Ind. Eng. Chem. Res. 2007, 46, 5453-5462
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Viscosity, Density and Excess Volume of Acetone + Carbon Dioxide Mixtures at High Pressures Kun Liu and Erdogan Kiran* Department of Chemical Engineering, Virginia Polytechnic Institute and State UniVersity, Blacksburg, Virginia 24061
The densities and viscosities of acetone, carbon dioxide, and acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide were determined at nominal temperatures of 325, 348, 373, and 398 K and at pressures up to 35 MPa using a falling-cylinder type high-pressure viscometer. The densities of carbon dioxide and acetone + carbon dioxide mixtures were found to show crossovers at around 18 MPa for mixtures with CO2 content less than 50 wt % and at around 23 MPa for mixtures with CO2 content greater than 50 wt % at 325 K, which shifts to higher pressures with temperature. Acetone displayed higher viscosities than the mixtures. At 325 K, the mixtures were found to show negative excess volumes at all compositions for pressures lower than 28 MPa. The excess volumes become less negative with increasing pressure and are positive above 28 MPa for high carbon dioxide content; at pressures above 55 MPa, they become positive for all compositions. Assessments of several mixing rules for viscosity show that logarithmic equations work well at low temperatures, while simple linear combinations of viscosity or kinematic viscosity work better at higher temperatures. Viscosity of the mixtures could be correlated with density; however, there were no direct correlations between excess viscosity and excess volume. Analysis of the excess Gibbs free energy for the flow suggests strong chemical interactions. Introduction The binary fluid mixtures of carbon dioxide with organic solvents at high pressures are widely used in extractions and separations, chemical reactions, and material processing.1-5 Depending upon the composition, these mixtures are either carbon dioxide modified with an organic “cosolvent” or are organic solvents modified with carbon dioxide. Even though processing with carbon dioxide at low levels of organic solvent additives as cosolvents is of continuing interest, in recent years there has been a growing activity in using carbon dioxide expanded liquids.6,7 The terminology of expanded liquids is however used without always clear documentation if indeed the mixtures show positive excess volumes. In our laboratory, we are interested in organic solvents modified with carbon dioxide such as alkanes + carbon dioxide, tetrahydrofuran (THF) + carbon dioxide, and, more recently, acetone + carbon dioxide as tunable solvents for polymerizations and polymer modifications. We have investigated the volumetric properties of a series of organic solvent + carbon dioxide mixtures in the past.8-10 We now present new data on the densities, viscosities, and excess volumes of acetone + carbon dioxide mixtures. A number of studies have already appeared on mixtures of acetone + carbon dioxide. Reaves and co-workers11 measured the critical points for acetone + carbon dioxide mixtures for acetone compositions up to 7.0 mol %. Day et al.12 and Chang et al.13 reported phase equilibria in acetone + carbon dioxide mixtures at temperatures in the range 291-313 K at pressures up to 8 MPa. Additional data at 323 and 333 K have been recently reported.14-16 The liquid-vapor phase boundaries of these mixtures at high pressures were determined by Chen et al.17 and Wu et al.18 The densities and excess volumes were reported by Po¨hler and Kiran8 and Wu et al.19 Some transport properties of these mixtures such as the diffusion coefficient of * To whom correspondence should be addressed. Tel.: (540) 2311375. E-mail:
[email protected].
acetone in carbon dioxide were also reported.20,21 Even though phase equilibria has been studied, the high-pressure viscosity data for these mixtures is limited. To our knowledge, only Tilly and co-workers22 reported viscosities for acetone concentrations between 1 and 5 mol % at 313 and 323 K and at pressures up to 24 MPa. We have recently reported viscosity data for acetone, and for solutions of poly(methyl methacrylate) and poly(caprolactone) in acetone or in acetone + carbon dioxide mixtures.23,24 We now report on the densities and viscosities for acetone, carbon dioxide, and acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide at nominal temperatures of 325, 348, 373, and 398 K and at pressures up to 35 MPa. The flow activation volumes and flow activation energies that are derived from the variation of viscosity with pressure and temperature are also reported. Free volume-based density correlations and close-packed volumes obtained from such correlations are also presented. For the mixtures, we report the excess volume over the full composition range. We also present a comparative assessment of several mixing rules for predicting the viscosities of these mixtures. Experimental Section Apparatus and Procedures. A high-pressure-high-temperature falling-cylinder type viscometer shown in Figure 1 was used to determine the viscosity and density of the mixtures simultaneously. The system, which has been discussed in detail in our previous publications,23,24 is basically a view-cell with a variable volume part (VVP), a fall tube (FT), and a fluid circulation loop. The pressure is adjusted at any loading and temperature, by changing the position of a movable piston (PI). The position of the piston (and, thus, the internal volume) is recorded at any given temperature and pressure. Knowing the internal volume permits the determination of the density at a given T and P since initial mass loading is known. The fall of the sinker is initiated by demagnetization of the pull-up magnet
10.1021/ie070274w CCC: $37.00 © 2007 American Chemical Society Published on Web 07/11/2007
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Figure 1. Schematic diagram of the viscometer system and the data-processing procedure: SL, solvent line; PFL, pressurizing fluid line; PM, pull-up magnet; TLP, top loading port; FLP, front loading port; SW, sapphire window; VVP, variable volume part housing for piston; EMS, electromagnetic stirrer; PI, piston; FS, ferromagnetic slug; PPS LVDT, piston position sensor linear variable differential transformer; S, sinker; V, LVDT signal; D, sinker fall distance; Vt, terminal velocity; and FT, fall tube.
(PM). The fall time of the sinker is monitored by three linearvariable differential transformer units (LVDT I, II, and III) positioned along the fall tube. The signal from each LVDT (as voltage reading) is recorded as a function of time when the sinker falls through the full length of the fall tube and is further processed to generate distance versus fall time plots for the sinker from which the terminal velocity (Vt) is determined. The terminal velocity along with density is then used to determine viscosity using the following equation
η)
1 (F - Ff)K Vt s
(1)
where Fs is the density of the sinker, Ff is the density of the fluid, Vt is the terminal velocity of the sinker, and K is a calibration constant, which is determined by measuring the terminal velocity and density of systems of known viscosities. With this instrument, the system temperature and pressure are measured with an accuracy of (0.1 K and (0.06 MPa, respectively. With this instrument, densities and viscosities can be determined with an accuracy of 1.5 and 4%, respectively.25 Materials. Acetone (Burdick & Jackson) with a purity of 99.5% and CO2 (Airgas) with a minimum purity of 99.9% were used without further purification. Results and Discussion Table 1 summarizes the viscosity and density data for pure acetone, carbon dioxide, and their mixtures. For the mixtures, the table also includes excess volume, excess viscosity, excess Gibbs free energy of viscous flow, and Grunberg-Nissan interaction parameter, which will be discussed later. The present measurements were mostly carried out at pressures greater than 12 MPa, which are higher than the critical pressures reported for these mixtures.8 The mixtures are either supercritical or exist as liquid mixtures at most of the measurement conditions. Density. Figure 2 displays the variation of density with pressure for each mixture at the nominal temperature of 325 K. The density data for pure acetone and pure carbon dioxide are at 323 and 320 K, respectively. Data from an earlier study8 for acetone and carbon dioxide are also included at these temper-
atures for comparisons. Despite the measurement systems being different, the reproducibilities of the density values are remarkable. Even though the densities obtained in the view-cell studies were slightly higher, the difference remains within 1.5%. We have also included in the figure recent literature data on the densities of acetone + carbon dioxide mixtures with 52 wt % carbon dioxide at 323 K,17 which are compared with the present data for 50 wt % carbon dioxide mixtures. The compositions and temperatures are close but different, and densities values are within 1.3% of each other. For the 52% mixture, literature data is given only for low temperatures and, therefore, we could compare only the data at 323 K. Density increases with pressure for all mixtures, but ∂F/∂P for carbon dioxide is much larger than that for the mixturessleading to a density crossover around 18 MPa for mixtures containing 50 wt % CO2. Density crossover is a well-known behavior in mixtures of CO2 with organic solvents.8-10 Figure 3 shows the density variation with pressure at a higher nominal temperature, T ) 348 K. The density crossover pressures are observed to increase to around 30 MPa (for CO2 content > 50 wt %) and 35 MPa (for CO2 content > 50 wt %). Figure 4 displays the variation of density with temperature for the mixture containing 10 wt % carbon dioxide at 7, 14, 21, 28, and 35 MPa. The densities show essentially a linear decrease with temperature at all the pressures. Viscosity. Figure 5 shows the variation of viscosity with pressure for pure acetone, carbon dioxide, and their mixtures at the nominal temperature of 325 K. The literature viscosity data26 for carbon dioxide at 320 K are also included in the figure for comparisons. The insert is an enlargement of the carbon dioxide data. Mixtures all show viscosities lower than that of acetone, and the viscosity reduction increases with the carbon dioxide content. A 60% reduction in viscosity is observed for the mixture containing 50 wt % carbon dioxide. Figure 6 illustrates the variation of viscosity with temperature for mixtures containing 10 wt % carbon dioxide at 7, 14, 21, 28, and 35 MPa. The viscosities were found to show a linear decease with temperature in the range studied. Flow Activation Volume and Flow Activation Energy. We have analyzed the variation of viscosity with pressure for all
Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5455 Table 1. Density (G), Viscosity (η), Excess Volume (VE), Excess Viscosity (∆η), Excess Gibbs Free Energy of Viscous Flow (GVE), and Grunberg-Nissan Interaction Parameter (d12) of Acetone + Carbon Dioxide Mixtures acetone/CO2 ) 90/10
acetone T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
323 323 323 323 323 348 348 348 348 348 373 373 373 373 373 398 398 398 398 398
7.5 14.3 21.4 27.8 35.0 8.1 14.4 21.4 28.3 35.1 8.3 14.7 21.3 28.6 35.3 8.2 13.5 20.5 27.9 33.7
0.7584 0.7631 0.7704 0.7773 0.7838 0.7370 0.7462 0.7546 0.7623 0.7697 0.7177 0.7285 0.7384 0.7474 0.7555 0.6919 0.7058 0.7174 0.7282 0.7374
0.290 0.367 0.362 0.377 0.383 0.244 0.253 0.255 0.262 0.264 0.200 0.203 0.215 0.214 0.232 0.169 0.162 0.182 0.184 0.205
325 325 325 325 325 348 349 349 349 349 374 374 374 374 374 399 399 399 399 399
7.9 14.3 21.2 28.2 34.7 7.4 14.7 21.4 28.3 34.8 7.1 14.3 21.3 28.3 35.2 7.0 14.5 21.3 27.9 34.9
0.7641 0.7736 0.7832 0.7902 0.7983 0.7373 0.7503 0.7619 0.7702 0.7793 0.7192 0.7305 0.7401 0.7488 0.7599 0.6999 0.7070 0.7183 0.7305 0.7389
0.281 0.289 0.294 0.307 0.311 0.236 0.243 0.247 0.254 0.260 0.191 0.201 0.206 0.210 0.215 0.160 0.164 0.169 0.175 0.182
VE (cm3/mol)
∆η (mPa‚s)
GVE (kJ/mol)
d12
-1.043 -0.837 -0.265 -0.269
-0.038 -0.030 -0.032 -0.036
-0.021 -0.062 0.034 -0.099
0.022 -0.149 0.071 -0.370
-1.068 -0.408
0.017 0.019
0.403 0.510
1.332 1.558
-0.530 -0.573
0.020 0.004
0.680 0.229
1.975 0.688
acetone/CO2 ) 75/25 T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
325 324 326 324 323 349 349 349 349 349 373 374 373 373 373 398 398 398 398
7.8 15.0 21.0 28.0 34.9 7.4 14.0 21.2 28.2 35.0 7.5 14.3 21.0 27.9 34.7 16.5 21.3 28.0 34.5
0.7708 0.7850 0.7977 0.8051 0.8145 0.7378 0.7584 0.7721 0.7815 0.7934 0.7203 0.7321 0.7415 0.7532 0.7668 0.7083 0.7192 0.7354 0.7409
0.225 0.233 0.241 0.252 0.259 0.185 0.193 0.199 0.203 0.211 0.164 0.171 0.178 0.185 0.191 0.141 0.147 0.156 0.162
VE (cm3/mol)
acetone/CO2 ) 50/50 ∆η (mPa‚s)
E
GV (kJ/mol)
d12
-2.077 -1.548 -0.212 -0.128
0.015 0.017 0.013 0.012
0.258 0.108 0.319 0.062
0.553 0.243 0.492 0.033
-2.468 -0.910
0.009 0.011
0.462 0.687
0.881 1.118
-1.493 -1.398
0.030 0.021
1.294 0.494
2.020 0.805
T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
325 325 325 325 325 348 348 348 348 348
7.1 14.2 21.2 28.1 34.9 7.3 14.2 21.2 28.1 35.1
0.7885 0.8134 0.8303 0.8389 0.8511 0.7401 0.7705 0.7903 0.8011 0.8175
0.137 0.145 0.152 0.161 0.168 0.113 0.120 0.127 0.133 0.141
373 373 374 374
15.7 21.3 28.3 35.2
0.7353 0.7502 0.7685 0.7840
0.111 0.119 0.125 0.132
398 398 398
22.8 27.9 34.4
0.7216 0.7378 0.7430
0.083 0.090 0.096
acetone/CO2 ) 25/75 T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
326 326 326 326 326 350 350 350 350 374 374
7.40 14.54 21.01 27.87 35.17 14.99 21.53 28.24 34.88 27.78 34.99
0.6653 0.7949 0.8339 0.8435 0.8603 0.6995 0.7773 0.7923 0.8125 0.7185 0.7512
0.105 0.111 0.117 0.125 0.131 0.093 0.098 0.105 0.112 0.095 0.104
VE (cm3/mol)
∆η (mPa‚s)
GVE (kJ/mol)
d12
-4.385 -3.264 -0.849 -0.652
-0.046 -0.043 -0.051 -0.057
0.181 -0.173 0.242 -0.218
0.518 -0.098 0.340 -0.375
-4.691 -1.790
-0.018 -0.010
0.116 0.622
0.430 0.941
-3.691 -3.175
0.014 -0.009
1.485 0.211
2.151 0.443
carbon dioxide d12
T (K)
P (MPa)
F (g/cm3)
η (mPa‚s)
0.659 0.048 0.635 -0.037
1.785 0.341 1.296 -0.282
320 320 320 320
13.8 20.0 27.2 34.1
0.7305 0.8035 0.8705 0.9127
0.057 0.073 0.085 0.095
-0.003 0.010
0.311 1.057
1.062 2.257
355 355
23.9 31.5
0.7793 0.7983
0.051 0.063
0.026 0.001
2.121 0.432
4.242 0.906
369 369
28.6 34.4
0.6823 0.7430
0.047 0.059
VE (cm3/mol)
∆η (mPa‚s)
GVE (kJ/mol)
-2.917 -2.633 0.716 0.858
-0.008 -0.009 -0.021 -0.030
-4.191 -0.377 -0.813 -0.722
temperatures and that with temperature for all pressures given in Table 1 in a manner shown in Figures 5 and 6 and correlated the data using the relationships27,28
η ) A exp(VqP/RT)
(2)
η ) B exp(Eq/RT)
(3)
and
where η is the viscosity, A and B are constants, Vq and Eq are the flow activation volume and flow activation energy, P is the pressure, R is the gas constant, and T is the temperature. The parameters for these equations are given in Tables 2 and 3 along with the correlation coefficients and average absolute deviation (AAD) values. The flow activation energies were in the range of 5-10 kJ/mol, with the value for most mixtures being ∼8 kJ/mol and independent of pressure. The flow activation volumes range from 5 to 41 cm3/mol. For all the systems, the
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Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007
Figure 2. Variation of density with pressure at the nominal temperature of 325 K for acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide. Data for pure acetone and CO2 are at 323 and 320 K, respectively (see Table 1).
Figure 5. Variation of viscosity with pressure at the nominal temperature of 325 K for acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide. Acetone data is at 323 K and carbon dioxide data is at 320 K (see Table 1).
Figure 3. Variation of density with pressure at the nominal temperature of 348 K for acetone and acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide. Data for pure carbon dioxide is at 355 K (see Table 1).
Figure 6. Variation of viscosity with temperature for acetone + carbon dioxide mixture containing 10 wt % carbon dioxide at the nominal pressures of 7, 14, 21, 28, and 35 MPa.
pressures. The data was correlated using a free volume-based equation27,28
η ) C exp
Figure 4. Variation of density with temperature for acetone + carbon dioxide mixtures containing 10 wt % carbon dioxide at the nominal pressures of 7, 14, 21, 28, and 35 MPa (see Table 1).
activation volumes show an increase with temperature, and at a given temperature, Vq appears to also increase with carbon dioxide content in the mixture. Viscosity-Density Correlation and Close-Packed Volume. Figure 7 shows the variation of viscosity with density for acetone, carbon dioxide, and acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide. This figure clearly demonstrates the change (reduction) in viscosity in going from acetone to carbon dioxide for all temperatures and
(
D 1 - V0F
)
(4)
where C and D are constants, F is the density, and V0 is the close-packed volume for the mixtures. The Hooke-Jeeves and quasi-Newton method with convergence criterion of 0.0001 were used to find the parameters. The close-packed volumes, constants C and D, correlation coefficients, and AADs of the correlations are summarized in Table 4. The close-packed volumes decrease from 0.98 cm3/g (for acetone) to 0.45 cm3/g (for carbon dioxide). In an earlier study, we reported a closepacked volume of 0.29 cm3/g for CO2 based on correlations that were obtained from data generated at higher temperatures in the range 380-420 K.27 In the present study, the temperatures are much lower, with the range being 320-370 K. It should also be noted that, for CO2, close-packed volume that is predicted with the van der Waals model is 0.44 cm3/g, which is similar to the values obtained from the experimental data at the present temperature range. Figure 7 is very instructive in showing the extent to which the viscosity is reduced by the addition of carbon dioxide if the density was held constant, as well as to what extent the mixture must be compressed if the same viscosity was to be maintained for a given mixture. It should be pointed out that the data for each fluid or fluid mixture in Figure 7 represent a wide range of P/T conditions. The
Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5457 Table 2. Parameters for Viscosity Correlation with Pressure (eq 2) activation volume, V* (cm3/mol) system/ temperature (K) acetone acetone/CO2 ) 90/10 acetone/CO2 ) 75/25 acetone/CO2 ) 50/50 acetone/CO2 ) 25/75 system/ temperature (K) CO2
A (104) (mPa‚s)
AADa (103) (mPa‚s)
correlation coefficient R
325
348
373
398
325
348
373
398
325
348
373
398
325
348
373
398
5 11 15 20 22
9 10 13 23 28
16 12 17 27 39
26 16 26 41
2.89 2.72 2.16 1.30 0.99
2.41 2.29 1.80 1.07 0.81
1.92 1.88 1.58 0.98 0.67
1.52 1.54 1.23 0.63
0.82 0.97 0.99 0.99 0.99
0.84 0.99 0.98 0.99 0.99
0.95 0.96 0.99 0.98 0.99
0.72 0.99 0.99 0.98
6 2 1 0 0
4 1 1 0 0
1 1 1 1 0
3 1 1 1
320 7
355 9
370 12
320 0.42
355 0.25
370 0.40
0.95
0.99
0.99
3
2
0
Average absolute deviation ) |XO - XP|/N, where XO is the value observed, XP is the value predicted from the model, and N is the number of the data points. a
Table 3. Parameters for Viscosity Correlation with Temperature (eq 3) activation energies, E* (kJ/mol)
B (105) (mPa‚s)
AAD (103) (mPa‚s)
correlation coefficient R
system/pressure (MPa)
7
14
21
28
35
7
14
21
28
35
7
14
21
28
35
7
14
21
28
35
acetone acetone/CO2 ) 90/10 acetone/CO2 ) 75/25 acetone/CO2 ) 50/50 acetone/CO2 ) 25/75
8 8 7 8
10 8 7 6 7
8 8 7 8 7
8 8 7 8 6
6 8 6 8 5
1.67 1.37 2.04 0.68
1.24 1.37 1.67 0.71 0.83
2.49 1.51 1.85 0.75 0.92
2.04 1.51 2.25 0.92 1.51
3.72 1.85 2.25 1.01 2.25
0.99 0.99 0.99 0.99
0.98 0.99 0.99 0.95 0.99
0.99 0.99 0.99 0.90 0.99
0.99 0.99 0.99 0.90 0.99
0.99 0.99 0.99 0.90 0.97
3 2 2 0
7 4 3 3 0
5 4 3 6 0
4 2 4 6 1
0 2 3 6 2
Table 4. Parameters for Viscosity Correlation with Density (eq 4) Doolittle equation parameters correlation AAD (102) V0 (cm3/g) coefficient R (mPa‚s)
system
C (mPa‚s)
D
acetone acetone/CO2 ) 90/10 acetone/CO2 ) 75/25 acetone/CO2 ) 50/50 acetone/CO2 ) 25/75 CO2
1.20E-02 1.00E-03
0.80 2.67
0.98 0.67
0.91 0.94
0.7 1.5
1.00E-03
2.67
0.64
0.93
1.2
1.00E-03
2.67
0.57
0.93
0.8
1.00E-03
2.67
0.54
0.93
1.3
1.00E-03
2.67
0.45
0.95
0.4
n
Mmix )
correlations that are given in the present paper provide a description of the viscosities and the densities of the system at all these P/T conditions. The correlations that are better descriptors of viscosity versus density may be generated at each temperature. Excess Volume. The excess volumes were calculated as n
V )V E
mix
-
xiVi ∑ i)1
tally. Mmix and Mi are the molecular weights for the mixture and the component i, respectively. The mixture molecular weights Mmix are calculated as
(5)
where VE is the molar excess volume (cm3/mol), Vmix is the mixture molar volume (cm3/mol), and xi and Vi are the mole fraction and the molar volume for component i. The mixture molar volume Vmix and the component molar volume Vi are calculated from
Vmix ) Mmix/Fmix
(6)
Vi ) Mi/Fi
(7)
and
where Fmix and Fi are the densities of the mixture and the pure component i, respectively, which were determined experimen-
Mixi ∑ i)1
(8)
Figure 8 shows the variation of excess volume with carbon dioxide content at 325 K and 14, 21, 28, and 35 MPa. Since the experimental data for pure components were at slightly different temperatures and pressures, data were extrapolated to the temperature and pressure of each mixture before calculations of the excess quantities were carried out. The excess volumes from an earlier study8 for limited compositions of this mixture that were obtained at higher pressures (35 and 55 MPa) are also included to accentuate the trends. The excess volumes are negative for all compositions at low pressures (14 and 21 MPa). With an increase in pressure, excess volume becomes positive for mixtures with high carbon dioxide contents. At 28 MPa, positive excess volume is displayed for the mixture with a carbon dioxide content of 75%. As the pressures are increased, positive excess volumes are observed for mixtures at lower CO2 content. At 55 MPa, positive excess volumes are observed over a wide range of compositions. The negative excess volumes for these mixtures indicate that overall volume of the mixture decreases upon mixing compared to simple linear additions. The concept of “expanded liquids” is frequently used in connection with two-phase systems at low carbon dioxide pressures. One should, however, exercise caution in that these systems may not necessarily mean that the volume of the organic liquid is actually expanded. It may even be reduced. If excess volumes are negative, the favorable attribute of the “liquid” arises from a combination of compositional effects and a change in the overall mixture density, rather than simply from a change in the volume (i.e., expanding) of the organic solvent. Figure 9 shows the variation of excess volume with carbon dioxide content at 373 K for 28 and 35 MPa. The excess volumes are negative and are similar at these high pressures.
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Figure 7. Variation of viscosity with density for acetone, carbon dioxide, and acetone + carbon dioxide mixtures containing 10, 25, 50, and 75 wt % carbon dioxide.
Figure 9. Variation of excess volume with carbon dioxide content for acetone + carbon dioxide mixture at 373 K and 28 and 35 MPa.
Figure 8. Variation of excess volume with carbon dioxide content for acetone + carbon dioxide mixture at 325 K and at 14, 21, 28, and 35 MPa. Excess volumes at 35 and 55 MPa are from ref 8.
Figure 10. Variation of viscosity with carbon dioxide content for acetone + carbon dioxide mixture at 325 K and 28 MPa. The viscosities include the experimental data (filled symbol) and the calculated values (open symbols) from four different mixing rules. See text for the mixing rules.
However, comparison with Figure 8 shows that, at the same pressure, a higher temperature may lead to more negative excess volumes. Correlations for Mixture Viscosity. Four different mixing rules were evaluated for their predictive ability of the mixture viscosities, expressed by the following equations: n
ηmix )
xiηi ∑ i)1
(9)
n
ln ηmix )
xi ln ηi ∑ i)1
(10)
n
ηmixVmix )
xiηiVi ∑ i)1
(11)
(12)
Figure 11. Variation of viscosity with carbon dioxide content for acetone + carbon dioxide mixture at 373 K and 28 MPa. The viscosities include the experimental data (filled symbols) and the calculated values (open symbols) from four different mixing rules. See text for the mixing rules.
Here ηmix and ηi are the viscosities of the mixture and the component i, respectively. Vmix and Vi are molar volumes. The logarithmic viscosities given by eqs 10 and 12 are known as the “Grunberg-Nissan”29 and “Katti-Chaudhri” mixing rules, respectively. Equations 11 and 12 involve the product “ηV”, which is the kinematic viscosity. Figures 10 and 11 show the comparisons of the predictions with the experimental data at
28 MPa at two different temperatures. (The predictions corresponding to each experimental data point are specifically shown in these figures and should not be confused with the actual experimental data points shown with filled symbols). At 325 K, the logarithmic mixing rules describe the viscosity well, but at the higher temperature, the simple linear combinations are observed to give better results. In the viscosity range from 0.04 to 0.38 mPa‚s, the average absolute deviation (AAD) between
n
ln(ηmixVmix) )
xi ln(ηiVi) ∑ i)1
Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5459
Figure 12. Variation of excess viscosity with carbon dioxide content (mass %) for acetone + carbon dioxide mixture at 325 K and at 14, 21, 28, and 35 MPa.
Figure 14. Variation of excess viscosity with excess volume for acetone + carbon dioxide mixtures containing 0, 10, 25, 50, 75, and 100 wt % carbon dioxide at 325 and 373 K at 28 MPa.
Figure 13. Variation of excess viscosity with carbon dioxide content (mass %) for acetone + carbon dioxide mixture at 373 K and at 28 and 35 MPa.
the models and the experimental data, depending upon the model and the temperature, is calculated to be in the range from 0.01 to 0.04 mPa‚s. Excess Viscosity. The excess viscosities (∆η), defined as viscosity deviations from the arithmetic average of the component viscosities, were calculated according to n
∆η ) ηmix -
xiηi ∑ i)1
(13)
These were evaluated for possible correlations with fluid composition and/or the excess volume. Figures 12 and 13 show the variation of excess viscosity with carbon dioxide content at 325 and 373 K at different pressures. Here, the curves are simply fits to data and do not represent any model. The magnitude and sign of the excess viscosity depend on the fluid composition. The excess viscosity is positive and goes through a maximum for the mixture containing 25% carbon dioxide at both temperatures. Excess viscosities are negative for other mixtures at 325 K but become positive at 373 K. At 325 K, pressure appears to influence more these mixtures with higher carbon dioxide content. Excess viscosity becomes less positive with increasing pressure. Figure 14 shows the variation of excess viscosity with excess volume. No simple trends are observed. While the excess viscosities are positive at 325 K, they are mostly negative at 373 K. Even though one anticipates a more clear and direct correlation between excess viscosity and excess volume, the present
Figure 15. (Top) Electron donor-acceptor complexes between acetone and carbon dioxide35 where R1 ) 132.8°, r1 ) 2.745 Å; R2 ) 180.0 °, r2 ) 2.774 Å. (Bottom) Dimer structures of carbon dioxide: the slipped parallel arrangement with C-C distance of 3.6 Å (d1 ) 3.6 Å, d11 ) 1.9 Å, d12 ) 3.1 Å) and T-shaped arrangement with C-C distance of 4.2 Å (d2 ) 4.2 Å).38
data and limited literature on other systems indicate that this is often not the case. For example, in a recent publication30 on mixtures of N-methylacetamide with chloroethanes and chloroethenes, no correlations could be established between the sign of the excess viscosity and the sign of excess volume either. This was rationalized by noting that the excess viscosity must depend not only on the intermolecular interactions but also on the sizes and shapes of the component molecules. In order to elucidate the importance of interactions between unlike molecules, they evaluated the excess Gibbs free energy of viscous flow (GVE) and Grunberg-Nissan interaction parameters (d12) using the equations
GVE ) RT[ln ηmixVmix - (x1 ln η1V1 + x2 ln η2V2)]
(14)
and
d12 ) (ln ηmix - x1 ln η1 - x2 ln η2)/(x1x2)
(15)
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Figure 16. Visualization of compositional variations in carbon dioxide-acetone mixtures. The diagrams consider possibilities for different forms of CO2 dimers and CO2-acetone complexes for different CO2-acetone ratios in the mixtures.
We have carried out such an analysis with our data as well. The calculated values of GVE and d12 are summarized in Table 1. Literature indicates that positive GVE values arise from specific chemical interactions while negative values indicate the dominance of physical interactions (arising from induction forces, dispersion forces, and so on).30,31 If d12 values are positive, the interactions between unlike molecules are strong, whereas they become weak with negative values.30,31 Except for the mixture containing 10% carbon dioxide at 325 K, essentially all values of GVE and d12 in Table 1 are positive, which suggests strong interactions between acetone and carbon dioxide at the conditions investigated. The specific interaction between the carbon atom in carbon dioxide with the carbonyl group in acetone has been predicted in ab initio simulations32,33 and confirmed also in spectroscopic experiments34,35 in the literature. These studies conducted for 1:1 mixtures indicate formation of two types of electron donoracceptor (EDA) complexes of carbon dioxide and acetone, which are illustrated in Figure 15. The carbon atom in CO2 is the electron acceptor center, and the oxygen atom of the carbonyl group in acetone is the electron donor center. For carbon dioxide, literature indicates the presence of pairwise interactions leading to the formation of dimers.36-39 The dimers are either in a slipped parallel geometry or in a T-shaped saddle geometry with a C-C separation of 3.6 or 4.2 Å, respectively. These are also shown in Figure 15. A crossed geometry has also been indicated for carbon dioxide dimers.36 Carbon dioxide trimers have been predicted as well.36 Of these, the slipped parallel arrangement is indicated to be favored.37 There has been no report on how these interactions in carbon dioxide + acetone mixtures change with pressure, temperature, or fluid composition except a recent investigation where Raman spectral changes have been reported for carbon dioxide-acetone mixtures at 313 K at pressures from 0.5 to 9 MPa.35 Even though the spectral band intensity representative of CO2-acetone complex increased up to 3 MPa (where the liquid-phase molar content of CO2 is reported to be 0.43), no significant change was observed with a further increase in pressure 35. Figure 16, which is a simplified illustration depicting mixtures with different carbon dioxide-to-acetone ratios, provides some insights to the effect of composition. For the 1:1 mixture, we assume that all carbon dioxide molecules associate with the acetone molecules, forming complexes of either type I or II. For mixtures with high CO2 content, a portion of carbon dioxide is tied with acetone, forming the complex, and the remainder is assumed as existing as unassociated molecules or as dimers. For mixtures with high acetone concentration, a portion of acetone is tied with carbon dioxide, forming the complex, and
the remainder is free acetone. The formation of dimers in CO2 and the nature of the association with acetone depicted in Figures 15 and 16 would suggest that mixtures with high carbon dioxide content would be more sensitive to pressure, whereas those with high acetone content would be more sensitive to temperature. This is indeed observed in Figures 12 and 13. The data in Figures 8 and 9 and the negative excess volumes are consistent with strong interactions. At 325 K, association effects are more effective and lead to greater volume reduction at lower pressures. When pressure is increased and both fluids become dense, the relative reduction in occupied volume in the mixture becomes less, reducing the relative impact of association. When temperature is increased, the more negative excess volumes observed at higher pressures suggest that the degree of association may be lessened at higher temperatures but is promoted at higher pressures that would help bring the components to their closer proximity. Negative excess volume, with other factors being the same, would imply an increase in the free volume in the mixture and, thus, lead to an expectation of a negative excess viscosity. In Figure 12, with an initial increase in the carbon dioxide content of the mixture, the formation of the acetone-CO2 complex generates sufficient free volume and leads to negative excess viscosity. Since the mixture is dominated with acetone, the net outcome overmasks any effect of the larger size and potentially higher viscosity of the acetone-CO2 complex. With a further increase in the carbon dioxide content in the mixture, the relative amount of the complex increases, and even though free volume still leads to a negative excess viscosity, the size effect of the complex appears to set in, resulting in a positive excess viscosity for the mixtures containing 25 wt % carbon dioxide. At higher carbon dioxide content and as a 1:1 molar mixture is approached and more and more of the acetone molecules become tied in the acetone-carbon dioxide complex, the additional carbon dioxide molecules now appear to serve as diluent molecules, leading to the negative excess viscosities. As the pure carbon dioxide end of the spectrum is approached, excess viscosity goes to zero. A clear description of excess viscosity behavior at different temperatures and pressures is, however, difficult without additional information on how the complex formation is influenced by these factors and which form of the complex has higher viscosity. Figure 14 would suggest that, at higher temperatures where excess viscosity is positive while excess volume is negative, the size and shape of the acetone-carbon dioxide complex must play a more significant role as compared to the free volume reduction. Free volume reduction appears to be a
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Analysis of the excess Gibbs free energy of viscous flow shows that the intermolecular interactions are strong and specific (chemical) interactions are dominant in the mixtures at the conditions investigated. Literature Cited
Figure 17. Variation of viscosity with excess volume for acetone + carbon dioxide mixture at 325 K and 14, 21, 28, and 35 MPa. On each curve, from the top to the bottom, the carbon dioxide contents for every point are 0, 10, 25, 50, 75, and 100 wt %.
Figure 18. Variation of viscosity with excess volume for acetone + carbon dioxide mixture at 373 K and 28 and 35 MPa. On each curve, from the top to the bottom, the carbon dioxide contents for every point are 0, 10, 25, 50, 75, and 100 wt %.
more dominating factor at lower temperatures, leading to the observed negative excess viscosities. Figures 17 and 18 show the variation of the actual viscosity of the mixtures with excess volume at 325 and 373 K for different mixtures at different pressures. Along the direction of the arrows, data points correspond to mixtures with 0, 10, 25, 50, 75, and 100 mass % carbon dioxide. For the pure components, excess volume is zero. Even though no simple correlation could be identified for excess viscosity and excess volume, Figures 17 and 18 both show that, in the direction along the arrows at each pressure, the mixture viscosities always decrease with an increase in carbon dioxide content. Conclusions The densities of carbon dioxide and acetone + carbon dioxide mixtures show different crossover pressures at different carbon dioxide concentrations, and these crossover pressures increase with temperature. The mixture viscosities display a decrease upon the addition of carbon dioxide. The flow activation volumes and flow activation energies range from 5-10 kJ/mol and 5-41 cm3/mol, respectively. The close-packed volume shows a decrease with the addition of carbon dioxide from 0.98 to 0.45 g/cm3. As the pressure is increased, the excess volumes become more positive, and as the temperature is increased, the excess volumes become more negative. There is no simple correlation between excess viscosity and excess volume.
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ReceiVed for reView February 21, 2007 ReVised manuscript receiVed May 9, 2007 Accepted May 30, 2007 IE070274W
