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  1. matériaux avancés pour la catalyse et la santé Adsorption and Intrusion Methods for the Characterization of Mesoporous Materials F. Di Renzo1*, A. Galarneau1, F. Quignard1, S. Valange2, Z. Gabelica3, J.-P. Bellat4 direnzo@enscm.fr 1Institut Charles Gerhardt Montpellier, UMR 5253 CNRS-UM2-ENSCM-UM1, Matériaux Avancés pour la Catalyse et la Santé, ENSCM, 8 rue Ecole Normale, 34296 Montpellier, France 2Laboratoire de Catalyse en Chimie Organique, Université de Poitiers, Poitiers, France 3LPI-GSEC, ENSCMu, Université de Haute Alsace, Mulhouse, France 4Institut Carnot de Bourgogne, UFR ST, Université de Bourgogne, Dijon, France

  2. matériaux avancés pour la catalyse et la santé Adsorption and Intrusion Methods for the Characterization of Mesoporous Materials ● an inventory of superposed phenomena ● surface tension, liquid-solid interfaces and capillarity ● new standard materials allow a new look at old models ● shape effects and the limits of capillarity ● non-wetting fluids and still more shape effects

  3. N2 adsorption-desorption isotherms at 77 K for mesoporous silicas prepared by different methods the relative pressure of the capillary condensation step indicates the pore size 21 nm 9.5 nm 10.3 nm 2 cm3 g-1 1.5 cm3 g-1 adsorbed gas volume 1.2 cm3 g-1 840 m2 g-1 490 m2 g-1 280 m2 g-1 the amount of nitrogen adsorbed at the top of the condensation step indicates the pore volume the amount adsorbed at the top of the first adsorption step indicates the surface area N2 inside the pores is a dense phase and presents nearly the density of liquid N2 for N2, ρliq/ρgas = 647 MCM-41 structured by CTMA swollen by TMBSBA-15 structured by PEO-PPO-PEO triblock copolymer Sylopol commercial precipitated silica

  4. Layer adsorption : spread over the whole pressure field according to a known law BET equation (multilayer Langmuir) n adsorbed amount nm monolayer capacity p/p° relative pressure c parameter related to the difference of adsorption heat between monolayer and following layers Isotherm interpretation : separation of superposed phenomena (which, happily, do not depend on pressure in the same way) Condensation : occurs at pressure values which depend on the pore size Kelvin equation γ surface tension R gas constant T temperature Vm molar volume r mesopore core radius Contributions of capillary condensation and multilayer adsorption can be easily separated if mesopores present a narrow pore size distribution

  5. an isotherm of mesoporous solid and its comparison plot N2 adsorption at 77 K on Lichrosphere 60 chromatographic silica comparison plots are useful to evidence different mechanisms in the adsorption isotherm

  6. comparison plot Y Y experimental isotherm X P reference isotherm aerosil 200 fumed silica X P in a comparison plot, for each pressure value the adsorbed amount on the examined sample is compared with the adsorbed amount on the reference sample reference adsorbent SBET 187 m2 g-1 slope of the comparison plot 3.9 Scomparison plot = 187 x 3.9 = 730 m2 g-1 in good agreement with SBET 740 m2 g-1

  7. a positive deviation of the comparison plot indicates that a more effective mechanism of adsorption is superposed to the growth of the adsorbed layer t-plot and αS-plot: two types of comparison plots t-plot: reference adsorbed amount expressed as average thickness of the monolayer (assumption of constant density of the condensed phase) thickness t = 1Å = 0.345 µmol m-2 = 15.4 cm3 (STP) m-2 αS-plot: the unit of the abscissae is the reference adsorbed amount at p/p° 0.4, an isotherm region expected to be often rid of condensation phenomena

  8. If cohesive forces of the liquid are stronger than the adhesive forces at the interface, the sum of forces at the surface is directed towards the interior of the liquid. This induces a pressure rise inside the liquid. The force balance inside a liquid droplet allows to correlate this pressure to the droplet size through the surface tension. http://citt.ufl.edu/Marcela/Sepulveda/html water surface tension at 20 °C = 0.0728 N m-1 Young-Laplace law

  9. contact angle Ө in the presence of a solid, the contact angle depends on the sum of the surface tensions at the triple point σvapour-liquidcos Ө + σliquid-solid = σvapour-solid non-wetting wetting

  10. 2σcos(Ө) capillary rise Surface tension around the perimeter of the tube results in a force with a vertical component that drives water upwards.  The movement continues until the force due to surface tension equals the weight of the water column. h capillary rise σ surface tension Ө contact angle r capillary radius ρ liquid density g gravity acceleration

  11. physicochemical equilibrium (Gibbs-Duhem at constant T) mechanical equilibrium (Young-Laplace) dμliq = dμvap dpliq-dpvap = d(2σ/rm) Vliqdpliq = Vvapdpvap d(2σ/rm) = dpvap (Vliq-Vvap) / Vliq Vliq negligible compared to Vvapvapour as perfect gas d(2σ/rm) = - RTdpvap / (Vliq Pvap) integrating between (rm, p) and (∞, p°) ln (p/p°)= - 2σVliq / (RT rm) Kelvin equation

  12. the driving force of capillary condensation and drop coalescence is the decrease of the liquid-vapour interface area Kelvin equation 2σVm surface = high energy state William Thomson Lord Kelvin (1824-1907)

  13. ln (p/p°) = - 2 σ VL / (R T rm) Kelvin equation the correlation between curvature of the meniscus and pore size depends on the shape of the pore rp = rm + t wp = rm + 2t Schematic representation of adsorbed layer and capillary meniscus in cylindrical (lefthand) and slit-shaped (rigthhand) pores

  14. MCM-41, J.S. Beck et al., JACS 114 (1992) 10834 Did the availability of new reference materials modify our understanding of the adsorption phenomena? MCM-48V. Alfredsson and M.W. Anderson, Chem. Mater. 8 (1996) 1141 SBA-15, Z. Liu et al., ChemPhysChem (2001) 229

  15. Correlations between cell size, pore size, wall thickness, surface area and mesoporous volume for MCM-41-like silicas r = (a - t)/2 radius of inscribed circle Deq = 1.05 (a - t) diameter of circle with the same area as the hexagon A. Galarneau et al., Micropor. Mesopor. Mater., 27 (1999) 297; Stud. Surface Sci. Catal., 142 (2002) 1057.

  16. Correlations between cell size, pore size, wall thickness, surface area and mesoporous volume for MCM-48 silicas A. Galarneau et al., Microp. Mesop. Mater., 83 (2005) 172 B. Coasne et al., Langmuir, 22 (2006) 11097

  17. Cross-sectional areas of nitrogen molecule: 16.2 Å2 over silylated silica (value usually used in syrface area calculations) 13.5 Å2 over rehydroxylated silica L. Jelinek, E.s. Kovats, Langmuir 10 (1994) 4225

  18. Ca-alginate aerogel F. Quignard, M. Robitzer, F. Di Renzo New J. Chem. 32 (2008) 1300 negative deviation of the αS-plot of a solid with less mesopores than the reference some mesoporosity in a reference solid assumed as non-porous Reference isotherm of N2 adsorption at 77 K on Aerosil fumed silica αS-plot for a Ca-alginate aerogel

  19. effect of the nature of the surface on the comparison plots N2 adsorption-desorption isotherms at 77 K (lefthand) and corresponding αS-plot (righthand) for a non-microporous SBA-15 silica (filled symbols) and a sample functionalized with C16 hydrocarbon chains (void symbols)

  20. t-plots for the adsorption of N2 at 77 K on polysaccharide aerogels Comparison plots of the adsorption of N2 at 77 K on (filled circles) ionotropic alginate, (void circles) alginic acid, and (void squares) carrageenan aerogels. The lines represent best-fit linear correlations extrapolated to αS = 0. Comparison plots of the adsorption of N2 at 77 K on (filled triangles) chitosan and (void triangles) chitin aerogels. The lines represent best-fit linear correlations extrapolated to αS = 0.

  21. κ-carrageenan agarose alginic acid chitosan chitin energetical parameters of the adsorption of N2 at 77 K on polysaccharide aerogels Correlation between the energetical parameter C of the BET equation and the intercept of the αS plots of polysaccharide aerogels with different surface groups: acetylated amines (chitin, void triangles), amines (chitosan, filled triangles), hydroxyls (agar, void lozenges), sulphates (carrageenan, void squares), carboxylic groups (alginic acid, void circles), and salified carboxylates (alginate, filled circles). St. Andrews cross for the Aerosil fumed silica used as reference isotherm.

  22. alginic acid chitin isosteric heats of adsorption of Ar on polysaccharide aerogels Net molar energy of adsorption of argon on (filled circles) Ca-alginate and (void triangles) chitin aerogels and (St. Andrews' crosses) fumed silica.

  23. Different shapes of hysteresis of type IV isotherms H4 H1 narrow mesopore size distribution H2 ink-bottle pores H3 broad pore size distribution with smaller pores accessible through the larger ones H4 similar to H3 in the presence of microporosity

  24. lower limit of the hysteresis loop: catastrophic desorption Schematic representation of the N2 adsorption-desorption isotherms at 77 K and corresponding pore size distributions for materials with 10 nm cavities and entrance sizes between 2 and 10 nm

  25. limit of reversible pore filling adsorption isotherms of N2 at 77 K on (a) SBA-15, (b) TMB-swollen MCM-41, and (c) MCM-41 silicas

  26. corresponding state graph for the limit of reversible pore filling D. Maldonado et al. J. Porous Mater. 14 (2007) 279 reduced temperature and pressure of the limits of reversible pore filling for N2 (void squares), Ar (filled squares), Xe (filled triangles), O2 (void lozenges), CO2 (void triangles), cyclopentane (void circles), benzene (St. Andrews crosses), 2,2-dimethylbutane (crosses). Tc and pc are the critical conditions.

  27. piping head delivery head maximum suction head suction head He = (Patm - Pv) / γ the suction head of a pump is limited by the evaporation of the liquid Suction Head as Affected by Temperature

  28. Clausius-Clapeyron calculations of the enthalpies of evaporation at the limit of reversible pore filling P. Trens et al., Langmuir 21 (2005) 8560

  29. The pore size can be tuned by the synthesis method Adsorption/desorption isotherms of nitrogen at 77 K  MCM-41 3 nm (synthesis with CTAB) ▲ MCM-41 4 nm (synthesis with CTAB, swelled with trimethylbenzene)  MCM-41 5.5 nm (synthesis with CTAB, swelled with dodecylamine)  MCM-41 10 nm (synthesis with CTAB, swelled with trimethylbenzene)

  30. Enthalpies of adsorption of n-hexane as a function of coverage as calculated from (left hand) the adsorption data and (right hand) the desorption data on () MCM-41 3 nm, (▲) MCM-41 4 nm, (■) MCM-41 5.5 nm, (O) SBA-15 10 nm. Dashed line: condensation heat of hexane. D. Maldonado et al. J. Porous Mater. 14 (2007) 279

  31. Condensation enthalpies of n-hexane as a function of the pore size. Isosteric data from adsorption () and desorption () results. Continuous line: calculated condensation enthalpy. Dotted line: condensation enthalpy on a flat liquid surface.

  32. pore surface adsorbed layer core filled by capillary condensation When the meniscus advances, the interface between adsorbed layer and vapour disappears In small mesopores, the energetical contribution of the interface affects the enthalpy of capillary condensation In the hypothesis of constant density of the adsorbed phase, the fraction of interface molecules can be evaluated from the adsorption isotherm Nm = monolayer amount by BET equation

  33. 2σcos(Ө) capillary rise and capillary depression non-wetting fluid Ө > 90° h capillary rise σ surface tension Ө contact angle r capillary radius ρ liquid density g gravity acceleration wetting fluid Ө < 90°

  34. Washburn-Laplace law for cylindrical pores ΔP = (2γ/R) cosθ γ(Hg)0.485 N m-1 if θ = 140° R = -743/ΔP R = nm ΔP = MPa corelation pressure-pore size depending on contact angle

  35. Mercury porosimetry on SBA-15 sample prepared at 130°C field of superposition with the data from nitrogen adsorption Pore size calculated for θ = 140° 50 nm 3 nm 0.7 µ 20 nm 7.5 nm structural porosity 1.0 ml/g intergranular porosity 2.2 ml/g grain packing

  36. Porosity of SBA-15s from nitrogen adsorption at 77 K pore size calculated by the method of Broekhoff and de Boer pore size increases with the temperature of the second step of the synthesis A. Galarneau et al., Langmuir 17 (2001) 8328

  37. structural porosity of SBA-15s from mercury intrusion pore size calculated for contact angle θ = 140° hysteresis loop is wider for larger pores

  38. Intrusion of water in MCM-41 grafted with octyldimethylsilane Intrusion = Propagation Pint RP-1 Pext  RP-4 Retraction Propagation Extrusion depends on cavitation (nucleation of the vapour phase) B. Lefèvre et al., J. Colloid Surface A 2004, 241, 265. empyrical Kloubek-Rigby-Edler correlation for mercury retraction Rigby and Edler, J. Colloid Interf. Sci.2002, 250, 175

  39. mercury porosimetry underevaluates the pore size for interconnected pore systems comparison of the pore size measured by mercury intrusion and N2 adsorption for MCM-41 (squares), SBA-15 (triangles) and porous glass (circles) samples.

  40. Carbon replica of SBA-15 prepared at 100°C The carbon rods formed inside the mesopores do not fall apart when the silica template is dissolved in HF Liu, Terasaki, Ohsuna, Hiraga, Shin, Ryoo, ChemPhysChem (2001) 229

  41. Carbon replica of SBA-15 prepared at 100°C Disordered bridges connecting ordered parallel mesopores Liu, Terasaki, Ohsuna, Hiraga, Shin, Ryoo, ChemPhysChem (2001) 229

  42. Connections between pores depend on the conditions of synthesis Pt-3522C Pt-3532C 50 nm SBA-15 prepared at 60 °C The platinum rods of the replica do fall apart (same effect for MCM-41) SBA-15 prepared at 100 °C Interconnected pores: the platinum replica does not fall apart Galarneau, Cambon, Di Renzo, Ryoo, Choi, Fajula, New J. Chem. 27 (2003) 73

  43. 180° 130° 110° Pression of intrusion and retraction of mercury as a function of pore size from nitrogen adsorption solids with pore interconnections physical impossibility: contact angle higher than 180°

  44. a higher pressure is needed to overcome the rim of a pore widening Evolution of the contact angle and the radius of the meniscus when mercury advances in a cylindrical pore with increasing diameter Kloubek, Powder Technol.1981, 29, 63; Galarneau et al., J. Phys. Chem. C 2008, 112,12921 surface roughness corresponds to an increase of contact angle R* = ratio of the rough surface area to its projection on the average plane cos θrough = R* cos θflat Wenzel, J. Phys. Colloid Chem. 1949, 53, 1466

  45. Academic Press, 1999 Academic Press, 1982