ARTICLE pubs.acs.org/IECR
Behavior of the Environmentally Compatible Absorbent 1-Butyl-3methylimidazolium Tetrafluoroborate with 2,2,2-Trifluoroethanol: Experimental Densities at High Pressures and Modeling of PVT and Phase Equilibria Behavior with PC-SAFT EoS Moises R. Curras,† Javier Vijande,† Manuel M. Pi~neiro,† Luis Lugo,† Josefa Salgado,‡ and Josefa García*,† † ‡
Departamento de Física Aplicada, Edificio de Ciencias Experimentais, Universidade de Vigo, E-36310 Vigo, Spain Laboratorio de Propiedades Termofísicas, Departamento de Física Aplicada, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain ABSTRACT: A novel refrigerant-absorbent system for absorption refrigeration based on ionic liquids as absorbents and a fluoroalcohol as the refrigerant is analyzed. New data of densities at several temperatures in the 283.15-333.15 K range and several pressures up to 40 MPa have been measured. Experimental data have been used to study the behavior and influence of the temperature, pressure, and composition on the isothermal compressibility and the isobaric thermal expansion coefficient. In addition, vapor pressures and saturated density data of the refrigerant 2,2,2-trifluoroethanol were used to determine PC-SAFT parameters, whereas for the absorbent 1-butyl-3-methylimidazolium tetrafluoroborate the molecular parameters were optimized using density data at atmospheric pressure. Using these calculated PC-SAFT parameters, PVT behavior, derived properties and vapor pressures were reasonably well predicted.
1. INTRODUCTION Since the energy crisis of the 1970s, considerable attention has been given to energy conservation and the use of nonconventional energies for heating and cooling applications. Absorption systems, being principally heat operated, can utilize low-potential thermal sources like solar energy, waste heat, low-pressure steam, etc. These systems consume a reduced amount of high-grade electrical/mechanical energy compared to the vapor compression systems. Therefore, absorption systems can significantly contribute to improvements in energy consumption efficiencies and also to energy conservation. Absorption refrigeration has been mainly confined to industrial applications because of corrosive or toxic refrigerant/absorption solvent combinations and the need for rather complex equipment due to absorbent volatility.1 Thus, in order to find new refrigerant-absorbent mixtures for absorption systems, novel absorbents based on ionic liquids (ILs) are currently being studied. ILs, presenting almost negligible vapor pressure, can be combined with a variety of working fluids, and they can contribute significantly to overcoming the cited drawbacks for this technology. In light of these two aspects and with the aim of reducing the equipment complexity, which is originally caused by the absorbent fluid volatility, absorption refrigeration systems have attained renewed importance.2 ILs are organic salts that are liquid at room temperature. They do not evaporate and are stable as liquids over a wide temperature range.3 Also, they are able to dissolve several refrigerants, which makes them potential candidates for use in absorption refrigeration systems. The large variety of new possible combinations of anions and cations is rapidly increasing the number of ILs under study. However, an important limitation to the use of ILs is r 2011 American Chemical Society
the lack of knowledge about how the structure of the IL may affect its physicochemical properties. In this context, the thermophysical properties of pure ILs and mixtures could provide information not only about the structure of the fluid but also about the intermolecular interactions, which are the basis for the improvement of thermodynamic models for the representation of the behavior of ILs in any of their applications. The thermophysical properties of solutions containing fluorinated or partly fluorinated alcohols have received significant attention in the past decade. Fluoroalcohols deserve consideration, in view of practical applications in heat machines, as refrigerants in Rankine thermal engines.4 Thus, in this work, 2,2,2-trifluoroethanol (TFE) was selected as the refrigerant. In addition, preliminary calculations1 of the 1-butyl-3-methylimidazolium bromide ([bmim][Br]) and 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) þ TFE mixtures indicate that they represent a viable possibility for absorption refrigeration. TFE has good solubility in the suggested ILs because of the permanent ion-dipole interaction. It is also worthwhile to note that both ionic compounds [bmim][Br] and [bmim][BF4] can be easily separated from TFE by a heat input (boiling) because ILs have no detectable vapor pressure but TFE is volatile. However, other thermophysical property values needed for design, such as the heat of solution, heat capacity, viscosity, density, surface tension, and thermal conductivity of the absorbent solution, are not available yet. Thus, it is necessary to Received: September 10, 2010 Accepted: January 20, 2011 Revised: January 14, 2011 Published: March 03, 2011 4065
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Industrial & Engineering Chemistry Research perform measurements and calculations before a specific IL combined with TFE can be used in a refrigerator system. So far, information about the thermophysical properties of TFE þ IL mixtures is quite limited, especially under high pressure, and how the structure of ILs may affect the thermophysical properties of these mixtures is also unknown. Recently, densities, excess molar volumes, and mixing enthalpies at atmospheric pressure of TFE þ 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]) or [bmim][BF4] have been reported by Curras et al.5 This previous study has been extended now by determining new density data and derived properties of the absorbent [bmim][BF4] with the refrigerant TFE at 10 isobars up to 40 MPa and at 6 temperatures in the 283.15-333.15 K temperature range. Because the hydrostatic principle is used to maintain the pressure difference between the components in a refrigeration system, an absorbent solution with higher density is preferred to minimize the overall height of the refrigerator.2 Thus, the solution density also becomes a very important parameter. Furthermore, the measured density data have also been used to study the behavior and influence of the temperature, pressure, and composition on the isothermal compressibility and the isobaric thermal expansion coefficient in order to analyze the behavior of their thermodynamic properties and the relationship with their molecular characteristics. On the other hand, a careful characterization of the ILs for a specific application can be obtained by experimental techniques, simulations, and/or theoretical approaches. A main advantage of a theory or an equation of state (EoS) versus experimental techniques is the speed and low cost of these calculations in order to estimate or even purely predict experimental data. For instance, molecular dynamics and Monte Carlo simulations have been shown to accurately predict the pure IL properties and IL þ CO2 properties from ab initio6-8 calculations, but they are computationally demanding. Therefore, there is a remarkable interest in simple models that might be more useful for applied process engineering computations.9 In order to model IL mixtures with several gases, research efforts have been focused on using EoS model types SAFT (tPC-PSAFT6,10,11 or softSAFT12,13) or a square-well chainlike fluid EoS (SWCF-EoS14,15) to calculate PVT, solubility, vapor-liquid equilibrium (VLE), etc. Also, classical cubic EoS, such as Redlich-Kwong (RK16-27) or Peng-Robinson (PR28,29), have been used to obtain the density, heat of absorption, and VLE of CO2 þ IL systems. An excellent review about the modeling can be found in ref 8. In this work, we have modeled the volumetric behavior, derived properties (isothermal compressibility and isobaric thermal expansion), and VLE of TFE þ [bmim][BF4] systems using the so-called perturbed-chain statistical associating fluid theory (PC-SAFT) version.30,31 To our knowledge, the suitability of this version for correlation and estimation of these properties in systems containing ILs has not been studied yet, but this model has offered accurate results in the estimation of volumetric and equilibrium properties of complex structure halogenated molecules such as hydrofluoroethers,32 commercial lubricants,33 etc.
2. EXPERIMENTAL SECTION 2.1. Products. The chemicals used in this study are commercially available and supplied by Sigma-Aldrich; 2,2,2-trifluoroethanol (TFE) has a molar mass of Mw = 100.04 g mol-1 and a chemical purity of >99.9%; 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) has a chemical purity of >97.0% and Mw = 226.02 g mol-1. A coulometric Karl-Fisher titration
ARTICLE
(Mettler Toledo DL32) on water was performed before and after each series of measurements, and it was found that there was no variation of the water quantity in the samples. The water content of [bmim][BF4] used was 410 ( 50 ppm. 2.2. Densities. The density was measured with an Anton Paar DMA 512 P/60 vibrating-tube densimeter. A schematic and a detailed description of the experimental setup and procedures can be found in works by Pi~neiro et al.34 and Curras et al.5 The calibration of the densimeter was performed according to the method of Lagourette et al.35 Temperature regulation is achieved through a jacket filled with water surrounding the experimental cell, whose temperature is controlled by a Prolabo thermostat. The temperature is measured by a CKT100 platinum thermometer, placed close to the experimental cell and previously calibrated with an uncertainty of (0.05 K by AIMEN, Vigo, Spain, whereas the pressure is controlled by a HBM manometer connected close to the experimental cell, which had been calibrated using a double weight gauge (Budenberg, uncertainty of (0.05 MPa). For preparation of the mixtures, IL and TFE were introduced in septum-sealed vials of 20 mL that were initially filled with argon. The binary mixtures were prepared by mass using a precision digital AND balance with an uncertainty of (5 10-5 g. The vials were not totally filled, leading to the presence of a vapor phase (typically 4 mL) containing TFE. The average uncertainty on the mole fraction composition is estimated as (3 10-5. The samples were introduced in the densimeter cell under vacuum conditions. The overall experimental uncertainty in the reported density values has been calculated by the law of propagation of uncertainty, resulting in a value of (4 10-4 g cm-3.
3. RESULTS AND DISCUSSION Original density measurements of TFE þ [bmim][BF4] over the entire composition range were performed up to 40 MPa and from 283.15 to 333.15 K with an interval of 10 K. Densities are reported in Table 1. It is known that the fluid viscosity has an effect on the experimental determination of the density if a vibrating-tube device is used. Unfortunately, only atmospheric pressure viscosity values of [bmim][BF4] þ TFE mixtures36 are available. Thus, the correction was applied only at this pressure in the measured temperature range. The correction factor recommended by Anton Paar for the model DMA 512P densimeter has been used to calculate the correction factor, ΔF:37 pffiffiffi ΔF ¼ ð-0:5 þ 0:45 ηÞ 10-4 ð1Þ F where F represents the density value obtained from the densimeter calibration and the measured periods, ΔF is the difference between this F value and the “corrected” density value due to the effect of viscosity, and η is the dynamic viscosity of the sample (in units of mPa s) obtained experimentally.36 The range of validity of eq 1 is for viscosities of 400 mPa s, the correction factor becomes constant and equal to 5 10-4. Between 100 and 400 mPa s, the correction factor follows an intermediate behavior. For [bmim][BF4] and the two lowest temperatures (283.15 and 293.15 K), the viscosity is higher than 100 mPa s and lower 400 mPa s; thus, the equation used in the correction was the one obtained by Fandi~no et al.37,38 The density uncertainty calculated for [bmim][BF4] at atmospheric pressure ranges from 2 10-4 to 4 10-4 g cm-3 in the 303.15-333.15 K temperature range; in the case of the lowest temperatures 4066
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Table 1. Experimental Densities G kg m-3, of x[bmim][BF4] þ (1 - x)TFE between 283.15 and 333.15 K up to 40 MPa P/MPa x[bmim][BF4]
0.1
1
5
10
0.0000
1408.2
1409.4
1415.4
1422.7
0.1032
1360.8
1361.8
1366.4
1371.8
0.2129
1322.2
1322.9
1326.7
0.2990
1299.8
1300.5
0.4022
1279.1
0.5028
15
20
25
30
35
40
1429.5
1436.1
1442.4
1448.5
1454.2
1459.8
1377.0
1382.0
1387.0
1391.6
1396.2
1400.7
1331.1
1335.4
1339.6
1343.6
1347.6
1351.4
1355.2
1303.7
1307.7
1311.5
1315.2
1318.9
1322.3
1325.7
1329.1
1279.7
1282.5
1286.0
1289.4
1292.7
1295.9
1299.0
1302.1
1305.1
1262.9
1263.3
1265.9
1269.0
1272.1
1275.1
1278.1
1280.9
1283.6
1286.5
0.5808
1252.3
1252.7
1255.0
1258.0
1260.8
1263.6
1266.4
1269.1
1271.7
1274.3
0.6912 0.8062
1239.6 1228.5
1240.0 1228.8
1242.2 1230.9
1244.9 1233.3
1247.5 1235.8
1250.1 1238.3
1252.7 1240.7
1255.3 1243.1
1257.7 1245.3
1260.1 1247.5
0.8945
1221.2
1221.5
1223.5
1225.9
1228.2
1230.5
1232.8
1235.1
1237.2
1239.4
1.0000
1213.3
1213.6
1215.5
1217.8
1220.0
1222.2
1224.3
1226.5
1228.5
1230.6
0.0000
1391.1
1392.5
1399.0
1406.6
1413.8
1420.8
1427.4
1433.7
1439.8
1445.7
0.1032
1346.9
1347.9
1352.7
1358.3
1363.9
1369.2
1374.2
1379.2
1384.0
1388.6
0.2129
1310.1
1310.9
1314.8
1319.4
1324.0
1328.3
1332.5
1336.6
1340.6
1344.4
0.2990 0.4022
1288.8 1269.0
1289.5 1269.6
1292.9 1272.7
1297.0 1276.2
1301.0 1279.7
1304.8 1283.1
1308.5 1286.5
1312.2 1289.8
1315.8 1292.9
1319.2 1296.0
0.5028
1253.4
1254.0
1256.7
1260.0
1263.0
1266.1
1269.3
1272.2
1275.0
1277.9
0.5808
1243.3
1243.8
1246.4
1249.3
1252.3
1255.2
1258.1
1260.9
1263.5
1266.2
0.6912
1231.2
1231.7
1234.0
1236.8
1239.4
1242.2
1244.8
1247.3
1249.9
1252.4
0.8062
1220.5
1221.0
1223.1
1225.7
1228.1
1230.7
1233.1
1235.5
1237.8
1240.1
0.8945
1213.3
1213.8
1215.8
1218.2
1220.6
1223.0
1225.4
1227.6
1229.9
1232.1
1.0000
1205.9
1206.2
1208.2
1210.5
1212.8
1215.0
1217.2
1219.4
1221.5
1223.7
0.0000 0.1032
1373.8 1332.9
1375.4 1334.1
1382.2 1339.1
1390.4 1345.1
1398.0 1350.8
1405.3 1356.4
1412.2 1361.6
1418.9 1366.8
1425.3 1371.8
1431.4 1376.5
0.2129
1298.1
1299.0
1303.0
1307.8
1312.5
1317.1
1321.4
1325.7
1329.9
1333.8
0.2990
1277.9
1278.7
1282.2
1286.4
1290.6
1294.6
1298.4
1302.2
1305.9
1309.4
0.4022
1259.1
1259.8
1262.9
1266.7
1270.3
1273.9
1277.3
1280.6
1283.9
1287.0
0.5028
1244.3
1244.9
1247.6
1251.1
1254.3
1257.5
1260.6
1263.7
1266.6
1269.5
0.5808
1234.6
1235.2
1237.7
1240.9
1243.9
1246.9
1249.8
1252.6
1255.1
1258.1
0.6912
1223.1
1223.6
1226.0
1228.8
1231.7
1234.3
1237.0
1239.7
1242.2
1244.8
0.8062 0.8945
1212.8 1205.8
1213.3 1206.3
1215.4 1208.3
1218.1 1210.8
1220.7 1213.3
1223.2 1215.7
1225.7 1218.1
1228.1 1220.4
1230.5 1222.7
1233.0 1224.9
1.0000
1198.6
1199.0
1201.0
1203.4
1205.7
1208.0
1210.2
1212.5
1214.7
1216.8
0.0000
1356.1
1357.8
1365.1
1373.8
1381.9
1389.5
1396.9
1403.9
1410.5
1416.9
0.1032
1319.0
1320.2
1325.5
1331.8
1337.8
1343.6
1349.0
1354.4
1359.6
1364.6
0.2129
1286.1
1287.0
1291.3
1296.4
1301.2
1305.9
1310.4
1314.9
1319.1
1323.4
0.2990
1267.0
1267.8
1271.6
1276.0
1280.3
1284.4
1288.4
1292.3
1296.1
1299.8
0.4022
1249.4
1250.2
1253.3
1257.3
1261.1
1264.7
1268.2
1271.6
1275.0
1278.2
0.5028 0.5808
1235.2 1226.0
1235.9 1226.7
1238.8 1229.3
1242.2 1232.6
1245.7 1235.7
1248.9 1238.7
1252.1 1241.8
1255.2 1244.7
1258.3 1247.5
1261.2 1250.3
0.6912
1215.0
1215.6
1218.0
1220.9
1223.9
1226.6
1229.4
1232.1
1234.7
1237.3
0.8062
1205.1
1205.6
1207.9
1210.7
1213.4
1215.9
1218.6
1221.0
1223.4
1225.8
0.8945
1198.3
1198.8
1200.9
1203.5
1206.0
1208.5
1210.9
1213.3
1215.7
1217.9
1.0000
1191.4
1191.9
1193.9
1196.3
1198.8
1201.1
1203.4
1205.7
1207.9
1210.0
0.0000
1338.0
1339.8
1347.6
1356.8
1373.6
1381.3
1388.6
1395.6
1402.4
T = 283.15 K
T = 293.15 K
T = 303.15 K
T = 313.15 K
T = 323.15 K 1365.4 4067
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Table 1. Continued P/MPa x[bmim][BF4]
0.1
1
5
10
15
20
25
30
35
40
0.1032 0.2129
1304.9 1274.3
1306.2 1275.2
1311.7 1279.7
1318.3 1285.0
1324.7 1290.1
1330.6 1295.0
1336.4 1299.7
1342.0 1304.3
1347.4 1308.8
1352.6 1313.1
0.2990
1256.4
1257.3
1261.0
1265.7
1270.2
1274.4
1278.6
1282.6
1286.6
1290.4
0.4022
1239.7
1240.5
1243.8
1247.8
1251.7
1255.5
1259.1
1262.7
1266.2
1269.6
0.5028
1226.4
1227.1
1230.0
1233.5
1237.1
1240.4
1243.8
1247.0
1250.1
1253.2
0.5808
1217.5
1218.2
1220.9
1224.2
1227.4
1230.6
1233.6
1236.7
1239.6
1242.5
0.6912
1207.0
1207.7
1210.1
1213.2
1216.2
1219.1
1221.9
1224.7
1227.3
1230.0
0.8062
1197.6
1198.1
1200.4
1203.2
1205.9
1208.6
1211.2
1213.8
1216.4
1218.9
0.8945 1.0000
1190.9 1184.4
1191.4 1184.9
1193.6 1186.9
1196.1 1189.4
1198.7 1191.8
1201.4 1194.2
1203.8 1196.5
1206.3 1198.9
1208.7 1201.2
1211.0 1203.5
0.0000
1319.1
1321.0
1329.5
1339.4
1348.5
1357.2
1365.4
1373.1
1380.4
1387.5
0.1032
1290.6
1292.0
1297.9
1304.9
1311.5
1317.8
1323.9
1329.7
1335.3
1340.7
0.2129
1262.4
1263.4
1268.2
1273.7
1279.0
1284.1
1289.0
1293.7
1298.4
1302.8
0.2990
1245.8
1246.7
1250.7
1255.5
1260.1
1264.5
1268.9
1273.0
1277.1
1281.1
0.4022
1230.0
1230.8
1234.3
1238.5
1242.5
1246.4
1250.2
1253.8
1257.4
1260.9
0.5028 0.5808
1217.4 1209.0
1218.1 1209.6
1221.2 1212.6
1224.9 1216.0
1228.5 1219.3
1232.0 1222.6
1235.4 1225.7
1238.7 1228.7
1241.9 1231.8
1245.2 1234.8
0.6912
1199.1
1199.7
1202.3
1205.5
1208.5
1211.5
1214.5
1217.3
1220.1
1222.8
0.8062
1190.1
1190.6
1193.0
1195.9
1198.8
1201.6
1204.1
1206.7
1209.3
1211.8
0.8945
1183.6
1184.1
1186.4
1189.1
1191.8
1194.4
1196.9
1199.4
1201.8
1204.2
1.0000
1177.4
1177.8
1180.0
1182.5
1185.0
1187.6
1189.9
1192.3
1194.6
1196.9
T = 333.15 K
(283.15 and 293.15K), the uncertainties are 5 10-4 and 4 10-4 g cm-3, respectively. The correction factors due to fluid viscosity are lower than the density, around 10-5 g cm-3. Thus, the corrections due to the viscosity were not taken into account. In the case of the [bmim][BF4] þ TFE mixtures, the viscosity decreases drastically (from 360.43 mPa s for pure [bmim][BF4] to 42.31 mPa s) for a TFE mole fraction of 0.3913 at 278.15 K. As usual, for higher temperatures and mole fractions of TFE, the viscosities decrease; thus, the correction factor will be much lower than the density uncertainty. Consequently, the correction factor was not taken into account for either mixture. The experimental density values of x[bmim][BF4] þ (1 x)TFE mixtures were correlated with a Tait-type equation:39 FðT, pref Þ ! FðT, pÞ ¼ ð2Þ BðTÞ þ p 1 - C ln BðTÞ þ pref where FðT, pref Þ ¼
2 X
Ai T i
ð3Þ
i¼0
is the reference density, C is an adjustable parameter, pref is the reference pressure (0.1 MPa), and B(T) is a second-order polynomial expressed as 2 X Bi T i ð4Þ BðTÞ ¼ i¼0
The set of the fitting coefficient values (Ai, Bi, C) of the Tait equation and the standard deviations s are listed in Table 2.
The considered IL has densities between 1213.3 and 1177.4 kg m-3 at 0.1 MPa and in the temperature range 283-333 K and between 1230.6 and 1196.9 kg m-3 at 40 MPa in the same temperature range. In order to compare our data with those obtained from the literature, the overall average relative deviation (ARD %) and maximum deviation (MD %) were used and were defined as n 1X zexp - zlit: ð5Þ ARD % ¼ 100 n 1 zexp 0
1 n X z z 1 lit: A exp MD % ¼ maximum@100 n i ¼ 1 zexp
ð6Þ
with n, zexp, and zlit. being the total number of data and the experimental and literature magnitudes, respectively. The density of pure [bmim][BF4] was extensively studied in the literature (more than 800 experimental data points40) at atmospheric pressure. Nevertheless, density data at high pressures are very scarce. At atmospheric pressure, we have found higher deviations with the data of Harris et al.,41 Suarez et al.,42 Branco et al.,43 and Huddleston et al.44 Harris et al.41 used two samples of [bmim][BF4] with different content in water and halides. The scatter between both samples is 1.1%, and with our data, the scatter is 1.0% for one sample and 1.3% for the other. These differences can be due to not only the different purity mixtures but also differences in the sample handling and in the experimental technique adopted. The errors in relating the temperature of the measurements to a common scale or the calibration should also be taken into account. The scatter of the 4068
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Table 2. Tait Parameters A0, A1, A2, C, B0, B1, and B2 of the Tait Equation Used To Smooth the Experimental Densities of x[bmim][BF4] þ (1 - x)TFE as a Function of the Temperature (from 283.15 to 333.15 K) and Pressure (up to 40 MPa) along with the Standard Deviations x[bmim][BF4] 0.0000
0.1032
0.2129
0.2990
0.4022
0.5028
0.5808
0.6912
0.8062
0.8945
1.0000
A0/kg m-3
1701.3
1722.9
1693.8
1656.0
1599.8
1573.8
1537.1
1510.4
1490.3
1485.1
1461.2
A1/kg m-3 K-1
-0.4056
-1.1737
-1.4134
-1.4093
-1.2639
-1.2600
-1.1310
-1.0854
-1.0610
-1.0880
-1.0109
A2 103/kg m-3 K-2 C
-2.226 0.0855
-0.371 0.0859
0.356 0.0853
0.534 0.0844
0.462 0.0822
0.581 0.0831
0.439 0.0832
0.454 0.0829
0.480 0.0818
0.550 0.0853
0.477 0.0853
B0/MPa
335.089
372.7534
421.372
433.1082
508.4553
508.3933
435.7849
339.9447
516.6946
484.3257
501.7664
B1/MPa K-1
-1.2330
-1.2934
-1.4641
-1.4458
-1.8588
-1.7475
-1.2067
-0.4954
-1.5900
-1.2383
-1.2688
B2 103/MPa K-2
1.14
1.18
1.42
1.37
2.04
1.84
0.962
-0.209
1.58
0.97
0.99
s/kg m-3
0.07
0.04
0.04
0.04
0.05
0.05
0.08
0.04
0.06
0.04
0.04
density measurements data of Suarez et al.42 and Branco et al.43 can be due to the fact that these data were measured with a pyrex dilatometer tube under argon and with a micropycnometric technique, respectively. For Huddleston et al.,44 the deviations with our data can be due to the water content (reported as 4530 ppm). On the other hand, analysis of the data at different pressures for [bmim][BF4]45,46 and TFE47,48 indicates relative deviations between our experimental densities and those of the literature lower than 0.5%, except for a value at the higher pressure (40 MPa), as can be seen in Figure 1. In particular, for [bmim][BF4], our high-pressure density data presented a global ARD % of 0.08% and a MD % of 0.3% from the literature values (Jacquemin et al.45 and Sanmamed et al.46). For TFE, a comparison with the literature values48 resulted with a global ARD % of 0.03% and a MD % of 0.06%. For [bmim][BF4], we can observe that ARD % values increase with pressure in the case of the density data of Jacquemin et al.,45 but the same behavior is not observed in the case of data from Sanmamed et al.,46 while for TFE, they decrease with pressure. Because the temperature was not the same for literature data and this work, interpolated densities have been obtained from the Tait equation when necessary. Thermal Coefficients. Calculation of the thermal coefficients leads to useful information on the dependence of the volumetric properties on temperature and pressure. The coefficient of thermal expansion, Rp, is related to variation of the density with temperature. 1 DF ð7Þ Rp ¼ F DT p The isothermal compressibility, κT, is related to variation of the density with pressure. ! 1 DF kT ¼ ð8Þ F Dp T
It must be underlined that the differences in the values of the thermal coefficients from the literature are due to not only differences in the density values but also the fitting equations used. The temperature dependence of the isothermal compressibility was calculated from analytical differentiation of the Tait equation, with respect to pressure and also using numerical derivates, because Cerdeiri~ na et al.49 and Watson et al.50 stated that Rp was highly dependent on the temperature trend of B and Rp(T,pref), which could lead to different Rp values.
Figure 1. Relative deviations of the literature densities from our data as a function of the pressure. (a) [bmim][BF4]: Jacquemim et al.45 at (]) 322.31 K and (2) 293.5 K; Sanmamed et al.46 at (b) 283.15 K, ([) 293.15 K, (0) 298.15 K, (9) 303.15 K, (4) 308.15 K, (O) 313.15 K, and (1) 318.15K. (b) TFE: Kabata et al.48 at (b) 310 K, (O) 320 K, and (1) 330 K.
In a similar way, isobaric thermal expansivity data were also determined by analytical calculation from the Tait equation and also use of the alternative numerical derivative. The ARD % values obtained for both properties using the two ways cited (analytical or numerical derivatives) were 0.2% and 0.8%, respectively, at all temperatures, pressures, and mole fractions of Table 1. Figure 2 shows that Rp for [bmim][BF4] decreases with temperature, while it increases for TFE. This behavior is in 4069
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Figure 2. Isobaric thermal expansivities, Rp, obtained from eq 7 versus temperature, T, at two pressures. (a) [bmim][BF4]: (2) 0.1 MPa and (4) 40 MPa; (b) TFE (9) 0.1 MPa, and (0) 40 MPa. (—) Polynomial fitting to guide the eyes.
agreement with the results obtained in recent articles of Troncoso et al.51 and Navia et al.52 These authors have measured Rp(T,p) and Cp(T,p) using accurate experimental techniques, and they have shown that for ILs (∂Rp/∂T)p < 0 while (∂Cp/∂p)T > 0. Troncoso et al.51 explain this behavior, which is different from classical molecular liquids, due to the strong and long-range nature of Coulombic interactions that result in small reduced temperatures for ILs at the experimental working temperature. Thus, ILs are in these conditions a close-packed fluid where thermal fluctuations are small and cohesion predominates. These coefficients of [bmim][BF4] are typically small and vary smoothly with T and p, as is found in the case of POE53 lubricants, with high viscosities. In Figure 3, the values of Rp and κT obtained from the Tait equation are compared with those of the literature.52,54 For [bmim][BF4], our thermal coefficients, compared with those presented by Jacquemin et al.45 also obtained from the Tait equation, present an ARD % of 1.0% for Rp and of 8.9% for κT, at 293 K and two pressures (0.1 and 40 MPa). In addition, in comparison with experimental thermal coefficients of Tekin et al.,54 our data give an ARD % of 1.6% for Rp and 2.9% for κT, respectively, at 323.15 K and a pressure range from 0.73 to 40 MPa, whereas with the values of Navia et al.52 ARD % is 1.1% in the temperature and pressure ranges from 283 to 333 K and from 5 to 40 MPa. Taking into account that the
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Figure 3. Thermal coefficients against the pressure for the pure [bmim][BF4] at two temperatures: (a) Rp and (b) κT. Values obtained from eq 7: (- - -) 293.15 K and (-) 323.15 K. Experimental points: (9) 323.15 K, Tekin et al.;54 (2) 293.15 K, Navia et al.;52 (() 323.15 K, Navia et al.52
literature uncertainties of Rp vary between 2% and 10%, we consider that the comparison is satisfactory. Within the considered T and p conditions, as could be a priori expected, TFE is more compressible than [bmim][BF4]. For the mixtures, between mole fractions of 0.1 and 0.3 of [bmim][BF4], there are crossing points for Rp (Figure 4a). Thus, at low mole fractions of [bmim][BF4], Rp increases with T, whereas at high mole fractions, it decreases, in agreement with the pure liquids. As is expected, κT decreases when the mole fraction of [bmim][BF4], pressure, and temperature increase (Figure 4b). Excess Molar Volumes. The excess molar volume, VE, was calculated from the density measurement in the same temperature and pressure ranges according with the equation xM1 þ ð1 - xÞM2 xM1 ð1 - xÞM2 ð9Þ VE ¼ F F1 F2 where x stands for the mole fraction of [bmim][BF4], M1 and M2 are the molar masses of [bmim][BF4] and TFE, respectively, and F, F1, and F2 are the densities of the mixture, [bmim][BF4], and TFE, respectively. The results of VE are positive in temperature (283-323 K) and in the overall pressure ranges, as we have 4070
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interactions occurring at low concentrations. We have plotted in Figure 6 VE/x[bmim][BF4]xTFE against x[bmim][BF4]. The behavior obtained in this figure corresponds to the general case observed in mixtures of molecules of different size and polarity, as is the case. According with the dependence showed in Figure 6, with a maximum around xbmimBF4 = 0.2, following the explanations of Desnoyers and Perron,55 a complex could be formed between the two components. In addition, at low concentrations of IL a certain degree of association could occur between the OH groups of TFE compound. For this reason, PVT and vapor pressures were modeled using the PC-SAFT equation including the usual association term.
Figure 4. Thermal coefficients for x[bmim][BF4] þ (1 - x)TFE against the mole fractions of [bmim][BF4]. Calculated points from the Tait equation. (a) 0.1 MPa: (9) 323.15 K, (() 293.15 K. (b) 40 MPa: (2) 323.15 K, (b) 293.15 K. (—) Polynomial fitting to guide the eyes.
previously found at atmospheric pressure.5 We have observed that at lower pressures (0.1 and 5 MPa) and higher temperature (333 K) this property is very small, and the excess molar volume values fall within the uncertainty of this property ((0.06 cm3 mol-1). Experimental data were fitted to a Redlich-Kister-type equation, and the parameters are given in Table 3, together with the standard deviation. We have chosen the Redlich-Kister equation to fit the experimental data because it is the equation classically used to fit such data. The use of more than two parameters would lead to a lower deviation between experimental and calculated points by adding an inflection to the curve, but in qualitative terms, the representation would not be improved. Figure 5 shows that VE increases with the pressure and decreases with the temperature. A maximum in VE occurs at a mole fraction of this IL near 0.4 for all systems displayed in this figure. At atmospheric pressure, the mixing enthalpies were measured for this system at 298.15 and 323.15 K.5 The mixtures of [bmim][BF4] with TFE are endothermic over the entire composition range. In addition, the excess molar volumes are also positive. Excess thermodynamic quantities illustrate the sign and magnitude of the nonideality of the system given the solution, but YE/x(1 - x) gives a much better account of the origin of the nonideality,55 and it is more sensitive than YE to
4. PC-SAFT MODELING Gross and Sadowski30,31 developed the PC-SAFT EoS after Chapman et al.56 introduced the SAFT based on Wertheim’s thermodynamic perturbation theory of first order.57-60 The PCSAFT approach is a modification of the SAFT equation by Huang and Radosz.61,62 One of the most relevant differences is that in PC-SAFT the dispersive forces are accounted for by applying a perturbation theory of second order using an expression for the radial pair distribution of a hard-chain reference fluid, while in the original SAFT equation,61,62 a hard-sphere reference is used in the dispersion term. The different extensions and implementations of PC-SAFT made it readily applicable to describing volumetric behavior and phase equilibrium calculations of different types of fluids, including associating or nonassociating fluids, linear, homonuclear, and heteronuclear chains, pure fluids, and mixtures. In the framework of the PC-SAFT equation,30,31 the compressibility factor Z is described as the contribution of different terms: the ideal gas contribution (Zid = 1), a hard-chain contribution (Zhc), a perturbation contribution of the dispersive forces (Zdisp) accounting for the attractive interactions, and a contribution due to the associating molecular interactions (Zassoc). In general, Zhc is related to three pure-component parameters: the segment number mi, the segment diameter σi, and the segment energy parameter εi. Zdisp also depends on these three parameters. The association term is introduced to describe the chemical association interactions present in compounds as alcohols. This association term depends on two more characteristic parameters: the association energy (εAB) and the effective association volume (κAB). Gross and Sadowski30 extended this EoS to mixtures applying the van der Waals one-fluid mixing rules being employed to determine the parameters for a pair of unlike segments: ð10Þ σ ij ¼ ðσi þ σ j Þ=2 εij ¼
pffiffiffiffiffiffiffi εi εj ð1 - kij Þ
ð11Þ
where σi and εi are the segment diameter and the segment energy parameter of molecule i, respectively, and an adjustable binary interaction parameter (kij) was introduced to correct the unlike energetic interactions. A challenging test for this theory would be to check the capability of the equation to provide thermodynamic properties of refrigerant þ novel absorbent (such as IL) mixtures. To our knowledge, there is no study available of the application of the PC-SAFT equation to describe densities and derivative properties of ILs. Only Andreu and Vega12,13 modeling the solubility 4071
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Table 3. Redlich-Kister Parameters A and B Used To Smooth VE with the Temperature (from 283.15 to 333.15 K) and Pressure (up to 40 MPa) together with Standard Deviations (s) P/MPa 0.1
1
5
10
15
20
25
30
35
40
A 106/m3 mol-1
1.60
1.62
1.73
1.89
2.01
2.10
2.19
2.28
2.34
2.41
B 106/m3 mol-1 K-1 s 106/m3 mol-1
-0.93 0.03
-0.91 0.03
-1.01 0.03
-1.06 0.03
-1.19 0.02
-1.27 0.02
-1.37 0.02
-1.47 0.02
-1.49 0.02
-1.49 0.02
A 106/m3 mol-1
1.40
1.42
1.58
1.75
1.90
2.03
2.11
2.21
2.29
2.37
B 106/m3 mol-1 K-1
-0.79
-0.85
-0.96
-1.09
-1.12
-1.24
-1.36
-1.40
-1.45
-1.50
s 106/m3 mol-1
0.04
0.04
0.03
0.03
0.03
0.03
0.02
0.02
0.02
0.02
A 106/m3 mol-1
1.14
1.17
1.35
1.56
1.72
1.87
1.98
2.11
2.23
2.28
B 106/m3 mol-1 K-1
-0.68
-0.71
-0.85
-1.00
-1.12
-1.20
-1.32
-1.34
-1.39
-1.51
s 106/m3 mol-1
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.03
A 106/m3 mol-1
0.77
0.82
1.07
1.28
1.48
1.67
1.82
1.94
2.04
2.13
B 106/m3 mol-1 K-1
-0.46
-0.51
-0.65
-0.88
-1.00
-1.07
-1.25
-1.30
-1.40
-1.43
s 106/m3 mol-1
0.05
0.05
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
A 106/m3 mol-1
0.32
0.38
0.66
0.95
1.17
1.38
1.55
1.71
2.29
1.95
B 106/m3 mol-1 K-1
-0.14
-0.21
-0.39
-0.57
-0.79
-0.96
-1.10
-1.18
-1.45
-1.31
s 106/m3 mol-1
0.06
0.06
0.05
0.05
0.04
0.04
0.04
0.03
0.02
0.03
T = 283.15 K
T = 293.15 K
T = 303.15 K
T = 313.15 K
T = 323.15 K
T = 333.15 K A 106/m3 mol-1 B 106/m3 mol-1 K-1
0.50 -0.29
0.77 -0.56
1.06 -0.72
1.24 -0.84
1.47 -0.93
1.60 -1.03
1.72 -1.12
s 106/m3 mol-1
0.06
0.05
0.05
0.04
0.04
0.04
0.04
Table 4. Characteristic Parameters of PC-SAFT for TFE and [bmim][BF4] ARD % -1
MW (g mol )
σ (Å)
m
ε/kB (K)
TFE
100.040
2.3966
6.2592
177.38
0.011 021
[bmim][BF4]
226.024
3.2724
8.1885
356.98
0.089 610
compound
behavior of CO2, H2, and Xe in ILs using soft-SAFT, Karakatsani and Economou,63 and Karakatsani et al.11 modeling6,64 phase behavior of CO2 and gas solubility in ILs with the tPC-PSAFT equation where the equation is similar to PC-SAFT but with a polar term. In addition, Ji and Adidharma7 represented densities of ILs using a heterosegmented SAFT. In this work, the original PC-SAFT model, including the association term, was used to model PVT, derived properties, and phase equilibria of the pure liquids (TFE and [bmim][BF4]) and their mixtures. ILs and TFE were modeled using a square-well potential with an associating site for taking into account the specific interactions between the cation and anion and the hydroxyl group of TFE, respectively. In the optimization of the PC-SAFT molecular parameters, we have used a code developed in our group that includes a genetic algorithm (GA).65 The GAs were first introduced by Holland66 and are adequately described in the literature.67,68
κ
AB
ε /kB (K)
T range (K)
Psat
Fliq,sat
287.60
310-420
1.4
1.1
240.83
283-333
AB
Fpatm.
0.3
5. THEORETICAL RESULTS AND DISCUSSION Calculation of Molecular Parameters. A compulsory step before applying the equation to mixtures is to obtain the molecular parameters of the pure compounds. For TFE, the parameters were calculated using vapor pressures and saturated densities,47 and for the IL, they were fitted to the experimental density data at the atmospheric pressure presented in this work (Table 4). The ARD % values in the correlations in the case of TFE were 1.4% for vapor pressures and 1.1% for saturated liquid densities. ARD % for density data at atmospheric pressure was 0.3% for [bmim][BF4]. PVT and Vapor Pressures. The model was able to predict with good accuracy the PVT behavior of pure compounds. For TFE,48 the ARD % value obtained was 1.2% from 0.1 to 200 MPa and from 310 to 420 K. In the case of [bmim][BF4], the ARD % value obtained was 0.3% from 0.1 to 40 MPa and from 283.15 to 333.15 K. As can be seen above, in all cases the ARD % values for 4072
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Figure 6. V E/x[bmim][BF4]xTFE of the [bmim][BF4] þ TFE system as a function of the [bmim][BF4] mole fraction. Calculated points: (2) 283.15 K, 40 MPa, (b) 0.1 MPa; (9) 303.15 K, 40 MPa, (() 303.15 K, 0.1 MPa.
Figure 5. Excess molar volumes of x[bmim][BF4] þ (1 - x)TFE mixtures against the mole fraction of [bmim][BF4] at two temperatures and two pressures. Experimental points: (a) 283.15 K, (2) 40 MPa, (9) 0.1 MPa; (b) 303.15 K, (() 40 MPa, (b) 0.1 MPa. ( -) Redlich-Kister equation.
the predictions of compressed densities of pure liquids are similar to those obtained, saturated densities or densities at atmospheric pressure. The equation was able to capture the general trend of the density with the pressure for the pure components but higher differences are found with the temperature (Figure 7). Better results could be obtained if the parameters of the PC-SAFT version used in this work were adjusted to all compressed densities. The PVT behavior of the [bmim][BF4] þ TFE system was also predicted with PC-SAFT. At low mole fractions of [bmim][BF4], the experimental mixture densities are lower than the predictions, whereas the opposite occurs at high mole fractions of [bmim][BF4]. As in the pure liquids, the equation was able to capture the general trend of the density with the pressure for the mixtures but higher differences are found with the temperature. Thus, PC-SAFT gives the general tendency of the thermal coefficients, Rp and κT, but quantitatively higher discrepancies are found for Rp (ARD % = 37), whereas for κT, ARD % = 6 in comparison with the data obtained from Tait equation. In addition, at a first stage, a kij parameter at each temperature was calculated by using experimental vapor pressures.1 The different kij values obtained in the intervals of temperature from 315.2 to
Figure 7. Compressed densities for TFE and [bmim][BF4] at high pressures and several temperatures. Experimental points: (a) TFE,48 (9) 310 K, ([) 350 K, (2) 390 K, (b) 420 K; (b) [bmim][BF4] (this work), (9) 293 K, ([) 303 K, (2) 313 K, (b) 323 K. (- ) PC-SAFT predictions.
469.4 K oscillated between -0.026 and -0.070. These binary parameter values, kij, are all negative with small absolute values and 4073
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obtained than for the composition x[bmim][BF4] = 0.2278. On the other hand, the fact that the linearity of kij decreases when the mole fraction of [bmim][BF4] increases may also be connected with the fact that the molecular parameters of pure components are in a lower temperature range than the vapor pressures of mixtures when the mole fraction of [bmim][BF4] increases. Moreover, the kij parameter fitted for each temperature could be correcting the experimental uncertainties, and because of this, irregular fluctuating lines describing the PC-SAFT predictions were obtained. In order to clarify this fact, we decided to use a constant value of 0.052 obtained as an average value of the whole kij set. In Figure 9, we can observe now the straight lines corresponding to the PCSAFT predictions, but ARD % increases from 1.2% to 11.6%. Thus, PC-SAFT is able to quantitatively reproduce the vapor pressures1 of these mixtures with a single binary interaction parameter depending on the temperature, but as usual, higher discrepancies are obtained if a unique kij is used. Nevertheless, qualitatively the results are still rather good.
Figure 8. Interaction binary parameter, kij, against the temperature for the x[bmim][BF4] þ (1 - x)TFE system: (a) x[bmim][BF4] = 0.2278 and (b) x[bmim][BF4 ] = 0.7993. Symbols are the optimized parameter kij. Straight lines are determined with linear temperature correlations of kij.
Figure 9. Vapor pressures of x[bmim][BF4] þ (1 - x)TFE against the inverse of the temperature. Experimental points:1 ([) x = 0.2278, (2) x = 0.3990, (9) x = 0.6390, (b) x = 0.7993. (- -) PC-SAFT predictions using a constant kij = -0.052.
have a linear trend with temperature, but this linearity decreases when the mole fraction of [bmim][BF4] increases, as can be seen in Figure 8. At the intermediate compositions x[bmim][BF4] = 0.3990 and x[bmim][BF4] = 0.6390, more similar results for kij are
6. CONCLUSIONS The densities of x[bmim][BF4] þ (1 - x)TFE mixtures were measured at several temperatures (283-333 K) and up to 40 MPa. From these density values, derived properties, Rp and κT, and excess molar volumes were calculated. It was observed that the thermal coefficients are typically small and exhibit small variations with T and p. Concerning excess molar volumes, they are positive in the temperature range (283-323 K) and up to 40 MPa. In addition, we have observed that at lower pressures (0.1 and 5 MPa) and higher temperature (333 K) this property is very small, and their values are comparable to the uncertainty of this property (0.06 cm3 mol-1). From a fundamental point of view, the excess properties illustrate the sign and magnitude of the nonideality, but YE/x(1 - x) gives a much better handle on the origin of the nonideality55 and is more sensitive than YE to interactions that occur at low concentrations. Concerning modeling, the PC-SAFT equation was used, including its association term. Good density estimations of pure liquids, [bmim][BF4] and TFE, together with those of the mixtures at high pressures were obtained. The equation was able to capture the general trend of the density with pressure, but higher differences are found with temperature. Thus, using PCSAFT, higher discrepancies are found for the Rp estimation. Finally, the PC-SAFT equation gives good results for vapor pressures of [bmim][BF4] þ TFE, which means that this model could be useful for practical estimations within the refrigeration industry. For refrigeration by absorption, a system with an absorbent solution with negative or small positive mixing enthalpy and higher density is preferred. Nevertheless, it must be reminded that other properties must be examined as well to reinforce the conclusions on their reliability. ’ AUTHOR INFORMATION Corresponding Author
*Tel/Fax: 0034-986812295. E-mail: fafi
[email protected].
’ ACKNOWLEDGMENT This work was supported by the Spanish-French joint action (PICASSO-HF2007-0053) and by Xunta de Galicia (PGIDIT07PPXIB314132PR). In addition, the authors 4074
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Industrial & Engineering Chemistry Research gratefully acknowledge A. A. H. Padua, M. F. Costa Gomes, and P. Husson of the French Laboratoire of Thermodynamique et Interactions Moleculaires (Blaise Pascal University and CNRS) for their help. L.L. would also like to acknowledge the financial support of the Ramon y Cajal Grant Program from the Ministerio de Ciencia e Innovacion, Spain.
’ REFERENCES (1) Kim, K. S.; Shin, B.-K.; Lee, H.; Zielgler, F. Refractive index and heat capacity of 1-butyl-3-methylimidazolium bromide and 1-butyl-3methylimidazolium tetrafluoroborate, and vapor pressure of binary systems for 1-butyl-3-methylimidazolium bromide þ trifluoroethanol and 1-butyl-3-methylimidazolium tetrafluoroborate þ trifluoroethanol. Fluid Phase Equilib. 2004, 218, 215–220. (2) Saravanan, R.; Maiya, M. P. Comparison of methanol-based working fluid combinations for a bubble pump-operated vapour absorption refrigerator. Int. J. Energy Res. 1998, 22, 715–731. (3) Sen, M.; Paolucci, S. Using carbon dioxide and ionic liquids for absorption refrigeration. 7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006. (4) Gente, G.; La Mesa, C. Water-Trifluoroethanol Mixtures: Some Physicochemical Properties. J. Solution Chem. 2000, 29, 1159–1172. (5) Curras, M. R.; Costa Gomes, M. F.; Husson, P.; Padua, A. A. H.; García, J. Calorimetric and volumetric study on binary mixtures 2,2,2trifluoroethanol þ (1-butyl-3-methylimidazolium tetrafluoroborate or 1-ethyl-3-methylimidazolium tetrafluoroborate). J. Chem. Eng. Data 2010, 55, 5504–5512. (6) Economou, I. G.; Karakatsani, E. K.; Logotheti, G. E.; Ramos, J.; Vanin, A. A. Multi-scale Modeling of Structure, Dynamic and Thermodynamic Properties of Imidazolium-based Ionic Liquids: Ab initio DFT Calculations, Molecular Simulation and Equation of State Predictions. Oil Gas Sci. Technol. 2008, 63, 283–293. (7) Ji, X.; Adidharma, H. Thermodynamic modeling of ionic liquid density with heterosegmented statistical associating fluid theory. Chem. Eng. Sci. 2009, 64, 1985–1992. (8) Vega, L. F.; Vilaseca, O.; Llovell, F.; Andreu, J. S. Modeling ionic liquids and the solubility of gases in them: Recent advances and perspectives. Fluid Phase Equilib. 2010, 294, 15–30. (9) Ayala, A. E.; Stadtherr, M. A. Modeling Properties of Mixtures Containing Ionic Liquids: How Good Are Cubic Equations of State? 01A23: Ionic Liquids, Thermodynamics and Transport II. AIChE Annual Meeting, Salt Lake City, UT, 2007. (10) Kroon, M. C.; Karakatsani, E. K.; Economou, I. G.; Witkamp, G.; Peters, C. J. Modeling of the Carbon Dioxide Solubility in Imidazolium-Based Ionic Liquids with the tPC-PSAFT Equation of State. J. Phys. Chem. B 2006, 110, 9262–9269. (11) Karakatsani, E. K.; Economou, I. G.; Kroon, M. C.; Peters, C. J.; Witkamp, G. tPC-PSAFT Modeling of Gas Solubility in ImidazoliumBased Ionic Liquids. J. Phys. Chem. C 2007, 111, 15487–15492. (12) Andreu, J. S.; Vega, L. F. Capturing the Solubility Behavior of CO2 in Ionic Liquids by a Simple Model. J. Phys. Chem. C 2007, 111, 16028–16034. (13) Andreu, J. S.; Vega, L. F. Modeling the Solubility Behavior of CO2, H2, and Xe in [Cn-mim][Tf2N] Ionic Liquids. J. Phys. Chem. B 2008, 112, 15398–15406. (14) Wang, T.; Peng, C.; Liu, H.; Hu, Y. Description of the pVT behavior of ionic liquids and the solubility of gases in ionic liquids using an equation of state. Fluid Phase Equilib. 2006, 250, 150–157. (15) Wang, T.; Peng, C.; Liu, H.; Hu, Y.; Jiang, J. Equation of State for the Vapor-Liquid Equilibria of Binary Systems Containing Imidazolium-Based Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 4323–4329. (16) Shiflett, M. B.; Yokozeki, A. Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids: [bmim][PF6] and [bmim][BF4]. Ind. Eng. Chem. Res. 2005, 44, 4453–4464. (17) Yokozeki, A.; Shiflett, M. B. Solubility of CO2 in Room Temperature Ionic Liquid [hmim][Tf2N]. J. Phys. Chem. B 2007, 111, 2070–2074.
ARTICLE
(18) Shiflett, M. B.; Yokozeki, A. Ammonia Solubilities in RoomTemperature Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 1605–1610. (19) Shiflett, M. B.; Yokozeki, A. Global Phase Behaviors of Trifluoromethane in Ionic Liquid [bmim][PF6]. AIChE J. 2006, 52, 3952–3957. (20) Yokozeki, A.; Shiflett, M. B. Vapor-liquid equilibria of ammonia þ ionic liquid mixtures. Appl. Energy 2007, 84, 1258–1273. (21) Yokozeki, A.; Shiflett, M. B. Hydrogen purification using roomtemperature ionic liquids. Appl. Energy 2007, 84, 351–361. (22) Shiflett, M. B.; Kasprzak, D. J.; Junk, C. P.; Yokozeki, A. Phase behavior of {carbon dioxide þ [bmim][Ac]} mixtures. J. Chem. Thermodyn. 2008, 40, 25–31. (23) Shiflett, M. B.; Yokozeki, A. Binary and Ternary Phase Diagrams of Benzene, Hexafluorobenzene, and Ionic Liquid [emim][Tf2N] Using Equations of State. Ind. Eng. Chem. Res. 2008, 47, 8389–8395. (24) Kumelan, J.; Kamps, A. P. S.; Tuma, D.; Yokozeki, A.; Shiflett, M. B.; Maurer, G. Solubility of Tetrafluoromethane in the Ionic Liquid [hmim][Tf2N]. J. Phys. Chem. B 2008, 112, 3040–3047. (25) Yokozeki, A.; Shiflett, M. B.; Junk, C. P.; Grieco, L. M.; Foo, T. Physical and Chemical Absorptions of Carbon Dioxide in RoomTemperature Ionic Liquids. J. Phys. Chem. B 2008, 112, 16654–16663. (26) Shiflett, M. B.; Yokozeki, A. Phase Behavior of Carbon Dioxide in Ionic Liquids: [emim][Acetate], [emim][Trifluoroacetate], and [emim][Acetate] þ [emim][Trifluoroacetate] Mixtures. J. Chem. Eng. Data 2009, 54, 108–114. (27) Yokozeki, A.; Shiflett, M. B. Separation of Carbon Dioxide and Sulfur Dioxide Gases Using Room-Temperature Ionic Liquid [hmim][Tf2N]. Energy Fuels 2009, 23, 4701–4708. lvarez, V. H.; Machado, J. J. B.; Paulyb, J.; (28) Carvalho, P. J.; A Daridon, J. L.; Marrucho, I. M.; Aznar, M.; Coutinho, J. A. P. High pressure phase behavior of carbon dioxide in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids. J. Supercrit. Fluids 2009, 48, 99–107. lvarez, V. H.; Schr€oder, B.; Gil, A. M.; (29) Carvalho, P. J.; A Marrucho, I. M.; Aznar, M.; Santos, L. M. N. B. F.; Coutinho, J. A. P. Specific Solvation Interactions of CO2 on Acetate and Trifluoroacetate Imidazolium Based Ionic Liquids at High Pressures. J. Phys. Chem. B 2009, 113, 6803–6812. (30) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244–1260. (31) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510–5515. (32) Vijande, J.; Pi~ neiro, M. M.; Bessieres, D.; Saint-Guirons, H.; Legido, J. L. Description of PVT behaviour of hydrofluoroethers using the PC-SAFT EOS. Phys. Chem. Chem. Phys. 2004, 6, 766–770. (33) Garcia, J.; Youbi-Idrissi, M.; Bonjour, J.; Fernandez, J. Experimental and PC-SAFT volumetric and phase behavior of carbon dioxide þ PAG or POE lubricant systems. J. Supercrit. Fluids 2008, 47, 8–16. (34) Pi~ neiro, M. M.; Bessieres, D.; Legido, J. L.; Saint-Guirons, H. PFT Measurements of Nonafluorobutyl Methyl Ether and Nonafluorobutyl Ethyl Ether between 283.15 and 323.15 K at Pressures up to 40 MPa. Int. J. Thermophys. 2003, 24, 1265–1276. (35) Lagourette, B.; Saint-Guirons, H.; Boned, C.; Xans, P. Densimeter calibration method versus temperature and pressure. Meas. Sci. Technol. 1992, 3, 699–703. (36) Salgado, J.; Regueira, T.; Fernandez, J.; Vijande, J.; García, J. Temperature dependence of the density and viscosity of 2,2,2-trifluoroethanol þ two ionic liquids ([bmim][BF4] and [bmim][PF6]): analysis of these properties with the anion. 1st Iberian Meeting on Ionic Liquids, Aveiro, Portugal, June 15-16, 2009. (37) Fandi~ no, O.; Pensado, A. S.; Lugo, L.; Comu~ nas, M. J. P.; Fernandez, J. Compressed Liquid Densities of Squalane and Pentaerythritol Tetra(2- ethylhexanoate). J. Chem. Eng. Data 2005, 50, 939–946. (38) Fandi~ no, O.; García, J.; Comu~ nas María, J. P.; Lopez, E. R.; Fernandez, J. PFT Measurements and Equation of State (EoS) Predictions of Ester Lubricants up to 45 MPa. Ind. Eng. Chem. Res. 2006, 45, 1172–1182. 4075
dx.doi.org/10.1021/ie101880t |Ind. Eng. Chem. Res. 2011, 50, 4065–4076
Industrial & Engineering Chemistry Research (39) Cibulka, I.; Hnedkovsky, L. Liquid Densities at Elevated Pressures of n-Alkanes from C5 to C16: A Critical Evaluation of Experimental Data. J. Chem. Eng. Data 1996, 41, 657–668. (40) http://ilthermo.boulder.nist.gov/ILThermo/mainmenu.uix. (41) Harris, K. R.; Kanakubo, M.; Woolf, L. A. Temperature and Pressure Dependence of the Viscosity of the Ionic Liquid 1-Butyl-3methylimidazolium Tetrafluoroborate: Viscosity and Density Relationships in Ionic Liquids. J. Chem. Eng. Data 2007, 52, 2425–2430. (42) Suarez, P. A. Z.; Einloft, S.; Dullius, J. E. L.; de Souza, R. F.; Dupont, J. Synthesis and physical-chemical properties of ionic liquids based on l-n-butyl-3-methylimidazolium cation. J. Chem. Phys. 1998, 95, 1626–1639. (43) Branco, L. C.; Rosa, J. N.; Ramos, J. J. M.; Afonso, C. A. M. Preparation and Characterization of New Room-Temperature Ionic Liquids. Chem.—Eur. J. 2002, 8, 3671–3677. (44) Huddleston, J. G.; Visser, A. E.; Reichert, W. M.; Willauer, H. D.; Broker, G. A.; Rogers, R. D. Characterization and comparison of hydrophilic and hydrophobic room temperature ionic liquids incorporating the imidazolium cation. Green Chem. 2001, 3, 156–164. (45) Jacquemin, J.; Husson, P.; Padua, A. A. H.; Majer, V. Density and viscosity of several pure and water-saturated ionic liquids. Green Chem. 2006, 8, 172–180. (46) Sanmamed, Y. A.; Gonzalez-Salgado, D.; Troncoso, J.; Romani, L.; Baylaucq, A.; Boned, C. Experimental methodology for precise determination of density of RTILs as a function of temperature and pressure using vibrating tube densimeters. J. Chem. Thermodyn. 2010, 42, 553–563. (47) Kabata, Y.; Yamaguchi, S.; Takada, M.; Uematsu, M. Densities of 2,2,2-trifluoroethanol in the temperature range from 310 K to 420 K. I. Saturated-liquid densities. J. Chem. Thermodyn. 1992, 24, 1019–1102. (48) Kabata, Y.; Yamaguchi, S.; Takada, M.; Uematsu, M. Densities of 2,2,2-trifluoroethanol in the temperature range 310-420 K. II. Compressed-liquid densities at pressures up to 200 MPa. J. Chem. Thermodyn. 1992, 24, 785–796. (49) Cerdeiri~na, C. A.; Tovar, C. A.; Gonzalez-Salgado, D.; Carballo, E.; Romaní, L. Isobaric thermal expansivity and thermophysical characterization of liquids and liquid mixtures. Phys. Chem. Chem. Phys. 2001, 3, 5230–5236. (50) Watson, G.; Lafitte, T.; Zeberg-Mikkelsen, C. K.; Baylaucq, A.; Bessieres, D.; Boned, C. Volumetric and derivative properties under pressure for the system 1-propanol þ toluene: A discussion of PC-SAFT and SAFT-VR. Fluid Phase Equilib. 2006, 247, 121–134. (51) Troncoso, J.; Cerdeiri~na, C. A.; Navia, P.; Sanmamed, Y. A.; Gonzalez-Salgado, D.; Romaní, L. Unusual Behavior of the Thermodynamic Response Functions of Ionic Liquids. J. Phys. Chem. Lett. 2010, 1, 211–214. (52) Navia, P.; Troncoso, J.; Romaní, L. Isobaric Thermal Expansivity for Ionic Liquids with a Common Cation as a Function of Temperature and Pressure. J. Chem. Eng. Data 2010, 55, 595–599. (53) Fandi~no, O.; Pensado, A. S.; Lugo, L.; Lopez, E. R.; Fernandez, J. Volumetric Behaviour of the Environmentally Compatible Lubricants Pentaerythritol Tetraheptanoate and Pentaerythritol Tetranonanoate at High Pressures. Green Chem. 2005, 7, 775–783. (54) Tekin, A.; Safarov, J.; Shahverdiyev, A.; Hassel, E. (p, F, T) Properties of 1-butyl-3-methylimidazolium tetrafluoroborate and 1-butyl-3-methylimidazolium hexafluorophosphate at T = (298.15 to 398.15) K and pressures up to p = 40 MPa. J. Mol. Liq. 2007, 136, 177–182. (55) Desnoyers, J. E.; Perron, G. Treatment of Excess Thermodynamic Quantities for Liquid Mixtures. J. Solution Chem. 1997, 26, 749–755. (56) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New reference equation of state for associating liquids. Ind. Eng. Chem. Res. 1990, 29, 1709–1721. (57) Wertheim, M. S. Fluids with highly directional attractive forces. I. Statistical thermodynamics. J. Stat. Phys. 1984, 35, 19–34. (58) Wertheim, M. S. Fluids with highly directional attractive forces. II. Thermodynamic Perturvation Theory and integral equations. J. Stat. Phys. 1984, 35, 35–47.
ARTICLE
(59) Wertheim, M. S. Fluids with highly directional attractive forces. III. Multiple attraction sites. J. Stat. Phys. 1986, 42, 459–476. (60) Wertheim, M. S. Fluids with highly directional attractive forces. IV. Equilibrium polymerization. J. Stat. Phys. 1986, 42, 477–492. (61) Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 2284–2294. (62) Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules: Extension to Fluid Mixtures. Ind. Eng. Chem. Res. 1991, 30, 1944–2005. (63) Karakatsani, E. K.; Economou, I. G. Phase equilibrium calculations for multi-component polar fluid mixtures with tPC-PSAFT. Fluid Phase Equilib. 2007, 261, 265–271. (64) Karakatsani, E. K.; Economou, I. G.; Kroon, M. C.; Bermejo, M. D.; Peters, C. J.; Witkamp, G. Equation of state modeling of the phase equilibria of ionic liquid mixtures at low and high pressure. Phys. Chem. Chem. Phys. 2008, 10, 6160–6168. (65) Vijande, J.; Pi~ neiro, M. M.; Mosteiro, L.; Legido, J. L. Estimation of carbonate-alcohol interaction parameters for Nitta-Chao group contribution model: application of a Genetic Algorithm. Fluid Phase Equilib. 2003, 212, 165–174. (66) Holland, J. H. Adaptation in Natural and Artificial Systems; University of Michigan: Ann Arbor, MI, 1975. (67) Goldberg, D. E. Genetic Algorithms in Search, Optimization and Machine Learning; Addison-Wesley: Reading, MA, 1989. (68) Mitchell, M. An Introduction to Genetic Algorithms; MIT Press: Cambridge, MA, 1998.
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