Supporting Information to Thermodynamics of Supercritical Carbon Dioxide Mixtures Across the Widom Line

Supercritical carbon dioxide (scCO2) mixtures are essential for many industrial applications. However, the knowledge of their thermophysical properties in the extended critical region is insufficient. Here, supercritical liquid- and gas-like regions dominated by distinct dynamics and thermodynamics exist and are demarcated by the so-called Widom line. The nature of the anomalies observed for several thermophysical properties at the crossover between these two regions is the subject of a lively debate. Hence, the extended critical region of scCO2 and seven of its binary mixtures with hydrogen, methane, ethane, isobutane, benzene, toluene or naphthalene is studied with respect to thermodynamic, transport and structural properties on the basis of molecular dynamics simulations and equation of state calculations. The Widom line is evaluated employing five criteria and a new empirical equation is proposed for its prediction. Further, the crossover anomalies are investigated in the light of pseudo-boiling theory, diffusion and viscosity as well as structural characteristics given by the radial distribution function.


Technical details
The simulations in the N pT ensemble to determine the density were equilibrated for 3 · 10 4 time steps and followed by a production run of 2 · 10 6 steps. The simulations in the N V T ensemble were equilibrated for 5 · 10 5 time steps and followed by a production run of 20 ·10 6 to 24 ·10 6 steps.
A fifth-order Gear predictor-corrector scheme with an integration time step of 0.994 fs was used to solve Newton's equations of motion. The velocity scaling algorithm was employed to control the temperature. The pressure was kept constant by the Andersen barostat 1 with a piston mass of 2.2 · 10 9 kg m −4 . The cubic simulation volume with periodic boundary conditions contained 5000 molecules throughout. The cut-off radius was set to 21Å. Lennard-Jones long range interactions were considered analytically employing angle averaging 2 and the reaction field method with conducting boundary conditions (ϵ RF = 1) was used for the dipolar interactions.
Correlation functions were calculated from an average of 4 · 10 5 independent time origins and a sampling length of 40 ps throughout. This extensive length of the autocorrelation functions was chosen to avoid long-time tail corrections. The separation between the time origins was chosen such that all correlation functions achieved time independence and decayed at least to 1/e of their normalized value. Statistical uncertainties were estimated by the block averaging technique of Flyvberg and Petersen 3 . Uncertainties of the derived thermodynamic properties were estimated by the error propagation law.

Average relative deviation
In order to quantify the deviations between simulation and empirical data for a given mixture, the average relative deviation (ARD) was calculated by where n is the number of data points studied, z sim and z emp are the thermodynamic quantities calculated from simulation and empirical data, respectively. Table S1: Binary interaction parameter ξ for the seven binary CO 2 mixtures considered in this work. The parameters were fitted to VLE data with a procedure described in preceding work 4 . The parameters of the employed force fields are listed in the MolMod database 5 .

Molecular models and validation
Mixture ξ CO 2 + hydrogen 1 CO 2 + methane 0.974 CO 2 + ethane 0.955 CO 2 + isobutane 0.985 CO 2 + benzene 0.995 CO 2 + toluene 0.96 CO 2 + naphthalene 1 Figure S1: Vapor-liquid equilibria of CO 2 mixtures with isobutane (bottom) or toluene (top). Solid lines for CO 2 + isobutane denote data from the GERG-2008 EOS 6 and for CO 2 + toluene they denote data from the Peng-Robinson EOS (k ij = 0.108) 7 . Crosses represent experimental data for CO 2 + isobutane 8 and for CO 2 + toluene 9,10 , whereas circles depict molecular simulation results. Red vertical marks on the very right stand for the supercritical states of interest. Figure S2: Vapor-liquid equilibria of CO 2 mixtures with hydrogen (bottom) or methane (top). Solid lines denote data from the GERG-2008 EOS 6 and crosses represent experimental data for CO 2 + hydrogen 11 and CO 2 + methane 12 . Circles depict molecular simulation results. Red vertical marks on the very right stand for the supercritical states of interest. Figure S3: Vapor-liquid equilibria of CO 2 + naphthalene. Crosses represent experimental data 13 , whereas circles depict molecular simulation results. Red vertical marks on the very right stand for the supercritical states of interest. 6 Finite size corrections Figure S4: Finite size corrections of the intra-diffusion coefficient of CO 2 and its mixture with 1 mol% of benzene for three temperature-pressure pairs. Circles represent the original simulation data. Squares represent the intra-diffusion coefficients corrected with the approach of Yeh and Hummer 14 and the triangles represent data corrected with the approach of Leverant et al. 15 . 7 Figure S5: Finite size corrections of the intra-diffusion coefficient of CO 2 and its mixture with 1 mol% of toluene for three temperature-pressure pairs. Circles represent the original simulation data. Squares represent the intra-diffusion coefficients corrected with the approach of Yeh and Hummer 14 and the triangles represent data corrected with the approach of Leverant et al. 15 . Figure S6: Finite size corrections of the intra-diffusion coefficient of CO 2 and its mixture with 1.5 (top), 1 (center) and 0.5 mol% (bottom) of ethane at three temperatures along p = 9 MPa. Circles represent the original simulation data. Squares represent the intra-diffusion coefficients corrected with the approach of Yeh and Hummer 14 and the triangles represent data corrected with the approach of Leverant et al. 15 . 9 Figure S7: Finite size corrections of the intra-diffusion coefficient of CO 2 and its mixture with 1.5 (top), 1 (center) and 0.5 mol% (bottom) of isobutane along p = 9 MPa and T = 315 K. Circles represent the original simulation data. Squares represent the intra-diffusion coefficients corrected with the approach of Yeh and Hummer 14 and the triangles represent data corrected with the approach of Leverant et al. 15 . Figure S8: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 1.0 mol% of hydrogen (blue) or benzene (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + hydrogen and the mixture model by Blackham and Lemmon 17 for CO 2 + benzene. Dotted lines the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 11 Figure S9: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 0.5 mol% of hydrogen (blue) or benzene (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + hydrogen and the mixture model by Blackham and Lemmon 17 for CO 2 + benzene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 12 Figure S10: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 1.5 mol% of ethane (blue) or toluene (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + ethane and the mixture model by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 13 Figure S11: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 1.0 mol% of ethane (blue) or toluene (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + ethane and the mixture model by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. Figure S12: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 0.5 mol% of ethane (blue) or toluene (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + ethane and the mixture model by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. Figure S13: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 1.5 mol% of methane (blue) or isobutane (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 and the GERG-2008 EOS 6 for CO 2 + methane or CO 2 + isobutane. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. Figure S14: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 1.0 mol% of methane (blue) or isobutane (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 and the GERG-2008 EOS 6 for CO 2 + methane or CO 2 + isobutane. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. Figure S15: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixtures with 0.5 mol% of methane (blue) or isobutane (red) at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner for CO 2 16 and the GERG-2008 EOS 6 for CO 2 + methane or CO 2 + isobutane. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter.

18
Figure S16: Temperature dependence of the thermodynamic properties of the scCO 2 mixture with 0.6 mol% of naphthalene at p = 9 MPa (black), 10 MPa (red) and 12 MPa (blue). Symbols show the present molecular simulation results. Density (circles) and residual enthalpy (triangles up) are shown at the top, residual isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. No experimental or equation of state data were available for comparison.

19
Figure S17: Temperature dependence of the thermodynamic properties of the scCO 2 mixture with 0.5 mol% of naphthalene at p = 9 MPa (black), 10 MPa (red) and 12 MPa (blue). Symbols show the present molecular simulation results. Density (circles) and residual enthalpy (triangles up) are shown at the top, residual isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. No experimental or equation of state data were available for comparison. 20 Figure S18: Temperature dependence of the thermodynamic properties of the scCO 2 mixture with 0.3 mol% of naphthalene at p = 9 MPa (black), 10 MPa (red) and 12 MPa (blue). Symbols show the present molecular simulation results. Density (circles) and residual enthalpy (triangles up) are shown at the top, residual isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. No experimental or equation of state data were available for comparison.

21
Figure S19: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixture with 1.0 mol% benzene at p = 10 MPa (red) as well as scCO 2 (blue) and its mixture with 1.0 mol% benzene at p = 12 MPa (green). Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner EOS for CO 2 16 and the mixture model for by Blackham and Lemmon 17 for CO 2 + benzene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 22 Figure S20: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixture with 0.5 mol% benzene at p = 10 MPa (red) as well as scCO 2 (blue) and its mixture with 0.5 mol% benzene at p = 12 MPa (green). Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner EOS for CO 2 16 and the mixture model for by Blackham and Lemmon 17 for CO 2 + benzene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 23 Figure S21: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixture with 1.5 mol% toluene at p = 10 MPa (red) as well as scCO 2 (blue) and its mixture with 1.5 mol% toluene at p = 12 MPa (green). Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner EOS for CO 2 16 and the mixture model for by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 24 Figure S22: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixture with 1.0 mol% toluene at p = 10 MPa (red) as well as scCO 2 (blue) and its mixture with 1.0 mol% toluene at p = 12 MPa (green). Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner EOS for CO 2 16 and the mixture model for by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 25 Figure S23: Temperature dependence of the thermodynamic properties of scCO 2 (black) and its mixture with 0.5 mol% toluene at p = 10 MPa (red) as well as scCO 2 (blue) and its mixture with 0.5 mol% toluene at p = 12 MPa (green). Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the EOS by Span and Wagner EOS for CO 2 16 and the mixture model for by Blackham and Lemmon 17 for CO 2 + toluene. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter.   Figure S26: Temperature dependence of the thermodynamic properties of scCO 2 and its mixture with 20 mol% (red) and 40 mol% (blue) of methane at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the GERG-2008 EOS 6 for CO 2 + methane. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity from EOS. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. 29 Figure S27: Temperature dependence of the thermodynamic properties of scCO 2 and its mixture with 60 mol% (red) and 80 mol% (blue) of methane at p = 9 MPa. Symbols show the present molecular simulation results. Density (circles) and enthalpy (triangles up) are shown at the top, isobaric heat capacity (triangles down) and speed of sound (squares) in the center, isothermal compressibility (diamonds) and volume expansivity (hexagons) at the bottom. Dashed and solid lines represent the GERG-2008 EOS 6 for CO 2 + methane. Dotted lines indicate the Widom line temperature determined by the maximum of the isobaric heat capacity from EOS. Statistical uncertainties were omitted when they are either within symbol size or lead to visual clutter. Figure S28: Analysis of pseudo-boiling with the approach of Banuti 18 for pure scCO 2 . The underlying data for this analysis were taken from the EOS by Span and Wagner for CO 2 16 . Symbols depict molecular simulation data. Solid lines represent the asymptotes of the liquid enthalpy h L (blue) and the ideal gas enthalpy h IG (red). Dotted lines represent the pseudo-boiling start temperature T -(blue), the Widom line temperature T W (black) and the pseudo-boiling end temperature T + (red). The Widom line temperature was determined by the maximum of the isobaric heat capacity. The pseudo-boiling start T -(blue) and end T + (red) temperatures were determined by the intersection point of the asymptote of the pseudo-boiling enthalpy h PB (orange) with h L and h IG , respectively. Figure S29: Pseudo-boiling of scCO 2 (black) and its mixtures with 1.5 mol% of ethane (blue) or toluene (red) along the isobar p = 9 MPa. Circles represent simulation data. Dashed lines represent the EOS by Span and Wagner for CO 2 16 , the GERG-2008 EOS 6 for CO 2 + ethane and the mixture model by Blackham and Lemmon 17 for CO 2 + toluene. The Widom line temperature is indicated by the dotted lines. The pseudo-boiling start Tand end T + temperatures enclose the extended Widom region as depicted by solid lines. Figure S30: Pseudo-boiling of scCO 2 (black) and its mixtures with 1.5 mol% of methane (blue) or isobutane (red) along the isobar p = 9 MPa. Circles represent simulation data. Dashed lines represent the EOS by Span and Wagner for CO 2 16 and the GERG-2008 EOS 6 for CO 2 + methane and CO 2 + isobutane. The Widom line temperature is indicated by the dotted lines. The pseudoboiling start Tand end T + temperatures enclose the extended Widom region as depicted by solid lines. Table S2: Quantitative analysis of pseudo-boiling on basis of EOS data for the studied CO 2 mixtures with 0.5, 1.0 and 1.5 mol% of the solute along the isobar p = 9 MPa. The scCO 2 mixtures with benzene and toluene were additionally analyzed at p = 10 MPa and 12 MPa. The Widom line temperature was determined by the isobaric heat capacity maximum.

Transport properties
Intra-diffusion coefficients Figure S32: Temperature dependence of the intra-diffusion coefficients of binary mixtures of scCO 2 (black) with 1 mol% of ethane (dark green), isobutane (dark yellow), benzene (red), toluene (blue) or naphthalene (green) along the isobar p = 9 MPa. Circles represent the intra-diffusion coefficient of the solute and solid lines represent the intra-diffusion coefficient of scCO 2 . The inset shows the results for hydrogen (grey) and methane (dark red) over a larger intra-diffusion coefficient range. Figure S33: Temperature dependence of the intra-diffusion coefficients of binary mixtures of scCO 2 (black) with 1.5 mol% of ethane (dark green), isobutane (dark yellow), benzene (red), toluene (blue) or naphthalene (green) along the isobar p = 9 MPa. Circles represent the intra-diffusion coefficient of the solute and solid lines represent the intra-diffusion coefficient of scCO 2 . The inset shows the results for hydrogen (grey) and methane (dark red) over a larger intra-diffusion coefficient range.

Shear viscosity
The kinetic η kk , configurational η cc and kinetic-configurational η kc contributions to the shear viscosity are given by: where V stands for the volume, T for the temperature and i and j denote different molecules of any species that interact with the potential u. The upper indices x and y stand for the spatial vector components, e.g., for velocity v x i or site-site distance r x ij .
39 Figure S34: Temperature dependence of the kinetic η kk (brown triangles), configurational η cc (green triangles) and kinetic-configurational η kc (grey squares) contributions to the shear viscosity of scCO 2 along the isobar p = 9 MPa (top), 10 MPa (center) and 12 MPa (bottom). The dotted line indicates the Widom line temperature calculated with the criterion of Bell et al. 19 . The inset shows the temperature dependence of the shear viscosity of scCO 2 (red) and its mixtures with 0.5 (top), 1 (center) and 1.5 mol % (bottom) of ethane (blue) or toluene (red) along the isobar p = 9 MPa. In the inset, circles show simulation data and solid lines EOS data. The reference correlation for the shear viscosity by Laesecke et al. 20 was used for pure scCO 2 . An extended corresponding states approach 21 was used for the mixtures. 40 Figure S35: Temperature dependence of the kinetic η kk (brown triangles), configurational η cc (green triangles) and kinetic-configurational η kc (grey squares) contributions to the shear viscosity of scCO 2 mixtures with 0.6 (top) and 0.3 mol% (bottom) of naphthalene along the isobar p = 9 MPa. The dotted line indicates the Widom line temperature calculated with the criterion of Bell et al. 19 . The inset shows the temperature dependence of the shear viscosity of scCO 2 (red) with 0.5 (top) and 1.5 mol% (bottom) of methane (blue), isobutane (red) as well as with 0.3 mol% (bottom) and 0.6 mol% (top) naphthalene (green) along p = 9 MPa. In the inset, circles show simulation data and solid lines EOS data. The reference correlation for the shear viscosity by Laesecke et al. 20 was used for pure scCO 2 . An extended corresponding states approach 21 was used for the mixtures.

Average coordination number
The average coordination number N A-B (r) between like and unlike molecules can be calculated from the integral of the radial distribution function g A-B (r) where r min is the position of the first minimum and ρ B the number density of the site molecular species B.
Microscopic structure of scCO 2 mixtures Figure S36: Correlation length (open symbols) and half of the edge length of the cubic simulation volume (crosses) for scCO 2 diluted with 0.5 (top), 1.0 (center) and 1.5 mol% (bottom) of benzene (red), toluene (blue) and naphthalene (green) over temperature along the isobar p = 9 MPa. Figure S37: Microscopic structure of the scCO 2 mixture with 1.5 mol% of benzene at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and C 6 H 6 -C 6 H 6 (bottom left) are shown for five temperatures: 300 K (red), 310 K (green), 317.5 K (black), 320 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), C 6 H 6 -C 6 H 6 (red) and CO 2 -C 6 H 6 (blue) as a function of temperature are depicted by crosses. Figure S38: Microscopic structure of the scCO 2 mixture with 0.5 mol% of benzene at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and C 6 H 6 -C 6 H 6 (bottom left) are shown for five temperatures: 300 K (red), 310 K (green), 315.5 K (black), 320 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), C 6 H 6 -C 6 H 6 (red) and CO 2 -C 6 H 6 (blue) as a function of temperature are depicted by crosses. Figure S39: Microscopic structure of the scCO 2 mixture with 1.0 mol% of hydrogen at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and H 2 -H 2 (bottom left) are shown for five temperatures: 290 K (red), 300 K (green), 308.5 K (black), 310 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), H 2 -H 2 (red) and CO 2 -H 2 (blue) as a function of temperature are depicted by crosses. Figure S40: Microscopic structure of the scCO 2 mixture with 1.0 mol% of ethane at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and C 2 H 6 -C 2 H 6 (bottom left) are shown for five temperatures: 300 K (red), 310 K (green), 312 K (black), 320 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), C 2 H 6 -C 2 H 6 (red) and CO 2 -C 2 H 6 (blue) as a function of temperature are depicted by crosses. Figure S41: Microscopic structure of the scCO 2 mixture with 1.0 mol% of isobutane at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and C 4 H 10 -C 4 H 10 (bottom left) are shown for five temperatures: 290 K (red), 300 K (green), 314.5 K (black), 320 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), C 4 H 10 -C 4 H 10 (red) and CO 2 -C 4 H 10 (blue) as a function of temperature are depicted by crosses Figure S42: Microscopic structure of the scCO 2 mixture with 1.0 mol% of toluene at p = 9 MPa. Center-of-mass radial distribution functions g(r) for CO 2 -CO 2 (top left) and C 7 H 8 -C 7 H 8 (bottom left) are shown for five temperatures: 290 K (red), 300 K (green), 317 K (black), 320 K (pink) and 340 K (blue). The magnitude of the first peak (top right) and the average coordination number (bottom right) for CO 2 -CO 2 (black), C 7 H 8 -C 7 H 8 (red) and CO 2 -C 7 H 8 (blue) as a function of temperature are depicted by crosses.