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1 Fluid adsorption in mesopores: critical remarks on the validity of thermodynamics for confined systems Harald Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry Leipzig University, Linnéstrasse 2, D-04103 Leipzig, hmorgner@rz.uni-leipzig.de The phenomenon of adsorption hysteresis: more than 1 response for 1 set of boundary conditions The role of time Treatment of processes in confined systems in the literature The goal: a theory for confined systems that treats time realistically CompPhys2013 Leipzig November 28-29,2013

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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

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

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4 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

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5 Introduction Theoretical Simulation Results Metastability Concept of metastable states calls for a corresponding ground state and, thus, for a characteristic life time against decay into the ground state sys : characteristic time of the system for decay into the ground state exp : the characteristic duration of an experiment 3 cases can be encountered exp sys exp > sys

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6 Introduction Theoretical Simulation Results time dependence in QM sys = /2 exp sys exp sys exp sys

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7 Introduction Theoretical Simulation Results Metastability Concept of metastable states calls for a corresponding ground state and, thus, for a characteristic life time against decay into the ground state sys : characteristic time of the system for decay into the ground state exp : the characteristic duration of an experiment exp sys requires time dependent theoretical treatment (does not exist) exp >> sys time independent theory appropriate, e.g. TD exp > sys

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8 H. Morgner J. Chem. Chem. Eng. 5 (2011) 456 - 472 Introduction Theoretical Simulation Results Curves of States: exp << sys exp << sys Confined systems: COS (curves of states) are appropriate concept bistability rather than metastable states

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9 Introduction Theoretical Simulation Results Curves of States: lifetimes H. Morgner J. Chem. Chem. Eng. 7 (2013) 260 - 274

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10 Introduction Theoretical Simulation Results search for a time dependent theory Treatment of changes in confined systems in the literature Langevin equation O.T. Valls and G.F. Mazenko, Numerical study of the growth kinetics for a Langevin equation, Phys. Rev. B 34 (1986) 7941-7950 O.T. Valls and G.F. Mazenko, Nucleation in a time dependent Ginzburg-Landau model: A numerical study, Phys. Rev. B 42 (1990) 6614-6622 F. Restagno, L. Bocquet, and T. Biben, Metastability and Nucleation in Capillary Condensation, Phys. Rev. Lett. 84 (2000) 2433-2436 F. Restagno, L. Bocquet, J. Crassous, E.Charlais, Slow kinetics of capillary condensation in confined geometry: experiments and theory, Colloids and Surfaces A 206 (2002) 66-77 Grand Canonical Monte Carlo (GC MC) A.V. Neimark and A. Vishnyakov, Phase Transitions and Criticality in Small Systems: Vapor-Liquid Transition in Nanoscale Spherical Cavities. J.Phys.Chem. B 110 (2006) 9403-9412

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11 Original Langevin equation for Brownian motion (1908) of a particle: friction noise Application for confined systems: relaxation perturbation relaxation Relaxation into equilibrium: Introduction Theoretical Simulation Results Langevin equation

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12 Introduction Theoretical Simulation Results Test of Langevin equation Application for confined systems: relaxation perturbation relaxation Relaxation into equilibrium: Langevin(-like) equation:Onsager: realistic transport of matter Onsager equation: continuity equation relaxation perturbation Relaxation into equilibrium: not equivalent !!!

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13 Introduction Theoretical Simulation Results Test of Langevin(-like) equation

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14 Introduction Theoretical Simulation Results Test of Langevin(-like) equation Evolution of the load during pressure jump from COS( ) to COS( ). The time scale refers to the physical transport by Onsager diffusion. The abscissa of the curve arising from Langevin(-like) equation is scaled to match the end point.

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15 Introduction Theoretical Simulation Results Test of Langevin(-like) equation Langevin(-like) equation:Onsager: realistic transport of matter Onsager equation:

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16 Introduction Theoretical Simulation Results Test of Langevin(-like) equation Langevin(-like) equation: Onsager: realistic transport Onsager equation:

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17 Neimark& Vishnyakov J.Phys.Chem. B110 (2006) 9403-12 spherical pore with virtual interface to gas reservoir Introduction Theoretical Simulation Results GC MC

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18 (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 Introduction Theoretical Simulation Results GC MC

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19 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 Introduction Theoretical Simulation Results GC MC

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20 Introduction Theoretical Simulation Results general time dependent theory still to be developed Literature: Treatment of changes in confined systems does not reflect realistic processes general time dependent theory for confined systems is still to be developed Thank you critical remarks welcome ! Langevin(-like) equation no underlying realistic transport process no realistic trajectory time needed for transport of matter is disregarded Grand Canonical Monte Carlo (GC MC) criterion for acceptance of step is energy time needed for transport of matter is disregarded systematic search for suitable fluctuations or combinations thereof

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21 A referee report from ADSORPTION, Springer, December 2012 Reviewer #1: The author suggests an alternative thermodynamic language to treat the adsorption hysteresis based on the concept of the curves of states (COS)instead of the isotherms defined in a proper statistico-mechanical ensemble. This reviewer is skeptical that the suggested approach provides for a new knowledge about the hysteresis phenomena. There is an extensive body of papers and reviews on thermodynamics and dynamics of adsorption hysteresis, and the consensus in adsorption community is that the hysteresis is related to the long-living metastable states and high energy barriers between the metastable and stable states, see e.g. most recent review of P.Monson and D.D.Do and co-authors. The introduction of the COS concept, which is in conflict with the well-established thermodynamics, may mislead students and beginning researchers, who are not knowledgeable in this field. The introduction of the COS concept, which is in conflict with the well-established thermodynamics, may mislead students and beginning researchers, who are not knowledgeable in this field.

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

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23 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

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24 Diffusion treated by Onsager ansatz driving force: gradient of chemical potential pressure in gas reservoir Introduction Theoretical Simulation Results pressure jump experiments

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25 Introduction Theoretical Simulation Results pressure jump experiments

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26 Introduction Theoretical Simulation Results pressure jump experiments

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27 Introduction Theoretical Simulation Results pressure jump experiments

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28 Introduction Theoretical Simulation Results pressure jump experiments

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29 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

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30 occurrence = fluc / P stat r 200 nm = 5 nm Introduction Theoretical Simulation Results fluctuations in gas reservoir pore wall

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31 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

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32 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

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33 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 !

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34 Simulation: adsorption in cylindrical pore of infinite length EOS

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35 Introduction Theoretical Simulation Results resume true GCE isotherm equilibrium from kinetics

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36 Introduction Theoretical Simulation Results resume

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37 Introduction Theoretical Simulation Results temperature variation

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38 Introduction Theoretical Simulation Results temperature variation

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39 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]

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40 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

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41 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

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42 H.Morgner (2010)

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43 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)

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44 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.

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45 Thermodynamics: EOS equilibrium states, coexistence

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46 Thermodynamics: EOS lowering grand potential lowering free energy equilibrium states, coexistence decay of metastable states

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47 Introduction Theoretical Simulation Results Curves of States: relation to TD

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48 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

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