Relation between Volume Expansion and Hydrogen Bond Networks

Oct 11, 2010 - We experimentally determined the density and mole fraction of CO2 (xCO2) for CO2−alcohol (methanol, ethanol, propanol, butanol, isopr...
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J. Phys. Chem. B 2010, 114, 13628–13636

Relation between Volume Expansion and Hydrogen Bond Networks for CO2-Alcohol Mixtures at 40 °C Tsutomu Aida, Takafumi Aizawa,* Mitsuhiro Kanakubo, and Hiroshi Nanjo National Institute of AdVanced Industrial Science and Technology, Research Center for Compact Chemical Process, 4-2-1 Nigatake, Miyagino-ku, Sendai 983-8551, Japan ReceiVed: February 26, 2010; ReVised Manuscript ReceiVed: September 15, 2010

We experimentally determined the density and mole fraction of CO2 (xCO2) for CO2-alcohol (methanol, ethanol, propanol, butanol, isopropyl alcohol, and tert-butyl alcohol) mixtures and performed molecular dynamics (MD) simulations to study the mechanisms of volume expansion at 40 °C. The volume as calculated by vapor-liquid equilibrium (VLE) data increased with decreasing alkyl chain length, although there was no effect of branched alkyl groups. Analysis of the hydrogen bond network showed that the average number of hydrogen bonds per alcohol molecule decreased with increasing branched methyl groups. At pure alcohol condition, large size hydrogen bond networks were made. With further addition of CO2 molecules, it became difficult to contain the large hydrogen bond networks. Furthermore, the hydrogen bond networks changed to a cyclic pentamer or tetramer, and volume expansion occurred. 1. Introduction There has been an increase in the number of reports for CO2expanded liquid mixtures. The phenomenon of liquid-phase volume expansion resulting from the addition of CO2 to many organic solvents has been utilized for industrial processes.1-8 CO2-expanded liquids provide the substitution of the organic solvents. Further development of CO2-expanded liquid requires accurate experimental data. Organic compounds appropriate for the CO2-expanded liquids are ketones, acetates, alcohols, and so on. Many researchers measure the vapor-liquid equilibrium (VLE) data of expanded liquid and show an expansion coefficient.9-12 In our previous work, we measured the density and carbon dioxide mole fraction (xCO2) of the liquid phase for CO2-ketone and CO2-acetate mixtures and studied the volume expansion mechanism for these mixtures with MD simulations.13-15 Here, we chose to examine expanded CO2-alcohol mixtures. The greatest difference between the previously measured organic compounds (ketones and acetates) and the alcohols is the existence of a hydrogen bond. Many researchers have studied the physical properties of alcohols. Shi et al. measured the viscosity of CO2-methanol and CO2-ethanol mixtures between CO2 mole fractions of 0.15 and 0.80 at temperatures of 25-40 °C.16,17 As xCO2 increased, the slope of the decline in viscosity changed from steep to shallow. Reports of VLE data for CO2-methanol, -ethanol,18,19 -propanol.20 and -butanol21 at 40 °C showed that there were few differences in xCO2 due to pressure. Xu et al. studied the hydrogen bond structure of CO2-ethanol mixtures by Monte Carlo (MC) simulation.22 They reported that the average number of hydrogen bonds was higher than 1 at xCO2 < 0.9 and that the fraction of linear hydrogenbonded structures was higher than that of cyclic hydrogenbonded structures at a temperature of 55 °C and a pressure of 20 MPa. However, there have been few if any reports clarifying the volume expansion mechanism for CO2-alcohol mixtures. * To whom correspondence should be addressed. Tel.: +81-22-237-5211. Fax: +81-22-237-5224. E-mail: [email protected].

Our objective in this paper is to clarify the mechanism of volume expansion for CO2-normal or blanched alkyl alcohol mixtures at 40 °C through experimental and MD simulation analyses. 2. Experimental Section Apparatus and Procedure. The density and xCO2 at 40 °C were measured using apparatuses used in a previous study.13 The uncertainties in temperature and pressure were (0.1 °C and (0.01 MPa, respectively. Density was measured using a vibrating tube densimeter (Anton Paar, DMA HPM, and mPDS 2000 V3). The composition of the mixture was determined by gas chromatographic analysis with a flame ionization detector (GC-FID; Agilent Technology, GC-7890A) using a capillary column (DB-1, 30 m × 0.32 mm × 0.25 µm) by the initial standard method. The temperature gradients of the oven are shown in Table 1. The injector and detector temperatures were kept at 250 °C. Helium was used as the carrier gas at a flow rate of 1.5 mL/min. The internal standard was propyl acetate (methanol, butanol), methyl ethyl ketone (ethanol, isopropyl alcohol), or methanol (propanol, tert-butyl alcohol). The maximum fluctuation in density was (0.002 g/cm3, and the measurement error for xCO2 was (0.005. xCO2 was determined to obtain the number of alcohol molecules in the sample loop. xCO2 is defined as

xCO2 )

(FCO2Vsample loop)/MW,CO2 (FCO2Vsample loop)/MW,CO2 + nalcohol

(1)

where FCO2 is the density of CO2 in the sample loop, Vsample loop is the volume of the sample loop (697 µL), MW,CO2 is the molecular weight of CO2, and nalcohol is the number of alcohol molecules in the sample loop. Materials. All reagents used in this study were purchased from Wako Pure Chemical Industries Co., Ltd. Methanol (purity of at least 99.8%), ethanol (purity of at least 99.5%), propanol (purity of at least 99.5%), butanol (purity of at least 99%),

10.1021/jp1017339  2010 American Chemical Society Published on Web 10/11/2010

Volume Expansion of CO2-Alcohol Mixtures at 40 °C

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TABLE 1: Temperature Gradient of the Oven in This Study material methanol ethanol propanol

temperature gradient 40 10 15 40 20 30 40 20 25

material

°C (initial, hold time is 3 min) °C/min by 60 °C (no hold time) °C/min by 90 °C (hold time is 1 min) °C (initial, hold time is 1 min) °C/min by 80 °C (no hold time) °C/min by 110 °C (hold time is 1 min) °C (initial, hold time is 2 min) °C/min by 60 °C (no hold time) °C/min by 110 °C (no hold time)

temperature gradient

butanol isopropyl alcohol and tert-butyl alcohol

40 10 30 40 20 30

°C (initial, hold time is 1 min) °C/min by 70 °C (no hold time) °C/min by 130 °C (no hold time) °C (initial, hold time is 2 min) °C/min by 80 °C (no hold time) °C/min by 110 °C (no hold time)

TABLE 2: Experimental Results of Liquid-Phase Density and xCO2 for CO2-Alcohol Mixtures methanol

ethanol

propanol

P (MPa)

Fmix (g/cm )

xCO2

P (MPa)

Fmix (g/cm )

xCO2

0.00 0.51 1.01 1.51 2.02 2.51 3.01 3.50 4.01 4.49 5.01 5.50 6.01 6.49 6.98 7.55

0.7722 0.7782 0.7837 0.7888 0.7936 0.7982 0.8027 0.8069 0.8114 0.8157 0.8202 0.8242 0.8278 0.8300 0.8286 0.8059

0.026 0.053 0.080 0.109 0.135 0.162 0.194 0.227 0.263 0.308 0.346 0.395 0.443 0.495 0.623

0.00 1.06 2.05 3.07 4.07 4.76 5.44 6.04 6.37 6.74 7.02 7.25 7.44 7.56 7.65 7.72

0.7729 0.7808 0.7874 0.7935 0.7994 0.8040 0.8085 0.8124 0.8142 0.8147 0.8132 0.8073 0.7938 0.7705 0.7425 0.7014

0.065 0.130 0.182 0.240 0.297 0.351 0.395 0.439 0.500 0.547 0.603 0.680 0.740 0.787 0.838

P (MPa)

Fmix (g/cm3)

xCO2

P (MPa)

Fmix (g/cm3)

xCO2

0.00 1.06 2.02 3.04 4.04 4.84 5.52 6.14 6.58 6.93 7.06 7.26 7.63 7.75 7.85 7.89 7.95

0.7934 0.7982 0.8019 0.8058 0.8101 0.8142 0.8182 0.8224 0.8256 0.8278 0.8285 0.8291 0.8245 0.8161 0.8004 0.7723 0.7333

0.067 0.125 0.161 0.231 0.280 0.342 0.424 0.456 0.530 0.559 0.593 0.662 0.717 0.771 0.825 0.863

0.00 1.05 2.08 3.04 4.04 4.84 5.34 5.65 5.95 6.24 6.53 6.83 7.04 7.21 7.37 7.53 7.72

0.7722 0.7776 0.7818 0.7856 0.7897 0.7932 0.7955 0.7969 0.7978 0.7981 0.7968 0.7914 0.7808 0.7646 0.7355 0.7000 0.6251

0.062 0.138 0.184 0.257 0.328 0.377 0.421 0.460 0.501 0.568 0.629 0.698 0.750 0.805 0.851 0.899

3

butanol

3

P (MPa)

Fmix (g/cm3)

xCO2

0.00 1.03 2.01 3.07 4.06 4.84 5.52 6.11 6.50 6.80 7.06 7.33 7.54 7.63 7.70 7.78 7.82 7.87

0.7872 0.7928 0.7973 0.8020 0.8066 0.8109 0.8152 0.8190 0.8215 0.8231 0.8232 0.8203 0.8102 0.7966 0.7767 0.7361 0.7041 0.6565

0.060 0.107 0.171 0.235 0.284 0.346 0.406 0.452 0.495 0.541 0.605 0.675 0.722 0.771 0.831 0.860 0.893

ispopropyl alcohol

isopropyl alcohol (purity of at least 99.7%), and tert-butyl alcohol (purity of at least 99%) were used without further purification. To collect alcohol in a GC-FID sampling flask and bottle, distilled water was used. Propyl acetate (purity of at least 97%) and methyl ethyl ketone (purity of at least 99%) were used as internal standards for GC-FID. High-purity CO2 (purity greater than 99.99%) was obtained from Tanuma Sanso. Simulation Details. The potential model used in this work on alcohols was the TraPPE-UA model,23,24 and the bond harmonic potential was used as the AMBER potential.25 The potential model for CO2 was developed by Tuckerman and Langel.26 Both models are flexible and represented as a sum of intra- and intermolecular potentials. The intramolecular potential uses a bond length in addition to angular and torsion potentials. The intermolecular potential uses a Lennard-Jones 12-6

tert-butyl alcohol P (MPa)

Fmix (g/cm3)

xCO2

0.00 1.03 2.06 3.06 4.05 4.84 5.53 6.04 6.36 6.65 6.93 7.14 7.35 7.55

0.7649 0.7688 0.7715 0.7740 0.7767 0.7789 0.7799 0.7781 0.7731 0.7634 0.7448 0.7224 0.6872 0.6372

0.077 0.141 0.232 0.325 0.431 0.533 0.620 0.687 0.742 0.800 0.839 0.882 0.911

potential and a Coulomb potential. For mixtures, we assumed the Lorentz-Berthelot rules in determining the interactions between alcohol and CO2 molecules. A cutoff radius of 0.4LBOX Å (LBOX is the length of the simulation box) was been applied for all Lennard-Jones interactions, and the reaction field method was used to account for long-range electrostatic interactions.27 All simulations were performed with NVT ensembles, and the total number of molecules was 500. The simulation volume was determined by our experimental data on densities and xCO2. The temperature was kept at 40 °C by velocity scaling28 (50 ps). The equations of motion were solved using the velocity Verlet technique31 and the multiple time scale algorithm.32 The multiple time scale algorithm for methanol (Honma et al.33) and CO2 (Aida and Inomata34) were in good agreement with other simulation data.

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Figure 1. Expansion coefficient versus pressure for CO2-alcohol mixtures at 40 °C.

Plots of the expansion coefficient for CO2-alcohols at 40 °C are shown in Figure 1. Volume expansion had two states, a slowly changing state (xCO2< 0.6) and rapidly changing state (xCO2 > 0.6). The expansion coefficient decreased with increasing alkyl chain length but was unaffected by the presence of branched alkyl groups. On the other hand, the following assumptions about the expansion coefficient were adopted: (I) The partial molar volume is not changed at all xCO2. (II) While adding the CO2 molecules, alcohol molecules in the liquid phase could not move to vapor phase. (III) The partial molar volume of CO2 is 50 cm3/mol. From the above assumptions, eq 2 was expressed by

V/V0 ) Vtotal /V0 The time step was 0.2 fs for intramolecular dynamics and 1 fs for intermolecular dynamics. Statistical sampling of the simulation was performed for 200 ps after 100 ps of equilibration.

) (Valcohol + VCO2)/V0

3. Results and Discussion

) 1 + VCO2 /V0

) (V0 + VCO2)/V0

Experimental Results. Table 2 summarizes the density and xCO2 data for CO2-alcohol mixtures at 40 °C. In Table 2, the density data at 0.00 MPa is the density of the alcohols in the atmosphere. The relation of xCO2 to pressure was almost the same for normal alkyl alcohol. Our experimental results were in good agreement with other reports.18-21 We evaluated the expansion coefficient (V/V0) of the liquid phase for CO2-alcohol mixtures at 40 °C using experimental data and the following equation.35

V/V0 )

F0{MW,CO2xCO2 + MW,alcohol(1 - xCO2)} FmixMW,alcohol(1 - xCO2)

)1+ )1+

j alcoholnalcohol) j CO nCO )/(V (V 2 2 j CO xCO )/(V j alcoholxalcohol) (V 2 2

j CO xCO )/ ) 1 + (V 2 2 j alcohol(1 - xCO )} (3) {V 2

(2)

where F0 is the liquid-phase density of pure alcohol at atmospheric pressure, MW,alcohol is the molecular weight of the alcohol, and Fmix is the liquid-phase density at the measured pressure.

where Vtotal, VCO2, and Valcohol are total volume and the molar j CO and V j alcohol are the partial molar volume of CO2 and alcohol, V 2 volume of CO2 and alcohol, and xalcohol is the mole fraction of alcohol. Here, Valcohol is used by our experimental data (methanol, 41.49 cm3/mol; ethanol, 59.61 cm3/mol; propanol, 76.35 cm3/ mol; butanol, 93.42 cm3/mol; isopropyl alcohol, 77.83 cm3/mol; tert-butyl alcohol, 96.90 cm3/mol). As an example, the results of comparing eqs 2 and 3 about ethanol and isopropyl alcohol are shown in Figure 2. The values are almost constant at lower xCO2 regions. However, the deviation appeared at higher xCO2 regions. These phenomena appeared at all other CO2-alcohol mixtures in this study. There seems not to be a rapid volumetric change. On the other hand, the deviation appeared at higher xCO2 regions. These results suggested that a rapid volumetric change could not occur at lower xCO2 regions and partial molar volume is changed at higher xCO2 regions. In further analyses, we calculated the partial molar volume by Peng-Robinson equation of state (PR-EOS).36 The xCO2 correlated with the PR-EOS, which is written as

P) a ) 0.45724

RT a - 2 V-b V + 2bV - b2

R2Tc2 [1 + (0.37464 + 1.54226ω Pc 0.26992ω2)(1 - Tr1/2)]2 b ) 0.0778

Figure 2. Results of competition with eqs 2 and: (a) ethanol; (b) isopropyl alcohol.

(4)

RTc Pc

(5) (6)

where R is the ideal gas constant, T is the temperature (313.15 K), V is the molar volume, Tc and Pc are the critical temperature

Volume Expansion of CO2-Alcohol Mixtures at 40 °C

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TABLE 3: Binary Interaction Coefficient (kij) for CO2-Alcohol Mixtures material

kij

material

kij

methanol ethanol propanol

0.081 0.091 0.089

butanol isopropyl alcohol tert-butyl alcohol

0.087 0.105 0.099

Figure 5. Radial distribution functions for (a) methanol oxygenmethanol oxygen and (b) methanol oxygen-methanol hydrogen.

Figure 3. Partial molar volume versus xCO2 for CO2-alcohol mixtures at 40 °C: (a) alcohols; (b) CO2.

Figure 6. Average number of hydrogen bonds per alcohol molecule (nHB).

and pressure of the pure component, Tr is the reduced temperature (Tr ) T/Tc), and ω is an acentric factor. Critical parameters were obtained from the literature.37 The following mixing rules are recommended. N

N

∑ ∑ xixjaij

(7)

aij ) (1 - kij)√aiaj

(8)

am )

i)1 j)1

N

bm )

N

∑ ∑ xixjbij

(9)

i)1 j)1

bij ) (1 - lij)

Figure 4. Self-diffusion coefficients for (a) alcohols and (b) CO2 in the liquid phase.

(bi + bj) 2

(10)

where kij and lij are the binary interaction coefficients. In this study we supposed that lij ) 0. kij was obtained by fitting the PR-EOS to the measured data by minimizing the absolute average deviation in pressure. The values of kij are given in Table 3.

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j i) using the PRWe calculated the partial molar volume (V EOS parameters and the following equation:37

ji ) V

{ ( [[ ∑

)

bi RT 1+ VL - bm VL - bm N

xkaik -

2

k

2ambi(VL - bm) VL(VL + bm) + bm(VL - bm)

]}/

]/

[VL(VL + bm) + bm(VL - bm)]

[

2am(VL + bm) RT 2 (VL - bm) {VL(VL + bm) + bm(VL - bm)}2

]

(11)

where VL is the molar volume of the liquid phase calculated by the PR-EOS. Figure 3 shows the partial molar volume of CO2-alcohols determined using the PR-EOS and the parameter kij. There is a large difference about the partial molar volume at pure condition in the experimental value and the calculated value. It is well-known that although the values of the volume calculated by using the equation of state (Peng-Robinson, Soave-Redlich-Kwong, and so on) fitting along with the composition differ from those obtained experimentally, the tendencies of the volume and the density are similar. However, the region of xCO2 in which the partial molar volume is almost constant was the same as the result of Figure 2. We assume that the result of partial molar volume calculated by

Figure 7. Distribution of cluster size.

PR-EOS is proper. In adding CO2 molecules to the pure-alcohol condition, the partial molar volume changed in one of two ways: a gradual or a rapid state. Especially, the partial molar volume of alcohol becomes negative at high xCO2 region. These tendencies have been observed for several CO2-organic compound mixtures.13,15,39,40 The partial molar volume was higher for longer alkyl chain lengths. The partial molar volume of branched alkyl alcohols was smaller than that of normal alkyl alcohols of equal molecular weight. The CO2 molecules were allocated to the occupied volume of alcohols, and alcohol molecules might be made large hydrogen bond networks at regions of lower xCO2. With further addition of CO2 molecules, these interspaces were filled and CO2 molecules break the large hydrogen bond networks. This phenomenon causes negative partial molar volume of alcohols. The partial molar volume for branched alkyl alcohol was smaller than that for normal alkyl alcohol, although the expansion coefficient was almost the same. In our previous study of CO2-acetate mixtures, the expansion coefficient increased with decreasing partial molar volume. We assumed that the volume expansion mechanism for CO2-alcohol mixtures was different from that of CO2-acetate mixtures. Simulation Results. We calculated the self-diffusion coefficient using the following Einstein relation to investigate molecular mobility in the liquid through simulations.

D ) lim tf∞

1 2 〉 〈[b(t) r - b(0)] r 6t

(12)

Figure 4 shows the resulting self-diffusion coefficients for alcohol and CO2 molecules. For both molecules, self-diffusion

Volume Expansion of CO2-Alcohol Mixtures at 40 °C

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TABLE 4: Distribution of Cluster Size for Measurement Alcohols fn

xCO2

1 2 3 4 5 6 7 8 9 10

0.000 0.009 ( 0.001 0.008 ( 0.001 0.009 ( 0.001 0.010 ( 0.001 0.013 ( 0.002 0.013 ( 0.003 0.014 ( 0.002 0.013 ( 0.002 0.014 ( 0.002 0.014 ( 0.002

0.228 0.012 ( 0.001 0.009 ( 0.001 0.011 ( 0.002 0.014 ( 0.002 0.015 ( 0.003 0.019 ( 0.003 0.017 ( 0.003 0.016 ( 0.005 0.015 ( 0.004 0.015 ( 0.002

Methanol 0.308 0.012 ( 0.001 0.009 ( 0.001 0.011 ( 0.001 0.016 ( 0.004 0.022 ( 0.005 0.024 ( 0.008 0.026 ( 0.008 0.021 ( 0.006 0.019 ( 0.005 0.021 ( 0.008

0.496 0.018 ( 0.005 0.012 ( 0.003 0.011 ( 0.003 0.026 ( 0.006 0.034 ( 0.011 0.031 ( 0.008 0.029 ( 0.009 0.023 ( 0.007 0.023 ( 0.007 0.018 ( 0.005

0.622 0.028 ( 0.004 0.017 ( 0.004 0.017 ( 0.002 0.032 ( 0.008 0.055 ( 0.009 0.054 ( 0.011 0.044 ( 0.014 0.033 ( 0.012 0.036 ( 0.009 0.037 ( 0.016

1 2 3 4 5 6 7 8 9 10

0.000 0.009 ( 0.001 0.007 ( 0.001 0.007 ( 0.001 0.022 ( 0.006 0.030 ( 0.002 0.024 ( 0.008 0.020 ( 0.005 0.016 ( 0.004 0.015 ( 0.002 0.016 ( 0.004

0.298 0.015 ( 0.003 0.009 ( 0.001 0.011 ( 0.002 0.036 ( 0.010 0.037 ( 0.007 0.025 ( 0.004 0.022 ( 0.004 0.029 ( 0.006 0.025 ( 0.006 0.028 ( 0.009

Ethanol 0.604 0.028 ( 0.004 0.014 ( 0.003 0.021 ( 0.006 0.062 ( 0.012 0.071 ( 0.014 0.057 ( 0.015 0.035 ( 0.006 0.042 ( 0.015 0.037 ( 0.014 0.038 ( 0.015

0.740 0.042 ( 0.011 0.032 ( 0.014 0.019 ( 0.006 0.133 ( 0.046 0.169 ( 0.042 0.078 ( 0.022 0.081 ( 0.018 0.063 ( 0.038 0.050 ( 0.010 0.033 ( 0.017

0.838 0.084 ( 0.013 0.037 ( 0.015 0.046 ( 0.014 0.167 ( 0.034 0.290 ( 0.064 0.162 ( 0.042 0.074 ( 0.015 0.042 ( 0.032 0.005 ( 0.005 0.002 ( 0.002

1 2 3 4 5 6 7 8 9 10

0.000 0.010 ( 0.001 0.007 ( 0.001 0.008 ( 0.001 0.030 ( 0.013 0.043 ( 0.006 0.038 ( 0.011 0.028 ( 0.005 0.014 ( 0.005 0.015 ( 0.006 0.017 ( 0.006

0.346 0.016 ( 0.003 0.009 ( 0.001 0.008 ( 0.002 0.028 ( 0.004 0.048 ( 0.012 0.037 ( 0.011 0.033 ( 0.004 0.020 ( 0.009 0.016 ( 0.005 0.012 ( 0.007

Propanol 0.606 0.023 ( 0.003 0.019 ( 0.005 0.019 ( 0.003 0.092 ( 0.034 0.098 ( 0.025 0.101 ( 0.024 0.085 ( 0.013 0.055 ( 0.032 0.024 ( 0.016 0.016 ( 0.010

0.770 0.050 ( 0.011 0.019 ( 0.006 0.022 ( 0.010 0.203 ( 0.050 0.137 ( 0.039 0.061 ( 0.009 0.055 ( 0.051 0.023 ( 0.021 0.019 ( 0.012 0.030 ( 0.028

0.892 0.106 ( 0.012 0.054 ( 0.020 0.042 ( 0.032 0.138 ( 0.055 0.175 ( 0.067 0.079 ( 0.042 0.138 ( 0.070 0.089 ( 0.065 0.026 ( 0.023 0.029 ( 0.029

1 2 3 4 5 6 7 8 9 10

0.000 0.010 ( 0.001 0.006 ( 0.001 0.007 ( 0.001 0.029 ( 0.005 0.029 ( 0.004 0.030 ( 0.010 0.015 ( 0.005 0.017 ( 0.006 0.013 ( 0.004 0.013 ( 0.002

0.342 0.014 ( 0.001 0.009 ( 0.002 0.010 ( 0.003 0.031 ( 0.009 0.064 ( 0.021 0.035 ( 0.011 0.019 ( 0.007 0.028 ( 0.015 0.034 ( 0.006 0.027 ( 0.012

Butanol 0.592 0.030 ( 0.007 0.014 ( 0.005 0.015 ( 0.006 0.055 ( 0.016 0.135 ( 0.030 0.135 ( 0.017 0.050 ( 0.016 0.069 ( 0.028 0.042 ( 0.020 0.041 ( 0.004

0.772 0.048 ( 0.003 0.026 ( 0.013 0.021 ( 0.008 0.216 ( 0.009 0.208 ( 0.028 0.095 ( 0.028 0.066 ( 0.045 0.033 ( 0.025 0.048 ( 0.030 0.010 ( 0.005

0.862 0.082 ( 0.031 0.031 ( 0.017 0.050 ( 0.017 0.223 ( 0.055 0.255 ( 0.092 0.237 ( 0.038 0.070 ( 0.050 0.012 ( 0.007 0.001 ( 0.001 0.000

1 2 3 4 5 6 7 8 9 10

0.000 0.013 ( 0.002 0.007 ( 0.001 0.009 ( 0.001 0.030 ( 0.006 0.056 ( 0.007 0.033 ( 0.014 0.015 ( 0.003 0.015 ( 0.005 0.012 ( 0.003 0.014 ( 0.003

0.328 0.017 ( 0.002 0.013 ( 0.001 0.013 ( 0.003 0.061 ( 0.013 0.089 ( 0.009 0.058 ( 0.008 0.028 ( 0.009 0.027 ( 0.010 0.023 ( 0.009 0.026 ( 0.009

Isopropyl Alcohol 0.630 0.048 ( 0.014 0.026 ( 0.011 0.029 ( 0.018 0.212 ( 0.028 0.181 ( 0.028 0.082 ( 0.010 0.034 ( 0.029 0.024 ( 0.017 0.022 ( 0.007 0.015 ( 0.006

0.750 0.051 ( 0.013 0.031 ( 0.001 0.040 ( 0.019 0.245 ( 0.029 0.265 ( 0.091 0.121 ( 0.024 0.067 ( 0.022 0.035 ( 0.019 0.031 ( 0.016 0.016 ( 0.016

0.898 0.184 ( 0.075 0.096 ( 0.066 0.110 ( 0.031 0.285 ( 0.061 0.154 ( 0.085 0.067 ( 0.033 0.038 ( 0.029 0.023 ( 0.023 0.000 0.000

1 2 3 4 5 6 7 8 9 10

0.000 0.037 ( 0.005 0.029 ( 0.004 0.055 ( 0.005 0.491 ( 0.011 0.160 ( 0.019 0.072 ( 0.009 0.038 ( 0.004 0.024 ( 0.006 0.017 ( 0.004 0.016 ( 0.007

0.326 0.066 ( 0.008 0.043 ( 0.005 0.077 ( 0.020 0.449 ( 0.032 0.186 ( 0.026 0.057 ( 0.010 0.024 ( 0.008 0.021 ( 0.009 0.019 ( 0.003 0.012 ( 0.003

tert-Butyl Alcohol 0.620 0.122 ( 0.041 0.083 ( 0.024 0.125 ( 0.017 0.466 ( 0.067 0.150 ( 0.023 0.036 ( 0.010 0.017 ( 0.011 0.006 ( 0.003 0.003 ( 0.002 0.001 ( 0.001

0.742 0.192 ( 0.057 0.115 ( 0.041 0.169 ( 0.031 0.339 ( 0.108 0.107 ( 0.023 0.029 ( 0.018 0.006 ( 0.005 0.002 ( 0.002 0.000 0.000

0.912 0.472 ( 0.203 0.143 ( 0.027 0.132 ( 0.081 0.152 ( 0.137 0.028 ( 0.028 0.000 0.000 0.000 0.000 0.000

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Figure 8. Fractions of linear and cyclic pentamer (tetramer, in the case of tert-butyl alcohol) clusters: (0) linear cluster; (O) cyclic cluster.

coefficients increased linearly at regions of lower xCO2, but increased rapidly for xCO2 > 0.6. The trend in the diffusion coefficient for CO2-methanol at 50 °C was similar to that reported in the literature (Shukla et al.41 and Aida and Inomata34). Both self-diffusion coefficients decreased with increasing alkyl chain length. Comparing compounds of equal molecular weight, the self-diffusion coefficients for branched alkyl alcohols were higher than those for normal alkyl alcohols. From the results of Figure 3, the motility of the alcohol molecules increased when the partial molar volume was small. On the other hand, the partial molar volumes of CO2 molecules were almost the same. The larger partial molar volume of the alcohol molecule hampers and reduces the motility of the CO2 molecule. To analyze the orientation of the other atoms around CO2, we calculated radial distribution functions (RDF). Figure 5 shows the (a) methanol oxygen-methanol oxygen RDF (gO-O(r)) and the (b) methanol oxygen-methanol hydrogen RDF (gO-H(r)) for pure methanol and at xCO2 ) 0.622. The gO-H(r) did not include intramolecular hydrogen in the next sentence. The maximum peaks were positioned at 2.7 Å in gO-O(r) and at 1.7 and 3.3 Å in gO-H(r), respectively. These peaks appeared for all conditions and mixtures, and their positions were related to the hydrogen-bond structure. Shilove et al. have pointed out that the angle between oxygen-oxygen alignment and the oxygen-hydrogen bond (θO-OH) was almost

distributed below 30° during hydrogen bond formation.42 We defined the molecule pairs forming hydrogen bonds using the following three assumptions: the oxygen-oxygen distance is less than 3.5 Å, the oxygen-hydrogen distance is less than 2.6 Å, and the angle θO-OH is below 30°. Many researchers have also adopted this angular assumption.43-47 In light of the above, the calculated average number of hydrogen bonds per alcohol molecule (nHB) is presented in Figure 6. Alkyl chain length had no influence on the nHB. However, the nHB for branched alkyl alcohols was smaller than that for normal alkyl alcohols. Isopropyl alcohol and tert-butyl alcohol each had a steric hindrance near the hydrogen bond so that the hydrogen bonds of branched alkyl alcohols were easier to break than those of normal alkyl alcohols. We also calculated the cluster-size distributions (fn) for hydrogen-bonded networks of size n (n ) 1, 2, 3,...) as shown in Figure 7 and Table 4. The fraction of pentamers tended to be highest for all alcohols except in tert-butyl alcohol in which the tetramer was highest. The tendency for the pentamer or tetramer fraction to be highest can be understood from the results of studies on pure methanol (Wallen et al.48) and pure tertbutyl alcohol (Sassi et al.49). The pentamer or tetramer fraction increased when xCO2 increased, especially when xCO2 was greater than 0.6. Breaking down a large-size hydrogen bond network into monomers may require steps via pentamers or tetramers.

Volume Expansion of CO2-Alcohol Mixtures at 40 °C The fractions of linear and cyclic pentamers/tetramers are shown in Figure 8. As xCO2 increased, cyclic pentamer clusters tended to increase while linear clusters decreased. With the exception of methanol, the fraction of cyclic pentamers was always higher than that of linear pentamers. For methanol, the fraction of cyclic pentamers was higher at xCO2 > 0.4. At regions of lower xCO2, alcohols made large hydrogen bond networks and CO2 molecules were allocated in the free spaces of those networks. With further addition of CO2 molecules, these spaces were filled to capacity and it became difficult to contain them in the large hydrogen bond networks. So the large hydrogen bond networks changed to cyclic pentamers, and volume expansion occurred. For tert-butyl alcohol, the cyclic tetramer fraction tended to decrease while the linear tetramer increased with increasing xCO2. Nevertheless the fraction of cyclic clusters was always higher. The number of cyclic tetramers was highest with pure tert-butyl alcohol. When maintenance of the cyclic tetramer became difficult, these clusters changed to monomers and the volume expanded. Although these phenomena might have occurred for isopropyl alcohol, which also has steric hindrance, we could not see the effect in this study. We suggest that the mechanism of volume expansion for tert-butyl alcohol is different from that for other alcohols measured in this study. 4. Conclusions In this paper, we showed that the relation between volume expansion and xCO2 were connected to the hydrogen bond network. The average number of hydrogen bonds per alcohol molecule was unaffected by alkyl chain length but decreased with the presence of branched methyl groups. A large number of CO2 molecules dissolved in branched alkyl alcohols at lower pressure because there is more occupied volume in the branched alkyl alcohols than in the normal alkyl alcohols. Large-size hydrogen-bond networks changed into cyclic pentamers or tetramers. Volume expansion accompanied these changes in hydrogen bond networks. References and Notes (1) McLeod, M. C.; Kitchens, C. L.; Roberts, C. B. CO2-expanded liquid deposition of ligand-stabilized nanoparticles as uniform, wide-area nanoparticle films. Langmuir 2005, 21, 2414–2418. (2) Reverchon, E. Supercritical antisolvent precipitation of micro- and nano-particles. J. Supercrit. Fluids 1999, 15, 1–21. (3) Chamblee, T. S.; Weikel, R. R.; Nolen, S. A.; Liotta, C. L.; Eckert, C. A. Reversible in situ acid formation for b-pinene hydrolysis using CO2 expanded liquid and hot water. Green Chem. 2004, 6, 382–386. (4) Bothun, G. D.; White, K. L.; Knutson, B. L. Gas antisolvent fractionation of semicrystalline and amorphous poly(lactic acid) using compressed CO2. Polymer 2002, 43, 4445–4452. (5) Mingotaud, A. F.; Be`gue, G.; Cansell, F.; Gnanou, Y. Free-radical polymerization of styrene in CO2/ethanol mixed supercritical fluid. Macromol. Chem. Phys. 2001, 202, 2857–2863. (6) Xu, Q.; Han, B.; Yan, H. Precipitation polymerization of methyl methacrylate in tetrahydrofuran with compressed CO2 as antisolvent. J. Appl. Polym. Sci. 2003, 88, 2427–2433. (7) Musie, G.; Wei, M.; Subramaniam, B.; Busch, D. H. Catalytic oxidations in carbon dioxide-based reaction media, including novel CO2expanded phases. Coord. Chem. ReV. 2001, 219, 789–820. (8) Nishi, K.; Morikawa, Y.; Misumi, R.; Kaminoyama, M. Radical polymerization in supercritical carbon dioxides use of supercritical carbon dioxide as a mixing assistant. Chem. Eng. Sci. 2005, 60, 2419–2426. (9) Kordikowski, A.; Schenk, A. P.; Van Nielen, R. M.; Peters, C. J. Volume expansions and vapor-liquid equilibria of binary mixtures of a variety of polar solvents and certain near-critical solvents. J. Supercrit. Fluids 1995, 8, 205–216. (10) Adrian, T.; Maurer, G. Solubility of carbon dioxide in acetone and propionic acid at temperatures between 298 and 333 K. J. Chem. Eng. Data 1997, 42, 667–672.

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