1. 1 Time dependent aspects of fluid adsorption in mesopores Harald Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry Leipzig University, Linnéstrasse 2, D-04103 Leipzig, hmorgner@rz.uni-leipzig.de Introduction to the phenomenon of adsorption hysteresis Shortcomings of standard thermodynamics for confined systems The alternative concept of COS (=Curves of States) Time dependent treatment: pressure jump experiments revealing dynamic behavior properties & role of fluctuations CompPhys2012 Leipzig November 29-30,2012

2. 2 R.Rockmann PhD Thesis 2007 U Leipzig Adsorption Hysteresis in Porous Material SBA-15: silica pores with two open ends narrow pore size distribution Introduction Theoretical Simulation Results adsorption from vapor phase

3. 3 Adsorption Hysteresis in Porous Material H.Morgner (2010) J.Phys.Chem. C 114 8877-83 Introduction Theoretical Simulation Results adsorption from vapor phase

4. 4 grand canonical boundary conditions canonical boundary conditions H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472 Introduction Theoretical Simulation Results Curves of States: introduction

5. 5 H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472 COS(  ) two IF COS(  ) one IF Introduction Theoretical Simulation Results Curves of States: filling pattern

6. 6 H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472 grand potential Introduction Theoretical Simulation Results Curves of States: relation to TD

7. 7 Neimark&Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 both branches contain a set of microstates these sets are subsets of one common state (equilibrium). Thus, both branches form only one state true GCE isotherm „….the true GCE isotherm cannot be sampled in practical simulations….“ Introduction Theoretical Simulation Results attempts to save TD

8. 8 Diffusion treated by Onsager ansatz driving force: gradient of chemical potential  pressure in gas reservoir  Introduction Theoretical Simulation Results pressure jump experiments

9. 9 Introduction Theoretical Simulation Results pressure jump experiments

10. 10 Introduction Theoretical Simulation Results pressure jump experiments

11. 11 Introduction Theoretical Simulation Results pressure jump experiments

12. 12 Introduction Theoretical Simulation Results pressure jump experiments

13. 13  eq    PONR  fluc  PONR time needed to lifetime of fluctuation:  fluc fluctuation effective if  fluc >  PONR Introduction Theoretical Simulation Results fluctuations in gas reservoir shift pore to PONR from pressure jump

14. 14  occurrence =  fluc / P stat r  200 nm  = 5 nm Introduction Theoretical Simulation Results fluctuations in gas reservoir pore wall

15. 15  eq  fluc average time elapsed until effective fluctuation occurs  occurrence Stat. TD provides statistical probability P stat P stat =  fluc /  occurrence  occurrence =  fluc / P stat Introduction Theoretical Simulation Results fluctuations in gas reservoir

16. 16  eq  occurrence  10 1377 [s]  occurrence  10 1370 [y] TD of confined systems: COS (curves of states) are appropriate concept bistability rather than metastable states Introduction Theoretical Simulation Results lifetime of short lived state  occurrence  10 1360 [14·10 9 y] H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472  occurrence =  fluc / P stat

17. 17 GCE and CE isotherms of LJ fluid confined to a 15.8  spherical pore at subcritical temperature, kT/  =1.02. (a) Practical GCMC isotherm is monotonic and reversible, CE isotherm generated with the IGGC method, and true GCE isotherm calculated from the CE isotherm (eq 9). The position of VLE is determined from the Maxwell rule (eqs 6). Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 Arguments from other authors system with virtual interface to reservoir

18. 18 Arguments from other authors system with virtual interface to reservoir (c) Fluctuation of the number of molecules during the GCMC run at point A. Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 spherical pore with virtual interface gas reservoir: fluid density is homogeneous with respect to 2 dimensions (both angles) fluid density can vary only with respect to 1 dimension (radius)

19. 19 Neimark&Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 Comparison of systems system with virtual interface to reservoir vs. system with real interface to reservoir spherical pore with virtual interface to gas reservoir: boundary conditions allow homogeneous density with respect to 2 dimensions (both angles) isotherm is one coherent curve (EOS) cylindrical pore with real interface to gas reservoir: boundary conditions allow homogeneous density with respect to only 1 dimension (polar angle) isotherm consists of two separated curves (COS) concept of present work Thank you critical remarks welcome !

20. 20 Simulation: adsorption in cylindrical pore of infinite length  EOS

21. 21 Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 Arguments from other authors system with virtual interface to reservoir spherical pore with virtual interface to gas reservoir: fluid density is homogeneous with respect to 2 dimensions (both angles) fluid density can vary only with respect to 1 dimension (radius)

22. 22 Introduction Theoretical Simulation Results resume true GCE isotherm equilibrium from kinetics

23. 23 Introduction Theoretical Simulation Results resume

24. 24 Introduction Theoretical Simulation Results temperature variation

25. 25 Introduction Theoretical Simulation Results temperature variation

26. 26 Introduction Theoretical Simulation Results resume  eq  occurrence  10 338 [14·10 9 y] TD of confined systems: COS (curves of states) are appropriate concept bistability rather than metastable states H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472  occurrence [77.35K]  10 1000.  occurrence [130K]

27. 27 Introduction Theoretical Simulation Results time dependence in QM  intrinsic =  /2   exp   intrinsic  exp   intrinsic  exp   intrinsic

28. 28 Adsorption Hysteresis in Porous Material Quotations from literature: 1 D.Wallacher et al., Phys. Rev. Lett. 92, (2004) 195704-1.. in the experimental system the metastable states just do not have time enough to relax... 1 Metastable states...... appear to be the most important aspect. 1...a failure of the system to equilibrate. 2 This explains why hysteresis, although representing a departure from equilibrium, is so reproducible in experiment. 2 2 R.Valiullin et al., Nature Letters, 443 (2006) 965-8

29. 29 Adsorption Hysteresis in Porous Material Quotations from literature: 1 J. Puibasset et al. J.Chem.Phys. 131 (2009) 124123-1/10 However, even in experiments in which accessible observation times are much longer than in simulations, a hysteresis is usually observed, whose properties are quite reproducible. 1

30. 30 H.Morgner (2010)

31. 31 H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472 COS and concept of applying canonical boundary conditions COS allow to retrieve isotherm Introduction Theoretical Method Results Curves of States (shape)

32. 32 H.Morgner (2010) Fig.6 Effect of pore shape on curves of states COS. Five different pore shapes are shown. The dotted line indicates the onset of the gas reservoir, i.e. homogeneous distribution of component A in the vapor phase. Below every pore shape, the corresponding COS are displayed. For clarity, the conventional isotherms are omitted, but can be easily reconstructed with the aid of the COS.

33. 33 Thermodynamics: EOS  equilibrium states, coexistence

34. 34 Thermodynamics: EOS  lowering grand potential lowering free energy equilibrium states, coexistence decay of metastable states