Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of

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Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of n-Hexane and Carbon Dioxide Probed by Dynamic Light Scattering, Raman Spectroscopy, and Molecular Dynamics Simulations Tobias Klein, Wenchang Wu, Michael Heinrich Rausch, Cédric Giraudet, Thomas M. Koller, and Andreas Paul Fröba J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03568 • Publication Date (Web): 11 Jun 2018 Downloaded from http://pubs.acs.org on June 12, 2018

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The Journal of Physical Chemistry

Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of n-Hexane and Carbon Dioxide Probed by Dynamic Light Scattering, Raman Spectroscopy, and Molecular Dynamics Simulations Tobias Klein, Wenchang Wu, Michael H. Rausch, Cédric Giraudet, Thomas M. Koller,* and Andreas P. Fröba Institute of Advanced Optical Technologies – Thermophysical Properties (AOT-TP), Department of Chemical and Biological Engineering (CBI) and Erlangen Graduate School in Advanced Optical Technologies (SAOT), FriedrichAlexander-University Erlangen-Nürnberg (FAU), Paul-Gordan-Straße 6, 91052 Erlangen, Germany ABSTRACT: This study contributes to a fundamental understanding how the liquid structure in a model system consisting of weakly associative n-hexane (n-C6H14) and carbon dioxide (CO2) influences the Fickian diffusion process. For this, the benefits of light scattering experiments and molecular dynamics (MD) simulations at macroscopic thermodynamic equilibrium were combined synergistically. Our reference Fickian diffusivities measured by dynamic light scattering (DLS) revealed an unusual trend with increasing CO2 mole fractions up to a CO2 concentration of about 70 mol%, which agrees with our simulation results. The molecular impacts on the Fickian diffusion were analyzed by MD simulations, where kinetic contributions related to the Maxwell-Stefan (MS) diffusivity and structural contributions quantified by the thermodynamic factor were studied separately. Both the MS diffusivity and the thermodynamic factor indicate the deceleration of Fickian diffusion compared to an ideal mixture behavior. Computed radial distribution functions as well as a significant blue-shift of the CH-stretching modes of n-C6H14 identified by Raman spectroscopy show that the slowingdown of the diffusion is caused by a structural organization in the binary mixtures over a broad concentration range in the form of self-associated n-C6H14 and CO2 domains. These networks start to form close to the infinite dilution limits and seem to have their largest extent at a solute-solvent transition point at about 70 mol% of CO2. The current results not only improve the general understanding of mass diffusion in liquids, but also serve to develop sound prediction models for Fick diffusivities.

INTRODUCTION Depending on the chemical and structural characteristics of the components in a binary liquid mixture, strongly varying trends for the concentration dependency of the Fick diffusivity can be observed.1-5 Systems containing similarly sized and/or weakly associative components typically show an ideal diffusive behavior with a linear concentration dependency.4 In the case of molecules with larger size differences and highly associative groups such as alcohols, strong deviations from the ideality can be found.4 Recently, diffusion experiments, molecular simulations, and excess Gibbs models were combined to identify the influence of kinetic and structural properties on the Fick diffusivity of alcohols in aromatics and ketones.5 It was found that the slowing-down of the molecular diffusion process is directly connected to the formation of molecular networks in the mixture. While such effects on the diffusive mass transport are obvious in the presence of strong hydrogen bonding, it remains unclear how the Fick diffusivity is affected by structural and kinetic effects for mixtures consisting of weakly polar or nonpolar molecules. Most respective publications6-8 focus only on the infinite dilution regime, which cannot depict the influence of the liquid structure on the Fickian diffusion.

Fickian diffusion is often the rate limiting step in operations where other phenomena such as chemical reaction or heat transfer occur simultaneously.9 In heterogeneous catalysis, for example, mass diffusion rates of volatile reactants and products through the liquid phase are typically much lower than reaction rates at the catalytic surface. Thus, the diffusion process strongly affects the kinetics and selectivity of catalytic reactions,10 but also of separation processes,11 or the production of customized materials.12 The underlying theory in form of Fick’s first law of diffusion

J1 = −ct D11∇x1

(1)

describes the molar flux J1 of component 1 in a binary mixture with component 2 at the total molar concentration ct in a steady state.13 The driving force for mass diffusion is the gradient in the mole fraction of component 1, ∇x1. The corresponding transport coefficient, which often features a pronounced concentration dependency, is one single Fick mutual diffusivity D11. Until now, only experiments can serve as indispensable methods to obtain a general understanding of the Fickian diffusion process. Most diffusion measurements are based on the analysis of the relaxation of either a macroscopic

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gradient4,5,14-16 or microscopic fluctuations under steadystate conditions.17-22 With the latter method, possible additional mass transfer contributions such as advection are limited, which allows for the study of solely concentration-driven diffusive mass transport. In this context, the analysis of spontaneous short-ranged fluctuations at macroscopic thermodynamic equilibrium by dynamic light scattering (DLS) has proven to be a reliable method for the accurate determination of the Fick diffusivity. It was used in connection with gaseous mixtures,23 liquid systems at atmospheric pressure,1,2 systems in the nearcritical and supercritical region,24 and liquids containing dissolved gases.7,20,21 The efforts associated with diffusion experiments motivate the development of corresponding prediction methods. Several theoretical25,26 and semiempirical27,28 models for predicting D11 have been suggested based on accurate experimental results. Yet, all these models are only valid for specific systems and not fully transferable to arbitrary mixtures or thermodynamic states. Most promising models are restricted to the regime close to infinite dilution where the tracer diffusivity is valid. While the latter property can be estimated within about 10%,7,28,29 the concentration dependency of D11 still cannot be predicted satisfactorily in most cases.4 On the path to such predictions, molecular dynamics (MD) simulation has evolved to a promising tool for the calculation of thermophysical properties including the Fick diffusivity.30 Since this theoretical approach provides also insight into the fluid behavior on a molecular level, helping to deduce structureproperty relationships. Yet, the reliability of simulations depends on how accurately the molecular models can reproduce the molecular structure and dynamics, which has to be validated against experimental data. Owing to discrepancies in nomenclature in literature, it is worth summarizing the different types of mass diffusion in a binary mixture, their characteristic coefficients, and their connections relevant for the present study. The Fick diffusivity D11 is the product of the mutual MaxwellStefan (MS) diffusivity Ð12 and the thermodynamic factor Γ11,9

D11=Ð12 Γ 11 .

If any cross-correlations between like and unlike molecules are neglected, the often used Darken relation31 for the concentration dependency of the MS diffusivity,

Ð12,Darken = x2 D1 + x1D2 ,

x2 x Λ11 + 1 Λ22 − 2Λ12 . x1 x2

(4)

can be derived rigorously from eq 3. This expression requires only the knowledge of the concentration dependency of the two self-diffusivities D1 and D2 at the thermodynamic state of interest. These diffusivities describe the mobility of the individual molecules in the mixture caused by the Brownian motion in the absence of a driving force for diffusion. Close to infinite dilution of either component, the tracer diffusivities D1x1→0 and D2x2→0 are obtained. Self-diffusivities are obtained by nuclear magnetic resonance32 or by MD simulations via the mean square displacement of the species in the Einstein regime.33 Many correlations based on the Darken relation34 as well as empirical Vignes-type models3 were developed to predict Ð12. For systems with associating molecules or where hydrogen bonding and distinct electrostatic interactions are present, such predictions generally fail.3,4 Besides the kinetic contributions expressed by the MS diffusivity, the molecular organization described by the thermodynamic factor plays a further important role in the Fickian diffusion; see eq 2. This structural quantity is a measure for the deviation from an ideal solution with Γ11 = 1 which holds also at infinite dilution. According to the Flory-Huggins model,35,36 the deviation from ideality is the sum of a combinatorial and residual contribution. The latter is an enthalpic effect arising from dispersive interactions between molecules of similar size and tends to decrease Γ11. The combinatorial contribution becomes dominant for molecules of strongly different sizes and increases Γ11. The thermodynamic factor cannot be measured, but relative information on structural changes with varying thermodynamic state can be accessed by vibrational spectroscopy.37 The determination of Γ11 requires the activity coefficient of either species. The latter can be derived from experimental vapor–liquid equilibrium data,38 equations of state (EoSs),39 or excess Gibbs energy models,4 but can still not be obtained accurately in many cases.30 The thermodynamic factor can be determined via the calculation of the three Kirkwood-Buff (KB) coefficients Gij∞ for systems of infinite size by30

(2)

Eq 2 reflects the strategy of separating the kinetic and structural contributions to Fickian diffusion used in equilibrium MD simulations. In the MS formalism, the kinetic property Ð12 represents an inverse friction coefficient between two components 1 and 2, which can be obtained from the three phenomenological Onsager coefficients,31

Ð12 =

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Γ11 = 1 − x1

∞ ∞ ∞ ) c2 (G11 + G22 − 2G12

∞ ∞ ∞ + G22 − 2G12 1 + c2 x1 (G11 )

,

(5)

where c2 is the molar concentration of species 2. Obtaining reliable KB coefficients via MD simulation by integrating the respective radial distribution functions is challenging due to the poor convergence of the integrals.24 Therefore, thermodynamic factors are often calculated by EoSs and combined with MS diffusivities from MD simulations to deduce Fick diffusivities.4,5,26 With the perspective of identifying structure-property relationships for the future development of predictive models for D11, the influence of the liquid structure on the Fickian diffusion in a liquid containing weakly associative substances is investigated. For a model binary system, the

(3)

Λ11 and Λ22 include both self-correlations of the individual molecules and cross-correlation of like molecules of species 1 and 2. Distinct cross-correlations between the molecules of different species are expressed by Λ12. x1 and x2 are the mole fractions of component 1 and 2. The Onsager coefficients, which can only be calculated, describe to which extent the net velocity or displacement of all individual molecules are temporally correlated.

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non-polar molecules n-hexane (n-C6H14) and carbon dioxide (CO2) with large mutual solubility, but no distinct associative interactions have been chosen. To contribute to a fundamental understanding how the liquid structure affects the diffusive mass transport, experimental and simulation methods in macroscopic thermodynamic equilibrium are combined synergistically. The DLS technique has been advanced for providing accurate reference data for the Fick diffusivities over the entire concentration range. Raman spectroscopy has been applied not only to determine the mixture composition, but also to analyze structural changes in the liquid. The MD simulation method has been advanced for the prediction of Fick diffusivities for the system of interest without the use of EoSs. Moreover, it reveals the liquid structure and decouples the kinetic and thermodynamic effects on the mass diffusion process.

with different polarization scattering geometries. The polarized (IVV) and depolarized (IHV) scattering intensities are obtained by changing the incident polarization to vertical or horizontal (first index V or H), while the polarization of the scattered light collected by the spectrometer is fixed to vertical (second index V). The isotropic spectrum Iiso as a function of the wavenumber ν% can be calculated by41 Iiso (ν%) =

(7)

The resulting spectrum corresponds to the diagonal terms of the Raman tensor which purely reflect vibrational motion. A scheme of the optical and electronic setup used in this study for combined DLS and PDRS experiments is illustrated in Figure 1A. Details on the DLS setup including the sample preparation system, the measurement cell, and the temperature control system20 as well as on the PDRS setup37 can be found in our previous publications. Briefly, the output of a frequency-doubled Nd:YVO4 laser (λ0 = 532 nm) is split into two beams which are focused into the sample cell (SC) by a set of mirrors (M) and a lens (L). The intensity of both beams can be adjusted by a combination of a half-wave plate (λ/2) and a polarization beam splitter (PBS) as well as by a gray filter (GF). The incident angle of the main beam shown by the solid green line is adjusted via the mirror M6, and measured with a rotational table using the autocollimation technique with an uncertainty of 0.01° (k = 2). Two stops spaced by about 1 m installed behind the sample cell define the detection direction for DLS. The reference beam illustrated by the dashed green line is superimposed with the quasi-elastic scattered light to achieve heterodyne conditions. The resulting signal is collected by two photomultiplier tubes (PMTs). The CF is calculated by two correlators featuring different correlation channel arrangements; see ref 7. Before or after the recording of independent CFs, the main beam is positioned in normal incidence and an additional half-wave plate (λ/2(*)) is placed in front of the sample cell to switch between V and H polarization for the incident beam. Eight independent IHV and IVV spectra are collected under a scattering angle of 90° relative to the incident beam using two lenses, a mirror, a PBS, a long pass filter (LPF), and a QE65Pro spectrometer. For all light scattering experiments, the input laser power never exceeded 400 mW and no beam expansion was observed. Furthermore, a CCD camera was installed at the remaining optical access to observe the vapor-liquid equilibrium (VLE) of the binary mixtures under white light conditions; see Figure 1B. From this, the swelling of the liquid phase with increasing pressures is clearly visible. Carbon dioxide (CO2, M = 44.01 g mol-1) provided by Linde AG with a specified purity of more than 99.995 vol % and a spectroscopic sample of n-hexane (nC6H14, M = 86.18 g mol-1) provided by Merck KGaA with a specified purity of more than 99.0 mass % were used. The experimental protocols used in this study are the same as

METHODS Rayleigh and Raman Scattering. When coherent light irradiates a transparent fluid in macroscopic thermodynamic equilibrium, scattered light can be observed in all directions. While quasielastic scattering allows the determination of various thermophysical properties in an absolute way,18 inelastic scattering provides information on the composition of mixtures and about molecular vibrations.40 Thus, light scattering experiments are a suitable way to establish structure-property relationships. Details on the methods can be found in the given references. Here, only the main principles of the methods are described. Quasielastic Rayleigh scattering from the bulk of a binary fluid mixture is governed by the relaxation of statistical microscopic fluctuations in temperature and concentration. With DLS, the mean relaxation times of both hydrodynamic modes at a defined scattering vector are analyzed by calculating the normalized pseudo crosscorrelation function of the scattered light intensity (CF) as a function of the delay time τ. The CF resulting from the superposition of the scattered light with reference light in the so-called heterodyne detection scheme consists of two decaying exponentials given by18 −1 −1 g(2) (τ ) = b0 + bt exp(− τ ⋅τ C,t ) + bc exp(− τ ⋅τ C,c ).

1 8 8 (i ) 4 ∑∑IVV(ν%) − 3IHV(j) (ν%) . 64 i =1 j =1

(6)

In eq 6, b0, bt, and bc are experimental constants. The mean lifetimes of the fluctuations in temperature and in concentration, τC,t and τC,c, are related to the thermal diffusivity a and the Fick diffusivity D11 as well as the squared modulus of the wavenumber q according to τC,t = (aq2)-1 and τC,c = (D11q2)-1. q depends on the wavelength of the laser in vacuo λ0 and the scattering angle Θs, which can be related to the angle of incidence Θi between the incident laser light outside the sample cell and the detection direction of the scattered light. The inelastic Raman scattering process is governed by molecular vibrations. In this study, the polarizationdifference Raman spectroscopy (PDRS) method was applied for retrieving quantitative information on molecular structure. The method is based on acquiring two spectra



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Figure 1. Schematic representation of the experimental investigations by DLS and Raman scattering. (A) Scheme of the optical and electronic setup. Abbreviations and line types are explained in the text. (B) Visual observation of the n-C6H14/CO2 sample in the measurement cell at T = 303.03 K and different pressures. (C) Example CFs at Θi = 4.8°, T = 303.03 K, and different pressures corresponding to the experimental conditions in (B). (D) Normalized averaged isotropic Raman intensities in the Fermi dyad domain of CO2 (left) and in the CH-stretching domain of n-C6H14 (right) at T = 303.03 K and different pressures p. The isosbestic point in the C-H stretching of nC6H14 is marked by a diamond. (E) VLE of the binary mixtures at the studied thermodynamic states obtained by our Raman spectroscopy measurements and by calculations using the PPR78 EoS. Error bars of the measured data were not included for legibility purposes.

those in refs 7 and 37. DLS and PDRS measurements were carried out in the bulk of the fluid at the saturated liquid state for temperatures T of 303.03, 322.94, and 347.72 K and pressures p between 0.03 and 9.12 MPa. At each thermodynamic state, macroscopic thermodynamic equilibrium could be achieved with temperature and pressure stabilities at least one order of magnitude below the uncertainty of the measuring devices. In all DLS measurements, the mean lifetimes associated with fluctuations in temperature were much shorter than those associated with fluctuations in concentration, allowing a simultaneous determination of the thermal diffusivity a and the Fick diffusivity D11. Example CFs recorded at Θi = 4.8°, T = 303.03 K, and three different pressures are shown in Figure 1C. The faster exponentially decaying mode related to the thermal diffusivity can be found in the short-time range below 21 µs, while the exponential describing the decay of concentration fluctuations expands over distinctly broader time ranges. For each thermodynamic state, the final D11 and a data are based on a statistical analysis of at least 12 independent measurements carried out for different q values. The normalized averaged isotropic spectra were extracted from the PDRS measurements; see eq 7. Exemplary Raman results are depicted in Figure 1D at T = 303.03 K and various pressures. Here, we focused on the wavenumber ranges characteristic for the Fermi resonance

modes of CO2 as well as for the CH-stretching of n-C6H14. For getting quantitative information from the spectra, all modes were adjusted by Gaussian shape using the PeakFit algorithm.42 The uncertainties specified in connection with the intensities as well as wavenumbers of each mode are equal to the root mean square deviation between the experimental and fitted values for Iiso. The corresponding mole fraction of CO2 in the liquid mixture, xCO2, was obtained from the intensity ratio Ir of two characteristic bands related to CO2 and n-C6H14 in the isotropic spectra after calibration according to40 xCO2 ( p, T ) =

1 . 1 + I r ( p, T ) ⋅ K (T )

(8)

For the intensity ratio, the second Fermi dyad 2ߥଶ of CO2 at (1388 ± 2) cm-1 and the CH2 symmetric stretching band of n-C6H14 at (2864 ± 1) cm-1 were used. The calibration factor K, which was found to increase linearly with increasing temperature, was determined by fitting Ir against the mole fraction of CO2 over a limited pressure and temperature range for which Henry’s law is valid. The corresponding Henry’s constants were extracted from experimental solubility data.43 For the 39 considered data points, the relative absolute average deviation as well as the bias between the modeled and experimental molar concentrations is 4% and 0.4%. For xCO2 ranging between 2.3 and 96.1 mol%, the average expanded uncertainty (k = 2) obtained from eq 8 is estimated to be 14%. As shown in Figure 1E, the VLE behavior obtained by our


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Raman measurements was found to be in good agreement with calculations using the PPR78 EoS, which can be considered as a reference EoS for this system.44 A comparison of our Raman-based results with further experimental literature data can be found in the Supporting Information. MD Simulations. All equilibrium MD simulations were carried out using the GROMACS package 5.1.2.45 The nonpolarizable force fields (FFs) used in the present study are characterized by pair-additive potential energy functions consisting of intramolecular and intermolecular interactions. Details on the functional form of the employed FF models and the corresponding parameters can be found in the respective references. For n-C6H14, the L-OPLS FF46 was used, while CO2 was modeled using the TraPPE FLEX FF.47 Both flexible models give an all-atom description of the molecules. Interaction parameters between unlike Lennard-Jones (LJ) interaction sites were calculated using standard Lorentz-Berthelot combination rules without using further binary interaction parameters. Both dispersive and electrostatic interactions are calculated within a cut-off of 1.6 nm, while long-range corrections are used to approximate their contributions beyond the cut-off. Equations of motion were integrated every 1 fs using the leap-frog algorithm. The Nosé-Hoover thermostat48,49 and Parrinello-Rahman barostat50,51 with coupling times of 1 ps and 14 ps, respectively, were used to control temperature and pressure. Periodic boundary conditions were employed in all directions of the cubic simulation boxes to mimic the bulk behavior of the compressed liquid phase close to saturation conditions. Here, the corresponding pressures were set by about 0.2 MPa above the saturation pressures to avoid any phase separation during the simulation run. Given this small pressure change, any effect on the diffusivity results can reliably be neglected. The same temperatures and pressures as studied by DLS were investigated by MD simulations. The respective mole fractions of CO2 at the corresponding temperature and pressure conditions ranging between 1 and 99 mol% were adjusted based on correlations of the solubility data reported by Li et al.43 These data are in agreement with the concentrations deduced by our Raman measurements. The use of 500 molecules for xCO2 < 0.7 and 700 molecules for higher concentrations resulted in edge box lengths of the simulation boxes between 4 and 5 nm. After energy minimization and equilibration, the temperature and pressure were set in an isothermal-isobaric ensemble (NpT) in 5 ns simulation runs. In a canonical ensemble (NVT) at the fixed densities, the selfdiffusivities and MS diffusivities were calculated from the positions of the center of masses of each molecule in simulations based on the same initial starting configurations. While for the calculation of the self-diffusivities only the first about 70 ns were sufficient for obtaining low statistical uncertainties, the MS diffusivities were calculated from extended runs between 500 and 600 ns to improve statistics. Data for the self- and MS diffusivities were extracted from the linear part in the plots of the displacements over the delay time. Finally, 50 ns NPT simulations were conducted to compute the radial distri-

bution functions required for the calculation of the thermodynamic factor. The MD simulation strategy for the computation of the thermodynamic factor of the studied system consisting of weakly associative components has previously been applied only for Lennard-Jones fluids52,53 and for binary and ternary liquid mixtures at ambient conditions.3,9 Details on specific procedures and aspects taken care of for transferring the strategy to the nC6H14/CO2 system are given in the Supporting Information. Five independent simulation runs using different initial configurations were carried out for all thermodynamic states to improve statistics.

RESULTS AND DISCUSSION In the following, accurate experimental data for the Fick diffusivities obtained by DLS and clearly showing the special concentration dependency for the model system n-C6H14/CO2 are presented. These data are of central importance for the current study and serve as a reference for comparison with the computed results from MD simulations. The Fickian diffusion is then analyzed by its separation into the kinetic contributions given by the selfdiffusion and MS diffusion coefficients as well as the structural contributions given by the thermodynamic factor. Regarding structural effects, microscopic information from radial distribution functions obtained from MD simulations is supported by Raman spectroscopy results. Fickian Diffusion. The Fick diffusivities D11 for the system n-C6H14/CO2 obtained by our DLS measurements in the saturated liquid phase are given in Table 1 and shown in Figure 2. In the graph as well as in the Supporting Information, also the D11 data computed by MD simulations based on eq 2 are given. Our experimental results are associated with an uncertainty of 3.6% (k = 2) averaged over all state points studied. For approximately constant xCO2, the D11 data increase with increasing temperature, which can also be related to decreasing viscosity. For the present results, the relatively weak effect of pressure on D11 found in the compressed liquid phase at a given composition and temperature17,54 cannot be dissociated from effects of concentration. This is due the fact that our DLS measurements were carried out at saturation conditions with two coexisting liquid and vapor phases in the sample cell. Regarding the concentration dependency of the measured Fick diffusivities, a clear non-ideality can be found for all temperatures studied. The decreasing trend of D11 with increasing xCO2 starting from xCO2 → 0 is related to the distinct increase of the mean lifetimes of concentration fluctuations τC,c between 0.31 and 5.03 MPa given in Figure 1D. In addition, the decrease of D11 with increasing xCO2 is more pronounced at larger temperature. Minima for the Fick diffusivity located at xCO2 ≈ 0.7 to 0.8 are observed at T = 303.03 and 322.94 K. The increasing diffusivities with further addition of CO2 is again reflected by the behavior of τC,c in Figure 1C. For 347.73 K, the expected minimum could not be detected due to the pressure restrictions of the used sample cell.



The slowing-down of the Fickian diffusion process with increasing CO2 concentration is not obvious because the addition of the component with smaller molecular size seems more likely to enhance the diffusion. The reason for the unexpected behavior has to be related to distinct structural changes in the liquid mixtures with varying concentration. At T = 303.03 K, D11 is reduced by 34% from the lowest mole fraction of CO2 of 0.035 to the minimum of D11. The strongly non-ideal behavior found for the studied liquid mixtures of weakly associative components is comparable to that of liquid mixtures containing more associative components such as cyclohexane and acetone,4 but for D11 values that are about a factor of 3 larger. Furthermore, in the present study, the deceleration of the Fickian diffusion process with increasing CO2 mole fraction was found to be more pronounced with increasing temperature. In literature,24,55,56 such an effect is related to the vicinity to the critical plait point, where the thermodynamic factor and thus D11 approach zero. However, predictions of the critical temperatures and critical pressures for all studied systems at the various compositions based on the PPR78 EoS44 indicate that the thermodynamic states associated to the minima for D11 are still far away from the vicinity to the critical plait point of the mixtures. This can also be evidenced by the clear observation of two stable phases in the measurement cell for all investigated systems. Table 1. Fick Diffusivities D11 as well as their Relative Uncertainties (k = 2) Measured by DLS for Binary Mixtures of n-C6H14 and CO2 at Different Temperatures, Pressures, and Measured or Estimated Mole Fractions of CO2.a p / MPa

xCO2

0.299 0.309 0.349 0.359 0.4121 0.534 0.700 1.049 1.496 1.999 2.403 3.012 3.050 3.490 4.042 4.090 4.473 4.535 4.895 4.995 5.033 5.508 5.596 5.797

0.035 0.034 0.039b 0.042 0.049 0.059b 0.086 0.124 0.194 0.240b 0.324 0.382 0.395b 0.464 0.534 0.571b 0.601 0.653b 0.722b 0.767 0.767 0.852 0.866 0.906b

109 D11 / (m2 s-1) T = 303.03 K 9.49 9.25 9.09 9.38 9.37 8.95 9.07 8.92 8.62 8.35 8.04 7.57 7.54 7.22 6.80 6.76 6.51 6.40 6.31 6.23 6.28 6.57 6.74 7.57

100 × ∆D11/D11

6.9 2.9 2.8 6.8 6.8 2.3 5.1 1.4 2.5 3.7 3.6 2.6 1.5 1.4 1.2 3.3 1.9 1.8 3.6 2.2 1.3 1.2 1.7 6.9

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6.051

0.961b

0.299 0.415 0.518 0.659 0.822 1.056 1.394 2.039 2.454 2.666 2.990 3.061 3.372 3.567 4.153 4.198 4.455 5.053 5.197 5.995 6.023 6.321 6.682 7.323 7.419

0.023 0.034 0.045 0.056 0.072 0.099 0.125 0.198 0.234 0.256b 0.291b 0.298 0.383 0.355b 0.422b 0.427b 0.446 0.529b 0.518b 0.629 0.685 0.724 0.721 0.827b 0.846

1.143 1.428 1.675 2.030 2.446 2.993 3.342 3.679 4.105 4.638 5.187 5.933 5.997 6.718 7.660 8.444 9.121

0.080 0.100 0.118 0.144 0.176 0.218 0.26 0.273 0.308b 0.353 0.400b 0.466b 0.472b 0.538 0.628b 0.706 0.775

7.92 T = 322.94 K 11.56 11.42 11.50 11.50 11.00 11.00 10.70 10.40 10.20 10.10 9.90 10.20 9.81 10.40 9.84 9.63 9.55 8.73 8.78 8.34 8.49 7.93 8.10 7.68 7.92 T = 347.73 K 13.30 13.40 14.10 13.30 13.40 13.40 13.04 12.70 12.80 12.10 11.80 11.60 11.50 11.20 10.10 9.49 8.33

3.8 8.9 10.6 4.2 7.4 3.3 3.8 3.9 1.6 1.7 2.0 2.4 7.6 5.7 8.5 8.3 5.3 2.0 2.3 4.8 2.9 2.2 0.7 2.4 2.8 5.3 4.3 4.1 3.6 2.5 3.0 3.1 2.2 3.3 2.6 1.7 1.4 2.8 1.7 4.7 3.2 4.0 1.2

a The expanded uncertainties Uc are Uc(T) = 0.015 K, Uc(p) = 6⋅10-4 MPa, and Uc(xCO2) = 0.14⋅xCO2. b The values are estimated from the fitting of experimentally obtained concentrations as a function of pressure.


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The Journal of Physical Chemistry cross-correlations of like molecules which can be expressed by ∆Λ11 = x2(Λ11/x1 – D1) and ∆Λ22 = x1(Λ22/x2 – D2). ∆Λ12 = 2Λ12 describes the distinct cross-correlations between molecules of unlike species. Representatively for all temperatures, Figure 3 shows the concentration dependency of the quantities outlined above as well as of the mutual MS diffusivity Ð12 computed by our MD simulations for the binary liquid mixture n-C6H14/CO2 at T = 303.15 K.

Figure 2. Fick diffusivities obtained by DLS measurements and MD simulations as a function of the mole fraction of CO2 at different temperatures. Uncertainties for the concentrations related to the DLS measurements are not shown for legibility purposes.

Our MD simulation results for the Fick diffusivity obtained from the independent calculation of MS diffusivity and thermodynamic factor based on eq 2 have an average statistical uncertainty of 8% (k = 2) for all thermodynamic states investigated. This uncertainty represents an improvement in comparison to typically reported uncertainties for simulated D11 data on the order of 30%.26,36 According to Figure 2, our simulation data agree well with the experimental results, except for the largest temperature and CO2 mole fractions above about 0.5. The concentration-dependent D11 minima are also captured by the simulations, but not as clear as in our experiments. As the molecular models used for n-C6H14 and CO2 have not been fitted to any mass diffusivity data investigated in the present study, the presented results are fully predictive. The simulation data cross the experimental data at specific concentrations. In detail, the models employed in our simulations overestimate the dynamics of CO2 especially at larger temperatures, and underestimate the dynamics of n-C6H14. This is in agreement with systematically larger simulated dynamic viscosities for pure n-C6H14 in comparison to reference data according to our previous study.7 The experimental and simulated D11 data raise the question regarding the molecular origin of the distinct slowing-down of the Fickian diffusion for the studied nC6H14/CO2 system. For finding an answer, we separately analyze the MD simulation results with respect to the kinetic and structural contributions to the Fickian diffusion process according to eq 2. Further structural insight from Raman spectroscopy will be employed to support derived conclusions regarding the non-ideality of the Fickian diffusion behavior. Kinetic Contributions. The MS approach treats the mutual diffusion process in the form of a purely kinetic, collective transport phenomenon in fluid mixtures. Nevertheless, structural contributions have an intrinsic impact on the MS diffusion process. In the following, species 1 refers to CO2 and species 2 to n-C6H14. The selfdiffusivities D1 and D2 represent the self-correlations of the individual molecules contributing to the Onsager coefficients Λ11, Λ22, and Λ12. The latter also include the

Figure 3. Kinetic contributions to the diffusion process for the binary liquid mixture of n-C6H14 and CO2 as a function of the mole fraction of CO2 at 303.15 K. Cross-correlations of the molecular displacements ∆Λii, self-diffusivities Di, and MS diffusivities Ð12 (eq 3) calculated by MD simulations. MS diffusivities Ð12,Darken deduced by the self-diffusivities according to eq 4. The line Ð12,ideal refers to a hypothetical MS diffusivity in an ideal mixture for which the simulated tracer diffusivities at the boundaries of the composition range are used.

The self-diffusivities of the lighter CO2 molecules are always larger than those of n-C6H14 molecules. Both selfdiffusivities increase with increasing mole fraction of CO2, which is most pronounced beyond x1 = 0.9. This could be related to the distinctly lower viscosity of pure CO2 compared to n-C6H14, which is also expressed in the clearly increasing D11 data with increasing xCO2 at high CO2 concentrations. Because of the generally sluggish dynamics of both components over a large concentration range, commonly employed predictive approaches34,57 significantly overestimate the concentration dependency of the selfdiffusivities. These schemes use the self-diffusivities of each species i at xi → 0 as well as xi → 1 and do not account for any interactions between molecules. The two computed tracer diffusivities D1x1→0 and D2x2→0 at the boundaries of the concentration range can be used to estimate a concentration-dependent hypothetical MS diffusivity Ð12,ideal (blue line) related to a mixture of ideally diffusing species, for which also the self-diffusivities would show a linear concentration dependency. We can observe that all Ð12 values obtained from our MD simulations according to eq 3 (dark-blue squares) are clearly smaller than Ð12,ideal, with a maximum relative reduction of 20% at x1 = 0.8. This shows that the reduced dynamics of the individual species found in connection with the



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Structural Contributions. The key question arising from the previous section is how the structural arrangement in the binary mixture of interest directly affects the Fickian diffusion process and how it is related to the nonidealities reflected by the kinetic contributions. To find respective answers, the thermodynamic factor Γ11 determined from MD simulations as well as the information available in the data employed to deduce Γ11 will be analyzed in the following together with results from Raman spectroscopy. Γ11 is required to calculate the Fick diffusivity D11 from Ð12 based on eq 2. In the present study, D11 is determined consistently only from MD simulations based on the same molecular models. To deduce reliable thermodynamic factors according to eq 5, the KB coefficients G11∞, G22∞, and G12∞ for systems of finite size are needed. They can be obtained from the integrals of the corresponding radial distribution functions (RDFs) g11∞(r), g22∞(r), and g12∞(r). gij(r) describes the variation of the number density of particle species i as a function of the distance r from a reference particle species j. While gij(r) = 1 indicates a uniform random distribution at a given r, gij(r) > 1 or gij(r) < 1 denote a local enrichment or depletion of particle i in the structure, respectively. Examples for the three different types of center-of-mass (COM) RDFs are shown in Figure 4A for the liquid mixture n-C6H14/CO2 at 303.15 K and various CO2 mole fractions. This structural information is supported by snapshots of the simulation boxes in Figure 4B depicting the binary mixtures and the corresponding n-C6H14 and CO2 domains separately for x1 = 0.5, 0.7, and 0.9. A clear difference in the RDFs related to like molecules can be found. The n-C6H14/n-C6H14 RDFs indicate a random distribution of alkane molecules around each other, featuring only one shell with weak n-C6H14 enrichment (g11 ≈ 1.2). This seems to be a result of the weak dispersive interactions found in non-polar alkanes. Furthermore, owing to the relatively large size of n-C6H14 molecules, other molecules are excluded from the vicinity of every central molecule. Such correlation hole effects have also been observed for longchained n-alkanes58 and polymer melts.59 The shoulder observable for low CO2 concentrations in front of the main peak may indicate a parallel arrangement of the alkyl chains. With increasing CO2 mole fraction, this shoulder vanishes which could be caused by the penetration of the gaps between aligned n-C6H14 molecules by CO2. The constant peak height in the n-C6H14/n-C6H14 RDF as well as the snapshots of the simulation boxes at x1 = 0.7 and 0.9 indicate that the voids provided by the CO2 solvent are filled by the n-C6H14 molecules in a more or less three-dimensional network. This observation agrees with the only slowly increasing self-diffusivities of n-C6H14 and CO2 up to about x1 = 0.9 according to Figure 3.

self-diffusivities is also reflected in the MS mutual diffusion process. This is apparently decelerated because of a molecular organization in the liquid bulk. In terms of the MS formalism, the molecular frictions between the two species are larger than in an ideal system where the species are randomly distributed and the interaction between like and unlike molecules is the same. To which extent the self- and MS diffusion processes are correlated can be analyzed by comparison of the Ð12 data computed by MD simulations with those predicted from the Darken relation eq 4, Ð12,Darken (light-blue squares). In agreement with theory, both types of MS diffusivities match at the boundaries of the concentration range. Beyond the infinite dilution limits, significant positive deviations of Ð12 from Ð12,Darken are present. The difference is equal to the sum of the cross-correlations in the diffusive process, ∆Λ11 + ∆Λ22 – ∆Λ12. All individual contributions are negative and show a minimum at x1 = 0.7. Negative crosscorrelations for like species cause a slowing-down of MS diffusion compared to an ideal mixture where no crosscorrelations are present. On the other hand, the correlations between unlike molecules are per se negative and increase Ð12. This increase seems to be largest when the nC6H14 and CO2 domains show their largest spatial extension. Since the impact of ∆Λ12 is larger than that of ∆Λ11 and ∆Λ22, the overall contribution is positive and amounts up to about 17% of Ð12 value at x1 = 0.7. The discussed trends for the concentration dependency of Ð12 were found in a similar way at the larger temperatures studied. The identified significant non-ideality is different from that found for commonly studied non-ideal systems at ambient conditions.4,9 The impact of the crosscorrelation terms related to that of the self-correlation terms for the present system is smaller than for binary liquid mixtures such as aceton-methanol4,9 or ethanolbenzene4 containing more associative hydrogen-bonding components. For the latter systems, strong selfassociation in form of alcohol clusters is responsible for the distinct increase in the MS diffusivity. Nevertheless, all these non-ideal systems including the one studied here show the same qualitative trend that any form of selfassociation results in a failure of the idealized Darken relation. Despite the weak enhancement of Ð12 compared to Ð12,Darken due to the sum of the cross-correlations found for the present system, Ð12 is still smaller than in an ideal system represented by Ð12,ideal in Figure 3. This is in contradiction to the trends for the mentioned more associative mixtures as well as for many other non-ideal systems4 where Ð12 is always larger than Ð12,ideal over the entire composition range. While nanosegregated alcohol clusters with large self-correlation terms contribute to an increase in Ð12, the slowing-down of the MS diffusion process for the n-C6H14/CO2 system seems to be caused by larger segregated non-polar n-C6H14 and polar CO2 domains or networks. These networks obviously find their largest spatial extent around x1 = 0.7, where the strongest friction between the two species occurs. To sum up, the kinetic contributions result in a slowing-down of the Fickian diffusion process for the studied model system.


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The Journal of Physical Chemistry These molecular insights into the liquid structure obtained from the MD simulations are supported by our experimental results from Raman spectroscopy. Example Raman spectra are shown in Figure 1D for T = 303.03 K. The left part of the figure shows that the isotropic Raman spectra of CO2 are characterized by a doublet of sharp and relatively intense contributions being two Fermi dyads shouldered with two hot bands.61 The first dyad at ν1 = (1282.9 ± 1.4) cm-1 and the second dyad located at 2ν2 = (1385.9 ± 1.4) cm-1 correspond to the symmetric stretching vibration and the first overtone of the bending vibration, respectively. For the Fermi dyads and the hot bands, we observe an intensity increase with increasing pressure which is in accordance with the VLE of the mixture. Because the intensity of the ν1 Fermi dyad is much lower than that of the 2ν2 one, the latter was chosen for the estimation of the mole fraction of CO2. The central bands of the ν1 and 2ν2 doublet are increased by 2.1 cm-1 and 4.0 cm-1, respectively, from the infinite dilution regime of CO2 up to the infinite dilution regime of n-C6H14. This blue shift for the Fermi dyads of CO2, which has also been observed by Besnard et al.62 for mixtures of CO2 and carbon disulfide, indicates again an increasing ordering of the CO2 molecules in the binary mixtures with increasing CO2 concentration. However, the relative shifts are smaller than the respective uncertainties, which makes the interpretation regarding the structural changes rather speculative. In contrast, the CH-stretching modes of n-C6H14 in the right part of Figure 1D are strongly affected by the increase of the CO2 concentration. While the wavenumber range of the CH-stretching remains constant, a clear blue shift is observable for all individual modes related to the CH- stretching and may give further insight into the molecular structure in the liquid phase. While a CH blue shift was evidenced by ab initio calculations and vibrational spectroscopy for systems with strong hydrogen bonding,63,64 it has not been observed or discussed in the literature for non-aqueous solutions as studied here. The shift to higher frequencies of the CH-stretching with increasing dilution of n-C6H14 is representative for molecular organization and may originate from the shrinkage of the C-H bond,65 the formation of dipole-dipole interactions,66 or conformational changes.63 According to our MD results, the average C-H bond length does not change with composition, debilitating the shrinkage hypothesis. Furthermore, the formation of dipole-dipole interactions between unlike molecules is improbable for the substances studied here. In contrast, the CH blue shift for alcohols upon water dilution reported by D’Angelo et al.63 was attributed to a “nanoaggregation” of alcohol molecules in the mixtures. A similar effect of self-association of n-C6H14 at large CO2 mole fractions was found from our simulation results shown in Figure 4. The found strong blue shift of the CH-stretching bands is accompanied by a temperature-independent so-called isosbestic point at (2896.2 ± 0.6) cm-1 at the cross-section between the antisymmetric and symmetric CH3 and CH2 stretching modes located on the left and the right side of

Figure 4. Insights into the microscopic structure of the studied binary liquid mixtures consisting of n-C6H14 and CO2 at T = 303.15 K and different CO2 mole fractions x1 by MD simulations. (A) COM-RDFs gij(r) between n-C6H14 and n-C6H14 (left), CO2 and CO2 (middle), and n-C6H14 and CO2 (right). (B) Snapshots of the simulation boxes with the binary mixtures and the associated n-C6H14 and CO2 domains visualized by using the VMD program.60 The hydrogen, carbon, and oxygen atoms are shown in green, grey, and red color, respectively.

For the CO2-CO2 RDFs, a distinct ordering with three solvation shells is observed, which is caused by the longrange nature of electrostatic interactions between the CO2 molecules. The oscillations spread out up to about 1.6 nm before the RDFs converge to a plateau of 1, indicating that the simulation box sizes are sufficiently large. The selfassociated domains of CO2 molecules inside the non-polar n-C6H14 framework are maintained over a broad concentration range and are apparent from the snapshots for x1 = 0.5 and 0.7. As a result of the two like RDFs discussed before, the unlike n-C6H14/CO2 RDFs show the behavior of two interconnected n-C6H14 and CO2 domains. The damping of the RDFs with increasing CO2 concentration can be interpreted by the formation of the domains of smaller CO2 molecules. The largest extent of the interconnected n-C6H14 and CO2 domains, which was attributed to x1 ≈ 0.7 according to our previous discussion, can be observed in the corresponding simulation boxes in Figure 4B. It seems that for this concentration, a solute-solvent transition takes place with the Fickian diffusion process being hindered most strongly due to the networks formed by both species. A significant effect of temperature on the shape of the RDFs could not be identified within the temperature range studied.



the isosbestic point, respectively. At this isosbestic point, the intensity of the CH-stretching bands does not change with changing CO2 mole fraction and temperature. The isosbestic point reveals often a change in the molecular structure by variation of the thermodynamic state. For example, in Raman investigations on water67 or waterbased mixtures,68 the signal intensity ratio between the left and the right side of the isosbestic point of water is used to quantify the changes in the reorganization of water molecules and their networks by means of hydrogen bonds with varying temperature. In our present study, the presence of an isosbestic point reflects most probably that the structure formation of n-C6H14 molecules in the CO2 voids is caused by a distinct conformational change when CO2 becomes the solvent. In fact, the ratio of the sums of the integrals of the peaks left and right to the isosbestic point can be seen as a measure of the conformational changes of the n-C6H14 chains and, thus, of the structure in the fluid. The ratio was found to be constant up to x1 ≈ 0.7, before it drops down sharply to another plateau. The above experimental and numerical results confirm our previous conclusions how the kinetic contributions to the diffusion process can be related to the changing liquid structure. The clustering of the CO2 molecules with increasing CO2 concentration is accompanied by a distinct molecular rearrangement of the n-C6H14 molecules in the CO2 voids around x1 = 0.7, which can be understood as a solute-solvent transition range. Neither the CO2 nor the n-C6H14 molecules preserve a constant local structure in the binary mixtures with varying concentration, but form more or less interconnected networks of CO2 and n-C6H14 domains outside the infinite dilution regimes. While the already discussed MD simulation results related to RDFs give a good view on structure formation on a molecular level, the thermodynamic factors Γ11 deduced from the RDFs via the KB coefficients according to eq 5 provide a more macroscopic information on the liquid structure. Nevertheless, they are required to bridge the gap between D11 and Ð12. All simulated Γ11 values given in Figure 5 as a function of the CO2 mole fraction are smaller than 1, where the temperature effect is not significant. In agreement with theory, the thermodynamic factor approaches 1 at infinite dilution. The values of Γ11 below 1 demonstrate that the Fickian diffusion is further decelerated compared to the MS diffusion because of the structural information captured by Γ11. The minimum of Γ11 with values between 0.66 and 0.72 at x1 = o.8 is located close to the CO2 mole fraction where the maximum deviation of Ð12 from the idealized Darken-relation has been found. Thermodynamic factors below 1 have also been found for similar n-alkane/CO2 systems36 and the already discussed alcohol-containing mixtures,4 as well as with the Flory-Huggins model.35 For the n-C6H14/CO2 system with a relatively small size difference and interacting mainly via dispersive interactions, enthalpic effects reducing Γ11 tend to be stronger than entropic effects, which become only significant for large size differences and increase Γ11.

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Figure 5. Thermodynamic factors obtained by MD simulations as a function of the mole fraction of CO2 at different temperatures.

Considering all discussed results for the n-C6H14/CO2 system, the concentration-dependent behaviors of both the kinetic contributions expressed by the MS diffusivity and the structural contributions quantified by the thermodynamic factor cause a deceleration of the Fickian diffusion process compared to ideal mixtures. This is a remarkable characteristic of the weakly associative nC6H14/CO2 system because only accelerating effects of the summarized kinetic contributions have been identified for strongly non-ideal liquid systems in the literature so far.4 The special behavior of the C6H14/CO2 system induces the experimentally observed initial decrease of D11 with increasing CO2 mole fraction, which can be attributed to a pronounced segregation of both n-C6H14 and CO2 domains in the liquid structure. Above x1 ≈ 0.8, the n-C6H14 domains are more and more dissolved, which can be related to the distinct increase of D11 in this regime.

CONCLUSIONS The present study contributes to the understanding how the changing liquid structure affects the Fickian diffusion process in a binary model system consisting of weakly associative n-C6H14 and CO2 molecules. A further development of the DLS method for studying the Fick diffusivities of such system over broad concentration and pressure ranges with small uncertainties allowed to identify the exceptional concentration dependency of D11 for the model system. These experimental data serve as reliable database for MD simulations that were employed to explore the reasons for the observed phenomenon. Quantitative agreement for the concentration dependence of the simulated and experimental Fick diffusivity was obtained for most of the studied states. The applied simulation strategy allowed to study the molecular origins of the nonideality of the Fickian diffusion, where kinetic and structural contributions could be analyzed separately. Compared to an ideal mixture, strong self-associations between like molecules reduce the dynamics of the molecules and, thus, the collective MS diffusivity, which is in contradiction to the findings for commonly investigated non-ideal systems. In contrast, the cross-correlations between all molecules slightly enhance the MS diffusion which, in total, is somewhat decelerated by the kinetic contributions. The structural analysis by MD simulations via radial distribution functions and Raman spectroscopy


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The Journal of Physical Chemistry A.; Vlugt, T. J. H. Fick Diffusion Coefficients in Ternary Liquid Systems from Equilibrium Molecular Dynamics Simulations. Ind. Eng. Chem. Res. 2012, 51, 10247-10258. (4) Guevara-Carrion, G.; Janzen, T.; Munoz-Munoz, Y. M.; Vrabec, J. Mutual Diffusion of Binary Liquid Mixtures Containing Methanol, Ethanol, Acetone, Benzene, Cyclohexane, Toluene, and Carbon Tetrachloride. J. Chem. Phys. 2016, 144, (12), 124501. (5) Janzen, T.; Gaponenko, Y.; Mialdun, A.; Guevara-Carrion, G.; Vrabec, J.; Shevtsova, V. The Effect of Alcohols as the Third Component on Diffusion in Mixtures of Aromatics and Ketones. RSC Adv. 2018, 8, 10017-10022. (6) Moultos, O. A.; Tsimpanogiannis, I. N.; Panagiotopoulos, A. Z.; Trusler, J. P.; Economou, I. G. Atomistic Molecular Dynamics Simulations of Carbon Dioxide Diffusivity in nHexane, n-Decane, n-Hexadecane, Cyclohexane, and Squalane. J. Phys. Chem. B 2016, 120, 12890-12900. (7) Giraudet, C.; Klein, T.; Zhao, G.; Rausch, M. H.; Koller, T. M.; Fröba, A. P. Thermal, Mutual, and Self-Diffusivities of Binary Liquid Mixtures Consisting of Gases Dissolved in nAlkanes at Infinite Dilution. J. Phys. Chem. B 2018, 122, 31633175. (8) Koller, T. M.; Heller, A.; Rausch, M. H.; Wasserscheid, P.; Economou, I. G.; Fröba, A. P. Mutual and Self-Diffusivities in Binary Mixtures of [EMIM][B(CN)4] with Dissolved Gases by Using Dynamic Light Scattering and Molecular Dynamics Simulations. J. Phys. Chem. B 2015, 119, 8583-8592. (9) Liu, X.; Schnell, S. K.; Simon, J.-M.; Bedeaux, D.; Kjelstrup, S.; Bardow, A.; Vlugt, T. J. H. Fick Diffusion Coefficients of Liquid Mixtures Directly Obtained from Equilibrium Molecular Dynamics. J. Phys. Chem. B 2011, 115, 12921-12929. (10) Pöhlmann, F.; Jess, A. Interplay of Reaction and Pore Diffusion During Cobalt-Catalyzed Fischer–Tropsch Synthesis with CO2-Rich Syngas. Catalysis Today 2016, 275, 172-182. (11) Hasib-ur-Rahman, M.; Siaj, M.; Larachi, F. Ionic Liquids for CO2 Capture ‒ Development and Progress. Chem. Eng. Process. 2010, 49, 313-322. (12) Putz, Y.; Grassberger, L.; Lindner, P.; Schweins, R.; Strey, R.; Sottmann, T. Unexpected Efficiency Boosting in CO2Microemulsions: A Cyclohexane Depletion Zone Near the Fluorinated Surfactants Evidenced by a Systematic Sans Contrast Variation Study. Phys. Chem. Chem. Phys. 2015, 17, 6122-6134. (13) Fick, A. Über Diffusion. Ann. Phys. 1855, 170, 59-86. (14) Zubeir, L. F.; Romanos, G. E.; Weggemans, W. M. A.; Iliev, B.; Schubert, T. J. S.; Kroon, M. C. Solubility and Diffusivity of Co2 in the Ionic Liquid 1-Butyl-3Methylimidazolium Tricyanomethanide within a Large Pressure Range (0.01 Mpa to 10 Mpa). J. Chem. Eng. Data 2015, 60, 1544-1562. (15) Cadogan, S. P.; Maitland, G. C.; Trusler, J. P. M. Diffusion Coefficients of CO2 and N2 in Water at Temperatures between 298.15 K and 423.15 K at Pressures up to 45 MPa. J. Chem. Eng. Data 2014, 59, 519-525. (16) Condemarin, R.; Scovazzo, P. Gas Permeabilities, Solubilities, Diffusivities, and Diffusivity Correlations for Ammonium-Based Room Temperature Ionic Liquids with Comparison to Imidazolium and Phosphonium RTIL Data. Chem. Eng. J. 2009, 147, 51-57. (17) Giraudet, C.; Bataller, H.; Croccolo, F. High-Pressure Mass Transport Properties Measured by Dynamic Near-Field

indicating a significant blue-shift of the CH-stretching modes of n-C6H14 revealed the presence of interconnected n-C6H14 and CO2 domains in the liquid bulk. These domains seem to find their largest extent around CO2 mole fractions of 0.7 where a solute-solvent transition takes place. In this concentration range, also the simulated thermodynamic factor found to be always smaller than 1 indicates the most pronounced deceleration of Fickian diffusion. The high degree of structural organization in the liquid bulk results in a significant reduction of the Fick diffusivity by about a factor of two compared to an ideal mixture. The identified structure-property relationships should contribute to the future development of sound prediction schemes for the Fick diffusivity of binary mixtures.

ASSOCIATED CONTENT Supporting Information. Details on the determination of the VLE experimental data and on the MD simulations with respect to the molecular models used, the calculation of self- and MS diffusivities, a comparison with reference data for density, viscosity, and self-diffusivity, and the methodology to obtain the thermodynamic factor. Self-diffusivities, MS diffusivities, thermodynamic factors, and Fick diffusivities obtained by MD simulations for the studied binary mixtures as a function of temperature, pressure, and concentration. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Phone: +49-9131-85-23279. Fax: +49-9131-85-25878. Email: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was financially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) within Project FR 1709/11-1 and by funding the Erlangen Graduate School in Advanced Optical Technologies (SAOT) within the German Excellence Initiative. The authors also gratefully acknowledge the computing resources and support provided by the Erlangen Regional Computing Center (RRZE).

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Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of

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