Structure of Alkylcarbonate + n-Alkane Mixed Fluids - The Journal of

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Structure of Alkylcarbonate + n‑Alkane Mixed Fluids Gregorio García,† José L. Trenzado,*,‡ Rafael Alcalde,† Ana Rodríguez-Delgado,‡ Mert Atilhan,§ and Santiago Aparicio*,† †

Department of Chemistry, University of Burgos, 09001 Burgos, Spain Departamento de Física, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas, G.C., Spain § Department of Chemical Engineering, Qatar University, Doha 2713, Qatar ‡

S Supporting Information *

ABSTRACT: The properties of dialkylcarbonate + n-alkane mixed fluids were studied both from macroscopic and from microscopic viewpoints using thermophysical measurements combined with classic molecular dynamics simulations and DFT quantum chemistry studies. The objective of this study is a whole range characterization of dialkylcarbonate-containing systems as fuel oxygenated additives. The reported results allowed analyzing the structure, dynamics, and intermolecular forces in these systems as a function of composition and temperature, paying attention to the mechanism of carbonate−n-alkane interaction for understanding the role of dialkylcarbonates in fuel properties.

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studied. Zhou et al.20 developed an equation of state modeling of the most relevant thermodynamic properties, in wide pressure and temperature ranges, which may serve as a reference model for this fluid. The properties of mixtures containing dialkylcarbonates have also been studied. Tojo et al.21 studied DMC + n-alkane mixtures showing expansion upon mixing, positive excess molar volume, and endothermic mixing process, with both properties increasing with increasing n-alkane length, and also studied vapor liquid equilibria. Rodri ǵ uez et al. 22 measured viscosity for DMC and diethylcarbonate (DEC) + n-alkane mixtures as a function of mixture composition and temperature, showing negative mixing viscosities, which is a proof of the weakening of intermolecular forces upon mixing. Additional thermodynamic studies, including modeling using several approaches, were reported by Gayol et al.,23 who also reviewed previous studies on volumetric properties of DMC or DME + n-alkane systems. Likewise, other relevant properties for alkylcarbonate + nalkane systems, such as surface tension,24 speed of sound,25 dielectric constant,25 refractive index,25 heat capacity,26 or critical behavior,27 were also studied. The available thermodynamic data allowed the study of mixing process and preferential solvation using the Kirkwood−Buff formalism.28 The understanding of liquid behavior of dialkylcarbonates from a molecular level viewpoint is also of relevance to improve their technological applications, and thus studies using computational chemistry methods have been reported. Okada29 carried out a molecular dynamics study on the conformational behavior of DMC showing the prevalence of cis−cis isomer. Studies by Gontrani et al.30 using molecular

INTRODUCTION The use of oxygenated additives to gasoline and diesel as suitable alternatives to leadalkyls for improving the octane number and the oxygen content emerged considering environmental and pollution control regulations. The most commonly applied oxygenated additives belong to the ether family of compounds, with particular interest in methyl tert-butyl ether (MTBE).1 The use of oxygenated additives is a remarkable improvement in comparison with previous technologies from both environmental and technological viewpoints, because it reduces the toxicity of the exhausts2 and maintains combustion performance.3 Nevertheless, the environmental problems rising from the use of compounds such as MTBE as gasoline additive,4 in particular drinking water pollution,5 together with the possibility of being a carcinogen agent,6 make necessary the use of new environmentally friendly and low toxic oxygencontaining additives. Therefore, dialkylcarbonates have been proposed as alternative compounds to methyl tert-butyl ether (MTBE) as gasoline additives,7−10 for meeting oxygenate specifications. Dialkylcarbonates, in particular dimethylcarbonate (DMC), are nontoxic,11 biodegradable,12 not atmospherically harmful,13 and environmentally friendly compounds,14−16 Moreover, emissions from fuels containing dialkylcarbonates as additives are lower than those using ether-based additives.17 Likewise, the available industrial technologies for producing DMC are cost-effective,7,12 and thus, from an economical viewpoint, DMC could be a suitable alternative to common additives such as MTBE. The relevance of dialkylcarbonates for the oil industry justifies that several studies have been carried out to understand their properties and liquid behavior. One of the most relevant aspects for the application of dialkylcarbonates as fuel additives is to study their thermodynamic behavior, and thus thermophysical properties18 and phase equilibria19 have been © 2014 American Chemical Society

Received: July 8, 2014 Revised: September 8, 2014 Published: September 8, 2014 11310

dx.doi.org/10.1021/jp506791m | J. Phys. Chem. B 2014, 118, 11310−11322

The Journal of Physical Chemistry B

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avoid moisture absorption. Ultrasound degassing was carried out before preparing mixtures. Binary mixtures for DMC + (n-heptane, n-octane, n-nonane, or n-decane) and DEC + (n-heptane, n-octane, n-nonane, or ndecane) were prepared in the whole composition range by weighing using an electronic balance (Mettler AE240, ± 0.0001 g), and thus leading to an average uncertainty of ±0.0004, for the mole fraction (x). Thermophysical properties were measured at ambient pressure for all of the studied systems. Density (ρ) measurements were carried out using an Anton Paar DMA 5000 oscillating U-tube densimeter, with the temperature being controlled by a Peltier system to ±1 × 10−3 K. The analysis of all of the uncertainty sources for density measurements led to ±1 × 10−5 g cm−3 estimated uncertainty. Kinematic viscosity (ν) measurements were done with a Schott-Geräte AVS-350 capillary viscometer (±1 × 10−2 s uncertainty for flow time), with temperature control to ±1 × 10−2 K using a Schott-Geräte CT1450/2 unit, and with cell temperature measurements to ±1 × 10−2 K with a platinum resistance thermometer. Viscometer calibration was traceable by the instrument manufacturer, thus leading to 0.4% average uncertainty. The average uncertainty of measured kinematic viscosity was 0.2%. DFT Calculations. The Gaussian 09 (revision D.01) package32 was used to compute the binding energy and the interaction mechanism of dialkylcarbonate + n-alkane pairs (1:1). Such calculations were carried out using the Becke gradient corrected exchange functional33 and Lee−Yang−Parr correlation functional34 with three parameter (B3LYP)35 method, along the 6-31+G** basis set. Binding energies, ΔE, were calculated as the differences among the pair energy and sum of corresponding monomer energies at the same theoretical level, with basis set superposition error (BSSE) corrected through the counterpoise procedure.36 Calculations using the CPCM (CPCM polarizable conductor calculation) approach were used to mimic the effect of surrounding n-alkane on the properties of interacting pairs.37 Optimized minima were checked trough their vibration frequencies. Interactions between different pairs were analyzed by mean of Atoms in Molecules (AIM)38 and Natural Bond Orbital (NBO)39 theories. The topological analysis of the electronic density over different interacting pairs was done using AIM2000 program.40 Besides, dyalkylcarbonates were optimized taking into account solvent effects by means of a solvation model (CPMC)41,42 using n-heptane as a solvent. These simulations were also carried out adding an implicit molecule of n-heptane, which allowed one to obtain some insights about solvent effect on dialkylcarbonates and n-alkanes interactions. Molecular Dynamics Simulations. Molecular dynamics simulations were carried out using the MDynaMix v.5.2 molecular modeling package.43 Mixtures for the DMC + nheptane system were simulated in the whole composition range, Table S2 (Supporting Information), whereas the DMC + (n-octane, n-nonane, or n-decane) systems were studied only at xDMC = 0.5, to infer the effect of n-alkane length on mixtures properties. Likewise, DEC + (n-heptane, n-octane, n-nonane, or n-decane) at xDEC = 0.5 were considered to analyze the effect of carbonate alkyl chain. Initial cubic simulation boxes, containing 400 total molecules and with density ∼0.5 g cm−3, were built for each system, using the Packmol program.44 NPT ensemble simulations, using cubic periodic boundary conditions, were carried out for all of the systems at 0.1 MPa and 293 K. Moreover, the DMC + n-heptane system was also studied at

dynamics simulations, experimentally confirmed by X-ray scattering, showed that 99% of the liquid DMC is composed of cis−cis conformer. Reddy and Balsubramanian31 carried out a quantum chemistry and molecular dynamics study on liquid DMC, their results showed wide disparities in the dipole moments of the cis−cis (1.0 D, prevailing one) and cis−trans (4.5 D, marginal populations), and thus DMC−DMC intermolecular interactions are very different for cis−cis and cis−trans isomers, which leads to clustering of the small populations of cis−trans isomers. Despite the importance of understanding the liquid behavior at the molecular level of liquid mixtures containing dialkylcarbonates and n-alkanes, to our knowledge, all of the available studies using computational chemistry methods were carried out for pure DMC, and thus further analysis of nanoscopic features controlling the properties of these mixtures is required. Therefore, a study on the thermodynamic and molecular level behavior of dialkylcarbonates mixed with n-alkane binary fluids is reported in this work. DMC and DEC, Figure 1, were

Figure 1. Molecular structure of dialkyl carbonates studied in this work calculated at the B3LYP/6-311++g** theoretical level. Atom color code: (gray) carbon, (red) oxygen, and (light gray) hydrogen. Atomic labeling used for molecular dynamics simulations is also reported.

selected because of their relevance as oxygenated additives for fuels, and n-heptane (C7), n-octane (C8), n-nonane (C9), and n-decane (C10) were selected as hydrocarbon models to simulate fuel properties. Therefore, alkylcarbonate + n-alkane binary mixtures were characterized in the full composition range as a function of temperature. Thermophysical characterization was carried out measuring volumetric and viscosity properties, because their relevance for industrial applications and because of the information on liquid structure that could be inferred from them. Likewise, theoretical studies using both classic molecular dynamics simulations (MD) and density functional theory (DFT) approaches allowed one to infer nanoscopic information about the structure, dynamics, and intermolecular forces in these fluids.

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METHODS Thermophysical Measurements. All of the studied compounds were obtained from commercial sources, with their purity and characteristics reported in Table S1 (Supporting Information). These fluids were stored out of light over molecular sieves (Fluka Union Carbide 0.4 nm) to 11311



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Figure 2. Density, ρ, viscosity, η, self-diffusion coefficient, D, and intermolecular interaction energy, Eint, for pure DMC and DEC. EXP stands for experimental values, and MD for values obtained in this work from molecular dynamics simulations. Experimental data are obtained from (a) density data from this work, (b) viscosity data from this work, and (c) self-diffusion coefficient data for DMC from Hayamizu et al.53 Error bars for MD results are reported; they were not reported for those cases in which error bars were smaller than point size.

predictions may be considered a validation of the applied force field parametrization. Thermal expansion coefficient, αp, obtained from experimental density data, was 1.242 and 1.160 m K−1 at 293 K, for DMC and DEC, respectively, whereas 1.087 m K−1 was obtained from molecular dynamics simulations for DMC at the same temperature. This 12.48% αp larger value for pure DMC from molecular dynamics simulation, despite the very low deviations in density predictions, may be considered as reasonable considering the complexity in predicting derived thermal coefficients using purely predictive approaches.49 Likewise, more reliable force field validation can be carried out using predicted vaporization enthalpy, ΔHVAP,50 because this property is strongly sensitive to the accuracy in the description of intermolecular forces in the liquid state by the considered force field. Experimental vaporization enthalpies at 1 atm are 38.30 and 44.69 kJ mol−1 at 293 K,51 for DMC and DEC, respectively, whereas molecular dynamics values, calculated as reported in a previous work (using a single dialkylcarbonate to mimic gas-phase properties),52 were 45.30 and 48.35 kJ mol−1 for DMC and DEC, respectively, which are 18.3% and 1.7% larger than experimental values. Experimental and simulated dynamic properties are reported in Figure 2b and c, where simulated dynamic viscosity was calculated using Green−Kubo method, and simulated centerof-mass self-diffusion coefficient from Einstein’s equation. DEC is more viscous than DMC, 29% larger at 293 K, in agreement with the larger vaporization enthalpy, which point to stronger intermolecular forces as the alkyl chain increases. Viscosity values obtained from molecular dynamics are 2.7 times larger on average than experimental ones for both compounds, which also lead to self-diffusion coefficients roughly 3 times lower, in agreement with previous simulations by Gontrani et al.30 Nevertheless, a good relationship between the predicted viscosity and self-diffusion coefficients is obtained, showing the fulfilling of Stokes−Einstein equation, as Hayamizu et al.53 showed for experimental results. Therefore, the applied force field parametrization may be considered as reliable for describing the main properties of the studied dialkylcarbonates. The structure of the pure dialkylcarbonates should be controlled both by geometrical and by steric factors rising from the sizes and shapes of the involved molecules, and from the intermolecular forces developed between alkylcarbonate molecules. Intermolecular interaction energy from molecular dynamics simulations is reported in Figure 2d, showing the

283, 303, and 313 K to analyze the temperature effect on liquid structure. Pressure and temperature were controlled using the Nose−Hoover method. Coulombic interactions were handled with the Ewald summation method,45 with a cutoff radius of 15 Å. Tuckerman−Berne double time step algorithm,46 with long and short time steps of 1 and 0.1 fs, was considered for solving the equations of motion. Lorentz−Berthelot mixing rules were used for Lennard-Jones terms. All of the systems were initially equilibrated in the NPT ensemble at the selected pressure and temperature for 1 ns, equilibration was assured through the analysis time evolution of potential energy, and then 5 ns NPT production runs were carried out. Force field parametrizations for all of the compounds are reported in Table S3 (Supporting Information). Internal force field parameters (bonds, angles, and dihedrals) and LennardJones parameters for dialkylcarbonates were obtained from Gontrani et al.30 Atomic charges for all of the molecules were calculated using ChelpG47 method for structures optimized at B3LYP/6-311++G** level using the Gaussian 09 (revision D.01) package.34 The n-alkanes force field parametrizations were checked through comparison of reference density data48 at 283, 293, 303, and 313 K, all at 0.1 MPa, with values obtained from NPT molecular dynamics simulation at the same temperatures and pressure, thus leading to average deviations in the studied temperature ranges of 1.47%, 1.35%, 1.38%, and 1.26%, for n-heptane, n-octane, n-nonane, and n-decane, respectively.

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RESULTS AND DISCUSSION Liquid-Phase Properties of Pure Dialkyl Carbonates. The characteristics of pure DMC in the liquid state were previously studied in the literature,30,31 although studies on DEC were not available. Experimental thermophysical properties measured in this work for pure dialkylcarbonates are reported in Table S4 (Supporting Information) in comparison with literature data showing good agreement. Density data are plotted in Figure 2a, leading to linear trends for both compounds, with DMC being denser than DEC. The calculated thermal expansion coefficients (αp) from experimental density data were 1.242 and 1.160 m K−1 at 293 K for DMC and DEC, respectively. Molecular dynamics simulations allow one to infer volumetric properties, which are compared to experimental ones in Figure 2a, showing excellent agreement: 0.16% absolute average deviation for DMC in the studied temperature range, and 1.43% for DEC at 293 K. These low deviations in density 11312



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second solvation shells of pure carbonates upon increasing temperature, in agreement with the very small decrease in Lennard-Jones intermolecular interaction energies reported in Figure 2d. A more detailed picture of the molecular arrangement in solvation shells can be obtained from spatial distribution functions reported in Figures 4 and 5. SDFs

prevailing role of van der Waals (Lennard-Jones) type interactions over purely Coulombic ones. Likewise, LennardJones interactions are larger for DEC than for DMC, which is in agreement with larger vaporization enthalpies, viscosities, and lower self-diffusion coefficients. Intermolecular forces decrease in a linear way with increasing temperature for DMC, although this change is only 4.7% on going from 283 to 313 K. The increasing alkyl chain in dialkylcarbonates leads to a decrease in density; on going from DMC to DEC, the increase in just one methyl group produces an 8.9% decrease in density. Likewise, αp coefficient for DEC is 6.3% lower than that for DMC. Therefore, to analyze the volumetric behavior in dialkylcarbonates, the void volume available was inferred using molecular dynamics simulations from the distribution of cavity sizes according to Margulis method,54 Figure S1 (Supporting Information). The cavity size distribution shows larger probabilities of cavities in the 0.3−1.0 Å range for DEC than for DMC, which would lead to a less compact fluid. Likewise, the free volume calculated for both carbonates, from the difference between the experimental molar volume, at 293 K, and the molecular volume calculate from Connolly method, is 34.61 cm3 mol−1 (0.38 cm3 g−1) and 46.58 cm3 mol−1 (0.40 cm3 g−1) for DMC and DEC, respectively, probing the presence of a larger void space in pure DEC than in DMC (∼5.3%). The structural properties of pure carbonates were analyzed using site−site radial distribution functions, RDFs, Figure 3.

Figure 4. Spatial distribution functions, SDFs, of DMC atoms around DMC molecule calculated for pure DMC at 293 K from molecular dynamics simulations. Color code: (red) O2, (pink) O1, (gray) C2, and (yellow) H1. Atom code as in Figure 1. Isosurfaces plotted at 3 times bulk density. SDFs reported from three different viewpoints (panels a, b, and c), with the orientation of DMC central molecule reported at the bottom of each panel. Alkyl hydrogen atoms are omitted for the sake of visibility.

Figure 5. Spatial distribution functions, SDFs, for O2 atoms around (a) DMC and (b) DEC molecules, calculated for pure dialkylcarbonates at 293 K from molecular dynamics simulations. Atom code as in Figure 1. Isosurfaces plotted at 3 times bulk density. Alkyl hydrogen atoms are omitted for the sake of visibility.

reported in Figure 4 show two caps of O2 atoms around both methyl groups, whereas the remaining atoms stay preferentially above and below the molecular plane for DMC,30,31 thus pointing to a specific molecular arrangement to allow the interaction between alkylic hydrogens and mainly carbonyl atoms. This spatial arrangement is slightly disrupted in DEC in comparison with DMC, Figure 5; the presence of an additional methyl group moves the preferential position of O2 atoms around the alkyl chain, but it strengthems the intermolecular interaction as reported in Figure 2d. The highly structured solvation shells raise the question of the residence times of molecules in the solvation shell around another molecule. For this purpose, the probability for an atom to remain within a sphere of radius R around a given atom was calculated for the values of the first and second minima (defined as first and second solvation shells) for com−com RDFs in Figure 3. In the case of pure DMC, Figure S4a (Supporting Information), the probability decay decreases with increasing temperature, but this effect is more remarkable for the first than for the second solvation shell. Residence times for pure DMC are 3 times larger for the first (in the 15−10 ps range) than for the second (in the 41−30 ps range) solvation shells. Likewise, probability decays are very similar for DEC than for DMC, with the residence time being slightly larger (4%

Figure 3. Site−site radial distribution functions, g(r), for pure DMC (continuous lines) and DEC (dashed lines) at 293 K obtained from molecular dynamics simulations. Atom code as in Figure 1. Values are shifted to improve visibility.

RDFs between center-of-mass (com) show two well-defined consecutive peaks with minimum at 4.75 and 7.50 Å, respectively, and although the intensity of these peaks is moderate, they point to carbonate−carbonate dipolar interaction. RDFs between carbonyl oxygen (O2) and methyl hydrogens (H1) show a weak, but well-defined, first peak at 2.74 Å, which could be considered a weak intermolecular hydrogen bond. Likewise, the large first peak between the methyl carbons (C2) and O2 atoms shows that interaction between neighbor molecules is carried out mainly through these sites, which is confirmed by the large C2−C2 first peak, showing the aggregation between alkylic domains. The effect of temperature on the structural properties of solvation shells is studied through Figures S2 and S3 (Supporting Information), showing linear and weak decreasing of populations in first and 11313



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Figure 6. Probability distribution functions for (a) molecular and (b) total dipole moment in pure DMC and DEC obtained from molecular dynamics simulations. In panel (a), all results are at 293 K.

at 293 K) for DEC than for DMC in the first shell and lower (− 22%) in the second shell. A remarkable feature for the analysis of dialkylcarbonate structure in the liquid phase is the isomers distribution. Reddy et al.31 showed from quantum chemistry calculations that the isolated DMC monomers in the gas phase had 0.32 and 3.98 D for the dipole moments of the cis−cis and cis−trans configurations, and thus the strength of intermolecular interactions is strongly dependent on the prevailing isomer in the liquid phase. Likewise, the dipole moment of cis− cis(trans−trans), cc-tt, DEC isomers is 0.64 D. Low dipole DMC cis−cis isomer prevails in the liquid phase as reported experimentally in ratios roughly 99:1 in comparison with cis− trans isomer,55,56 in agreement with previous molecular dynamics studies.31 The calculated isomer populations from the molecular dynamics simulations reported in this work may be inferred from the torsional distribution reported in Figure S5 (Supporting Information), showing large prevalence of DMC cis−cis isomer in ratio 99.5:0.5 to cis−trans isomer. The temperature effect on the DMC cis−cis to cis−trans ratio is almost negligible, changing from 99.8 at 283 K to 99.3 at 313 K. For the case of DEC, the percentage of low dipole cc-tt is 99.25%. Therefore, both for DMC and for DEC the low dipole isomers prevail over higher dipolar configurations. Nevertheless, the dipole moments of carbonate molecules in liquid phase are larger than those calculated for isolated gas-phase molecules, because of polarization in the liquid phase.31 The distributions of molecular dipole moments for DMC and DEC obtained from molecular dynamics simulations are reported in Figure 6a. In the case of DMC, a strong peak, with maxima at 0.85 D, corresponding to cis−cis isomers, is obtained together with a second weaker peak at 4.62 D, corresponding to cis− trans isomer. These DMC molecular dipole moments are remarkably larger than those in the gas phase, but this effect is more important for the cis−cis isomer, which increases 165% on going to liquid phase, whereas the cis−trans isomer only increases its dipole moment 16%, showing that cis−cis isomer is more polarizable than the liquid one. For DEC, the first peak at 1.68 D corresponds to the cctt isomer, which increases 163% in comparison with gas-phase monomers. The dielectric constants were calculated from molecular dynamics leading to 1.61 ± 0.05 and 1.73 ± 0.08 for DMC and DEC at 293 K, respectively, which are lower than the experimental values (3.1 and 2.8 for DMC and DEC).57 The total dipole moment in the simulation cells, calculated as the vectorial sum of all of the

molecular dipoles, is reported in Figure 6b, showing larger values for DEC than for DMC, and thus showing a stronger dipole medium for DEC, which would justify the larger Lennard-Jones interactions with increasing alkyl chain. Likewise, increasing temperature leads to a decrease in the total dipole moment for DEC, which would justify the temperature effects on the intermolecular interactions reported in Figure 2d. Therefore, the structure of pure dialkylcarbonates is characterized by the presence of cis−cis isomer, with very low concentrations of cis−trans isomers, which is maintained upon increase of alkyl chain. Upon increase of alkyl chains, the void space in the liquid increases, leading to a less effective packing, but this effect is overbalanced by the stronger intermolecular interactions for the larger chains, that despite the prevailing presence of low dipolar cis−cis isomers lead to remarkable van der Waals type interaction, which are characterized by well-defined and highly structured solvation shells around the carbonyl oxygen group and the alkyl chains. Study on the Dialkyl Carbonates + n-Alkane According to DFT. Previous to assessing interactions between dialkyl carbonates and n-alkanes, a conformational landscape has been analyzed for DMC and C7 interactions pairs. Because DMC shows the prevalence of cis−cis isomer,31 we have focused on the interaction between the cis isomer of DMC and n-alkanes. After interaction geometry landscape, 16 different configurations were used as starting geometry (Figure S6, Supporting Information). After checking the presence of real minima, this analysis yielded a total of six different interaction geometries, which along with information from molecular dynamics simulations and their relative energies were reduced to three different relative dispositions between DMC and C7 interactions pairs (labeled as I, II, and III, see Figure 7). Because alkyl chain length of both DMC and C7 seems to be not related to the relative disposition between both molecules, these three geometries were used as reference to optimize dialkyl carbonates n-alkane (1:1) interaction pairs. Optimized structures for alkyl carbonate and n-alkane pairs are shown in Figure 7. Table 1 collects the main molecular parameters of isolated dialkyl carbonates, and three pairs optimized at B3LYP/631+G(d,p). As shown, both dialkyl carbonates have similar structures (even in solvent), which are not affected upon interaction with n-alkanes. As said, for each couple we have focused on three relative dispositions between both molecules. Regardless of the selected conformer, the interaction between 11314



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carbonates and n-alkanes is always through an intermolecular bond between O2 of dialkyl carbonate and H from the ending methyl group of n-alkane (see Figure 7). Intermolecular distance between both molecules (d1, corresponding to intermolecular hydrogen-bond length) and several angles involving both molecules (θ1, θ2, and θ3) have been defined to assess the alkane length influence over interaction geometry. As seen in Table 1, chain length (for dialkyl carbonate of nalkane) does not have an important effect on the relative disposition between both molecules. Table 2 gathers biding energies (ΔE) corresponding to the interactions of dialkyl carbonates and n-alkanes for the selected configurations. Binding energies were corrected according to basis set superposition error, with the exception of CPCM calculations for which BSSE cannot be applied. Results of the ΔE show that all configurations yields very low values, ≃0.03 kcal mol−1, whatever the configuration and the selected compound, which is indicative of the interaction weakness between both molecules. As concerns the counterpoise corrections, it has a considerable impact on ΔE (in part due to their low values), and leads to a decrease of ΔE of around 0.9 kcal mol−1. Although corrected binding energies cannot be obtained for structures optimized in solvent, similar results

Figure 7. Optimized geometries for DMC−C7 pairs (similar structures are obtained for the remaining dialkyl carbonate n-alkanes pairs) along different viewpoints for conformations (a) I, (b) II, and (c) III.

Table 1. Main Structural Parameters for Isolated Dialkyl Carbonates and Dialkyl Carbonates + n-Alkane Pairsa DMC DMCb DEC DECb DMC−C7

DMC−C7b

DMC−C8

DMC−C9

DMC−C10

DEC−C7

DEC−C7b

DEC−C8

DEC−C9

DEC−C10

a

I II III I II III I II III I II III I II III I II III I II III I II III I II III I II III

C1−O2/Ǻ

C1−O1/Ǻ

O1−C1−O1/deg

O2−C1−O1/deg

d1/Ǻ

θ1/deg

θ2/deg

θ3/deg

1.211 1.213 1.213 1.214 1.213 1.213 1.213 1.214 1.214 1.213 1.213 1.213 1.213 1.213 1.213 1.213 1.213 1.213 1.213 1.214 1.214 1.214 1.215 1.215 1.215 1.214 1.214 1.214 1.214 1.214 1.214 1.214 1.214 1.214

1.342 1.340 1.341 1.340 1.340 1.340 1.340 1.339 1.339 1.340 1.340 1.340 1.341 1.340 1.341 1.341 1.341 1.341 1.341 1.340 1.340 1.340 1.339 1.339 1.339 1.340 1.340 1.340 1.340 1.340 1.340 1.340 1.340 1.340

107.9 107.9 108.0 108.0 107.9 108.0 108.0 107.9 108.0 108.0 107.9 108.0 108.0 107.9 108.0 108.0 107.9 108.0 108.0 108.0 108.1 108.1 108.0 108.1 108.1 108.0 108.1 108.1 108.0 108.1 108.1 108.0 108.1 108.1

126.1 126.1 126.0 126.0 126.2 126.0 126.0 126.2 126.0 126.0 126.2 126.0 125.9 126.2 126.0 125.9 126.2 126.0 126.0 126.2 126.0 125.9 126.2 126.0 125.9 126.2 126.0 126.0 126.2 126.0 125.9 126.2 125.9 126.0

2.627 2.657 2.645 2.668 2.696 2.645 2.634 2.658 2.632 2.635 2.658 2.639 2.632 2.658 2.648 2.617 2.654 2.625 2.659 2.686 2.679 2.615 2.655 2.636 2.615 2.647 2.632 2.609 2.654 2.625

143.9 119.0 119.3 144.2 116.2 119.3 143.4 119.0 138.6 143.3 119.0 120.5 142.8 119.0 121.6 143.9 119.1 122.4 144.2 117.6 118.9 145.9 119.1 118.0 146.2 119.3 118.9 147.6 119.1 123.3

10.2 19.2 71.8 9.6 19.4 71.8 10.3 20.1 48.5 10.4 20.0 78.4 13.4 20.6 82.7 8.5 20.3 64.1 8.1 21.3 64.8 9.4 21.2 71.4 8.3 21.0 71.6 5.00 21.5 70.3

27.4 38.0 48.3 27.7 40.3 48.4 27.2 32.7 58.5 26.7 37.1 51.1 23.2 36.6 55.6 26.6 36.7 48.5 27.3 37.3 50.1 29.8 31.7 44.7 30.3 36.0 49.1 29.8 35.8 47.2

See Figures 1 and 7 for labeling. bFrom calculations using n-heptane as solvent. 11315



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Table 2. Binding Energies (ΔEb), Electronic Density (ρ), Laplacian of Electronic Density (∇2ρ), and NBO Charge Transfer (ENBO) for Intermolecular Interactions between Dialkyl Carbonates + n-Alkane Pairs DMC−C7

DMC−C7a

DMC−C8

DMC−C9

DMC−C10

DEC−C7

DEC−C7a

DEC−C8

DEC−C9

DEC−C10

a

I II III I II III I II III I II III I II III I II III I II III I II III I II III I II III

ΔE/kcal mol−1

ΔEb/kcal mol−1

ρ/au

∇2ρ/au

ENBO/kcal mol−1

−0.048 −0.018 −0.010

−0.976 −0.967 −1.011 −0.817 −0.855 −0.929 −0.965 −0.970 −0.906 −0.959 −0.967 −1.019 −0.955 −0.970 −0.989 −1.005 −1.000 −1.046 −0.836 −0.881 −0.919 −0.988 −1.003 −1.064 −0.980 −1.000 −1.069 −0.966 −1.002 −1.054

0.0064 0.0061 0.0063 0.0060 0.0057 0.0064 0.0064 0.0061 0.0062 0.0063 0.0061 0.0064 0.0064 0.0061 0.0062 0.0066 0.0062 0.0065 0.0061 0.0059 0.0059 0.0066 0.0062 0.0065 0.0066 0.0064 0.0065 0.0066 0.0062 0.0065

0.0058 0.0054 0.0055 0.0053 0.0051 0.0056 0.0057 0.0054 0.0056 0.0057 0.0054 0.0056 0.0057 0.0054 0.0055 0.0059 0.0054 0.0057 0.0054 0.0052 0.0052 0.0059 0.0055 0.0057 0.0059 0.0055 0.0057 0.0059 0.0054 0.0058

1.23 1.09 1.20 1.22 1.05 1.23 1.49 1.12 1.24 1.36 1.18 1.22 1.37 1.18 1.17 1.43 1.21 1.31 1.23 1.09 1.12 1.41 1.20 1.31 1.41 1.23 1.25 1.42 1.20 1.28

−0.036 −0.024 −0.080 −0.028 −0.021 0.008 −0.012 −0.025 −0.017 −0.068 −0.035 −0.022

−0.069 −0.039 −0.004 −0.066 −0.033 −0.011 −0.065 −0.039 −0.011

From calculations using n-heptane as solvent. bValues obtained without BSSE corrections.

Figure 8. Experimental and molecular dynamics volumetric properties for xDMC + (1 − x)n-alkane. (a) Properties for xDMC + (1 − x)n-heptane at 293 K as a function of mixture composition; (b) properties for xDMC + (1 − x)n-heptane at x = 0.5 as a function of temperature, T; and (c) properties for xDMC + (1 − x)n-alkane at 293 K and x = 0.5, as a function of n-alkane number of carbon atoms, n.

about interaction weakness are obtained from simulations in nheptane as solvent. As said, weak interactions between dialkyl carbonates and nalkanes are expected. the intermolecular hydrogen bond between both molecules has been characterized through its structural parameters (d1 and θ1) along AIM and NBO theories (Tables 1 and 2). For all compounds, regardless of the configuration, intermolecular hydrogen-bond length is ≃2.6 Å. This length is somewhat higher than the typical hydrogen-bond length. High intermolecular lengths, along with low electronic

densities (from AIM theory) and low charge transfer between the O and H (from NBO), agree with low interaction strengths. Liquid-Phase Properties of Dialkyl Carbonate + nAlkane Systems. Experimental density and viscosity data are reported in Tables S5−S12 (Supporting Information), together with the excess molar volume, VE, and mixing viscosity, Δη, calculated from these data using well-known thermodynamic relationships,58 which are plotted as a function of composition and temperature in Figures S7−S10 (Supporting Information). 11316



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Figure 9. Radial distribution functions, g(r), between center-of-mass and the corresponding running integrals, N, for xDMC + (1 − x)n-heptane at 293 K.

The DMC + n-alkane and DEC + n-alkane binary systems lead to large positive excess molar volume upon mixing, Figures S7 and S9 (Supporting Information). The maxima of excess molar volume appear in the 0.4−0.5 DMC mole fraction, x, range, and the expansive behavior is reinforced with increasing alkane alkyl chain length, whereas it decreases on going from DMC to DEC for a fixed n-alkane. Excess molar volume for xDMC + (1 − x)n-heptane, together with density values, from experimental and molecular dynamics simulations is reported in Figure 8a. The molecular dynamics predictions are in excellent agreement with experimental results for density (0.28% absolute average deviation), and simulated results predict both the sign and the shape of the excess molar volume, but predictions are 42.3% larger on average than experimental values. The temperature effect on volumetric properties is analyzed in Figure 8b, where excellent agreement between experimental and molecular dynamics density data is inferred, but simulated excess molar volume is larger than the experimental. Moreover, the excess molar volume at equimolar mixtures for xDMC + (1 − x)n-heptane increases experimentally with temperature at a rate of 0.0093 cm3 × mol−1 × K−1, whereas this rate of change is 0.0240 cm3 × mol−1 × K−1 from simulations. The effect of n-alkane chain length on volumetric properties for DMC-containing systems is reported in Figure 8b, showing almost a linear increase of excess molar volume with increasing n-alkane number of carbon atoms, n, at 0.096 and 0.222 cm3 × mol−1 × n−1 rates from experimental and simulated results, respectively. Therefore, molecular dynamics simulations are able to capture the volumetric behavior of the studied binary systems, although predicting too large expansion effects in comparison with experimental measurements.

The expansive behavior upon mixing in xdialkylcarbonate + (1 − x)n-alkane systems suggests important structural changes of DMC and DEC when mixing with n-alkane. This effect was analyzed using RDFs as a function of mixture compositions for xDMC + (1 − x)n-heptane. Center-of-mass RDFs are reported in Figure 9 for mixtures at 293 K. The DMC−DMC RDFs reported in Figure 9a show that the first and second peaks do not change their position upon DMC dilution in n-heptane, running integrals show then only the number of DMC molecules surrounding a central one decreases with increasing alkane concentration, but the mechanism of interaction between neighbor DMC molecules does not change upon mixing with n-heptane. Results in Figure 9b for n-heptane−nheptane RDFs show a behavior parallel to that for DMC: nheptane molecules tend to self-aggregate without changing their intermolecular interaction mechanism in comparison with pure n-heptane. Therefore, these tend to self-aggregate both for DMC and for n-heptane, together with the RDFs for DMC−nheptane reported in Figure 9c, and show weak trends to develop interactions between DMC and n-heptane molecules, and the mixing mechanism should be controlled by a dilution of DMC clusters in n-heptane, for n-heptane-rich mixtures, and nheptane apolar domains in DMC, for DMC-rich mixtures. Nevertheless, results reported in Figure 10, in which the changes in the first (and second) solvation shells properties are reported, show that a highly nonlinear mixing behavior is obtained, which is in agreement with the strong nonideality of these mixtures reported in Figure 8. The number of DMC molecules surrounding a central DMC one decreases very suddenly on going from pure DMC to mixtures within the range of 0.8−0.9 mole fraction, for both the first and the second solvation shells, and thus, together with the large values 11317



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Figure 11. Spatial distribution functions, SDFs, for (a,c,e) n-heptane center-of-mass around DMC, and (b,d,f) DMC center-of-mass around n-heptane for xDMC + (1 − x)n-heptane at 293 K from molecular dynamics simulations. Isosurfaces plotted at 3 times bulk density. Alkyl hydrogen atoms are omitted for the sake of visibility.

Figure 10. Running integrals, N, obtained from the first (and second for DMC−DMC) minima in the corresponding center-of-mass radial distribution functions (Figure 9) for xDMC + (1 − x)n-heptane at 293 K. Values were calculated at 4.75 (first shell) and 7.65 (second shell) Å for DMC−DMC, 6.75 Å for C7−C7, and 6.85 Å for DMC−C7.

around the corresponding molecules as a function of mixture composition, Figure 12. The residence time of DMC molecules

obtained for DMC−C7 running integrals in the region of DMC-rich mixtures, show that n-heptane molecules have a disrupting effect on the DMC structuring. DMC molecules keep maintaining their trend to self-aggregate (because of their low trend to interact with n-heptane molecules) in the DMCrich regions, but n-heptane molecules enters in the second solvation shell of DMC molecules (second shell minimum for DMC−DMC RDFs appears at 7.65 Å and first minimum for DMC−C7 RDFs appears at 6.85 Å), thus leading to a smaller DMC−DMC cluster. This effect is very remarkable for very rich DMC mixtures (x > 0.8), but for x < 0.8 results reported in Figure 10 shows that both the numbers of DMC and n-heptane molecules in the first and second solvation shells do not change remarkably up to highly diluted regions (x < 0.3). For the region rich in n-heptane, the mechanism of interaction between n-heptane molecules does not change remarkably in comparison with pure liquid n-heptane, and the number of n-heptane molecules in the first solvation shell of a central n-heptane one does not change remarkably on going from pure n-heptane to equimolar DMC mixtures, Figure 10. SDFs analysis for DMC + n-heptane mixtures would allow us to analyze the spatial distribution of molecules both around DMC and n-heptane molecules. SDFs reported in Figure 11a,c,e show that molecular distribution around central DMC molecules is characterized by surrounding neighbor molecules placed preferentially around the terminal methyl groups, because of the preferential interaction of carbonyl oxygens through this position, with minor caps above the carbonyl group. This DMC−DMC short-range arrangement is maintained, but weakened, with increasing n-heptane mole fraction, and even at low DMC mole fractions DMC molecules are placed in this preferential position around neighbor DMC ones. Likewise, n-alkane molecules are clearly placed above and below the DMC molecular plane. The arrangement of molecules around central n-heptane ones is reported in Figure 11b,d,f, n-heptane molecules tend to arrange along the nheptane molecular axis, and DMC molecules are placed in almost the same regions. The solvation structure defined in Figure 11 leads to the question of molecular residence time for each type of molecule

Figure 12. Residence time, tres, of the center-of-mass of one type of molecule around another molecule for xDMC + (1 − x)n-heptane at 293 K from molecular dynamics simulations. tres was calculated from the exponential decay of conditional probability P(t) as in Figure S4 (Supporting Information). The radii R of the solvation spheres for the calculation of tres were 7.65 Å for DMC around DMC (second solvation sphere in Figure 9a), 6.75 Å for C7 around C7 (first solvation sphere in Figure 9b), and 6.85 Å for C7 around DMC (first solvation sphere in Figure 9c).

around a central DMC one first decreases vey steeply upon nheptane addition up to roughly 0.8 DMC mole fraction, and then it remains almost constant up to very diluted DMC solutions in n-heptane. This behavior points to a weakening of DMC−DMC interactions upon addition of small amounts of DMC and to a reinforcement of these interactions in highly diluted regions, with a dilution of DMC−DMC clusters in nheptane for the intermediate regions. n-Heptane molecules around DMC ones are more dynamic, leading to residence times almost one-half of those for DMC molecules in the DMC solvation sphere, but surprisingly increasing with DMC increasing mole fraction; that is to say, n-heptane molecules are more retained around DMC molecules for DMC-rich solutions. In the case of n-heptane−n-heptane interaction, they follow a parallel behavior to that of n-heptane−DMC; with increasing DMC mole fraction, n-heptane molecules remain 11318



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Figure 13. Intermolecular interaction energy, Eint, and vaporization enthalpy, ΔHvap, in xDMC + (1 − x)n-heptane at 293 K from molecular dynamics simulations. (a) van der Waals (Lennard-Jones) and (b) Coulombic contributions to Eint.

Figure 14. (a) Experimental dynamic viscosity, η, for xDMC + (1 − x)n-heptane at 293 K; (b) relationship between η and intermolecular potential energy, Ep(inter), for xDMC + (1 − x)n-heptane at 293 K; and (c) relationship between η and Ep(inter), for xDMC + (1 − x)n-heptane at x = 0.5 as a function of temperature. Red dashed line in panel (a) shows linear behavior for comparison purposes; labels in panel (b) show DMC mole fraction; and labels in panel (c) show temperature (in K). Lines in panels (a,b) are linear fits for comparison.

longer around DMC molecules, and this effect decreases nheptane mobility and allows a longer n-heptane−n-heptane interaction. These residence times are strongly related to the strength of intermolecular forces reported in Figure 13. Lennard-Jones contribution to the DMC−DMC intermolecular interaction energies are weakened upon mixing with n-hexane, but this effect is more remarkable in the 0.8−0.9 DMC mole fraction range, Figure 13a, which is also obtained for Coulombic contribution, Figure 13b. The effect of DMC on n-heptane−n-heptane interaction energies is only remarkable for high DMC mole fractions, thus confirming the weak effect of DMC molecules on pure n-heptane structuring. The behavior of DMC−C7 interaction energies is highly nonlinear, both in the van der Waals and in the Coulombic contributions. Lennard-Jones DMC−C7 interaction energies, Figure 13a, evolve reaching a minimum (in absolute value) for roughly equimolar mixtures. van der Waals forces between DMC and nheptane molecules are very strong for DMC-rich mixtures, but decrease steeply with increasing C7 mole fraction up to equimolar mixtures and then reinforcing again for n-heptanerich mixtures, with a similar behavior for Coulombic interactions although with weaker contributions. These results show the large effect of n-heptane on pure DMC structure, leading to n-heptane molecules being placed inside the DMC second solvation shells, and thus allowing efficient DMC−C7 interactions. Nevertheless, for n-heptane-rich mixtures, the trend to self-aggregate between alkane molecules leads to weaker DMC−C7 interactions in comparison with those for

DMC-rich mixtures. The behavior of simulated vaporization enthalpy is reported in Figure 13c, decreasing with increasing nheptane mole fraction but following a nonlinear trend; in particular, deviations from linearity are more remarkable for mixtures with compositions close to pure DMC and pure nheptane. The development of remarkable intermolecular forces between DMC and C7 molecules should lead to important changes in the dynamic properties of DMC + n-heptane mixtures in comparison with pure fluids. Results reported in Figure S8a (Supporting Information) show negative mixing viscosity for DMC + n-heptane for the studied temperature range reaching minima at roughly equimolar concentrations. The minima for mixing viscosity values reported in Figure S8a (Supporting Information) are in the 0.06−0.09 mPa s range for temperatures in the 283.15−313 K range, and thus it may be that very weak interactions are developed between DMC and C7 molecules. Nevertheless, dynamic viscosities are 0.409 and 0.623 mPa s for pure C7 and DMC, respectively, and thus the mixing of these two low viscous fluids should lead also to low viscous mixtures with low deviations from linearity. The behavior of dynamic viscosity for DMC + C7 mixtures at 293 K is reported in Figure 14a, and from these results it may be clearly concluded that deviations from linear behavior are remarkable despite the low viscosity values obtained for the mixtures. Dynamic viscosity in DMC + n-heptane is strongly related to intermolecular potential energy; results reported in Figure 14b,c show a well-defined linear relationship between 11319



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forces, and thus lower diffusion rates. Mixing viscosities reported in Figures S8 and S10 (Supporting Information) are negative for all of the n-alkanes, but decrease in absolute value with increasing n-alkane chain length, thus showing more viscous fluids for larger n-alkanes, in agreement with stronger intermolecular forces, Figure 16c. The DMC + (n-octane, nnonane, and n-decane) show w-shaped mixing viscosities at the lowest temperatures, especially at 293 K for n-decane (even reaching positive mixing viscosity), which is related to the large number of n-decane molecules surrounding DMC reported in Figure 16b, being an outlier of the linear trend for the remaining alkanes, and thus leading to strong heteroassociations between the n-decane and DMC. This w-shaped behavior does not appear for DEC mixtures; results in Figure 16b show that, although n-decane deviates from the linearity obtained for the remaining n-alkanes, this deviation is remarkably lower than for DMC systems, and it may be speculated that w-shaped mixing viscosity for DEC systems would be obtained for nalkanes larger than C12. The increase of dialkylcarbonate alkyl chain length leads to a decrease in positive excess molar volume (40% on average for the corresponding maxima) on going from DMC to DECbased mixtures. This may be justified considering that intermolecular interaction energies reported in Figure 16c are larger for DEC than for DMC systems, for all of the studied nalkanes, thus decreasing expansive behavior upon mixing with increasing dialkylcarbonate alkyl chain length. This is confirmed by the larger number of n-alkanes in the DEC first solvation sphere, for C8 and C9, in comparison with DMC systems reported in Figure 16b, and the slightly larger residence times reported in Figure 16d (with the exception of C10). The effect of dialkylcarbonate alkyl chain length on mixing viscosity is almost negligible, Figures S8 and S10 (Supporting Information); for example, the minima are −0.081 and −0.094 mPa s for DMC + C7 and DEC + C7 mixtures, respectively, at 293 K, and −0.076 and −0.079 mPa s for DMC + C10 and DEC + C10 mixtures, respectively, at 293 K. This almost null change on going from DMC to DEC rises from the fact that van der Waals intermolecular forces in pure DEC are stronger than those in pure DMC, as discussed in previous sections, Figure 2d, and therefore although DEC−n-alkane interactions are stronger than DMC−n-alkane ones, upon mixing the stronger DEC−DEC interactions are disrupted, and thus the balance

these two properties both for mole fraction and for temperature effects on viscosity. Likewise, simulated self-diffusion coefficients are reported in Figure 15, following a behavior parallel

Figure 15. Center-of-mass self-diffusion coefficients in DMC and nheptane molecules in xDMC + (1 − x)n-heptane at 293 K calculated from molecular dynamics simulations.

to that of dynamic viscosity as a function of mole fraction. Hence, the development of DMC−C7 intermolecular forces, mainly of van der Waals type, controls the dynamic behavior of these systems. Despite the apolar character of C7 molecules, the hydrocarbon interacts with the DMC molecule, leading to nonlinear changes in systems viscosity. The effect of n-alkane and dialkylcarbonate alkylic chain lengths on the properties and structure is analyzed in Figures S7−S10 (Supporting Information) and Figure 16. The maximum of excess molar volume increases linearly with increasing n-alkane chain length, for all of the studied temperatures, for both DMC and DEC. This behavior could be justified considering that increasing n-alkane chain length leads to larger interaction energies with the dialkylcarbonate, and also to large n-alkane−n-alkane interactions, Figure 16c, which are directly proportional to the number of alkyl carbon atoms. Nevertheless, the increment in n-alkane chain length decreases the number of n-alkane molecules in the first solvation sphere around the dialkylcarbonate, because of steric hindrance, Figure 16a,b, but at the same time increases the time these n-alkane molecules stay in the dialkylcarbonate solvation sphere, Figure 16d, because of the stronger intermolecular

Figure 16. Properties from molecular dynamics simulations for xDMC + (1 − x)n-alkane and xDEC + (1 − x)n-alkane, at x = 0.5 and 293 K. (a) Radial distribution functions, g(r), between the centers-of-mass of the corresponding dialkylcarbonate and n-alkane; (b) running integrals, N, obtained from the g(r) reported in panel (a) integrating up to the corresponding first minimum; (c) intermolecular potential energy, Ep(inter); and (d) residence time, tres, of the center-of-mass of n-alkane molecule around the center-of-mass of the corresponding dialkylcarbonate. n stands for the number of carbon atoms in the n-alkane. 11320



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computing Center of Castile and León (FCSCL, Spain) and Computing and Advanced Technologies Foundation of Extremadura (CénitS, LUSITANIA Supercomputer, Spain) for providing supercomputing facilities. The statements made herein are solely the responsibility of the authors.

between these two factors leads to almost null effects on mixing viscosity.

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CONCLUSIONS An experimental and computational study on the structure, dynamics, and thermophysical behavior of dialkylcarbonate + nalkane mixtures is reported in this work. The mixing process is characterized by expansion and negative mixing viscosity, which points to the prevailing role of van der Waals type heteroassociations between the n-alkane and the dialkylcarbonate disrupting the dipolar interactions between dilakylcarbonate molecules. Molecular dynamics results show that nalkanes occupy well-defined positions in the dialkylcarbonates solvation spheres, allowing interacting with neighbor carbonate molecules through the alkylic terminal groups with the carbonyl oxygen. Adding dialkylcarbonate molecules to the studied hydrocarbons does not disrupt remarkably the microscopic structuring of the liquid alkane. DFT simulations have allowed assessing interactions between dialkyl carbonates and n-alkane pairs and the molecular level. Three different configurations between dialkyl carbonates and n-alkanes have been optimized. However, length chain does not have an important effect on relative disposition between molecules. Binding energies, AIM, and NBO parameters gave information about interaction weakness. The simulated results show that despite the apolar character of the studied n-alkanes, remarkable structural changes upon mixing are inferred both from experimental and from computational approaches. Likewise, the residence times of n-alkanes in the solvation spheres around the carbonate increase with alkyl chains lengths, which would justify the dynamic behavior of these fluids.

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ASSOCIATED CONTENT

S Supporting Information *

Table S1 (purity and characteristics of used solvents), Table S2 (systems studied for molecular dynamics simulations), Table S3 (force field parametrization), Table S4 (thermophysical properties of pure compounds), Figure S1 (distribution of cavity sizes in pure solvents), Figure S2 (temperature effect on radial distribution functions for pure solvents), Figure S3 (running integrals in pure DMC), Figure S4 (residence time in pure solvents), Figure S5 (relevant dihedral angles in pure solvents), Figure S6 (conformational landscape for different interactions pairs), Tables S5−S12 (thermophysical properties of dialkylcarbonate + n-alkane mixtures), and Figures S7−S10 (excess and mixing properties of dilalkylcarbonate + n-alkane mixtures). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: jtrenzado@dfis.ulpgc.es. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.L.T. and A.R.-D. acknowledge the funding by Universidad de Las Palmas de Gran Canaria (Project ULPGC 07-011). Gregorio Garciá acknowledges the funding by Junta de Castilla y León, cofunded by European Social Fund, for a postdoctoral contract. We also acknowledge The Foundation of Super11321



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Structure of Alkylcarbonate + n-Alkane Mixed Fluids - The Journal of

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