Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene and carbon tetrachloride
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1 - 1 - 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 () Paderborn University, Germany
2 - 2 - 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
3 - 3 - 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
4 ms2: simulation tool for thermodynamic properties Molecular dynamics / Monte Carlo Arbitrary mixtures of rigid molecules Grand equilibrium method (for VLE) Several classical ensembles All static properties (thermal, caloric, entropic) Gradual insertion for entropic properties Transport properties (Green-Kubo) Consistent FORTRAN90 code Object oriented All loops vectorized MD and MC parallelized 3D visualization interface Glass et al., Comp. Phys. Commun. 185 (2014)
5 - 5 - Description of diffusion (1) nn 1 Fick: JJ ii = ρρ mm DD iiii jj=1 xx jj coefficients from experiment Maxwell-Stefan: nn xx jj uu ii uu jj jj ii=1 Đ iiii = 1 RRRR μμ ii coefficients from molecular simulation xx ii uu ii = 1 RRRR Λ iiii μμ jj nn jj=1 Onsager reciprocal relation: Λ iiii = Λ jjii Binary mixture: Đ iiii = xx jj xx ii Λ iiii + xx ii xx jj Λ jjjj Λ iijj Λ jjii Fick Maxwell-Stefan
6 - 6 - Description of diffusion (2) Fick Maxwell-Stefan Binary mixture: DD = ĐГ Г = 1 + xx 1 dd ln γγ 1 ddxx 1 Thermodynamic factor Г Describes the thermodynamic non-ideality of a mixture Ideal mixture: Г = 1 Thermodynamic instability (phase separation): Г < 0 Can be calculated from G E models (e.g. Wilson, NRTL, UNIQUAC) Fitting of the model parameters to experimental VLE data or to simulation data
7 - 7 - Green-Kubo formalism (1) Microscopic fluctuations around equilibrium Description of non-equilibrium phenomena Transport coefficients from time dependent autocorrelation functions of corresponding flux DD ii, DD iijj, ηη, λλ e.g. self-diffusion NN DD ii = 1 dddd vv 3NN ii ii 0 ii (0) vv ii (tt)
8 - 8 - Green-Kubo formalism (2) Transport coefficients: DD ii, DD iijj, ηη, λλ Self-diffusion DD ii = 1 NN 3NN ii dddd vv ii 0 ii (0) vv ii (tt) Onsager coefficients mutual diffusion DD iiii Shear viscosity Thermal conductivity NN ii Λ iiii = 1 3NN dddd vv ii,kk 0 vv jj,ll tt 0 kk=1 NN jj ll=1 ηη = 1 VVkk BB TT dddd JJ xxxx pp (0) JJ xxxx pp (tt) 0 λλ = 1 VVkk BB TT 2 dddd JJ qq xx (0) JJ xx qq (tt) 0
9 - 9 - Molecular models Methanol CCl 4 Ethanol Acetone - 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 Toluene Benzene Cyclohexane
10 Molecular models: new models Benzene Toluene CCl 4
11 Studied mixtures (1) Methanol CCl 4 Toluol Ethanol Aceton Benzol Cyclohexan 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 20 binary mixtures
12 Studied mixtures (2) Groups according to deviation of thermodynamic factor from ideal behavior Group I (less 10 %) Group II (10 %...45 %) Group III (>60 %) Ethanol + Methanol Benzene + Toluene Benzene + CCl 4 Cyclohexane + CCl 4 Toluene + CCl 4 Methanol + Acetone Ethanol + Acetone Acetone + Benzene Acetone + Toluene Acetone + CCl 4 Benzene + Cyclohexane Cyclohexane + Toluene Methanol + Benzene Methanol + Toluene Methanol + CCl 4 Ethanol + Benzene Ethanol + Cyclohexane Ethanol + Toluene Ethanol + CCl 4 All mixtures studied at T = K and p = 0.1 MPa Acetone + Cyclohexane
13 Predictive phenomenological models
14 Group I: Benzene + Toluene Self-diffusion Diffusion coefficients Shear viscosity Thermal conductivity
15 Group I: Fick diffusion Ethanol + Methanol Benzene + CCl 4 Cyclohexane + CCl 4 Toluene + CCl 4
16 Group II: Acetone + Benzene Self-diffusion Diffusion coefficients Shear viscosity Thermal conductivity
17 Group II: Fick diffusion Methanol + Acetone Ethanol + Acetone Acetone + Toluene Acetone + CCl 4 Benzene + Cyclohexane Cyclohexane + Toluene
18 Group III: Methanol + Toluene Self-diffusion Diffusion coefficients Shear viscosity Thermal conductivity
19 Group III: Fick diffusion Methanol + Benzene Methanol + CCl 4 Ethanol + Benzene Ethanol + Cyclohexane Ethanol + Toluene Acetone + Cyclohexane
20 Transport properties: average deviation Mean average deviation for all mixtures Fick diffusion: 16 % (calculated with Wilson model)
21 Radial distribution functions G I: Benzene + Toluene G II: Acetone + Benzene G III: Methanol + Toluene
22 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
23 Methanol + Benzene x 1 = 0.1 mol/mol
24 Methanol + Benzene x 1 = 0.1 mol/mol
25 Summary 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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