Time dependent aspects of fluid adsorption in mesopores

1. CompPhys2012 Leipzig November 29-30,2012 Time dependent aspects of fluid adsorption in mesopores • 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 Harald Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry Leipzig University, Linnéstrasse 2, D-04103 Leipzig, hmorgner@rz.uni-leipzig.de

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

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

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

5. Introduction TheoreticalSimulationResults Curves of States: filling pattern COS(b) two IF COS(a) one IF H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472

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

7. Introduction TheoreticalSimulationResults attempts to save TD • 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….“

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

9. Introduction TheoreticalSimulationResults pressure jump experiments

10. Introduction TheoreticalSimulationResults pressure jump experiments

11. Introduction TheoreticalSimulationResults pressure jump experiments

12. Introduction TheoreticalSimulationResults pressure jump experiments

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

14. Introduction TheoreticalSimulationResults fluctuations in gas reservoir pore wall r  200 nm  = 5 nm occurrence = fluc / Pstat pore wall

15. Introduction TheoreticalSimulationResults fluctuations in gas reservoir average time elapsed until effective fluctuation occurs occurrence Stat. TD provides statistical probability Pstat Pstat = fluc / occurrence occurrence = fluc / Pstat eq fluc

16. Introduction TheoreticalSimulationResults lifetime of short lived state 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 = fluc / Pstat occurrence  101377 [s] eq occurrence  101370 [y] occurrence  101360 [14·109y]

17. Arguments from other authors system with virtual interface to reservoir Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 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).

18. Arguments from other authors system with virtual interface to reservoir 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) (c) Fluctuation of the number of molecules during the GCMC run at point A.

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

20. Simulation: adsorptionin cylindrical pore of infinite length  EOS

21. Arguments from other authors system with virtual interface to reservoir Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 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. Introduction TheoreticalSimulationResults resume true GCE isotherm equilibrium from kinetics

23. Introduction TheoreticalSimulationResults resume

24. Introduction TheoreticalSimulationResults temperature variation

25. Introduction TheoreticalSimulationResults temperature variation

26. Introduction TheoreticalSimulationResults resume 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 eq occurrence  10338 [14·109y] occurrence[77.35K] 101000 . occurrence[130K]

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

28. Adsorption Hysteresis in Porous Material Quotations from literature: Metastable states ...... appear to be the most important aspect.1 .. in the experimental system the metastable states just do not have time enough to relax...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 1 D.Wallacher et al., Phys. Rev. Lett. 92, (2004) 195704-1 2 R.Valiullin et al., Nature Letters, 443 (2006) 965-8

29. Adsorption Hysteresis in Porous Material Quotations from literature: 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 1 J. Puibasset et al. J.Chem.Phys. 131 (2009) 124123-1/10

30. H.Morgner (2010)

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

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. Thermodynamics: EOS  equilibrium states, coexistence

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