InPROMT 2012, Berlin, 16. November 2012 DFG Transregio CRC 63 Molecular Modeling and Simulation of Phase Equilibria for Chemical Engineering Hans Hasse 1, Martin Horsch 1, Jadran Vrabec 2 1 Laboratory of University of Kaiserslautern 2 Thermodynamics and Energy Technology University of Paderborn
Modeling and Simulation in Chemical Engineering Bottom up Top down 2
Molecular Simulation with Force Fields Molecular Dynamics (MD) Numerical solution of Newtonian equations of motion Deterministic Static and dynamic properties Monte-Carlo (MC) Statistical method Energetic acceptance criteria Static properties only Reactive MC MD/MC Code: www.ms-2.de S. Deublein et al.: Comput. Phys. Commun. 182 (2011) 2350-2367 3
Molecular Model Type Example: Ethylene Oxide Rigid, non-polarizable Multicenter Lennard-Jones (LJ) + electrostatic sites United atom approach All properties from one model B. Eckl et al. Fluid Phase Equilib. 274 (2008) 16-26 4
Molecular Model Development Geometry: bond lengths bond angles QM Electrostatics: partial charges dipoles quadrupoles QM / VLE Dispersion, Repulsion: Lennard-Jones (LJ) potentials VLE B. Eckl et al. J. Phys. Chem. B 112 (2008) 12710-12721 5
Parameterizing of Molecular Models with VLE Data Multi-Objective Optimization Vapor-pressure Saturated liquid density Enthalpy of vaporization www.withfriedship.com 6
CAPEX Laboratory of Molecular Models from Multi-Objective Optimization: Pareto-based Approach Introduction by well known example Not feasible Pareto frontier Feasible Pareto optimality Improvement in any chosen objective leads inevitably to a decline in at least one other objective. Pareto frontier: best compromises Design by navigation on Pareto frontier OPEX 7
Lennard-Jones (LJ) Pair Potential r U 4 kb r r 12 6 Repulsion r / Attraction Radial symmetry Accounts for: Repulsion Dispersion Two parameters: Size Energy 8
Pareto-based Lennard-Jones Modeling of Argon Parameter space Objective space / K δδh v σ / Å δp δρ' 9
Pareto-based Lennard-Jones Modeling of Argon Parameter space Objective space / K δδh v σ / Å δp δρ' Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133 10
/ K Laboratory of Pareto-based Lennard-Jones Modeling of Methane Parameter space Objective space δδh v δp δρ' σ / Å Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133 11
Molecular Models of Fluids: Examples Phosgene Group CCl 2 O HCl C 6 H 6 C 6 H 5 -CH 3 C 6 H 5 -Cl o-c 6 H 4 -Cl 2 Ethylene Oxide Group C 2 H 4 O H 2 O HO(CH 2 ) 2 OH high economic interest difficult experiments few reliable data need for predictive modeling and simulation Excellent test cases for molecular modeling and simulation Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060 Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012) 7428-7440 12
Vapor Pressures 0 HCl ln(p / MPa) -5-10 ocl 2 -Benzene Benzene Phosgene Cl-Benzene Toluene -15 Symbols: Simulation Lines: Reference DIPPR 0.002 0.003 0.004 0.005 0.006 0.007 T / K 1 (1/ T ) / K Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060 13
Saturated Densities T / K 700 600 500 400 ocl 2 -Benzene Cl-Benzene Toluene Benzene Phosgene Symbols: Simulation Lines: Reference DIPPR 300 HCl 200 0 10 20 30 / mol/l Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060 14
Predictions: Transport Properties of Liquid HCl 20 6 Laboratory of D i / 10-9 m 2 s -1 15 10 5 / 10-4 Pa s 5 4 3 2 1 0 0.5 150 200 250 T / K 0 160 200 240 280 T / K / W m -1 K -1 0.4 0.3 0.2 0.1 + Prediction EMD Simulation Prediction NEMD Simulation Experiment (Literature) DIPPR Correlation p = 0.1 MPa 0.0 175 200 225 250 275 T / K G. Guevara-Carrion et al. Fluid Phase Equilib. 316 (2012) 46-54 15
Molecular Modelling of Mixtures A σ A, ε A A Predictions ξ = 1 or B σ AB, ε AB B State-independent parameter ξ fitted to one experimental data point p(t,x) oder H(T) σ B, ε B Unlike interaction A-B: Electrostatics fully predictive Lennard-Jones parameters from combination rules Modified Lorentz-Berthelot σ σ σ ε = + / 2 AB A B = ε ε AB A B T. Schnabel et al. J. Mol. Liq. 135 (2007) 170-178 16
17 Laboratory of Vapor-Liquid Equilibrium HCl + Chlorobenzene 1.02 0.3 423.15 K 15 0.2 0.1 p / MPa 10 0.05 0.10 0.0 393.15 K 5 283.15 K Symbols: simulation (full) experiment (cross) Lines: Peng-Robinson EOS 0 0.0 0.2 0.4 0.6 0.8 1.0 x HCl / mol mol -1 Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060
Application to Reaction Studies Phosgeneation, Liquid Mixture (110 C, 1 bar) Phosgene + Cl-Benzene + HCl + 2,4-Diaminetoluene 50 mol% 40 mol% 7 mol% 3 mol% Local concentration Overall concentration Study of radial pair correlation functions g ij () r local concentration c ji, overall concentration c j 18
8 7 g ij (r) g ij (r) Radial Pair Correlation Functions: Amine Groups HCl Important for Formation of Undesired Hydrochlorides 6 d H Cl Amine group N2 DAT.N2--HCl.Cl DAT.N2--HCl.H N2 8 7 6 Amine group N4 DAT.N4--HCl.Cl DAT.N4--HCl.H NH 2 (H in HCl) NH 2 (Cl in HCl) g(r) [-] 5 4 g(r) [-] 5 4 d H Cl 3 2 N4 3 2 1 1 0 0 2 4 6 8 0 2 4 6 8 r r /Å [Å] r /Å r [Å] 0 Deviations between overall and local concentration up to a factor of 8 HCl strongly prefers amine group N2 over N4 HCl docks preferentially with the proton at amine group N2 19
Proton Catalyzed Reaction Ethylene Oxide + Water 20
Proton Catalyzed Reaction Ethylene Oxide + Water + 21
Radial Pair Correlation Functions 22
Transient Radial Pair Correlation Functions Laboratory of 23
H EO / MPa H EO / MPa Henry s Law Constants of Ethylene Oxide EO in Water Laboratory of EO in (Water + Ethylene glycole) 30 30 500 K 20 20 10 10 350 K 0 Molecular Simulation Guide for eye 350 400 450 500 Physical solubility No chemical reactions 0 0.00 0.05 0.10 0.15 * T / K x EG / mol mol -1 Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012) 7428-7440 24
Spherical Vapor-Liquid Interfaces Droplet + metastable vapor liq Δp 2γ R γ Spinodal limit: For the external phase, metastability breaks down. gas 25
Spherical Vapor-Liquid Interfaces Droplet + metastable vapor Bubble + metastable liquid liq Δp 2γ R γ Spinodal limit: For the external phase, metastability breaks down. gas Planar limit: The curvature changes its sign and the radius R γ diverges. 26
Curvature Dependence of Surface Tension Equimolar radius (from density profile) R 0 R dr 0 R 2 2 R R R dr Laplace radius R 2 p Capillarity radius R 2 0 p density / -3 1 0.1 0.01 ρ 0 LJTS fluid T = 0.75 /k equimolar radius R capillarity radius R = 2 0 / p 0 5 10 15 20 distance from the centre of mass / ρ M. Horsch et al. Phys. Rev. E 85 (2012) 031605 27
Curvature Dependence of Surface Tension No evidence for curvature dependence of surface tension of small droplets M. Horsch et al. Phys. Rev. E 85 (2012) 031605 28
Planar Vapor-Liquid Interfaces Surface tension: Abundant studies on small droplets, i.e. simultaneous variation of curvature & size No previous studies on thin slabs with planar surfaces, i.e. variation of size only 29
Planar Vapor-Liquid Interfaces Lennard-Jones fluid Surface tension Density in center * T * T S / S / Evidence for finite size effects for very thin slabs S. Werth Physica A submitted (2012) 30
Wetting and Dispersive Fuid-Wall Interactions contact angle in degrees 180 150 120 90 60 30 0 Symbols: Simulation (LJTS) Lines: correlations Curve parameter: reduced temperature Reduced wall density 5.876 σ -3 three phase contact vapor (V) 1 /k contact angle Θ solid (S) liquid (L) 0.88 /k 0.73 /k 0.05 0.10 0.15 0.20 reduced fluid-wall dispersive energy Young s equation SV = SL + LV cos Θ M. Horsch et al., Langmuir 26 (2010) 10913-10917 31
Wetting and Dispersive Fuid-Wall Interactions y / σ 30 25 Density in droplet ρ / σ -3 Density profile center LJTS Simulation Correlation 20 15 ρ / σ -3 10 5 0 0 5 10 15 20 25 y / σ x / σ 32
Wetting, Adsorption and Surface Diffusion Laboratory of Molecular dynamics LJTS Model 33
Summary Molecular modeling and simulation in chemical engineering Atomistic force fields Molecular simulations of real systems are feasible Wide range of applications Fluid properties (static, dynamic, ) Surfaces (nucleation, wetting, adsorption, ) Reactions Challenges Complex molecules, electrolytes Fluid-wall interactions Bridging scales (long times, large systems, ) Computational efficiency, massive parallelization High potential (to be exploited ) 34
Acknowledgment People Stefan Becker Bernhard Eckl Manfred Heilig (BASF) Yow-Lin Huang Peter Klein (ITWM) Karl-Heinz Küfer (ITWM) Thorsten Merker Thorsten Schnabel Katrin Stöbener (ITWM) Stephan Werth Thorsten Windmann Funding DFG SPP 1155 DFG TFB 66 DFG SFB 706 DFG SFB 926 BMBF IMEMO RLP Research Center CM 2 35