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Development of a Polarizable Transferable Force Field for Vapor-Liquid Equilibria Calculations

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Development of a Polarizable Transferable Force Field for Vapor-Liquid Equilibria Calculations Development of a Polarizable Transferable Force Field for Vapor-Liquid Equilibria Calculations Von der Fakult¨atEnergie-, Verfahrens- und Biotechnik der Universit¨atStuttgart und dem Stuttgart Research Centre for Simulation Technology zur Erlangung der W¨urdeeines Doktors der Ingenieurwissenschaft (Dr.-Ing.) genehmigte Abhandlung Vorgelegt von Christian Waibel aus Schw¨abisch Gm¨und Hauptberichter: Prof. Dr.-Ing. Joachim Groß Mitberichter: Prof. Dr.-Ing. habil. Jadran Vrabec Tag der m¨undlichen Pr¨ufung:28.01.2019 Institut f¨urTechnische Thermodynamik und Thermische Verfahrenstechnik der Universit¨atStuttgart 2019 Erkl¨arungzu meiner Dissertation mit dem Titel: Development of a Polarizable Transferable Force Field for Vapor-Liquid Equilibria Calculations Hiermit erkl¨areich, dass ich die beigef¨ugteDissertation selbstst¨andigverfasst und keine anderen als die angegebenen Hilfsmittel genutzt habe. Alle w¨ortlich oder inhaltlich ¨ubernommenen Stellen habe ich als solche gekennzeichnet. Ich versichere außerdem, dass ich die beigef¨ugteDissertation nur in diesem und keinem an- deren Promotionsverfahren eingereicht habe und dass diesem Promotionsverfahren keine endg¨ultiggescheiterten Promotionsverfahren vorausgegangen sind. Ort, Datum Unterschrift Contents 1 Introduction 15 1.1 Vapor-Liquid Equilibria in Molecular Simulation . 15 1.1.1 Gibbs Ensemble Monte Carlo . 16 1.1.2 Grand Canonical Transition Matrix Monte Carlo . 18 1.2 Molecular Model . 23 1.2.1 Classical Force Fields . 23 1.2.2 Polarizable Force Fields . 25 1.3 Methods for Electrostatic Energy Calculation . 26 1.3.1 Ewald Summation . 27 1.3.2 Wolf Summation . 29 1.4 Outline of this thesis . 29 Bibliography . 30 2 Modification of the Wolf Method and Evaluation for Molecular Simula- tion of Vapor-Liquid Equilibria 35 2.1 Wolf Summation . 36 2.2 Molecular Simulation Technique . 41 2.2.1 Simulation Method . 41 2.2.2 Molecular Model . 42 2.2.3 Simulation Details . 43 2.3 Results and Discussion . 43 2.3.1 Wolf Parameter Estimation . 43 2.3.2 VLE Calculations . 47 2.4 Conclusion . 49 Appendix . 50 Bibliography . 51 3 A Modified Shifted Force Approach to the Wolf Summation 56 3.1 Wolf Summation . 58 3.1.1 Shifted Potential . 58 5 3.1.2 Shifted Force Potential . 60 3.1.3 A Modified Shifted Force Approach . 61 3.2 Molecular Simulation Technique . 65 3.2.1 Molecular Model . 65 3.2.2 Monte Carlo Simulations . 67 3.2.3 Molecular Dynamics Simulations . 69 3.3 Results and Discussion . 70 3.3.1 Correlation coefficients . 70 3.3.2 VLE calculations . 72 3.3.3 Dynamic Properties . 74 3.3.4 Dielectric Constant . 76 3.4 Conclusion . 77 Bibliography . 78 4 Transferability of Cross-Interaction Pair Potentials: Vapor-Liquid Phase Equilibria of n-Alkane/Nitrogen Mixtures Using the TAMie Force Field 84 4.1 Molecular Model . 87 4.2 Cross-Interaction Energy Parameters estimated from PCP-SAFT Equation of State . 88 4.3 Procedure for iterating cross-energy parameters in force fields . 90 4.4 Molecular Simulation Method . 91 4.5 Simulation Details . 92 4.6 Results and Discussion . 93 4.7 Conclusion . 98 Bibliography . 99 5 Polarizable Transferable Anisotropic United-Atom Force Field Based on the Mie Potential for Phase Equilibria: n-Alkanes, Ethers, and Nitrogen105 5.1 Force Field Development . 108 5.1.1 Intermolecular Energy . 108 5.1.2 Intramolecular Energy . 112 5.1.3 Optimization of Force Field Parameters . 112 5.2 Molecular Simulation Technique . 114 5.2.1 Monte Carlo Simulations . 114 5.2.2 Energy Minimization . 115 5.2.3 Electrostatics . 116 5.3 Results and Discussion . 117 5.3.1 Alkanes . 117 5.3.2 Ethers . 120 6 5.3.3 Nitrogen . 124 5.3.4 Mixtures . 127 5.4 Conclusion . 128 Bibliography . 130 6 Conclusion 138 Appendices 140 A Supporting Information to Chapter 2 141 A.1 Further Vapor-Liquid Equilibria Results . 141 B Supporting Information to Chapter 3 145 B.1 Details of the Configurational Bias Scheme . 145 B.2 Self Term of the Original Shifted Force Wolf Summation . 146 B.3 Energy Conservation . 147 B.4 Stockmayer Fluid . 148 Bibliography . 152 C Supporting Information to Chapter 4 153 C.1 Tail Correction for the TAMie Force Field . 153 C.2 Pure Component Properties of Nitrogen from modified TraPPE Force Field 153 C.3 Pure Component Properties for Propane from TraPPE-EH Force Field . 154 C.4 Pure Component Properties for n-Pentane from TraPPE-EH Force Field . 158 C.5 Binary interaction parameters kij for the PCP-SAFT equation of state . 160 C.6 Comparison of segment-wise καβ and molecule-wise κij parameter . 160 C.7 Vapor-liquid equilibrium predictions for nitrogen/alkane mixtures . 163 Bibliography . 168 D Supporting Information to Chapter 5 170 D.1 Simulation Details . 171 D.2 Uncertainty of Results . 172 D.3 Results - Polarizable PTAMie Force Field . 173 D.4 Results - Non-Polarizable TAMie Force Field . 180 Bibliography . 190 7 List of symbols Latin letters AAD absolute average deviation C collection matrix cij; cαβ; cab prefactor of Mie potential CORR correlation coefficient D self diffusion coefficient E system energy Ei electric field 0 Ei static electric field ERR relative deviation F force fobj objective function H histogram / probability distribution ∆LV h enthalpy of evaporation I^ij Iαβ correlation integrals J 0 atomic "hardness" k force constant k reciprocal space vector kB Boltzmann constant kij binary interaction parameter of PC-SAFT L box length M net dipole moment mij attractive exponent of Mie potential m^ segment number of PC-SAFT n new state of Monte Carlo move n iteration step N number of molecules nij; nαβ; nab repulsive exponent of Mie potential o old state of Monte Carlo move scaling of simulation effort O p pressure P transition probability P molecular number probability Pxy pressure tensor q partial charge Q partition function 8 ∆qi(Rc) net-charge within cutoff sphere r distance Rc cutoff radius s reduced coordinate SD standard deviation T temperature Tij dipole-dipole interaction tensor u potential U 0 constant of fluctuating charge model v velocity V volume x mole fraction Greek letters α damping parameter of Wolf summation α polarizability β inverse temperature scaled with the Boltzmann constant β scaling parameter of mDSF method δn phase shift of torsional potential 0 vacuum permittivity r relative dielectric constant ij; αβ; ab energy parameter of Mie potential ^ii energy parameter PC-SAFT η shear viscosity θ bending angle κ Ewald splitting (damping) parameter κij; καβ; κab binary interaction parameter between interaction sites Λ de Broglie wavelength µ chemical potential µ dipole moment ξij binary interaction parameter between species πacc acceptance probability ρ charge density ρ molecule density σij; σαβ size parameter of Mie potential σ^ii segment diameter PC-SAFT τ time step φ torsional angle 9 φ electrostatic potential φij adjustable parameter for kαβ estimation χ0 electro-negativity i;ab intramolecular interaction operator ! weighting function for bias Ω observable Subscripts a; b indices for interaction sites bend bending angle c value at critical point c core CBMC configurational bias Monte Carlo D charge-on-spring / shell / Drude model eq equilibrium i; j indices for interaction site / molecule / species / segment i index for sate condition inter intermolecular intra intramolecular k index for molecule number windows l bond max maximum min minimum n periodicity n new state of Monte Carlo move o old state of Monte Carlo move vdW van der Waals I,II indices of boxes in Gibbs ensemble α; β indices for interaction site θ angle φ torsion Superscripts bias quantity obtained with bias Coulomb Coulombic energy Ewald Ewald summation exp experimental Gibbs Gibbs ensemble 10 l, L liquid phase long long-ranged mod modified opt optimal pol polarizable sat saturation self self interaction set training set short short-ranged sim simulation tot total v, V vapor phase Wolf Wolf summation * reduced variable Abbreviations COS charge-on-spring DSF damped shifted force DSP damped shifted potential MC Monte Carlo MD molecular dynamics mDSF modified damped shifted force mSF modified shifted force NpT isobaric-isothermal ensemble NVT canonical ensemble PC-SAFT Perturbed-Chain Statistical Associating Fluid Theory ref reference SF shifted force SP shifted potential UA united atom VLE vapor-liquid phase equilibrium µV T grand canonical ensemble 11 Zusammenfassung Die Vorhersage thermodynamischer Eigenschaften f¨urStoffe mit nicht ausreichenden oder fehlenden experimentellen Daten ist eine Grundvoraussetzung f¨urdie Auslegung vieler Prozesse, insbesondere in der chemischen Industrie. Molekulare Simulationen in Kom- bination mit ¨ubertragbaren Kraftfeldern erm¨oglichen solche Vorhersagen. In dieser Ar- beit werden hierf¨urMonte Carlo Simulationen im großkanonischen Ensemble verwendet um Dampf-Fl¨ussigPhasengleichgewichte zu berechnen. Die Qualit¨atder Vorhersagen ist dabei stark von der G¨utedes verwendeten Kraftfeldes abh¨angig. Elektrostatische Wechselwirkungen sind Teil der meisten Kraftfelder und erfordern rechenaufw¨andigeAl- gorithmen zur Auswertung. Deshalb wird eine effiziente sph¨arische Abschneidemethode entwickelt, die auf der Wolf Summe basiert, und die Energie als auch die Kr¨aftepr¨azise wiedergibt. Um bin¨areMischungen besser beschreiben zu k¨onnen wird außerdem die An- wendung und Ubertragbarkeit¨ von kreuzweisen van der Waals Energie Parametern unter- sucht. Die Simulationsergebnisse zeigen dabei eine ausgezeichnete Ubereinstimmung¨ mit experimentellen Daten. Des Weiteren wird ein polarisierbares Kraftfeld f¨urAlkane, Ether und Stickstoff entwickelt, welches die elektronische Polarisation
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