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ThEt Thermodynamics and Energy Technology
PLMMP 2016, Kyiv Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene and carbon tetrachloride Jadran Vrabec Tatjana Janzen, Gabriela Guevara-Carrión, Yonny Mauricio Munoz Munoz Thermodynamics and Energy Technology (ThEt) Paderborn University, Germany
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ThEt Thermodynamics and Energy Technology
Motivation Diffusion coefficients are essential for modelling of complex systems and processes in science and engineering Problems: - Only few experimental data available,
especially for multicomponent mixtures - Measurements are challenging and time consuming - Theoretical and empirical approaches often fail
in predictions for strongly non-ideal mixtures Goal: - Establish precise predictive methods → Prediction of diffusion coefficients by molecular simulation
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ThEt Thermodynamics and Energy Technology
Molecular simulation
Calculation of macroscopic behavior from molecular interactions
- Molecular models based on force fields
- Equilibrium molecular dynamics - Force calculations to get
molecular trajectories → static and dynamic fluid properties
- Calculation of transport properties → Green-Kubo formalism
ms2: simulation tool for thermodynamic properties
Glass et al., Comp. Phys. Commun. 185 (2014) 3302
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ThEt Thermodynamics and Energy Technology
ms2: simulation tool for thermodynamic properties
• Molecular dynamics / Monte Carlo • Arbitrary mixtures of rigid molecules • Grand equilibrium method (for VLE) • Several classical ensembles
• Consistent FORTRAN90 code • Object oriented • All loops vectorized • MD and MC parallelized • 3D visualization interface
• All static properties (thermal, caloric, entropic) • Gradual insertion for entropic properties • Transport properties (Green-Kubo)
Glass et al., Comp. Phys. Commun. 185 (2014) 3302
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ThEt Thermodynamics and Energy Technology
Description of diffusion (1)
Fick: 𝑱𝑱𝑖𝑖 = −𝜌𝜌𝑚𝑚 �𝐷𝐷𝑖𝑖𝑖𝑖
𝑛𝑛−1
𝑖𝑖=1
𝛻𝛻𝑥𝑥𝑖𝑖
�𝑥𝑥𝑖𝑖 𝒖𝒖𝑖𝑖 − 𝒖𝒖𝑖𝑖
Đ𝑖𝑖𝑖𝑖
𝑛𝑛
𝑖𝑖≠𝑖𝑖=1
= −1𝑅𝑅𝑅𝑅
𝛻𝛻𝜇𝜇𝑖𝑖 Maxwell-Stefan:
Fick Maxwell-Stefan
coefficients from experiment
𝑥𝑥𝑖𝑖𝒖𝒖𝑖𝑖 = −1𝑅𝑅𝑅𝑅
�Λ𝑖𝑖𝑖𝑖𝛻𝛻𝜇𝜇𝑖𝑖
𝑛𝑛
𝑖𝑖=1
coefficients from molecular simulation
Đ𝑖𝑖𝑖𝑖 =𝑥𝑥𝑖𝑖𝑥𝑥𝑖𝑖Λ𝑖𝑖𝑖𝑖 +
𝑥𝑥𝑖𝑖𝑥𝑥𝑖𝑖Λ𝑖𝑖𝑖𝑖 − Λ𝑖𝑖𝑖𝑖 − Λ𝑖𝑖𝑖𝑖
Onsager reciprocal relation: Λ𝑖𝑖𝑖𝑖 = Λ𝑖𝑖𝑖𝑖
Binary mixture:
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ThEt Thermodynamics and Energy Technology
Description of diffusion (2)
Binary mixture: 𝐷𝐷 = ĐГ Г = 1 + 𝑥𝑥1𝑑𝑑 ln 𝛾𝛾1𝑑𝑑𝑥𝑥1
− Describes the thermodynamic non-ideality of a mixture − Ideal mixture: Г = 1 − Thermodynamic instability (phase separation): Г < 0
− Can be calculated from GE models (e.g. Wilson, NRTL, UNIQUAC)
− Fitting of the model parameters to experimental VLE data or to simulation data
Fick Maxwell-Stefan
Thermodynamic factor Г
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ThEt Thermodynamics and Energy Technology
Green-Kubo formalism (1)
Microscopic fluctuations around equilibrium → Description of non-equilibrium phenomena
Transport coefficients from time dependent autocorrelation functions of corresponding flux
e.g. self-diffusion
𝐷𝐷𝑖𝑖 =1
3𝑁𝑁𝑖𝑖� 𝑑𝑑𝑑𝑑 �𝒗𝒗𝑖𝑖
𝑁𝑁
𝑖𝑖
(0) ∙ 𝒗𝒗𝑖𝑖(𝑑𝑑)∞
0
𝐷𝐷𝑖𝑖 , 𝐷𝐷𝑖𝑖𝑖𝑖 , 𝜂𝜂, 𝜆𝜆
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ThEt Thermodynamics and Energy Technology
Green-Kubo formalism (2)
Transport coefficients: 𝐷𝐷𝑖𝑖 , 𝐷𝐷𝑖𝑖𝑖𝑖 , 𝜂𝜂, 𝜆𝜆
Self-diffusion 𝐷𝐷𝑖𝑖 =1
3𝑁𝑁𝑖𝑖� 𝑑𝑑𝑑𝑑 �𝒗𝒗𝑖𝑖
𝑁𝑁
𝑖𝑖
(0) ∙ 𝒗𝒗𝑖𝑖(𝑑𝑑)∞
0
Onsager coefficients → mutual diffusion 𝐷𝐷𝑖𝑖𝑖𝑖
Λ𝑖𝑖𝑖𝑖 =13𝑁𝑁� 𝑑𝑑𝑑𝑑 �𝒗𝒗𝑖𝑖,𝑘𝑘 0 ⋅
𝑁𝑁𝑖𝑖
𝑘𝑘=1
�𝒗𝒗𝑖𝑖,𝑙𝑙 𝑑𝑑𝑁𝑁𝑗𝑗
𝑙𝑙=1
∞
0
Shear viscosity
Thermal conductivity
𝜂𝜂 =1
𝑉𝑉𝑘𝑘𝐵𝐵𝑅𝑅� 𝑑𝑑𝑑𝑑 𝑱𝑱𝑝𝑝
𝑥𝑥𝑥𝑥 (0) ∙ 𝑱𝑱𝑝𝑝𝑥𝑥𝑥𝑥 (𝑑𝑑)
∞
0
𝜆𝜆 =1
𝑉𝑉𝑘𝑘𝐵𝐵𝑅𝑅2� 𝑑𝑑𝑑𝑑 𝑱𝑱𝑞𝑞𝑥𝑥 (0) ∙ 𝑱𝑱𝑞𝑞𝑥𝑥 (𝑑𝑑)∞
0
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ThEt Thermodynamics and Energy Technology
Molecular models
Methanol
Cyclohexane Toluene
Ethanol
CCl4 Acetone
Benzene
- Rigid molecules (united atom)
- Lennard-Jones sites, point charges, dipole, quadrupole
- Parameters optimized to saturated liquid density and vapor pressure, (self-diffusion)
- Mixing behavior: predicted
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ThEt Thermodynamics and Energy Technology
Molecular models: new models
Toluene CCl4 Benzene
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ThEt Thermodynamics and Energy Technology
Studied mixtures (1)
Methanol
Cyclohexan Toluol
Ethanol
CCl4
Aceton
Benzol
20 binary mixtures
Molecular models - Rigid molecules
(united atom) - Lennard-Jones sites,
point charges, dipole, quadrupole
- Parameters optimized to saturated liquid density and vapor pressure, (self-diffusion)
- Mixing behavior: predicted
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ThEt Thermodynamics and Energy Technology
Studied mixtures (2)
Group I (less 10 %)
Ethanol + Methanol Benzene + Toluene
Benzene + CCl4
Cyclohexane + CCl4 Toluene + CCl4
Group II (10 %...45 %)
Methanol + Acetone Ethanol + Acetone
Acetone + Benzene Acetone + Toluene
Acetone + CCl4
Benzene + Cyclohexane Cyclohexane + Toluene
Group III (>60 %)
Methanol + Benzene Methanol + Toluene
Methanol + CCl4
Ethanol + Benzene Ethanol + Cyclohexane
Ethanol + Toluene Ethanol + CCl4
Acetone + Cyclohexane
Groups according to deviation of thermodynamic factor from ideal behavior
All mixtures studied at T = 298.15 K and p = 0.1 MPa
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ThEt Thermodynamics and Energy Technology
Predictive phenomenological models
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ThEt Thermodynamics and Energy Technology
Group I: Benzene + Toluene
Diffusion coefficients
Shear viscosity
Thermal conductivity
Self-diffusion
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ThEt Thermodynamics and Energy Technology
Group I: Fick diffusion
Benzene + CCl4 Ethanol + Methanol
Cyclohexane + CCl4 Toluene + CCl4
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ThEt Thermodynamics and Energy Technology
Group II: Acetone + Benzene
Diffusion coefficients
Shear viscosity
Thermal conductivity
Self-diffusion
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ThEt Thermodynamics and Energy Technology
Group II: Fick diffusion
Methanol + Acetone Ethanol + Acetone Acetone + Toluene Acetone + CCl4 Benzene + Cyclohexane Cyclohexane + Toluene
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ThEt Thermodynamics and Energy Technology
Group III: Methanol + Toluene
Diffusion coefficients
Shear viscosity
Thermal conductivity
Self-diffusion
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ThEt Thermodynamics and Energy Technology
Methanol + Benzene Methanol + CCl4 Ethanol + Benzene Ethanol + Cyclohexane Ethanol + Toluene Acetone + Cyclohexane
Group III: Fick diffusion
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ThEt Thermodynamics and Energy Technology
Transport properties: average deviation
Mean average deviation for all mixtures
Fick diffusion: 16 % (calculated with Wilson model)
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ThEt Thermodynamics and Energy Technology
Radial distribution functions G I: Benzene + Toluene G II: Acetone + Benzene G III: Methanol + Toluene
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ThEt Thermodynamics and Energy Technology
Radial distribution functions
- Hydrogen bonding in mixtures with ethanol and methanol - Strong non-idealities in mixtures with one polar and one non-polar
component - RDF show that extensive clustering occurs in mixtures of group III - Micro-heterogeneity is present in these mixtures clusters can be quite large, but no phase separation - Even stronger thermodynamic non-idealities
lead to liquid-liquid equilibrium
e.g. Methanol + Cyclohexane
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ThEt Thermodynamics and Energy Technology
Methanol + Benzene x1 = 0.1 mol/mol
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ThEt Thermodynamics and Energy Technology
Methanol + Benzene x1 = 0.1 mol/mol
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ThEt Thermodynamics and Energy Technology
Method: - Prediction of transport coefficient by molecular simulation - Equilibrium MD, Green-Kubo formalism Results: - Mutual diffusion in different binary liquid mixtures - Further transport properties - Good predictons of all kind of mixtures Outlook: - Diffusion coefficients in mixtures with LLE - Diffusion coefficients in ternary mixtures
Summary