Insights into the Coal Extractive Solvent N-Methyl-2-pyrrolidone +

Energy & Fuels 2009, 23, 1591–1602

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Insights into the Coal Extractive Solvent N-Methyl-2-pyrrolidone + Carbon Disulfide Santiago Aparicio,* Marıá J. Da´vila, and Rafael Alcalde Department of Chemistry, UniVersity of Burgos, 09001 Burgos, Spain ReceiVed October 2, 2008. ReVised Manuscript ReceiVed December 31, 2008

A wide set of experimental and computational tools were used to characterize the N-methyl-2-pyrrolidone (NMP) + carbon disulfide mixed solvent in the full composition range. The interest in this solvent rose from its very efficient use for coal extraction through a mechanism still not fully understood. Thermophysical properties at ambient pressure together with pressure-volume-temperature (PVT) behavior were measured with the objective of providing the required data for the industrial use of the mixed fluid and to get insight into the fluid structure at the molecular level. NMR, FTIR, and solvatochromic studies were performed together with microwave dielectric relaxation spectroscopy (DRS) measurements, thus providing more information on the fluid’s structure and allowing one to relate the molecular level behavior with the measured macroscopic properties. Moreover, density functional theory (DFT) and classical molecular dynamics simulations (MD) were used to obtain a detailed picture of the intermolecular interactions within the fluid, at short and long ranges, and of other relevant features leading to the structure of the studied system. The whole study leads to a fluid’s picture in which carbon disulfide hinders the development of NMP/NMP intermolecular dipolar interactions, thus increasing the monomer population. We should remark that some properties reported in this work are in remarkable disagreement with previously reported studies, the most important one being the positive excess molar volume in the whole pressure-temperature range studied, which contrasts with the negative values reported in the literature. Previously reported properties are hardly justified with a coherent molecular level picture, whereas the whole collection of properties reported in this work leads to a more reasonable fluid’s structure.

1. Introduction The knowledge of coal structure is very important for many processes such as gasification or liquefaction, and thus it is a remarkable problem from both technological and economical viewpoints. This structure strongly influences the physical and chemical properties of the different coal types, and it is intimately related to the aggregation state of the molecules forming coal. A powerful method to study coal structure is the extraction and swelling using organic solvents, considering that the coal aggregation state determines the solubility. Thus, this extraction allows for the studying of the origins of coal aggregation in noncovalent interactions such as hydrogen bonding, van der Waals forces, or π-π interactions. Recent studies have proposed the use of multicomponent organic liquid mixtures for this purpose.1,2 Although several liquid mixtures have been studied, special attention has been paid to the NMP + CS2 system, showing remarkable efficiency for a variety of coals, especially at 1:1 volume ratio (mole fraction of NMP ≈ 0.40). This mixed solvent gives rise to very high extraction yields, especially for bituminous coals, working at room temperature conditions.3,4 Nonetheless, the extractive ability of * To whom correspondence should be addressed. E-mail: [email protected]. (1) Dyrkacz, G. R.; Bloomquist, C. A. A. Energy Fuels 2000, 14, 513– 514. (2) Dyrkacz, G. R.; Bloomquist, C. A. A. Energy Fuels 2001, 15, 1409– 1413. (3) Lino, M.; Takanohashi, H.; Osuga, H.; Toda, K. Fuel 1988, 67, 1639– 1647. (4) Lino, M.; Takanohashi, H.; Obara, S.; Tsueta, H.; Sakonawa, Y. Fuel 1989, 68, 1588–1593.

this fluid is not so high for low rank coals,5 although the ultimate reason of this behavior is not fully understood, as its origin is supposed to be in the different interacting sites in each coal through which the interaction with the solvent is developed. Several studies have been published trying to shed light into the molecular level origins of the remarkable extractive ability of NMP/CS2 mixed solvent, and in particular on the role of CS2 both in the liquid mixture structure and in the solvent interaction with coals. Nevertheless, the reasons of the special extractive ability of this particular mixture are still under discussion. A recent work6 reported a wide study using different experimental tools to characterize the mixed solvent, and some of the reported results were highly surprising, for example, negative excess molar volume in the whole composition range or a very anomalous sigmoid variation of viscosity with composition. These results were in clear disagreement with the first results of our research on this system, and thus a wide scope study was planned using several experimental and theoretical approaches to infer the molecular level structure of NMP/CS2 mixed solvent in wide pressure and temperature ranges and its relationship with the coal extractive ability of the studied fluid. The analysis of available literature allows one to infer several conclusions on the extractive ability of NMP/CS2 mixed solvent and the possible molecular origins of this behavior. Although extraction may be carried out at room temperature, it is more efficient at high temperatures, but when temperature is larger than 453.15 K, a reaction occurs between both molecules, (5) Takanohashi, T.; Yaganida, T.; Lino, M.; Mainwaring, D. E. Energy Fuels 1996, 10, 1128–1132. (6) Dyrkacz, G. Energy Fuels 2001, 15, 918–929.

10.1021/ef800838r CCC: $40.75  2009 American Chemical Society Published on Web 02/16/2009

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leading to the formation of N-methylpirrolidin-2-tiona.7,8 The same reaction product is produced at large pressures.9 Hence, the extraction process has to be developed at moderate conditions. NMP molecules are able to interact strongly with aromatic compounds, especially polycondensed aromatic ones,10 and this may be the origin of the solvent ability of NMP for coal macromolecules and of the different extraction yields for bituminous and low rank coals. Nonetheless, the ability to dissolve coal requires that NMP molecules permeate the coal structure to interact with coal macromolecules; NMP molecules are maybe too bulky to penetrate easily in the coal structure, and thus the interaction with coal macromolecules may be hindered. This low permeability of pure NMP molecules may also hinder the possible breaking effects on coal hydrogen bonds, and thus this low diffusion of NMP into the coal structure would justify the poor extractive ability of pure NMP solvent.11 Thus, considering the relationship between self-diffusion constant and viscosity through the Stokes-Einstein equation, the remarkable decrease of viscosity upon CS2 addition (64% on going from pure NMP to the 1:1 volume ratio mixture) would justify the improvement in extraction yields. Likewise, NMP molecules are strongly polar (4.09 D at 298.15 K),12 thus tending to develop effective dipolar intermolecular forces leading to different oligomers; these association complexes should increase viscosity, decrease molecular diffusion, and thus hinder the penetration in the coal structure. The addition of carbon disulfide to liquid NMP has a strong effect on these NMP intermolecular dipolar interactions, which are clearly weakened;10 this seems to be the most remarkable structural feature leading to coal extraction. Hence, to recap, two main factors seem to control the coal extraction process by the NMP/CS2 mixture: (i) The extraction is developed mainly through NMP/coal macromolecule interactions, although CS2 has been proposed to break some of the weaker coal interactions.13 (ii) The main role of CS2 seems to be breaking/weakening NMP intermolecular dipolar interactions, thus allowing it to penetrate the coal structure to interact with coal macromolecules, and thus weakening the coal intermolecular forces (mainly hydrogen bonding but also weaker van der Waals forces).13 Although the above-mentioned general facts controlling coal extraction are shared by different authors, this is not fully clarified with a molecular level study on the NMP/CS2 structure that allows one to quantify all of these trends. Thus, the approach proposed in this work tries to explore the molecular level nature of this complex solvent mixture using a collection of experimental and theoretical tools to analyze, on one side, the NMP pure solvent structure and, on the other side, how the addition of CS2 molecules changes it. The structure of the work is reported in Figure 1; to our knowledge, this is the first study in which computational methods are combined with highly accurate thermophysical properties, as a function of pressure and temperature, and with wide range spectroscopic measurements (7) Zong, Z.; Peng, Y.; Qin, Z.; Liu, J.; Wu, L.; Wang, X.; Liu, Z.; Zhou, S.; Wei, X. Energy Fuels 2000, 14, 734–735. (8) Fu, X.; Zhang, C.; Zhang, D.; Yuan, S. Chem. Phys. Lett. 2006, 420, 162–165. (9) Wang, B.; Wei, X.; Xie, K. J. Chem. Ind. China 2004, 55, 569– 574. (10) Shui, H.; Wang, Z.; Gao, J. Fuel Process. Technol. 2006, 87, 185– 190. (11) Ndaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842–845. (12) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Methods of Purification; John Wiley and Sons: New York, 1986. (13) Aida, T.; Suzuki, E.; Yammanishi, I.; Sakai, M. Prepr. Pap.-Am. Chem. Soc., DiV. Fuel Chem. 1999, 44, 623–628.

Aparicio et al.

Figure 1. Scheme of the work reported in this study.

(including state-of-the-art dielectric relaxation spectroscopy) to infer the particular characteristics of NMP/CS2 mixed solvent. 2. Materials and Methods 2.1. Solvents. NMP (Fluka, 99.9%) and CS2 (Fluka, 99.9%) were degassed by ultrasounds before any measurement, used without any additional purification, and kept out of the light over Fluka 0.4 nm molecular sieves. Their purity was measured by gas chromatography and checked by comparison of literature properties with measured ones at 298.15 K, Table 1. Mixture samples were prepared by weighing with a Mettler AT261 microbalance ((1 × 10-5 g) and syringing into vials with the same mixture volume to avoid preferential evaporation; thus, a precision of (1 × 10-4 in the mole fraction is obtained. 2.2. Ambient Pressure Thermophysical Properties. Density (F) and speed of sound (u) were measured simultaneously with an Anton Paar DSA 5000 instrument, where density was measured by an oscillating U-tube ((5 × 10-6 g cm-3) and speed of sound by measuring the traveling time of a sound pulse from the piezoelectric transducer to the detector ((0.5 m s-1). The cell temperature was controlled by a built-in solid-state thermostat and measured by internal platinum resistance thermometers ((1 × 10-2 K). Calibration was carried out using two reference standards, n-nonane (Fluka, purity >99.5%) and toluene (Sigma-Aldrich, purity >99.5%). Density values for these standards were obtained from the literature.20 Dynamic viscosity (η) was measured using an automated AMV200 Anton Paar rolling ball microviscometer. The cell temperature was controlled through a Julabo F25 external thermostat and measured with a platinum resistance thermometer ((1 × 10-2 K). The rolling time was measured to (1 × 10-2 s, and the precision for dynamic viscosity was (5 × 10-3 mPa s. Calibration was carried out using n-dodecane (Aldrich, >99.5%), hexan-1-ol (Fluka, >99.5%), octan-1-ol (Fluka, >99.5%), and decan-1-ol (Fluka, >99.5%) as standards.18,20 Refractive indices (nD) were measured in relation to the sodium D line by an automated Leica AR600 refractometer to (5 × 10-6. Temperature was controlled by a Julabo F32 external circulator and measured by a platinum resistance thermometer ((1 × 10-2 (14) Domanska, U.; Lachwa, J. J. Chem. Thermodyn. 2002, 34, 885– 893. (15) Al-Mashhadani, A. M. A.; Awwad, A. M. Thermochim. Acta 1985, 89, 75–80. (16) Assarson, P.; Eirich, F. R. J. Phys. Chem. 1968, 72, 2710–2719. (17) Zabransky, M.; Ruzicka, V.; Majer, V.; Domalski, E. J. Phys. Chem. Ref. Data Monogr. 6 1996. (18) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of Liquids; Hemisphere: New York, 1989. (19) Garcıá, V.; Fernańdez, J. E.; Caćeres, M.; Nuń˜ez, J. J. Chem. Thermodyn. 1993, 25, 555–559. (20) Lemmon, E. W.; McLinden, M. O.; Friend, D. G. Thermophysical Properties of Fluid Systems. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, June 2005; http://webbook.nist.gov.

N-Methyl-2-pyrrolidone + Carbon Disulfide

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Table 1. Experimental and Literature Thermophysical Properties of Pure Solvents at 298.15 K and Ambient Pressure (∼0.1 MPa)a solvent

F/g cm-3

η/m Pa s

u/m s-1

nD

kS/T Pa-1

kT/T Pa-1

RP/kK-1

Cp/J K-1 mol-1

Cv/J K-1 mol-1

NMP

1.02789b 1.02796c 1.02804d 1.25577b 1.2555f

1.707b 1.667e 1.666f 0.397b 0.352h

1545.4b

1.46882b 1.4675f

407.35b

531.86b

0.869b 0.837d

174.39b 174g

133.57b

1143.7b

1.62360b 1.62409f

608.79b

939.84b

1.192b 1.208i

77.59b 77.93g

50.25b

CS2

a Density, F, dynamic viscosity, η, speed of sound, u, refractive index, n , isentropic compressibility, k , isothermal compressibility, k , isobaric D S T thermal expansivity, Rp, molar isobaric heat capacity, Cp, and molar isochoric heat capacity, Cv. b This work. c Reference 14. d Reference 15. e Reference 16. f Reference 12. g Reference 17. h Reference 18. i Reference 19.

K). Calibration was performed using double degassed water (Millipore Milli-Q) and a standard oil (nD ) 1.51416) supplied by the manufacturer. Isobaric molar heat capacities (Cp) were measured to (1 × 10-2 J mol-1 K-1 using a Setaram micro DSC III calorimeter. It consists of two vessels (reference and measuring) surrounded by an array of highly sensitivity Peltier elements ((1 × 10-2) and lodged in a calorimetric block surrounded by a thermostatic liquid (n-undecane) that ensures a temperature homogeneity. The calorimeter works under the Calvet Principle, determining the variation of the heat flow to/from liquid, with both cells maintained to the same temperature. Measurements were performed according to the isothermal step method described in the literature,21 using n-hexane (Fluka, >99.5%) as reference material and butan-1-ol (Aldrich, >99.5%) as calibration liquid, whose cp values were obtained from Zabransky et al.17 Excess properties derived from experimental ones were calculated according to well-known ideality criteria.22,23 If an ideal term may not be defined, as for viscosity, and thus it is not proper to use the term excess, the so-called mixing property according to eq 1 is used. 2

∆Y ) Y -

∑xY

(1)

i i

i)1

where Y stands for the corresponding property. The Redlich-Kister equation24 was used to correlate excess and mixing properties for binary systems (XE) at atmospheric pressure, eq 2. k

XE ) x(1 - x)

∑ A (2x - 1)

j

j

(2)

j)0

2.3. Spectroscopical Measurements. UV-vis measurements were performed in a Hewlett-Packard spectrophotometer ((0.2 nm) with the temperature of the cell controlled with a Peltier element to (1 × 10-1 K. Reichardt’s dye (Aldrich 95%) was used for solvatochromic measurements according to a procedure previously reported.25 Attenuated total reflection infrared (ATR-FTIR) spectroscopy studies were developed with a Nicolet Nexus spectrometer together with a Smart Thermal ARK device. The ATR accessory contains a Zinc Selenide crystal, the temperature of which is controlled through a built-in controller, and measured through a RTD temperature sensor to (1 °C. Nuclear magnetic resonance (NMR) experiments were carried out using a Varian Unity Innova 400 MHz apparatus with the cell temperature controlled to (1 × 10-1 K. All chemical displacements are reported relative to those in pure NMP because no other reference was used to avoid any disruption in the mixture structure because of the presence of additional compounds. Microwave dielectric relaxation spectroscopy (DRS) measurements were performed according to a coaxial (21) Cerdeirinã, C. A.; Migues, I. A.; Carballo, E.; Tovar, C. A.; de la Puente, E.; Romanı´, L. Thermochim. Acta 2000, 347, 37–44. (22) Benson, G. C.; Kiyohara, O. J. Chem. Thermodyn. 1979, 11, 106– 1064. (23) Douheret, G.; Moreau, C.; Viallard, A. Fluid Phase Equilib. 1985, 22, 277–287. (24) Redlich, O.; Kister, T. Ind. Eng. Chem. 1948, 40, 345–348. (25) Garcıá, B.; Aparicio, S.; Alcalde, R.; Ruiz, R.; Da´vila, M. J.; Leal, J. M. J. Phys. Chem. B 2004, 108, 3024–3029.

reflection technique using a vector network analyzer (Agilent N5230A) in the 200 MHz to 20 GHz frequency range with an Agilent 85070E dielectric probe kit and an Agilent N4691B ECal electronic calibration module; the cell temperature was controlled with an external circulating bath and measured to (1 × 10-1 K with a platinum resistance thermometer, and the measurement and calibration procedures were previously reported.26 All spectroscopic experiments were carried out at 298.15 K and ambient pressure. 2.4. Pressure-Volume-Temperature (PVT) Measurements. The apparatus used for the PVT measurements was previously described in detail.27,28 The system is installed around a highpressure vibrating tube densimeter. The cell temperature is controlled and measured to (1 × 10-2 K, and the pressure was kept constant to (5 × 10-3 MPa and measured to (1 × 10-2 MPa. The pressure transducer and thermometer were previously calibrated through well-defined and traceable procedures. For proper apparatus calibration, a 14-parameter equation was used27 with n-hexane (Fluka, 99.9%) and water (Millipore, resistivity 18.2 mΩ cm) as reference fluids.20 The effect of sample’s viscosity on density readings is below the accuracy limit of measurements ((1 × 10-4 g cm-3); thus raw data without viscosity corrections were used along this work. Experimental density data were fitted successfully to the 10-parameter TRIDEN equation developed by Ihmehls and Gmehling.29 From the fitting equation, the derived properties isobaric expansivity, RP, isothermal compressibility, kT, and internal pressure, Pi, were calculated from corresponding thermodynamic relationships. Excess properties were defined according to reported ideality criteria.27 2.5. Density Functional Theory (DFT) Calculations. DFT calculations were carried out with the Gaussian 03 package30 according to the density functional theory (DFT), using the Becke gradient corrected exchange functional31 and Lee-Yang-Parr correlation functional32 with the three parameters (B3LYP)33 method. 6-311++g** basis set was used along this work. Atomic (26) Aparicio, S.; Alcalde, R.; Garcıá, B.; Leal, J. M. Chem. Phys. Lett. 2007, 444, 252–257. (27) Garcıá, B.; Aparicio, S.; Alcalde, R.; Da´vila, M. J.; Leal, J. M. Ind. Eng. Chem. Res. 2004, 43, 3205–3215. (28) Aparicio, S.; Garcıá, B.; Alcalde, R.; Da´vila, M. J.; Leal, J. M. J. Phys. Chem. B 2006, 110, 6933–6942. (29) Ihmehls, E. C.; Gmehling, J. Ind. Eng. Chem. Res. 2001, 40, 4470– 4477. (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (31) Becke, A. D. Phys. ReV. A 1988, 38, 3098–3100. (32) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (33) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652.


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Figure 2. (a) Excess molar volume, VE, (b) mixing dynamic viscosity, ∆η, (c) mixing refractive index, ∆nD, and (d) excess isobaric molar heat capacity, CEp , for the x1 NMP + (1 - x1) CS2 binary solvent, at 298.15 K and ambient pressure. (b) Experimental and (-) correlated values with eq 2.

charges were calculated to fit the electrostatic potential34 according to the Merz-Singh-Kollman (MK)35 scheme. Interaction energies for complexes, ∆E, were calculated as the differences among the complex and sum of monomers’ energies at the same theoretical level, with basis set superposition error (BSSE) corrected through the counterpoise procedure.36 2.6. Classical Molecular Dynamics (MD) Simulations. Classical molecular dynamics simulations were carried out using the TINKER molecular modeling package.37 All simulations were performed in the NPT ensemble; the Nose´-Hoover method38 was used to control the temperature and pressure of the simulation system. The motion equations were solved using the Verlet Leapfrog integration algorithm.39 The molecular geometries were restrained according to the shake algorithm.40 Long-range electrostatic interactions were treated with the smooth particle mesh Ewald method.41 The simulated systems consist of cubic boxes with 200 molecules to which periodic boundary conditions were applied in three directions. The simulations were performed using a cutoff L/2 Å radius for the nonbonded interactions, L being the box side. Initial boxes were generated using the PACKMOL program42 that uses the BOX-QUACAN43 local-minimization method to obtain adequate starting configurations. These boxes were minimized according to the MINIMIZE program in TINKER package to a 0.01 kcal mol-1 Å-1 rms gradient, and then several heating and quenching steps in the NVT ensemble up to 500 K were performed, after which a 100 ps NVT equilibration molecular dynamics simulation was run at the set temperature; finally, from the output NVT simulation configuration, a run of 500 ps (time step 1 fs) in the NPT ensemble at the set temperature and pressure was run, from which the first 100 ps was used to ensure equilibration (checked through constant energy) and the remaining 400 ps for data collection. The studied fluids have large self-diffusion coefficients, see Results and Discussion, and thus the simulation time is large enough to obtain representative results. NMP was described according to the socalled Optimized Potential for Liquid Simulations (all atom version) (34) Singh, U. C.; Kollman, P. A. J. Comput. Chem. 1984, 5, 129–145. (35) Besler, B. H.; Merz, K. M.; Kollman, P. A. J. Comput. Chem. 1990, 11, 431–439. (36) Simon, S.; Duran, M.; Dannenberg, J. J. J. Chem. Phys. 1996, 105, 11024–11031. (37) Ponder, J. W. TINKER: Software tool for molecular design, 4.2 ed.; Washington University School of Medicine, 2004. (38) Hoover, W. G. Phys. ReV. A 1985, 31, 1695–1697. (39) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, UK, 1989. (40) Rickaert, J. P.; Ciccotti, G.; Berendsen, H. J. J. Comput. Phys. 1977, 23, 327–341. (41) Essmann, U. L.; Perera, M. L.; Berkowitz, T.; Darden, H.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577–8593. (42) Martıńez, J. M.; Martıńez, L. J. Comput. Chem. 2003, 24, 819– 825. (43) Friedlander, A.; Martıńez, J. M.; Santos, S. A. Appl. Math. Opt. 1994, 30, 235–266.

j iE, and (b) partial excess Figure 3. (a) Partial excess molar volume, V j Ep,i, for the x1 NMP + (1 - x1) CS2 binary isobaric molar heat capacity, C solvent, at 298.15 K and ambient pressure. Values calculated with coefficients reported in Table S2 (Supporting Information).

OPLS-AA.44 MK charges obtained through B3LYP/6-311++g** calculations were used in the simulations.

3. Results and Discussion 3.1. Ambient Pressure Thermophysical Properties. Results at ambient pressure and 298.15 K are reported in Tables S1 and S2 (Supporting Information), and the most remarkable properties are plotted in Figures 2 and 3. These results are in disagreement with those previously reported by Dyrkacz,6 mainly for excess molar volume and viscosity. Dyrkacz reported6 negative excess molar volume, whereas our results show positive values in the whole composition range. The author reports the results just in a graphical way, thus hindering numerical comparison. The viscosity data reported by Dyrkacz are also totally different from the ones reported in this work; we obtain negative deviations from linearity, Figure 2, whereas Dyrkacz obtains a complex sigmoid behavior. First, although the author does not report the numeric data, from the plot we may infer the values for pure compounds: ηCS2 = 0.5 cp and ηNMP = 1.3 cp; these values are totally different from those reported previously in the literature for these solvents, Table 1, with differences around 42% for CS2 and 22% for NMP, whereas our values are in closer agreement with literature ones, Table 1. Dyrkacz6 justified their thermophysical results because of the development of heteroassociations between NMP/CS2 molecules or to the fit of CS2 molecules into the cavities rising from a NMP dominated fluid structure. In our opinion, none of the two considered options could justify such large negative values in excess molar volume; first, because NMP/CS2 interactions would be of dipolar nature, and thus not strong enough (and in any case weaker than the NMP/NMP ones that would be disrupted by the presence of CS2 molecules) to lead to large (44) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225–11236.


Figure 4. (a) Reichardt’s normalized parameter ENT and deviations of linearity for Reichardt’s normalized parameter ∆ENT ; (b) relative chemical shifts (referred to those in pure NMP), δr, for carbon in 13CCO, O, and for hydrogen in 13CCH2CO, b. (-) Lines for guiding purposes. Data for the x1 NMP + (1 - x1) CS2 binary solvent, at 298.15 K and ambient pressure.

negative volumes, and second, because NMP liquid structure is compact and in fact dilution of CS2 molecules should result in an expansive contribution, considering the more efficient packing of CS2 molecules in the pure fluid (as the large density of CS2 shows). Our results reported in Figures 2 and 3 show physically meaningful behavior: positive excess molar volume in the full composition range is consistent with negative mixing viscosity, negative mixing speed of sound, and negative mixing refractive index. This may be extended to the positive excess isentropic compressibility (not reported in Figure 2, but it may be calculated in a simple way from data reported in Table S1, Supporting Information, using well-known thermodynamic relationships) and positive excess isobaric heat capacity. These thermophysical results may be justified considering that the large dipole moment of NMP molecules leads to a remarkable dipolar ordering in the pure state. The addition of CS2 molecules leads to an expansive effect; hence, NMP dipolar interactions are disrupted/weakened by increasing quantities of CS2, and this is confirmed by the negative mixing refractive index. The CS2 increasing concentration gives rise to a less viscous fluid because of the disruption of dipolar NMP interaction, and it would justify the negative mixing viscosity in the full composition range. Positive excess isentropic and excess isobaric heat capacity also points to the disruption of the strong dipolar interaction in pure NMP by the addition of CS2 as the main effect in the behavior of this system. Thus, even if NMP/CS2 interactions were developed, this would not be the main effect on the mixture properties, as the reported excess and mixing properties show. Excess partial molar properties reported in Figure 3 are positive in the full composition range, thus discarding the existence of relevant NMP/CS2 heteroassociation complexes. 3.2. Spectroscopic Measurements. The different spectroscopic tools used in this work, UV-vis/solvatochromism, NMR, ATR-FTIR, and DRS, may shed light into the intermolecular interactions in this mixed fluid. Reichardt’s dye used in this work provides valuable information on the solvent polarity because it shows negative solvatochromism (hypsochromic shift of the absorption maxima as the solvent polarity increases).45 The measured wavenumber decreases smoothly in a linear fashion from the value for pure NMP with increasing CS2 concentration up to x(NMP) ≈ 0.3, then decreasing in a steeped way to a value close to zero for the apolar pure CS2; thus, a sudden structural change should happen for this concentration that is close to the 1:1 volume ratio used for optimal coal extraction. The calculated deviations of linearity for the Reichardt’s normalized parameter, ∆ENT ,25 are also reported in Figure 4a; this property shows positive values in the whole composition range with a large maximum at x(NMP) ≈ 0.3, and thus for this composition a reinforcement (45) Reichardt, C. Chem. ReV. 1994, 94, 2319–2358.


of the solvent polarity seems to appear. The molecular origins of this behavior are not simple; the large dipolar moment of NMP monomer molecules changes upon the formation of association complexes through dipolar interaction, and if cyclic dimers are formed dipolar moments almost cancel and thus a lower polarity would be obtained, but if linear chain aggregates prevail the dipole moment is slightly reinforced. Hence, the addition of CS2 molecules to NMP should have a main effect rising from the disruption of dipolar aggregates, and the increasing presence of NMP monomers, that would lead to an increasing solvent polarity as compared to both pure solvents (this would be more remarkable if cyclic dimers prevail in NMP fluid structure), which is in agreement with positive ∆ENT . If NMP/CS2 heteroassociates would be formed, this would increase also the solvent polarity, but in our opinion this effect would be less remarkable considering the close to null polarity of CS2. The maximum in ∆ENT function shows that once the NMP concentration is too low we have NMP monomers dispersed in an almost apolar media, and thus the polarity would decrease steeply as the CS2 concentration increases, thus pointing again to a weaker effect of NMP/CS2 heteroassociation on solvent polarity. NMR results are reported in Figure 4b, the values of the chemical shifts being referred to those in pure NMP, δr. Values for 13CCO, which show the behavior of carbon in NMP carbonyl group, decrease upon CS2 addition, although this decrease is extremely low (0.8% on going to x(NMP) ≈ 0.1), whereas the concentration effect on δr for 13CCH2CO (the hydrogens close to the carbonyl group) is most remarkable, increasing a 6.3% on going to x(NMP) ≈ 0.1. δr for 13CCH2CO shows that the hydrogens neighboring the carbonyl group suffer an increase in electron density upon CS2 addition, and this behavior may be justified considering that the CS2 molecules would interact with NMP through this position, thus enriching its charge density. δr shows an interesting behavior with composition, with a change of slope at xNMP ≈ 0.3, and thus showing again a remarkable structural change for this composition. Nonetheless, although this would point to the existence of NMP/CS2 dipolar interactions, these should be weak as the values of δr show. The change of δr for the carbon in the carbonyl group is too weak to extract reliable conclusions; nevertheless, the presence of CS2 molecules interacting with the neighbor CH group should subtract some charge from this position, and thus slightly decrease δr values. Moreover, the formation of NMP/NMP interactions, both cyclic and linear, should decrease the charge density in carbonyl carbon, although this effect is not clear from NMR results because upon CS2 addition the NMP monomer population increases, and thus this fact should contribute to an increase of charge density on carbonyl carbon. ATR-FTIR results may provide more detailed information on the intermolecular interactions within the studied system. Previously reported results46 for pure NMP have showed that the spectrum of NMP may be analyzed considering an equilibrium monomer/dimer (both cyclic and linear), with a large prevailing population of associated molecules. Moreover, FTIR studies on the NMP/CS2 system reported by Dyrkacz6 and Shui et al.10 have showed remarkable structural changes inferred from the spectral analysis, although conclusions on the formation of heteroassociates are not totally clear from their results. These studies centered their FTIR analysis mainly on the carbonyl NMP band and on the CS2 bending vibration; nevertheless, an analysis of the whole ATR-FTIR (46) Da´vila, M. J.; Alcalde, R.; Aparicio, S. Ind. Eng. Chem. Res. 2009, 48, 1036–1050.


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Figure 5. ATR-FTIR spectra for the x1 NMP + (1 - x1) CS2 binary solvent, at 298.15 K and ambient pressure. (a and b) NMP C-H stretching band; (c and d) CS2 υ1+υ3 combination band. Labels within (a) and (c) show values of x1. In (a) and (c), gray line shows spectra for x1 ) 0.4 (∼1:1 volume fraction), and in (b) and (d), gray symbol shows data for that mole fraction. In (b) and (d), (-) shows linear fits.

spectra as a function of composition obtained in this work has showed interesting features for the υ1+υ3 CS2 combination band (appearing around 2155 cm-1) and for the NMP C-H stretching band appearing in the 2800-3000 cm-1 range, Figure 5. This last band shows complex features rising from the superposition of the different C-H vibrations. We will center our discussion on these two bands because the remaining parts of the spectra were widely discussed in the literature.6,10 Results reported in Figure 5 show a completely different behavior for NMP mole fractions up to 0.4 (∼1:1 volume ratio) and from this composition up to pure NMP. NMP C-H stretching band decreases smoothly with increasing CS2 concentration, but when 0.4 mole fraction is reached the band intensity decreases in a steeped way. The area of this peak shows an analogous behavior with two regions clearly different separated by 0.4 mole fraction. A parallel behavior is observed for the ε1 + ε3 CS2 combination band, although this band increases smoothly with increasing CS2 concentration up to 0.4 NMP mole fraction, then increases steeply. Thus, a remarkable structural change in the studied solution appears for compositions around 0.4 NMP mole fraction. Although the interaction between NMP molecules leading to homoassociation complexes is done through the carbonyl position, this interaction also affects the properties of the ring CH groups, and thus of their vibrational behavior, and hence the results point to a remarkable population of NMP/NMP dipolar association complexes (linear and/or cyclic) up to around 0.4 NMP mole fraction; thus the trend of NMP molecules to form complexes is remarkable, even for low NMP concentrations. When 0.4 NMP mole fraction is reached, and more CS2 molecules are present, monomer population increases remarkably, thus leading to a steeped increase of CH band. The behavior of υ1+υ3 CS2 combination band may be explained considering the interaction of CS2 molecules with NMP monomers for NMP mole fractions up to 0.4 and with remarkable populations of NMP association complexes as NMP mole fraction increases.

Figure 6. Real, ε′, and imaginary, ε′′, components of the complex dielectric function of pure NMP at 298.15 K and ambient pressure. (b) Experimental data; (-, gray) fitting according to a single Debye process; (-, black) fitting according to two Debye processes; (- - -) process 1 and process 2 of the two-Debye fitting. Circles show the poor quality of the one-Debye fitting.

DRS is a powerful tool to study the structure and dynamics of complex fluids such as those studied in this work. The frequency dependence of the real, ε′, and imaginary, ε′′, components of the complex dielectric function, ε*, was analyzed by fitting experimental DRS spectra to a relaxation time distribution involving k Debye processes: k

ε*(ν) )

∆εi

∑ 1 + i2πντ + ε i)1

i

∞

(3)

where i stands for the imaginary unit, ν for the frequency, ε∞ for the dielectric constant in the high-frequency limit, ∆εi for the relaxation amplitude of the i process, and τi for the relaxation time. A bimodal approach, k ) 2, is used both for pure NMP and for NMP/CS2 mixtures in the whole composition range. Previous literature works47 considered a single Debye process to describe the relaxational behavior of pure NMP in this frequency range; nevertheless, the use of two Debye processes improves remarkably the quality of the fittings for pure NMP, this improvement being more remarkable for the high-frequency data, Figure 6. Although the second relaxational process, process 2, appears close to the high frequency limit of our experimental results, and thus it is not totally covered by our data, nonetheless, we have considered both processes for the proper description of experimental DRS results. The composition effect on DRS spectra for NMP/CS2 mixtures is reported in Figure S1 (Supporting Information) with the fitting parameters using two Debye processes in Table S3 (Supporting Information). No processes rising from CS2 are considered in the fitting because of its almost null DRS response in the studied frequency range, Figure S1 (Supporting Information); nev(47) Dachwitz, E. Z. Naturforsch. 1988, 43a, 285–286.



Table 2. Comparison between the Sum of ∆εi for Each Composition (Table S3, Supporting Information) and the * Reduced Value for pure NMP, ∆εNMP , and for x NMP + (1 - x) CS2 Binary Mixtures at 298.15 K and Ambient Pressure x

∑i2 ) 1 ∆εi

* ∆εNMP

0.1050 0.2127 0.3327 0.4349 0.5701 0.6494 0.7519 0.8591 0.9383 1 (NMP)

4.10 7.70 11.30 14.72 18.71 20.77 23.55 26.15 27.96 29.21

4.38 8.30 11.86 15.01 17.94 20.56 23.02 25.24 27.28 29.21

ertheless, this may be confirmed considering that the sum of ∆εi for each concentration equals the value for pure NMP * reduced, ∆εNMP , by the volume fraction, φ,47 Table 2. ∆εNMP ) (∆ε1 + ∆ε2)NMP

(4)

* ) ∆εNMP · φ ∆εNMP

(5)

The composition effect on the main DRS parameters is reported in Figure 7. Two relaxation processes rise from the analysis of DRS spectra, a faster one, process 1, and another slowest one, process 2. The amplitude of both relaxation processes evolves in a very different way upon increasing CS2 mole fraction, Figure 7a, whereas ∆ε1 decreases almost linearly, and ∆ε2 goes through a maximum around 0.4-0.5 NMP mole fraction. The molecules involved in each process may be inferred from the relationship between both amplitudes, Figure 7b; results show that the number of molecules suffering process 2 increases up to around 0.4 mole fraction (∼1:1 volume fraction), and then they remain almost constant; hence, a remarkable structural change appears in the solution for 0.4 NMP mole fraction. The concentration evolution of relaxation times reported in Figure 7c is also very different for both processes, whereas process 1 does not change remarkably, and thus molecules involved in this relaxation are not strongly affected by the increasing surrounding CS2 concentration, and process 2 evolves through a maximum at around 0.4 mole fraction. Hence, DRS results confirm the structural change appearing for 1:1 volume fraction in agreement with the other experimental results. We may speculate on the molecular level origin of both relaxation processes. Process 1 may be attributed to NMP molecules involved in dipolar interactions relaxing through rotational tumbling47 and surrounded by a media in which NMP molecules prevail. Process 2 may rise from NMP molecules relaxing also through rotational tumbling but surrounded by a media in which CS2 molecules prevail. Hence, a certain microheterogeneity may be inferred for the mixtures’ structure upon CS2 addition. Molecules suffering process 2 relax slower than those suffering process 1, although the difference is not remarkably large, and thus the increasing surrounding CS2 molecules seem to slightly hinder NMP relaxation. This behavior may rise from the increasing density as CS2 concentration increases; CS2 molecules surround efficiently NMP molecules, despite disrupting the dipolar ordering, and thus slightly hinder their relaxation. The behavior of static dielectric constant, εs, calculated according to eq 6, and the mixing property, εs,mix, eq 7, are reported in Figure 8. 2

εs )

∑ ∆ε + ε i

∞

(6)

i)1

εs,mix ) εs - (x · εs,NMP + (1 - x) · εs,CS2)

(7)

Composition evolution of εs is strongly nonlinear leading to a remarkably positive εs,mix. The maximum of εs,mix appears again at around 0.4 NMP mole fraction; this property points to an increase of effective dipoles in the mixture upon CS2 increasing concentration up to 0.4 mole fraction. This may be justified considering the increasing population of NMP monomer molecules surrounded by CS2 molecules, as these molecules are not able to interact with other NMP molecules; thus, having in mind that NMP/NMP dipolar interaction should decrease the effective dipolar moment, the increasing presence of CS2 molecules leads to a more polar media. These results are in agreement with solvatochromic data reported in previous sections. 3.3. PVT Behavior. PC-SAFT Modeling. Experimental and calculated PVT properties are reported in Tables S4-S8 (Supporting Information) for the 278.15-358.15 K and 0.1-60 MPa temperature and pressure ranges, respectively. The behavior of the thermophysical properties is the expected one: density increases with pressure and decreases with increasing temperature, and isobaric expansivity and isothermal compressibility increase with temperature and decrease with increasing pressure. Upon NMP addition to CS2, density decreases remarkably; nevertheless, despite the larger density of CS2-rich fluids as compared to NMP-rich ones, we should remark that the sizes and shapes of both molecules lead to very different molecular level characteristics. Pure CS2 is remarkably more dense than pure NMP, but CS2 is more compressible, Tables S5-S6 (Supporting Information), leading to a fluid with larger free spaces. To confirm this, we have calculated the intermolecular free length, Lf, from experimental density according to expressions previously reported,48,49 Figure 9. The longer is the free length, the larger is the free volume in the mixture, and thus the addition of CS2 to NMP leads to less compact fluids, confirming the disruptive effect of CS2 on NMP liquid structure. This is confirmed by the positive excess molar volume obtained for any pressure and temperature, Figure 10, decreasing with increasing temperature and increasing with increasing pressure. Internal pressure reported in Table S8 (Supporting Information) provides useful information on fluids’ structure and intermolecular forces strength, and it is also important for practical purposes because of its relationship with cohesive energy density, c, and thus with the Hildebrand solubility parameter, δH. Although the strength of intermolecular forces is truly reflected by c, for fluids in which no hydrogen bonding is present or dipolar moments are not too large, we may consider c = Pi. CS2 is an apolar molecule, and although NMP is a remarkably polar molecule, if we calculate δH from Pi values reported in Table S8 (Supporting Information) at 0.1 MPa and 298.15 K, we obtain δH ) 21.9 MPa0.5, which is only slightly lower than the literature value50 of 22.9 MPa0.5 obtained from experimental vaporization enthalpy data. Thus, we may consider that for the NMP + CS2 binary system, internal pressure reflects most of the intermolecular forces present in the fluid. The decreasing internal pressure with increasing CS2 mole fraction shows that intermolecular forces through dipolar interactions decrease upon CS2 addition to NMP, thus discarding the presence of remarkable interaction between both molecules and pointing again to the disrupting effect of CS2 on the molecular (48) Aparicio, S.; Alcalde, R.; Da´vila, M. J.; Garcıá, B.; Leal, J. M. J. Phys. Chem. B 2007, 111, 3167–3177. (49) Pandey, J. D.; Dey, R.; Chabra, J. Phys. Chem. Commun. 2003, 6, 55–58. (50) Hansen, C. M. Hansen Solubility Parameters: a User’s Handbook; CRC Press: Boca Raton, FL, 2000.


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Figure 7. Relaxation amplitude, ∆εi, and relaxation time, τi, for x NMP + (1 - x) CS2 binary mixtures at 298.15 K and ambient pressure. (b) Parameters from Table S3 (Supporting Information), (-) trend lines for guiding purposes. In panels (a) and (c): (black) process 1 and (gray) process 2.

Figure 8. Static dielectric constant, εs, and mixing static dielectric constant, εs,mix, for x NMP + (1 - x) CS2 binary mixtures at 298.15 K and ambient pressure. (b) Values from Table S3 (Supporting Information), (-) fitting curves for guiding purposes.

Figure 9. Temperature and pressure effect on intermolecular free length, Lf, for the x NMP + (1 - x) CS2 binary system.

Figure 10. Temperature and pressure effect on excess molar volume for x NMP + (1 - x) CS2 binary mixtures.

level structure as the main factor controlling the behavior of this mixed fluid. No literature data are available on excess enthalpy for the studied binary mixture up to our knowledge; we report in Figure 11 the pressure effect on this property at 298.15 K calculated from experimental PVT data according to procedures previously

reported.27 An exothermic contribution rises with increasing pressure because of the closer proximity of the molecules at higher pressures. Nevertheless, the larger entropic contribution leads to positive excess Gibbs pressure contribution; this behavior points to the importance of geometrical features on the mixture structure that should be more remarkable than intermolecular forces leading to the negative contributions to excess enthalpy. Moreover, the minima of the reported properties, Figure 11, appear close to 0.4 NMP mole fractions, pointing again to the remarkable structural changes at this composition. The industrial importance of the PVT properties for the studied system raises the question of the ability of the available theoretical models to describe the behavior of the mixed fluid in wide pressure/temperature ranges. Thus, in this work, we have used the PC-SAFT51 molecularly based equation of state to correlate PVT data and to predict additional properties. This equation of state was selected considering its theoretical background, its growing recognition both in academia and in industry, the reported literature successful studies for systems of very different nature, and its relative computational simplicity for process design purposes. Pure solvents’ parameters required for the calculations were obtained from the literature.51,52 The model was applied to mixtures using a simple monoparametric Berthelot-Lorentz-type mixing rule for the crossing term with a single binary interaction parameter, k12, for the whole temperature range. A least-squares procedure of experimental PVT data was carried out leading to k12 ) 0.0184 with a percentage absolute average deviation of 0.71%. Thus, the correlative ability of the model may be considered as very satisfactory despite the complexity of the studied mixture, Figure 12. The obtained good performance of the PC-SAFT model allows one to predict the global phase diagram for the NMP/ CS2 mixtures, using the binary interaction parameter obtained from PVT correlation, Figure 12d. The results obtained show a type I behavior according to van Konynenburg’s classification,53 and the predicted critical locus shows a maximum at 626.68 K/9.13 MPa. No experimental phase equilibrium data were found in the literature, and thus comparison with values predicted according to the PC-SAFT model was not possible; nevertheless, considering the accuracy of PVT correlations, phase equilibrium should be predicted with similar accuracy. 3.4. Molecular Dynamic Simulations. We have carried out classical molecular dynamics simulations for both pure fluids and for 0.1, 0.3, 0.5, 0.7, and 0.9 mixture mole fractions. For (51) Gross, J.; Sadowski, G. Ind. Eng. Chem. Res. 2001, 40, 1244– 1260. (52) Alcalde, R.; Aparicio, S.; Da´vila, M. J.; Garcıá, B.; Leal, J. M. Fluid Phase Equilib. 2008, 266, 90–100. (53) Van Konynenburg, P. H.; Scott, R. L. Philos. Trans. R. Soc. London, Ser. A 1980, 298, 495–540.



Figure 11. Pressure effect on the isothermal excess properties at T ) 298.15 K with respect to their values at 0.1 MPa (∆X ) X298.15,p - X298.15,0.1, where X stands for excess Gibbs energy, excess enthalpy, or excess entropy) for x NMP + (1 - x) CS2 binary system. Curves reported for 20, 40, and 60 MPa; arrows indicate increasing pressure.

Figure 12. (a-c) Comparison between (b) experimental and (-) PC-SAFT, k12 ) 0.0184, values of density, F, at different pressures for x NMP + (1 - x) CS2 binary system. From top to bottom in each panel, increasing temperature from 278.15 to 358.15 K in 10 K steps. (d) P-T projection of the global phase diagram calculated with the PC-SAFT model and k12 ) 0.0184 for x NMP + (1 - x) CS2 binary system; continuous lines show pure compounds vapor pressure, and dashed line shows critical locus.

Figure 13. Comparison between (-) experimental and (b) molecular dynamics, parameters from Tables S9 and S10 (Supporting Information), values of density, F, for x NMP + (1 - x) CS2 binary system. (O,- - -) Percentage absolute average deviation, % AAD. (a) Composition, (b) pressure, and (c) temperature effects on the quality of molecular dynamics density predictions.

each composition, simulations were performed at 0.1 MPa isobaric conditions for 278, 318, and 358 K, to analyze the temperature effect on the studied properties, and at 318 K isothermal conditions for 0.1, 30, and 60 MPa, to analyze the pressure effect. Carbon disulfide simulations were carried out according to a rigid molecule model previously described in the literature;54,55 this model has proven to give an accurate description of CS2 fluid’s structure in wide pressure/temperature ranges. NMP molecule was described according to the OPLS-AA forcefield, with Coulombic interactions described using MK atomic charges obtained from B3LYP/6-311++g** calculations. Parameters used along this work are reported in Tables S9 and S10 (Supporting Information). The validation of the forcefield parametrization was done by analyzing the agreement between experimental and predicted properties for different mixture compositions, temperatures, and pressures, Figure 13, thus assuring the reliability of structural features inferred from the simulations. A remarkable good (54) Xhu, S. B.; Lee, J.; Robinson, G. W. Mol. Phys. 1988, 65, 65–75. (55) Yamamoto, S.; Ishibashi, Y.; Inamura, I.; Katayama, Y.; Mishina, T.; Nakahara, J. J. Chem. Phys. 2006, 124, 144511.

agreement for density predictions is obtained for the studied composition, pressure, and temperature ranges, with deviations always below 2%. Nevertheless, simulated densities are almost always larger than experimental ones; only for NMP-rich mixtures are predicted values lower than experimental ones, Figure 13a. The use of MK charges for the description of NMP molecule may lead to a larger Coulombic energetic contribution that would be the origin of the slightly larger densities, although the small deviations with experimental density discard that this would lead to remarkable structural features. Hence, we may conclude that the selected forcefield parametrization captures accurately the main structural features that determine the NMP/ CS2 mixture structure. Structural features are analyzed using radial distribution functions, RDFs, for selected pairs. In Figure 14, the composition effect at isothermal/isobaric conditions on RDFs is reported. RDFs rising from NMP amide group features, O-O and N-N, show that NMP is a highly structured fluid despite the absence of specific interactions such as hydrogen bonding. In pure NMP, RDFs for O-O and N-N pairs show a first wide peak with a maximum at ∼6 Å followed by a valley at ∼8.1 Å. Moreover, RDF for the N-N pair shows a well-defined second peak at


Aparicio et al.

Figure 14. Composition effect on radial distribution functions, g(r), for x NMP + (1 - x) CS2 binary system at 318 K and 0.1 MPa. r ) interatomic distance.

Figure 15. Optimized geometry for the interaction between two NMP molecules obtained at B3LYP/6-311++g** theoretical level in gas phase. ∆E stands for the interaction energy.

Figure 16. Intermolecular energy, Einter, calculated from molecular dynamics simulations for x NMP + (1 - x) CS2 binary system at 318 K and 0.1 MPa. (b) Calculated values, (-) line for guiding purposes.

10.4 Å, and although this second peak seems to appear for the O-O pair, it is not well defined. Thus, these results point to a remarkable interaction between neighbor NMP molecules, interacting through dipolar interaction in pure NMP, and leading to two well-defined solvation shells. RDF for the interaction between neighbor N-methyl groups, CN-CN, shows also a first well-defined peak, although in this case it is narrower and the maximum position appears at 4 Å, which is remarkably closer than the position of the maxima for O-O and N-N RDFs first peak. These RDFs point to the prevailing existence of linear dimers, although slightly skewed, which are in agreement with the position of the RDFs maxima. Cyclic dimers, as proposed in the literature,6 would lead to molecular packings in which NMP molecules remain closer than the RDFs maxima show. Nonetheless, linear dimers should be not purely head-to-tail

interactions, in which dipole moments would be reinforced, because in this case the maximum of the CN-CN RDF should be almost the same as those for N-N, but skewed conformations leading to closer CN-CN packings, Figure 15. The effect of increasing CS2 concentration on these RDFs rising from NMP atoms is not very remarkable, Figure 14; on going to 0.5 mole fraction they are weakened, but the position of maxima does not change. Thus, the addition of CS2 seems to weaken the number of NMP molecules involved in the dipolar interaction, the molecules involved in NMP/NMP would continue interacting through the scheme proposed (as the position of the maxima show) with increasing CS2 concentration, and an increasing number of NMP monomers surrounded by CS2 would appear in the mixed fluids. RDFs for CS2 atoms, CS-CS and S-S, Figure 14, show maxima at shorter distances than those for NMP with narrower peaks. This has been justified in the literature using a local crystal-like model in which CS2 molecules are placed in T and parallel arrangements.55,56 These RDFs are weakened upon NMP addition; nevertheless, neither the position of the maxima nor the shape of the curves changes with increasing NMP concentration, and thus the structure of CS2 around NMP molecules seems to resemble that in pure CS2, and hence NMP solvation seem to be effective. RDFs that show NMP/CS2 mixed structural features (O-CS, N-CS, and CN-CS) are also reported in Figure 14. These RDFs show an effective solvation of NMP amide group by surrounding CS2 molecules, with two well-defined solvation spheres; this solvation may stabilize NMP monomers that will compete with dipolar associates, the population of which will decrease upon CS2 increasing concentration. In Figure S2 (Supporting Information), we show a representative snapshot of the simulations to visualize the mixed fluids’ structure, and the results show a remarkable population of NMP surrounded by CS2 molecules and discard the existence of specific CS2/NMP interactions, thus confirming that the main role of CS2 molecules is to hinder the development of NMP/NMP dipolar interactions. Moreover, the pressure and temperature effect on the studied RDFs are reported in Figures S3 and S4 (Supporting Information). The pressure effect is almost negligible in the studied pressure range (0.1-60 MPa), but an increasing temperature leads to a weakening of the RDFs, because of the greater molecular mobility; nonethe(56) Iijima, T.; Nishikawa, K. J. Mol. Struct. 1995, 352-353, 213– 218.



Figure 17. Mean square displacement, msd, and self-diffusion coefficient, D, calculated from msd according to Einstein’s relation, for x NMP + (1 - x) CS2 binary system. (a and b) Composition effect (from top to bottom: x ) 0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1) for 318 K and 0.1 MPa, (c and d) pressure effect (from top to bottom: P ) 0.1, 30, and 60 MPa) for x ) 0.5 and 318 K, and (e and f) temperature effect (from bottom to top: T ) 278, 318, and 358 K) for x ) 0.5 and 0.1 MPa. Arrows indicate increasing x (panel a), increasing pressure (panel b), and increasing temperature (panel c). Ea in panel f stands for the activation energy of diffusion process according to an Arrhenius-type behavior.

less, the structuring of the mixed fluid does not change remarkably as the position and shapes of the obtained peaks show. To analyze the effect of CS2 increasing concentration of NMP/NMP intermolecular forces, we have calculated from molecular dynamics simulation the intermolecular energy, Einter, which would measure the strength and extension of these forces, Figure 16. Results shows a remarkable decrease of Einter with increasing CS2 concentration up to a value almost constant reached around xNMP ≈ 0.4 (1:1 volume ratio), and thus for this concentration (for which the most effective coal extraction is obtained), the population of NMP/NMP association complexes seems to be negligible because Einter is almost the same as the value for pure CS2. In our opinion, this may justify the effectiveness of coal extraction for that composition: NMP dipolar interactions almost vanish, and thus the mixed fluid may penetrate more effectively in coal structure. Dynamic properties, such as self-diffusion coefficient (D), are important to characterize complex fluids’ structure, although they are not easily measurable. Thus, in this work, D was calculated from molecular dynamics simulations according to Einstein’s relation, eq 8: 1 D ) lim〈∆r(t)2 〉 6 tf∞

(8)

where the quantity in brackets is the mean square displacement, msd. It is plotted in Figure 17 to analyze the composition, Figure 17a, pressure, Figure 17c, and temperature, Figure 17e, effects. msd decreases remarkably with increasing NMP concentration; nevertheless, this change is not homogeneous, as up to around 0.4 NMP mole fraction it decreases more steeply, whereas for larger mole fractions the decrease is smoother. This behavior leads to a nonlinear composition evolution of D coefficient, Figure 17b, and two regions are clearly obtained separated at xNMP ≈ 0.4. Thus, a remarkable structural change happens for xNMP ≈ 0.4 that allows the molecules to move more freely and thus to diffuse faster; this may be produced by the weakening

of dipolar interactions and is clearly related to the behavior of intermolecular energy reported in Figure 16. The pressure effect on these dynamic properties, Figure 17c and d, is the expected one: slower diffusion as pressure increases, although the change with pressure is not linear with a remarkable change up to around 30 MPa and a smoother one for higher pressures. The temperature effect, Figure 17e and f, is almost linear, leading to an Arrhenius-type behavior that allows one to calculate the activation energy of the diffusion process, Ea. The obtained Ea value points to weakly interacting fluids. 4. Conclusions The wide scope study reported in this work, using a collection of experimental and computational tools, allows one to infer several relevant conclusions on the structure and properties of the NMP/CS2 mixed solvent that are relevant to characterize the behavior of this complex mixture in the coal extraction processes. These conclusions may be summarized as: (i) Thermophysical results reported in this work are in clear disagreement with those previously reported by Dyrkacz,6 especially with the negative values for excess molar volume that were not obtained in this work for any pressure and temperature considered. (ii) Results using spectroscopic, thermophysical, and computational tools discard the existence of NMP/CS2 interactions and point to fluids’ structure characterized by the disruption effect of CS2 on NMP dipolar ordering, thus leading to an increasing population of NMP monomers, properly solvated by carbon disulfide molecules, upon CS2 addition. (iii) All of the studied properties show sudden changes at x ≈ 0.4 (1:1 volume ratio) that may justify the efficiency of coal extraction for that composition. At this mole fraction, results show that the population of NMP monomers prevails remarkably over associated NMP/NMP complexes, thus leading to a mixed fluid that may permeate the coal structure, improving the extraction efficiency.

1602 Energy & Fuels, Vol. 23, 2009 Acknowledgment. The financial support by Junta de Castilla y Leoń, Project BU020A07, and Ministerio de Educacioń y Ciencia, Project CTQ2005-06611/PPQ (Spain), is gratefully acknowledged. Supporting Information Available: Ambient pressure thermophysical properties (Table S1); Redlich-Kister fitting coefficients of excess and mixing properties at atmospheric pressure (Table S2); DRS spectra (Figure S1); fitting coefficients of DRS spectra according to two Debye processes (Table S3); density as a function of pressure and temperature (Table S4), TRIDEN fitting coefficients of density as a function of pressure and temperature (Table S5);

Aparicio et al. isobaric thermal expansivity as a function of pressure and temperature (Table S6); isothermal compressibility as a function of pressure and temperature (Table S7); internal pressure as a function of pressure and temperature (Table S8); forcefield parameters for carbon disulfide (Table S9); forcefield parameters for NMP (Table S10); temperature effect on radial distribution functions (Figure S2); and pressure effect on radial distribution functions (Figure S3). This material is available free of charge via the Internet at http://pubs.acs.org. EF800838R

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