Adsorption Modeling of physisorption in porous materials Part 2

1. European Master Adsorption Modeling of physisorption in porous materials Part 2 Bogdan Kuchta Laboratoire MADIREL Université Aix-Marseille

2. Typicalhysteresisofadsorption-desorption cycle Hysteresis loops H1 and H2, are characteristic for isotherms of type IV (nanoporous materials). Loop of hysteresis H1 shows nearly vertical and parallel branches of the loop : it indicates a very narrow distribution of pore sizes. Loop of hysteresis H2 is observed if there are many interconnections between the pores.

3. Typicalhysteresisofadsorption-desorption cycle Loops of hysteresis H3 et H4, appear on isotherms of type II where there is no saturation. They are not always reproducible. Loop of hysteresis H3, is observed in porous materials formed from agregats, where the capillary condensation happens in a non-rigid framework and porosity not definitly defined. Loop of hysteresis H4 are often observed in structures built from planes that are not rigidly

4. n n p/p0 p/p0

5. n n p/p0 p/p0

6. n p/p0

7. Theories of adsorption Frundlich model Langmuir model BET

8. Theory of adsorption by Freundlich: x/m =  c1/n x – adsorbed mass m – mass of adsorbent c – concentration , n – experimental constants x/m lg(x/m) c Conclusion: adsorption is better at higher pressure lg(c)

9. Langmuir theory - 1 one type of » adsorption sites" - No lateral interactions - 1 site of adsorption allows 1 particle to be there: adsorption is limited to one layer N s = number of adsorption sites N a = number of adsorbed molecules  = fraction of the surface covered

10. Langmuir theory • Isotherm of Chemisorption • at low pressure bp << 1, so • Henry’s law • at high pressure, bp >> 1, si

11. Langmuir isotherm : influence of the coefficient ‘b’

12. Variations on Langmuir and Henry Henry Freundlich Langmuir Sips (Langmuir-Freundlich) Toth Jensen & Seaton

13. Variations of Langmuir and Henry

14. Methode « BET »

15. Théorie de Brunauer Emmett et Teller (BET) • Hypothèses • Starting from the second layer E1EL energy of molecules in liquid state } - 1 one type of » adsorption sites" - No lateral interactions E1=energy of adsorption of the first layer

16. q EL Basic hypothesis of the BET theory B 1 E1 E1 = Energy of adsorption for the first layer El = Energy of liquid state Energy of adsorption Relative pressure p/p°

17. so s1 s2 s3 A Basic hypothesis of the BET theory surface socovered with0 adsorbed layers ... s1 ... 1 ... ... ... ... si ... i Accessiblesurface A = so + s1 + … + si + ...

18. For s0 Rate of condensation of an empty surface Rate of evaporation from a surface covered with one layer = for s1 Rate of evaporation from the surface covered with two layers Rate of condensation on the surface covered with one layer = General, in the case of si Rate of condensation on a surface covered with i layers Rate of evaporation from a surface covered with i+1 layers = Derivation of the BET formula ki si-1 p = k-i si

19. Derivation of the BET formula ki si-1 p=k-i si Total surface of adsorbent Total quantity of adsorbed gas Asuming, that the layer properties are all the same C1(T)=exp(-E1/kT) Ci(T)=exp(-EL/kT)

20. À p° : donc : Derivation of the BET formula

21. Theory of Brunauer Emmett and Teller (BET) • Equations • N= number of layersx = p/p0 = relative equilibrium pressure • if N   • Transformed equation BET

22.  p / po N = 7 N = 25 à  N = 6 Influence of number of layers N on the shape of isotherms of adsorption (BET) N = 5 N = 4

23. Influence of the constant ‘C’ on the shape of isotherms of adsorption (BET)

24. Application for calculation of the adsorption surfaceexample : alumin NPL / N2 / 77 K Pente : Ordonnée :

25. Verifications of BET results example : alumin NPL / N2 / 77 K

26. Lateral interactions Normal interactions

27. Simulation of adsorption • Calculation of energy of adsorption • Simulation of isothermes (with different strength of interaction) • Analyse the results • Simulation Monte Carlo grand canonique (GCMC) • Tool: program GCMC (Fortran) Numerical challenge: 1. Simulations of equilibrium between gas and adsorbed phase 2. Modeling of interaction between pore walls and adsorbed particles

28. (gas) = (adsorbate) (gas, ideal) = 0(gas) + kBT ln(P) VT PVT - constant Working case: MC simulation of adsorption in a pore Problem: Fluid adsorption in cylindrical pores. Grand Canonical Monte Carlo VT- constant External ideal gas pressure P

29. Working case: MC simulation of adsorption in a pore P1 and T fixed R (radius) P2 and T fixed R (radius)

30. Working case: MC simulation of adsorption in a pore T = const p <N>  0.05 234.7 16.2 0.1 362.8 7.6 0.2 385.8 5.8 0.3 401.9 6.9 0.4 421.2 9.7 0.5 448.3 13.2 0.7 558.3 31.6 0.8 691.6 26.7 0.9 1259.1 8.3

31. Directory Run program (compiled) input files gcmc_H2.dat gcmc_H2_par.dat pos_inp.dat spline* execute Results files ene.ini - initial molecular energies ene.fin - final molecular energies mc.pos - molecular position after each bin mc_ene.dat - energies after each bin (wall and total) mc_ent.dat - energies pos_inp.res - analysis of results Rename : pos_inp.res pos_inp.dat OK STOP NO

32. mc.pos Nbin N x y z 1 154 10.886520 -14.887360 9.244424 10.898990 14.983010 21.000650 14.028510 11.913710 2.990251 -14.459990 11.605350 .722188 1.908520 18.285780 22.916110 1.256716 -18.238170 4.253842 13.606980 -12.499060 7.607756 -15.536920 -9.600965 16.492660 -15.764630 -9.760927 24.275380 -4.318254 -17.841070 23.939530 15.933630 -9.115001 17.567660 …………. …….. Nbin = 1 N = 154 Nbin = 1000 N = 258 Nbin = 2000 N = 615

33. Equilibrium situation T = const p <N>  0.05 234.7 16.2 0.1 362.8 7.6 0.2 385.8 5.8 0.3 401.9 6.9 0.4 421.2 9.7 0.5 448.3 13.2 0.7 558.3 31.6 0.8 691.6 26.7 0.9 1259.1 8.3 Mean values Variation -337.7 13.5 -1160.2 15.3 -1497.9 10.2 234.7 16.2

34. Experimental results of adsorption Milestones results • Isotherms • Energy of adsorption • Hysteresis properties

35. Approach thermodynamic – energie of adsorption = g u +pv -Ts = ug +pvg - Tsg u-Ts = ug +RT - Tsg (v = 0, pvg =RT) sg=sg,0 – Rln(p/p0) adsh = u- ug -RT  const. adss0 = s - sg,0  const. Adsorption is a phenomenon exothermic !!!

36. T1 T2 > T1 • Isosteric enthalpy p1 p2 p Approach thermodynamic – energie of adsorption

37. h 4 D ads 3 2 5 1 Basic types of adsorption energy curves Curves 3 and 4 correspond delocalized and localized adsorption on a homogeneous surface, with lateral interactions between molecules. Curve 2 appears in homogeneous systems with no lateral interaction. Curve 5 shows an existence of well defined fomains. Curve 1 is characteristic for heterogeneous surfaces. p/p0

38. . . Example:mesoporous system: MCM-41 et 77K CO & CH4 • Typical for heterogeneous surface •  adsh (2 kJ.mol-1) during the capillary condensation Kr •  adsh (5kJ.mol-1) during the capillary condensation solidification ? CO Kr CH4

39. Milestone properties • Capillary condensation is accompnied with histeresis of variable form Ar N2 lichrospher CPG

40. Milestone properties • Hysteresis disappears at some high temperature Argon / MCM41 (Morishige et al)

41. Argon Nitrogen 2.5 nm 4.0 nm 4.6 nm 2.5 nm 4.0 nm 4.6 nm Milestone properties • For each temperature, there is a size of pore (and/or equilibrium pressure), that the hysteresis disappears below this value. Llewellyn et al., Micro. Mater. 3 (1994) 345.

42. Adsorption - Desorption Isotherms : MCM41 à 77K Ar N2 CO Llewellyn et al., Surf. Sci., 352 (1996) 468.

43. Nitrogen / black of de carbon (Carbopack) M. Kruk, Z. Li, M. Jaroniec, W. B. Betz, Langmuir 15 (1999) 1435-1441.

44. na / mmol g-1 300°C 200°C 110°C 25°C p / p0 Adsorption on precipitated silica Isotherms : N2 & Ar à 77K P. J. M. Carrott & K. S. W. Sing, Ads. Sci. Tech., 1 (1984) 31. • The conditions of the sample preparation are very important!!!!