Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Molecular Modeling and Simulation of
Phase Equilibria for Chemical Engineering
Hans Hasse1, Martin Horsch1, Jadran Vrabec2
1Laboratory of Engineering Thermodynamics
University of Kaiserslautern 2Thermodynamics and Energy Technology
University of Paderborn
InPROMT 2012, Berlin, 16. November 2012
DFG Transregio CRC 63
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Modeling and Simulation in Chemical Engineering
Top down Bottom up
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Molecular Dynamics (MD)
Numerical solution of
Newtonian equations of motion
Deterministic
Static and dynamic properties
Molecular Simulation with Force Fields
Monte-Carlo (MC)
Statistical method
Energetic acceptance criteria
Static properties only
Reactive MC
S. Deublein et al.: Comput. Phys. Commun. 182 (2011) 2350-2367 MD/MC Code: www.ms-2.de
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Molecular Model Type
Rigid, non-polarizable
Multicenter Lennard-Jones (LJ) + electrostatic sites
United atom approach
All properties from one model
Example: Ethylene Oxide
B. Eckl et al. Fluid Phase Equilib. 274 (2008) 16-26
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Parameterizing of Molecular Models with VLE Data
www.withfriedship.com
Vapor-pressure
Saturated liquid density
Enthalpy of vaporization
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Multi-Objective Optimization
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
OPEX
CA
PE
X
Pareto optimality
Improvement in any chosen
objective leads inevitably to
a decline in at least one
other objective.
Molecular Models from Multi-Objective Optimization:
Pareto-based Approach
Introduction by well known example
Feasible
Not
feasible
Pareto frontier
Pareto frontier: best
compromises
Design by navigation on
Pareto frontier
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
12 6
4B
U
k r r
Lennard-Jones (LJ) Pair Potential
Radial symmetry
Accounts for:
Repulsion
Dispersion
Two parameters:
Size
Energy
Repulsion Attraction
r
8
/r
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Pareto-based Lennard-Jones Modeling of Argon
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σ / Å
/ K
δp
δΔ
hv
δρ'
Parameter space Objective space
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Pareto-based Lennard-Jones Modeling of Argon
Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133
10
σ / Å
/ K
Parameter space Objective space
δp
δΔ
hv
δρ'
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Pareto-based Lennard-Jones Modeling of Methane
Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133
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σ / Å
/ K
Parameter space Objective space
δp
δΔ
hv
δρ'
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Phosgene Group
C6H5-Cl C6H6 CCl2O o-C6H4-Cl2 HCl C6H5-CH3
Molecular Models of Fluids: Examples
Ethylene Oxide Group
C2H4O H2O HO(CH2)2OH
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. Ind. Eng. Chem. Res. 51 (2012) 7428-7440
Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
T / K0.002 0.003 0.004 0.005 0.006 0.007
ln(p
/ M
Pa)
-15
-10
-5
0HCl
Benzene
Cl-Benzene
Phosgene
Toluene
oCl2-Benzene
Vapor Pressures
Symbols: Simulation
Lines: Reference DIPPR
Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060
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1(1/ ) / KT
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
/ mol/l0 10 20 30
T /
K
200
300
400
500
600
700
HCl
Phosgene
oCl2-Benzene
Cl-Benzene
Toluene
Benzene
Saturated Densities
Symbols: Simulation
Lines: Reference DIPPR
Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Prediction EMD Simulation
Experiment (Literature) +
T / K150 200 250
Di /
10
-9 m
2 s
-1
0
5
10
15
20
T / K175 200 225 250 275
/
W m
-1 K
-1
0.0
0.1
0.2
0.3
0.4
0.5
T / K160 200 240 280
/ 1
0-4
Pa s
0
1
2
3
4
5
6
Prediction NEMD Simulation
Predictions: Transport Properties of Liquid HCl
p = 0.1 MPa
DIPPR Correlation
G. Guevara-Carrion et al. Fluid Phase Equilib. 316 (2012) 46-54
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Unlike interaction A-B:
Electrostatics fully predictive
Lennard-Jones parameters from combination rules
Molecular Modelling of Mixtures
AB A B+= / 2σ σ σ
AB A B
=ε ε ε
A A
B B
σA, εA
σB, εB
σAB, εAB
or
State-independent parameter ξ
fitted to one experimental
data point p(T,x) oder H(T)
ξ = 1 Predictions
Modified
Lorentz-Berthelot
T. Schnabel et al. J. Mol. Liq. 135 (2007) 170-178
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
xHCl
/ mol mol-1
0.0 0.2 0.4 0.6 0.8 1.0
p /
MP
a
0
5
10
15
283.15 K
423.15 K
393.15 K
0.05 0.10
0.0
0.1
0.2
0.3
Vapor-Liquid Equilibrium HCl + Chlorobenzene
Symbols: simulation (full)
experiment (cross)
Lines: Peng-Robinson EOS
1.02
Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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%
Study of radial pair correlation functions
,( )
j i
ij
j
local concentration cg r
overall concentration c
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Local concentration ≠ Overall concentration
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
r [Å]
0 2 4 6 8
g(r
) [-
]
0
1
2
3
4
5
6
7
8DAT.N2--HCl.Cl
DAT.N2--HCl.H
r [Å]
0 2 4 6 8
g(r
) [-
]0
1
2
3
4
5
6
7
8DAT.N4--HCl.Cl
DAT.N4--HCl.HdH–Cl
dH–Cl
Amine group N2
Radial Pair Correlation Functions: Amine Groups – HCl Important for Formation of Undesired Hydrochlorides
r /Å r /Å
gij(
r)
gij(
r)
Amine group N4
NH2 – (H in HCl)
NH2 – (Cl in HCl)
N4
N2
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
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Proton Catalyzed Reaction Ethylene Oxide + Water
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Proton Catalyzed Reaction Ethylene Oxide + Water
+
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Radial Pair Correlation Functions
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Transient Radial Pair Correlation Functions
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Henry’s Law Constants of Ethylene Oxide
Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012) 7428-7440
EO in Water EO in (Water + Ethylene glycole)
T / K xEG / mol mol-1
350 K
500 K
350 400 450 500
0
10
20
30
HE
O / M
Pa
0
10
20
30
HE
O / M
Pa
Molecular Simulation
Guide for eye
0.00 0.05 0.10 0.15
*
Physical solubility
No chemical reactions
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Spherical Vapor-Liquid Interfaces
• Droplet + metastable vapor
Spinodal limit: For the external
phase, metastability breaks down.
γR
γpΔ
2
25
liq
gas
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Spherical Vapor-Liquid Interfaces
• Droplet + metastable vapor
• Bubble + metastable liquid
Spinodal limit: For the external
phase, metastability breaks down.
Planar limit: The curvature changes
its sign and the radius Rγ diverges.
γR
γpΔ
2
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liq
gas
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Curvature Dependence of Surface Tension
distance from the centre of mass / 0 5 10 15 20
density
/
-3
0.01
0.1
1
T = 0.75 /k
equimolar radius R
LJTS fluid
distance from the centre of mass / 0 5 10 15 20
density
/
-3
0.01
0.1
1
T = 0.75 /k
equimolar radius R
capillarity radius
R = 20/p
LJTS fluid
2R
p
Laplace radius Capillarity radius 02
Rp
Equimolar radius
(from density profile) 2 2
0
0
R
R R
R
R dR R dR
M. Horsch et al. Phys. Rev. E 85 (2012) 031605
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ρ0
ρ∞
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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
Planar Vapor-Liquid Interfaces
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Lennard-Jones fluid
*T*T
/S /S
Evidence for finite size effects for very thin slabs
Surface tension Density in center
S. Werth Physica A submitted (2012)
Planar Vapor-Liquid Interfaces
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Wetting and Dispersive Fuid-Wall Interactions
reduced fluid-wall dispersive energy 0.05 0.10 0.15 0.20
conta
ct angle
in d
egre
es
0
30
60
90
120
150
180
0.88 /k 0.73 /k1 /k
Young‘s equation
SV SL LV = + cos Θ
solid (S)
liquid (L)vapor (V)
three phase contact
contact angle Θ
Symbols:
Simulation (LJTS)
Lines:
correlations
Curve parameter:
reduced temperature
Reduced wall density
5.876 σ-3
M. Horsch et al., Langmuir 26 (2010) 10913-10917
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Wetting and Dispersive Fuid-Wall Interactions
Simulation
Correlation
x / σ
y / σ
ρ / σ-3
ρ / σ
-3
y / σ
0
5
10
15
20
25
30
0 5 10 15 20 25
Density profile center Density in droplet
LJTS
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Wetting, Adsorption and Surface Diffusion
Molecular dynamics
LJTS Model
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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…)
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Acknowledgment
Funding
DFG SPP 1155
DFG TFB 66
DFG SFB 706
DFG SFB 926
BMBF IMEMO
RLP Research Center CM2
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
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