV P m a mma http://nano.materials.drexel.edu Adsorption Theories: BET adsorbate. of pressure relative and layer);1st of adsorption ofenergy to(relatedconstant BET C monolayer; form torequired gas of volume ; pressureat adsorbed gas of volume where )1(1 )( = = = = ? ? ? ? ? ?? += ? o m a o mm o a P P V PV P P CV C CVPPV P ? Modification of Langmuir isotherm ? Both monolayer and multilayer adsorption Adsorbate Adsorbent 15 http://nano.materials.drexel.edu Specific Surface Area Calculation CVP P CV C PPV P m o m o a 1)1( )( + ? ? ? ? ? ?? = ? imXY += im V m + = 1 P/P o 1 V[(P o /P)-1] 0-1 0-2 0-3 At least three data points in the relative pressure range 0.05 to 0.30 adsorbate ofWeight area surface Total csavm ANV = sample ofWeight area surface Total area) surface (SpecificSSA = http://nano.materials.drexel.edu Single Point BET ?Single-point method offers the advantage of simplicity and speed, often with little loss in accuracy. ( ) o am PPVV ?= 1 i.e. V m = 1/slope ?A relative pressure of 0.3 gives good general agreement with the multi-point method. ? Correction of single point “error” at P/P 0 = 0.3 by multiplying the single point BET value by C/C-2 decreases the difference. 5.957 8.056 4.286 4.923 Multi-point BET (m 2 /g) 5.194 6.867 3.664 4.241 Uncorrected single-point (m 2 /g) -12.8 -14.8 -14.5 -13.9 Uncorrected difference (%) 4 3 2 1 Sample No. +1.736.060 -0.568.011 -0.264.275 0.514.948 Corrected difference (%) Corrected single – point (m 2 /g) 16 http://nano.materials.drexel.edu Pore Size Distribution V a Pore diameter, d Narrow pore size distribution Broad pore size distribution Unimodal pore size distribution Pore diameter, d Multimodal pore size distribution The distribution of pore volume with respect to pore size is called a pore size distribution. V a ∑ = d a V volumePore http://nano.materials.drexel.edu Pore Size Distribution ?G ads = RT(lnP ads -lnP 0 ) ?G des = RT(lnP des -lnP 0 ) ?G des < ?G ads 1 P/P o (P/P o ) des (P/P o ) ads ?Adsorption or desorption isotherm. ?The desorption isotherm is preferred over adsorption isotherm. V a 17 http://nano.materials.drexel.edu Pore Size: Kelvin Equation ?Multilayer formation occurs in parallel to capillary condensation. ?Capillary condensation is described by the Kelvin equation. phase. condensed and solid ebetween th anglecontact re; temperatu constant; gas real meniscus; liquid theof curvature of radiusmean adsorbate; condensed of memolar volu tension;surface liquid ; adsorbate of pressure saturated adsorbate of pressure where cos 2 ln = = = = = = ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? θ γ θ γ T R V RT V r p p r p p k o k o θ k r http://nano.materials.drexel.edu Pore Size: Kelvin Equation trr kp += Actual radius of the pore Kelvin radius of the pore Thickness of the adsorbed layer Prior to condensation, some adsorption has taken place on the walls of the pore, r k does not represent the actual pore radius. θ t k r Adsorbed layer 18 http://nano.materials.drexel.edu Methods for Calculation of Pore Size Distribution ?BJH (Barrett, Joyner and Halenda) method ?DH (Dollimore Heal) method ?Dubinin-Astakhov method ?HK (Horvath-Kawazoe) method ?Saito-Foley method Mesoporous solids Microporous solids ?NLDFT (Non Local Density Functional Theory) and Monte Carlo simulation method Microporous and Mesoporous solids http://nano.materials.drexel.edu Porosity Measurement 19 http://nano.materials.drexel.edu Porosity Analyzer Outgassing station Analysis station Liquid nitrogen bath http://nano.materials.drexel.edu Steps for Measurement 3. Interpretation 2. Adsorption Analysis 1. Sample Preparation 20 http://nano.materials.drexel.edu 1. Sample Preparation (Outgassing) ? Surface contamination is removed by application of: ? Temperature ? Flowing gas (helium or nitrogen) or vacuum ? Backfill can be done using helium or adsorbate gas. ? According to IUPAC standards, materials should be outgassed for at least 16 hours. Adsorbate Helium Vacuum P o Outgassing station Analysis station Sample Cell http://nano.materials.drexel.edu 2. Adsorption Analysis ? Adsorbate (nitrogen, argon, carbon dioxide, krypton) ? Analysis temperature (liquid nitrogen, liquid argon, 0 o C) ? Quantity of sample (1 mg sample is sufficient) ? Number of points (single point, five points, seven points, eleven points, full analysis) Adsorbate Helium Vacuum P o Outgassing station Analysis station Sample Cell 21 http://nano.materials.drexel.edu 3. Interpretation 3 2 1 Volume adsorbed P/P o Points Weight of sample O U T P U T Pore shape Specific surface area Pore volume Pore size & distribution Results http://nano.materials.drexel.edu Critical Comments and Conclusion 22 http://nano.materials.drexel.edu Critical Comments : Choice of Adsorptive ? N 2(g) in N 2(l) is the most commonly used adsorbate. ? Not completely inert. ? Dipole movement and thus can have localized adsorption. ? Cross-sectional area of 0.162 nm 2 is questionable. ?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 ?Quantachrome Autosorb-I Operational Manual O x y g e n A r g o n N i t r o g e n C a r b o n m o n o o x i d e C a r b o n d i o x i d e K r y p t o n n - b u t a n e 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 C r os s- sect i onal ar ea, nm 2 http://nano.materials.drexel.edu O x y g e n A r g o n N i t r o g e n C a r b o n m o n o o x i d e C a r b o n d i o x i d e K r y p t o n n - b u t a n e 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 C r os s- sect i onal ar ea, nm 2 Critical Comments : Choice of Adsorptive ?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 ?Quantachrome Autosorb-I Operational Manual ? Ar (g) in Ar (l) is preferable but because of unavailability of Ar (l) (87K), N 2(l) (77 K) is used. ? Ar can reach to somewhat smaller pores than N 2 . ? Accurate measurement of micropores is possible using Ar. 23 http://nano.materials.drexel.edu O x y g e n A r g o n N i t r o g e n C a r b o n m o n o o x i d e C a r b o n d i o x i d e K r y p t o n n - b u t a n e 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 C r os s- sect i onal ar ea, nm 2 Critical Comments : Choice of Adsorptive ?S. Lowell & J. E. Shields, Powder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 ?Quantachrome Autosorb-I Operational Manual ? In case of activated carbon, CO 2 is often the most preferred adsorbate. ? Adsorption analysis of CO 2 takes less time. ? Limited to micropore analysis. http://nano.materials.drexel.edu Critical Comments : Validity of BET - Method ? The BET method depends on the cross- sectional area of adsorbate. ? Monolayer structure is same on all the surface. ? Localized monolayer coverage. K. S. W. Sing, The Use of Nitrogen Adsorption for the Characterisation of Porous Materials, Colloids and Surfaces, 187 – 188, 2001, 3 - 9 ? ? ? ? ? ?? += ? o mm o P P CV C CVPPV P )1(1 )( M ALV SSA av = Adsorbate Adsorbent 24 http://nano.materials.drexel.edu Critical Comments : Validity of Kelvin Equation θ γ cos 2 ln RT V r p p k o = ? ? ? ? ? ? ? ? ? ? ? Is relation between the meniscus curvature and the pore size and shape valid? ? Is it applicable for micropores and narrow mesopores? ? Does surface tension varies with pore width? θ F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 203, 1999 k r http://nano.materials.drexel.edu Critical Comments : Shape of Microporous Materials V a 1 P/Po Type I or Langmuir ?Type I isotherms don’t have hysteresis. ?Pore shape cannot be determined by isotherm. ?As various methods for pore size calculation are based on shape of pores, reliability of pore size calculation is questionable. F. Rouquerol, J. Rouquerol, K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 439-446, 1999 25 http://nano.materials.drexel.edu 2 nm 50 nm Micropores Mesopores Macropores de Boer’s t-methodCylindrical or Slit shapedBrunauer MP method ?Polanyi potential theory ?Independent of Kelvin equation -Dubinin-Astakhov method AssumptionMethods Cylindrical Slit Pore Shape HK method ?Everett and Powl method ?Independent of Kelvin equation Based on .. Saito-Foley method HK (Horvath-Kawazoe) method Critical Comments : Choice of Method ?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997 ?Quantachrome Autosorb-I Operational Manual http://nano.materials.drexel.edu 2 nm 50 nm Micropores Mesopores Macropores Kelvin equationCylindrical, Slit-shapedBJH (Barrett, Joyner and Halenda) method t-methodCylindrical DH (Dollimore Heal) method AssumptionMethods Pore Shape Based on .. Critical Comments : Choice of Method ?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997 ?Quantachrome Autosorb-I Operational Manual 26 http://nano.materials.drexel.edu 2 nm 50 nm Micropores Mesopores Macropores AssumptionMethods Cylindrical and slit Pore Shape Statistical thermodynamics Based on .. NLDFT (Non Local Density Functional Theory) and Monte Carlo simulation method Critical Comments : Choice of Method ?P. A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics, 53 – 152, 1997 ?Quantachrome Autosorb-I Operational Manual http://nano.materials.drexel.edu Conclusion ?Despite limitations, physisorption is often the technique of first choice for studying pore characteristics of solid materials. ?In spite of its artificial nature, the BET method is still the most popular technique for determination of surface area. ?All computational procedures for pore size analysis have limitations. The various assumptions include ideal pore shape, rigidity of structure and oversimplified model (capillary condensation or micropore filling). ?The current IUPAC classification contain six isotherms. Apart from these, there are many complex isotherms for which there is no procedure available for interpretation. ?The use of single gas adsorption cannot be expected to provide more than a semi-quantitative estimate of the micropore size distribution. It is always advisable to compare adsorption results with two or more gases. 27 http://nano.materials.drexel.edu Questions? Comments? Thank you! I love Pia. http://nano.materials.drexel.edu TEM of Ordered Nanoporous Carbon R. Ryoo, S. H. Joo and S. Jun, "Synthesis of Highly Ordered Carbon Molecular Sieves via Template-Mediated Structural Transformation", J. Phys. Chem. B 103, 7743 (1999). 28 http://nano.materials.drexel.edu TEM of Amorphous Carbon Carbon derived from boron carbide 5 nm http://nano.materials.drexel.edu SEM of Porous Aluminum http://cml.me.berkeley.edu/~jiayang/inter/english/eweb4-1.htm. Porous aluminum with pore-spacing about 100 nm (SEM, 70,000 X) 29 http://nano.materials.drexel.edu Common Adsorbates 0.205? -195.8 o C (liquid nitrogen)Kr 0.141? -183 o C (liquid argon)O 2 ? 0 o C, 25 o C ? -183 o C (liquid argon) ? -78 o C, -25 o C, 0 o C ? -183 o C (liquid argon). ? -195.8 o C (liquid nitrogen) ? -195.8 o C (liquid nitrogen) ? -183 o C (liquid argon). Temperature 0.195CO 2 0.163CO 0.162N 2 0.142Ar 0.469 Cross sectional area (nm 2 ) Gas C 4 H 10 http://nano.materials.drexel.edu Adsorption Analyzer 30 http://nano.materials.drexel.edu Adsorption Analyzer Adsorbate Helium Vacuum P o Outgassing station Analysis station Sample Cell Manifold (known volume) http://nano.materials.drexel.edu Adsorption Measurement 1. Adsorptive is passed through the sample at requested pressure. 2. Volume of gas adsorbed = difference in pressure of manifold. 3 2 1 Volume of gas adsorbed P/P o Points 31 http://nano.materials.drexel.edu Techniques for Porosity Analysis ?Larger pores (> 5 nm).SEM (Scanning Electron Microscope) ?Total porosity (open + close).SAXS (Small Angle X-Ray Scattering) ?Open porosity (pore size > 1.5 nm)Mercury Porosimetry ?Limited information regarding pore connectivity. ?Small pores if the materials contain ordered pores TEM (Transmission Electron Microscope) ?Open and closed pores. ? Open porosity (pore size: 0.4 nm - 50 nm) Gas Adsorption SANS (Small Angle Neutron Scattering) S. Lowell & J. E. Shields, Haowder Surface Area and Porosity, 3rd Ed. Chapman & Hall, New York, 1991 http://nano.materials.drexel.edu Factors Affecting Surface Area 1 m A i = Initial surface area = 6 m 2 0.1 m Number of fragments = 1000 A f = Final surface area = 1000 X 6 X (0.1) 2 m 2 A f /A i = 10 (Particle size) 2 α Surface area 1