Soft matter between soft solids. sorption-induced pore deformation and fluid phase behaviour [Elektronische Ressource] / vorgelegt von Gerrit Günther

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• Naturwissenschaften

Informations

• Publié par: technische_universitat_berlin
• Publié le: 01 janvier 2011
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 2 Mo

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SoftMatterbetweenSoftSolids.
Sorption-InducedPoreDeformationand
FluidPhaseBehaviour
vorgelegtvon
¨Dipl.-Chem.GerritGunther
ausBerlin
VonderFakultat¨ II–MathematikundNaturwissenschaften
derTechnischenUniversitat¨ Berlin
zurErlangungdesakademischenGrades
DoktorderNaturwissenschaften
Dr.rer.nat.
genehmigteDissertation
Promotionsausschuss:
Vorsitzender: Prof.Dr.PeterStrasser
Berichter: Prof.Dr.MartinSchoen
Berichterin: Prof.Dr.SabineKlapp
Berichter: Prof.Dr.ReinhardLipowsky
TagderwissenschaftlichenAussprache: 25.01.2011
Berlin2011
D83Abstract
Monte Carlo simulations in the semi-grand canonical ensemble are employed to in-
vestigatethesorptionstrainofmesoporousmaterialsandtheirinfluenceonthephase
behaviour of the confined fluid. For this purpose, a simple fluid is considered which
is confined between two parallel plane walls consisting of single wall particles. The
wallandfluidparticlesareofthesametypeandinteractingviaLennard–Jones(12,6)
potentials. The wall particles are not fixed to their lattice sites but bound to them
by harmonic potentials. By changing the force constant of this harmonic potential,
weare ableto control the softness of thewallfroman almostrigidstructuretomore
flexible walls. Flexible means that the wall particles can move farther from their
equilibriumpositionstoreacttothefluidtoagreaterextent.
Theporestrainiscalculatedasanensembleaverageofthepositionsofthewallpar-
ticlesandmayindicateeitheracontractionoranexpansionofthepore,dependingon
the interaction between the fluid and the wall particles. By tuning the parameters of
the model system, a strain isotherm is obtained which is in semi-quantitative agree-
ment with the data of small-angle X-ray diffraction experiments. Strain isotherms
over a wide temperature regime and thermodynamic conditions are computed to in-
vestigate the origin of sorption strain: if the confined fluid is in the gas-like phase,
the strain is dominated by the wetting characteristics of the fluid whereas at capil-
larycondensationtheporeshrinksonaccountoftheattractivefluid–wallinteraction.
Confining a liquid-like phase, the strain behaviour becomes independent of the fluid
characteristics and exhibits a nanomechnical property of the confining medium. In
thisregime,thecourseofthestrainisothermisexplainedbyasimplethermodynamic
analysis.
Ontheotherhand,thedeformabilityofmesoporeshasanimpactonthephasebe-
haviouroftheconfinedfluid. Thephasediagramforafluidinarigidporeandonein
a deformable pore are computed. By using finite-size scaling concepts the location
of the critical point is determined accurately for the fluid both in confinement and in
bulk. Compared with rigid pores, deformable pores affect the phase boundaries of
theconfinedfluidandhaveanimpactonthecriticaldensityofthefluid.
3Publications
• G. Gunther¨ , J. Prass, O. Paris and M. Schoen. Novel Insights into Nanopore
DeformationCausedbyCapillaryCondensation. PRL 101: 086104(2008).
• G.Gunther¨ andM.Schoen. SorptionStrainandtheirConsequencesforCapil-
laryCondensationinNanoconfinement . Mol.Simul.35(1-2): 138–150(2009).
• G. Gunther¨ and M. Schoen. Sorption Strain as a Packing Phenomenon. Phys.
Chem.Chem.Phys. 11: 9082–9092(2009).
• M.Schoen,O.Paris,G.Gunther¨ ,D.Muter¨ ,J.PrassandP.Fratzl. Pore-Lattice
Deformations in Ordered Mesoporous Matrices: Experimental Studies and
TheoreticalAnalysis. Phys.Chem.Chem.Phys.12(37): 11267–11279(2010).
• G. Gunther¨ and M. Schoen. Capillary Condensation in Deformable Meso-
pores: Wetting versus Nanomechanics. Molecular Physics 12: 11267–11279
(2010).
• M. Schoen and G. Gunther¨ . Phase Transitions in Nanoconfined Fluids: Syn-
ergistic Coupling between Soft and Hard Matter. Soft Matter 6: 5832–5838
(2010).
4Content
1 Introduction 9
2 Theory 13
2.1 PhenomenologicalThermodynamics . . . . . . . . . . . . . . . . . 13
2.2 EnsembleAverage . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 GrandCanonicalEnsemble . . . . . . . . . . . . . . . . . . . . . . 20
2.4 PairCorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 MonteCarloMethod . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 MarkovProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 AModelofFlexibleWalls 31
3.1 PoreFillinginOrderedMesoporousMaterials . . . . . . . . . . . . 31
3.2 DegreeofConfinement . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 HarmonicApproximation . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 ModelofThermallyCoupledWalls . . . . . . . . . . . . . . . . . 37
3.5 Semi-GrandCanonicalEnsemble . . . . . . . . . . . . . . . . . . . 41
3.6 SimulationDetails . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 PhaseBehaviour 49
4.1 SorptioninExperimentandTheory . . . . . . . . . . . . . . . . . 49
4.2 BulkPhaseTransition . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 PerturbationTheory . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 ReferenceModelofSmoothWalls . . . . . . . . . . . . . . 57
4.3.2 λ-Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.3 CalculationoftheSemi-GrandPotentialDensity . . . . . . 60
4.4 CapillaryCondensationBetweenFlexibleWalls . . . . . . . . . . . 64
4.4.1 ContactwithSorptionExperiments . . . . . . . . . . . . . 68
4.4.2 ComparisonwithRoughPoreModels . . . . . . . . . . . . 69
4.4.3withAnotherModelofDeformablePores . . . 70
4.5 CoexistingPhases . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5Content
4.5.1 ImprovedSGCMCAlgorithmtoExplorePhaseCoexistence 74
4.5.2 Universality . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5.3 FiniteSizeEffects . . . . . . . . . . . . . . . . . . . . . . 76
4.5.4 FiniteSizeScaling . . . . . . . . . . . . . . . . . . . . . . 77
4.5.5 PhaseDiagramofaFluidinFlexibleConfinement . . . . . 85
4.6 FluidStructurebetweenFlexibleWalls . . . . . . . . . . . . . . . . 87
4.6.1 LocalDensity . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6.2 In-PlanePairCorrelation . . . . . . . . . . . . . . . . . . . 89
5 PoreDeformation 93
5.1 StrainofIdealPores. . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 SorptionStrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.1 StrainDistributions . . . . . . . . . . . . . . . . . . . . . . 99
5.2.2 StrainUponPoreFilling . . . . . . . . . . . . . . . . . . . 101
5.3 PentaneinMCM-41: TheoryandExperiment . . . . . . . . . . . . 108
5.3.1 Small-AngleX-RayDiffraction . . . . . . . . . . . . . . . 108
5.3.2 LatticeStrainvs. PoreStrain . . . . . . . . . . . . . . . . . 112
5.4 ComparisonWithOtherStudies . . . . . . . . . . . . . . . . . . . 114
5.5 Stress–StrainRelation . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5.1 ForceandVirialExpressionofStress . . . . . . . . . . . . 118
5.5.2 StrainasaPackingPhenomenon . . . . . . . . . . . . . . . 119
5.6 StrainCausedbyGas-likePhases . . . . . . . . . . . . . . . . . . . 122
5.7 StrainbyLiquid-likePhases . . . . . . . . . . . . . . . . . 125
5.7.1 Quasi-KelvinEquation . . . . . . . . . . . . . . . . . . . . 125
5.7.2 NanomechanicalSubstrateProperties . . . . . . . . . . . . 129
5.7.3 ComparisonwithExperiment . . . . . . . . . . . . . . . . 132
6 Summary 133
Bibliography 137
A SubstrateDetails 155
A.1 ChoiceofUnitCellina2-DimensionalLattice . . . . . . . . . . . 155
A.2 MobilityofWallParticles . . . . . . . . . . . . . . . . . . . . . . . 156
A.3 SubstrateStructure . . . . . . . . . . . . . . . . . . . . . . . . . . 157
A.3.1 Solidvs.Liquid . . . . . . . . . . . . . . . . . . . . . . . . 158
A.3.2 LindemannCriterion . . . . . . . . . . . . . . . . . . . . . 159
B StressinDeformablePores 163
6Content
B.1 StressviatheForceRoute . . . . . . . . . . . . . . . . . . . . . . 165
B.2 StressviatheVirialRoute . . . . . . . . . . . . . . . . . . . . . . 166
C KelvinEquation 171
71
Introduction
Every substance changes its properties upon changing thermodynamic conditions
suchastemperature,pressureorvolume. Thepropertiesofasubstancearetherefore
determined by thermodynamic conditions, the so-called state. Upon
changing the state successively (such as increasing the temperature
whilekeepingpressureandvolumeconstant)wefindregionsinwhichpropertiesofa
substance change only slightly and continuously. Thus, states of such a region share
similarpropertiesandtheyarecollectivelysubsumedunderthetermphase. Butthere
are thermodynamic conditions at which a substance reacts to minor perturbations of
the state with a sharp, discontinuous change of a property. We de-
notethelatterphenomenonasphasetransition(offirstorderaccordingtoEhrenfest’s
classification [1]) which separates di fferent phases. For example, by increasing the
temperature water is transformed from a liquid to a gaseous phase, characterised by
a discontinuous, sharp drop of density at the liquid–gas phase transition. This phase
transition separates two regions in which the density changes only continuously and
thusbothphasesbasicallydifferindensity.
In general, a phase is a state of organisation of matter characterised by a specific
molecularinteractionanddegreeofsymmetry. Theinteractionofparticlesisobserv-
able through, e.g., the pair correlation function or structure factor [2] and increases
in the sequence gas–liquid–solid. On the other hand