Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone ... ·...

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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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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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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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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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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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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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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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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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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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Molecular models: new models

Toluene CCl4 Benzene

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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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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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Predictive phenomenological models

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Group I: Benzene + Toluene

Diffusion coefficients

Shear viscosity


Self-diffusion

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Group I: Fick diffusion

Benzene + CCl4 Ethanol + Methanol

Cyclohexane + CCl4 Toluene + CCl4

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Group II: Acetone + Benzene


Shear viscosity


Self-diffusion

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Group II: Fick diffusion

Methanol + Acetone Ethanol + Acetone Acetone + Toluene Acetone + CCl4 Benzene + Cyclohexane Cyclohexane + Toluene

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Group III: Methanol + Toluene


Shear viscosity


Self-diffusion

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Methanol + Benzene Methanol + CCl4 Ethanol + Benzene Ethanol + Cyclohexane Ethanol + Toluene Acetone + Cyclohexane

Group III: Fick diffusion

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Transport properties: average deviation

Mean average deviation for all mixtures

Fick diffusion: 16 % (calculated with Wilson model)

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Radial distribution functions G I: Benzene + Toluene G II: Acetone + Benzene G III: Methanol + Toluene

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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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Methanol + Benzene x1 = 0.1 mol/mol

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Methanol + Benzene x1 = 0.1 mol/mol

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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

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Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone ... ·...

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