Coarse-Grained Model for Perfluorocarbons and Phase Equilibrium

Jul 26, 2010 - State Key Laboratory of Materials-Oriented Chemical Engineering, College ... data, the GEMC simulation based on the CG model satisfacto...
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Ind. Eng. Chem. Res. 2010, 49, 8271–8278

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Coarse-Grained Model for Perfluorocarbons and Phase Equilibrium Simulation of Perfluorocarbons/CO2 Mixtures Qiu Du, Zhen Yang, Nannan Yang, and Xiaoning Yang* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, China

A coarse-grained (CG) model for perfluorocarbons (PFCs) with arbitrary chain length has been established in this work. The construction of the CG model is based on the all-atomic (AA) simulation results and the thermodynamics experimental data. The intramolecular parameters are obtained through reproducing the intramolecular bond and angle distributions from AA simulations. The intermolecular parameters are determined by fitting the experimental bulk densities and surface tensions. Comparison between the CG and AA simulations has confirmed that the CG model can reasonably represent the structure behavior of PFCs. Furthermore, the CG model has been also extended to simulate the vapor-liquid phase equilibria for the mixture of PFCs and carbon dioxide by using the Gibbs ensemble Monte Carlo (GEMC) method. As compared with the experimental data, the GEMC simulation based on the CG model satisfactorily reproduces the mixture phase equilibria. The developed CG model will be useful in simulating the self-assembly of PFC-based surfactants/blockpolymers in supercritical carbon dioxide fluid. 1. Introduction Perfluorocarbons (PFCs) are the petroleum-based compounds synthesized by substitution of hydrogen atoms of hydrocarbons by fluorine atoms. PFCs are chemically and biochemically inert because of their strong intramolecular interactions and weak intermolecular interactions.1 The atypical properties of PFCs make them extremely interesting in extensive fields.2-4 Presently, the PFC-based surfactants have potential applications5-8 in supercritical carbon dioxide (scCO2) fluid. On the other hand, block copolymers using fluoropolymers have also been commonly used as surfactants in scCO2 fluid.9-11 In particular; scCO2 fluid medium is particularly suitable for fluoropolymer synthesis.5 Theoretical and experimental studies12-14 have been carried out to elucidate the underlying mechanism of interactions between the fluorinated carbon chains and the CO2 molecules, which is the key factor for determining the special CO2-philicity of the fluorinated surfactants/polymers. However, there are still some controversies over whether there exists a specific interaction between the fluorinated groups and CO2 molecules. The molecular-level understanding of phase behavior and selfassembly structure of PFC based surfactants or polymers in scCO2 will help to clarify the complex mechanism and to develop new CO2-compatible surfactants.15 As a powerful complementary analysis tool, computer simulation approach can offer deep insight into the fundamental properties of various materials in different environments. However, it is not feasible to directly perform the all-atomic (AA) simulation for surfactant/polymer systems because of larger time and length scales, which often require enormous computational resources. Alternatively, various coarse-grained (CG) models have been developed to investigate large and complex systems with similar accuracy but less computational cost. In CG models, several neighboring atoms and monomers or even a whole chain is reasonably represented by one simple interaction site with an effective interaction potential.16 For surfactant/polymer systems, it has been suggested that CG * To whom correspondence should be addressed. E-mail: yangxia@ njut.edu.cn.

models can be successful and more efficient relative to AA models. For example, Marrink et al. developed a robust CG model17,18 (called MARTINI force field) to study the spontaneous aggregation of DPPC lipids into small unilamellar vesicles and bialyers;19-22 and subsequently the force field was also extended to proteins and carbohydrates.23,24 Compared to AA models, a considerable reduction in time scale can be achieved by 3-4 orders of magnitude by using CG models.17 Klein et al.25-28 developed a set of CG models for phospholipids, which has been used to explore the behavior of biomembrane selforganization and structure transformations of protein in complex fluids and biological systems. Lipowsky et al.29 successfully studied the self-assembly of surfactant molecules into bilayer membranes by using a CG model. To the best of our knowledge, no relevant CG model for fluorinated alkanes has been developed so far. Therefore, the main purpose of this study is to establish an appropriate CG model for PFC molecules, which can be transferred into the self-assembly simulation of fluorinated amphiphiles in scCO2 fluid. In this work, the previous construction strategy of the CG model30 was used. In the first step, the whole PFC molecule is reasonably partitioned into larger CG structure units to reduce the system complexity. The second step is to construct an effective force field to describe the interactions between the CG units. In this respect, the intramolecular parameters of the CG model are obtained through reproducing the AA molecular dynamics (MD) simulation results, and the intermolecular parameters are determined by fitting the experimental densities and surface tensions of PFCs. We further extended the CG model of PFC to the scCO2 fluid mixtures. The experimental vapor-liquid phase equilibrium of C6F14/CO2 mixture is used to adjust the compatibility between the PFC and CO2 molecules in the mixture model. Finally, we employ the CG model to study a series of vapor-liquid phase equilibria of various chain length PFC molecules in scCO2. 2. CG Model 2.1. Construction. In the CG representation for PFCs, we group three consecutive backbone carbon atoms along with their

10.1021/ie100935u  2010 American Chemical Society Published on Web 07/26/2010

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Figure 1. Illustration of the coarse-graining construction. For C9F20, the molecule is reduced to an effective chain of three CG sites. Carbon dioxide is represented by a single Lennard-Jones bead.

fluorine atoms into a single CG site. In this manner, we have two CG particle types, CT (-CF2CF2CF3) and CM (-CF2CF2CF2-). PFCs with arbitrary chain length could be grouped in the following way.31 The quotient of carbon atom number in a PFC chain and three is rounded to the nearest integer, which is the number of CG sites. The scaling weight, m, of each CG site can be derived from dividing the carbon atom number by the CG site number. Then the PFC chain is divided uniformly. Starting at one end of the chain, the first group that represents m atoms is marked off as the first CG site; subsequently another group, representing m atoms, is labeled as the second site (see Figure 1). In this way, the PFC chain is represented explicitly. Note that the coordinates of each CG site are located by the center of mass of the backbone carbon atoms and their fluorine atoms. Development of the CG model generally has two principle stages: (1) selection of proper potential forms and (2) parametrization.30 In the CG representation, the interacting sites are physically larger than those of the AA model and hence we need a potential with wider well.27 Accordingly, the non-bonded interactions among CG sites are described with a Lennard-Jones 9-6 potential, V(rij) )

27 ε [(σ /r )9 - (σij /rij)6] 4 ij ij ij

(1)

where εij is the well-depth parameter and σij is the van der Walls (vdW) diameter. rij is the distance between site i and j. Consecutive CG sites in a molecule are bonded by the harmonic potential, Vbond(rij) ) kb(rij - r0)2

(2)

where the equilibrium bond distance is denoted by r0, and kb is the bond force constant. The bond angle between three consecutive sites in a molecule is described by the following potential, Vbend(θijk) ) kθ(θ0 - θijk)2

(3)

where θijk is the bond angle formed by the three sites i, j, and k. θ0 is equilibrium angle and kθ is the bond angle force constant. In the present CG model, the torsional component is not considered.

Briefly, after grouping CG sites and selecting the effective potential forms, the CG model parameters could be obtained by reproducing selected target observables, which are either from experiments or from AA simulations of corresponding species.32 In this work, the intramolecular potential parameters of the CG model were obtained by matching the bond length and bond angle distributions of AA simulations. The intermolecular potential parameters were obtained by fitting the experimental values of bulk densities and surface tensions of PFCs. 2.2. Intramolecular Parameters. It is generally accepted that the intramolecular parameters are nearly independent of intermolecular ones,31 so the initial intermolecular parameters are assigned a set of approximate values based on experience (σCT ) 5.5 Å, εCT ) 0.40 kcal/mol). Once the intramolecular parameters are obtained, the intermolecular ones could be determined by fitting the experimental data. When this process is accomplished, the intramolecular parameters should be checked to see whether there are some pronounced changes. Frequently, slight adjustments are needed. The details of parametrization are introduced in the following section. The bond length and bond angle distributions are first generated from the AA simulations. For example, the bond stretching parameters r0 and kb for CT-CT bond are determined by reproducing the bond length distribution from the AA simulation of the bulk C6F14 phase. Similarly, the bond parameters for CT-CM and CM-CM bonds are obtained from the AA simulations of C9F20 and C12F26, respectively. The CT-CM-CT bending parameters are also determined by the bond angle distribution of C9F20. The CT-CM-CM and CM-CM-CM bending parameters are obtained in the same manner. 2.3. Intermolecular Parameters. For the non-bonded parameters, we begin with the C6F14 molecule to determine the parameters of CT sites. The target data is taken from the experiments of Caco and co-workers.33 The σCT and εCT parameters are adjusted until the MD simulations satisfactorily reproduce the experimental bulk densities and surface tensions, respectively. By tradition the size parameter is adjusted until the deviation between the CG simulation and experimental surface tension is smaller than 2 dyn/cm.27 The next step is to find out the non-bonded interaction parameters σCM and εCM based on the experimental data of C9F20, where the LorentzBerthelot (L-B) mixing rules34 were used for the cross terms. To treat PFC chains with arbitrary length, a scaling treatment for the CG parameters has been adopted.31 The scaling is done on perfluoroalkanes C3nF6n+2 to model perfluoroalkanes C3n(1F6n(2+2, where n is the CG site number. For example, the parameters for C6F14 are scaled to model C7F16, and the parameters for C9F20 are scaled to model C8F18. Generally speaking, the mass of site is modified by a scaling factor of 1 ( 1/3n; the equilibrium bond length is scaled by 1 ( 1/3n while the bond force constant is scaled by 1 - 1/3n. Furthermore, the ε parameters are multiplied by 1 ( C1/3n, while the σ parameters are multiplied by 1 ( C2/(3n)2. The scaling coefficients, C1 and C2, are determined until a reasonable agreement is achieved between the CG simulations and experiments for the bulk densities and surface tensions of C7F16 and C8F18. To calculate the surface tension, we first constructed a slab with PFCs located at the center of the simulation box in the NVT ensemble, which had an enough box length in the z-direction.35 This setup yields two air-PFC interfaces. Then the box was divided into Nsl equal slabs parallel to the xy plane.

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The local normal (Pn) and tangential (Pt) components of pressure tensor in individual slab z (z ) 1, 2, ..., Nsl) are given by36 Pn(z) ) kBT〈F(z)〉 -

1 Vsl

〈

(z)

z2ij dU(rij) dr ij

∑r (i,j)

〉

(4)

and Pt(z) ) kBT〈F(z)〉 -

1 2Vsl

〈

(z)

∑ (i,j)

x2ij + y2ij dU(rij) rij dr

〉

(5)

where 〈F(z)〉 is the average density in slab z, 〈〉 denotes an ensemble average, Vsl is the volume of the slab, and U(r) is the intermolecular potential. ∑(z) (i,j)means that the summation runs over all pairs of particles (i, j) of which at least one of the particles is situated in slab z. The surface tension, γ, is calculated according to the following formula,37 γ)

1 2

∫

Lz

0

dz [Pn(z) - Pt(z)]

(6)

where the first factor of 1/2 appears since there are two interfaces in the simulation box, Lz is the box length along the z-direction. 2.4. Interaction Parameters with CO2. To simulate the mixtures of PFCs and CO2, the interaction parameters between them must be determined. In this work, a single point model38 was used for CO2 molecules. It has been demonstrated by Sennapat et al.39 that this single-point model gives the same performance as the sophisticated EPM2 model40 in the description of the pressure density dependence of scCO2 fluid. To better describe the interactions, the conventional L-B mixing rules are corrected using the following equations, 1 σij ) (σi + σj), 2

εij ) ξ√εiεj

(7)

In the CG model, the cross-parameters of σij are simply calculated using the arithmetic mean, while for the εij parameters, it might be inadequate to describe the interactions for the unsymmetrical mixtures directly using the conventional L-B mixing rule. Therefore, a correcting coefficient ξ which controls the miscibility41 is introduced in eq 7. The coefficient ξ was determined by fitting the corresponding vapor-liquid phase equilibrium data for C6F14/CO2 system.42 2.5. Simulation Procedures. AA Simulation. We used the AA potential model for PFCs from the work of Watkins and Jorgensen.43 The atomic MD simulations of each PFC bulk phase were carried out in the NPT ensemble with application of the Nose-Hoover thermostat for maintaining the constant pressure and temperature. The periodic boundary conditions were employed in all three directions. Newton’s equation of motion was integrated using the velocity Verlet algorithm with a time step of 2 fs. The electrostatic interactions were calculated using the Particle Mesh Ewald method with a real-space cutoff of 9.0 Å and a tolerance of 10-8. The truncation length for the vdW interactions was 12.0 Å. Simulations were performed under the pressure of 1.0 atm, while the simulation temperatures were chosen ranging from 298.15 to 403.15 K to maintain the PFC bulk phase in the liquid state. At each run, the first 500 ps was for equilibration and the next 300 ps for the production stage. Furthermore, the atomic MD simulations for the mixture system with a single PFC AA molecule and 1000 CO2 molecules were implemented in the NPT ensemble at 323.15 K and

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pressures ranging from 6.0 to 9.0 MPa. Duration of 8.0 ns simulation was used for equilibration stage and 0.5 ns for production. CG Simulation. CG dynamics simulations were run with 700-1000 molecules for various PFC systems (from C6F14 to C15F32). Bulk phase systems were modeled in the NPT ensemble with the same conditions as for the AA simulations. The time step in the CG simulation was set to be 10.0 fs and the vdW interactions were truncated at 14.0 Å. For the vacuum-liquid slab systems, simulations were carried out in the NVT ensemble. The box length in z-direction was 700.0 Å while the length in the x- and y- directions was about 70.0 Å. The CG simulations can be usually run for 20-30 ns in the equilibrium step. The production run was conducted for 0.5 ns in the bulk phase, whereas 6.0 ns for the slab system. Additionally, the CG simulations for the mixture system with a single PFC molecule and 1000 CO2 molecules were run for a period of 60.0 ns in the equilibration stage and 0.5 ns for the production run. GEMC Simulation. The NPT Gibbs ensemble Monte Carlo (GEMC)44,45 simulations were performed for the mixtures of PFCs and CO2 at various temperatures and pressures. In the simulations, two cells were simultaneously simulated: one cell represents the PFC-rich liquid phase and the other cell for CO2rich gas phase. The total number of molecules was fixed, but molecules could be transferred from one cell to another. The volume of the two simulation cells is allowed to fluctuate to maintain the desired pressure. In the GEMC ensemble, the number of CO2 molecules in each simulation changes from 1200 to 3000, while the number of PFC molecules ranges from 70 to 800, depending on various concentrations. Four types of trial moves46 were conducted randomly in this simulation: translation, rotation, transfer between the two cells, and volume change in the bulk phase cell. For the first two types of moves, the molecule number in each phase is fixed and a randomly chosen molecule is moved. The acceptance probability is determined by the common Metropolis criterion.47,48 In these systems, the configuration-biased MC method49 was used for the molecule

Figure 2. Comparison of the bond length distributions obtained from CG and AA simulations. (a) CT-CT units of C6F14, (b) CT-CM units of C9F20, and (c) CM-CM units of C12F26.

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Ind. Eng. Chem. Res., Vol. 49, No. 17, 2010 Table 3. Potential Parameters of the CG Model for PFCsa Bond Parameters sites

kb (kcal/mol · Å2)

r0 (Å)

CT-CT CT-CM CM-CM

84.2 148.6 85.3

4.50 4.23 3.97

Bend Parameters sites

kθ (kcal/mol · rad2)

θ0 (deg)

CT-CM-CT CT-CM-CM CM-CM-CM

40.6 46.5 69.7

164.6 162.4 161.2

Lennard-Jones Parametersb sites

ε (kcal/mol)

σ (Å)

CT CM

0.5220 0.4023

5.20 5.65

a The Lennard-Jones CT-CM parameters are determined by the L-B mixing rules. b Interactions between CO2 are described using LJ 12-6 potential, while the rest interactions are all described using LJ 9-6 potential.

the CG probability distributions of PFCs are unimodal, which is consistent with the result of alkanes.31 This consistency suggests that the intramolecular CG parameters can reasonably capture the main intramolecular structure characteristics. Tables 1 and 2 list the comparisons of the bulk phase densities and surface tensions between the experimental data and the CG simulations, in which the experimental data for C6F14 and C9F20 were applied to determine the non-bonded parameters of CT and CM units in the PFC molecules. On the other hand, the experimental data for C7F16 and C8F18 were used to obtain the scaled parameters for C3n(1F6n(2+2 molecules, which are 0.9 for C1 and 1.20 for C2 in the scaling formula. As listed in Tables 1 and 2, there is a good agreement between the CG simulations and experimental results, with the mean deviation about 2% for densities and 4% for surface tensions. All obtained intramolecular and intermolecular interaction parameters for PFCs are given in Table 3. With the purpose of checking whether the CG model can represent the bulk phase structure of PFC molecules, we have compared the corresponding radial distribution functions (RDFs) between the AA and CG simulations for PFCs with different chain lengths. As shown in Figure 4a, there are two peaks in the RDFs of C6F14, where the first peak locates at 5.90 Å and the second at 10.60 Å. The peak positions agree well

Figure 3. Comparison of the bond angle distributions obtained from CG and AA simulations. (a) CT-CM-CT units of C9F20, (b) CT-CM-CM units of C12F26, and (c) CM-CM-CM units of C15F32.

creation/deletion during the transfer move between the two cells. Periodic boundary conditions were implemented in all three dimensions. The cutoff length used here for the calculation of the site-site interactions was 12.5 Å. Typical simulation run consists of 3 × 104-4 × 104 cycles with 1000 moves per cycle. The first 2 × 104 cycles were used for the equilibrium step, and the rest cycles were used to determine the equilibrium properties. 3. Results and Discussions We have developed the CG model for PFCs by reproducing the selected observables, which include the intramolecular bond probability distributions from the atomic simulation, and the experimental bulk density and surface tension data. The comparisons of the bond length distributions as well as the bond angle distributions between the AA and CG simulations are shown in Figures 2 and 3, respectively. We can see from these figures that the CG results show an excellent agreement with those of the AA model. As the finer structure details are averaged out,

Table 1. Comparison of Liquid Densities for PFCs between the Experiments and CG Simulationsa C6F14

a

C7F16

C8F18

C9F20

T/K

Fexp

Fsim

Fexp

Fsim

Fexp

Fsim

Fexp

Fsim

288.15 298.15 303.15 313.15

1.7023 1.6775 1.6625 1.6317

1.6898 1.6738 1.6635 1.6383

1.7553 1.7283 1.7145 1.6865

1.7334 1.7103 1.6968 1.6766

1.7902 1.7648 1.7519 1.7258

1.7799 1.7692 1.7595 1.7515

1.8122 1.7879 1.7757 1.7509

1.8307 1.8164 1.8114 1.8048

Fexp and Fsim correspond to density from experiment and simulation respectively. Density term is in g/cm3.

Table 2. Comparison of Surface Tensions for PFCs between the Experiments and CG Simulationsa C6F14

a

C7F16

C8F18

C9F20

T/K

σexp

σsim

σexp

σsim

σexp

σsim

σexp

σsim

288.15 293.15 298.15 303.15

12.50 11.83 11.36

12.31 11.43 11.13

13.60 13.08 12.58 11.97

12.61 11.96 11.70 10.75

14.48 13.94 13.54 12.88

13.34 12.24 12.05 11.93

15.22 14.74 14.14 13.71

15.08 14.63 14.18 13.56

σexp and σsim correspond to surface tension from experiment and simulation, respectively. Surface tension term is in dyn/cm.

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Figure 6. Vapor-liquid phase diagram for C7F16/CO2 mixture at 353.15 K. In each panel, the red cycles are for the calculation results based on the SAFT-VR equation of state and the blue line for simulation results.

Figure 4. Comparison of the RDFs for different units of (a) C6F14, (b) C9F20, and (c) C12F26 obtained from CG and AA simulations. The CG units involved are mentioned in the figure. The CT-CM and the CT-CT curves are offset vertically by one and two units, respectively, for clarity.

Figure 7. Vapor-liquid phase diagram for C8F18/CO2 mixture at (a) 293.15 K, and (b) 323.15 K. Symbols are same as in Figure 5.

Figure 5. Vapor-liquid phase diagram for C6F14/CO2 mixture at (a) 314.65 K, and (b) 353.25 K. In each panel, the red cycles are for the experimental data and the blue lines for simulation results.

between the AA and the CG simulations. It should be noted that some discrepancies can be observed between both simulations. For example, the first peak from the CG simulation is slightly higher than that from the AA simulation and the second peak from the CG data is a little wider. The similar comparisons of the RDFs between C9F20 and C12F26 are shown in Figures 4b and 4c. The present results advise that the CG model can reproduce the main features of PFC molecules. To demonstrate the compatibility of our CG model with scCO2 molecules, the vapor-liquid phase equilibria for binary mixtures of PFCs and CO2 were simulated by using the GEMC method. Figure 5a shows the simulated phase diagram for the C6F14/CO2 mixture at 314.65 K from the CG simulation together with the experimental data from Lezzi et al.42 In the simulation, the coefficient ξ in the corrected L-B mixing rules (eq 7) was found to be 0.82 by fitting the phase equilibrium of C6F14/CO2 mixture.

Satisfactory agreement is observed between the simulated and experimental phase coexistence curves, which separate the single-phase region from the two-phase region and typically end in the critical point of mixture. On the gas-phase branch of coexistence curve, the solubility of C6F14 in CO2 from simulation is relatively low, in agreement with the corresponding experimental results. On the liquid branch of the phase diagram, the mole fraction of CO2 from the simulation usually agrees well with the corresponding experimental data when the pressure is below 5.0 MPa. However, as the pressure increases, the simulation underestimates the CO2 mole fraction with the average relative deviation of 5%. The largest deviation occurs at 7.0 MPa, where the mole fraction of CO2 from the simulation is about 8% lower than the experimental data. Since the interaction parameters between the PFCs and the CO2 molecules have been obtained, we can directly use the current CG model to predict the phase behavior of any PFC/ CO2 system. Figure 5b shows the comparison of the simulated phase diagram with the experimental data42 for C6F14/CO2 system at a higher temperature of 353.25 K. Similar agreement is obtained for the phase diagram between the simulation and experiment. Figure 6 shows the comparison for C7F16/CO2 at 353.15 K between the molecular simulation and the calculation results based on the SAFT-VR equation of state.50 Although the simulation slightly overestimates the CO2 mole fraction on the liquid-phase branch as compared with the theoretical calculation, reasonable agreement is still observed between them. We have also made a comparison for the mixture of C8F18/ CO2 at 293.15 and 323.15 K. The simulated results along with the corresponding experimental data51 are shown in Figure 7, where only the liquid phase experimental data is available. The CG simulations have given a reasonable prediction not only for the solubility of CO2 molecules in the liquid phase branch,

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Figure 8. Comparison of RDFs for CT-CO2 units in C6F14/CO2 systems obtained from CG and AA simulations at (a) 6.0 MPa, (b) 7.0 MPa, and (c) 8.0 MPa.

but also for the variation trend in the gas-phase branch. As compared with the mixture of C6F14/CO2 system, the solubility of C8F18 in the gas phase region is lower, suggesting the solubility of PFCs in the CO2 phase decreases with the carbon atom number increasing. Although relatively larger differences appear at higher-pressure conditions, the simulated composition in the liquid phase branch is qualitatively in good agreement with the experimental data. The larger deviation at higher pressures may be ascribed to the effect of finite system size in the simulation cell, which becomes more serious as the critical point is approached.52 Another reason may arise from an inadequacy of this scaling treatment in the present CG model. The simple interaction site model in the CG approach can rationally reproduce the miscibility for PFC-CO2 and reflect the interactions between the PFC and CO2 molecules. Moreover, MD simulations, using both the CG and the AA models, were carried out to compare the solvation structure of CO2 molecules around the PFC molecule, which can be represented by the pair RDFs. Figure 8 shows the obtained RDFs at different pressures between CO2 and CT sites in the C6F14/CO2 system. There are always a high and sharp peak locating at 5.1 Å and a low and wide peak at 9.1 Å. Although the first peak height of the RDFs from the CG simulation is usually lower than that from the AA simulation, the overall solvation position in the RDFs agrees well between the two simulation methods. The difference of the first RDF peak height between the CG and the AA simulations may be attributed to the different mixture interaction strengths in the two simulation approaches. Because the coefficient ξ in the CG simulation was obtained by fitting the phase equilibrium data of C6F14/CO2 system, this coefficient should reasonably reflect the interactions between the PFC and the CO2 molecules. Therefore, this RDF comparison implies that the interaction parameter between PFC and CO2 in the AA model, only from the simple L-B mixing rule, is somewhat overestimated, which may lead to an enhanced solvation degree in the AA simulation, as compared with the result from the CG simulation. The corresponding RDFs of CT-CO2 and CM-CO2 for C9F20 in the scCO2 fluid at the pressures ranging from 7.0

Figure 9. Comparison of RDFs for CT-CO2 units at (a) 7.0 MPa, (b) 8.0 MPa, (c) 9.0 MPa; and CM-CO2 units at (d) 7.0 MPa, (e) 8.0 MPa, (f) 9.0 MPa in C9F20/CO2 systems obtained from CG and AA simulations.

Figure 10. Prediction for the vapor-liquid phase diagrams for several CnF2n+2/CO2 mixtures at 323.15 K. The inset shows the expanded curves on the gas-phase branches.

to 9.0 MPa are given in Figure 9. Similar agreement for the systems between the two simulations is obtained. According to the above results, the CG model can reasonably represent the temperature dependence of various available experimental data, even though, in the CG simulation, the intramolecular and intermolecular parameters were considered to be temperature independent. This treatment is consistent with the fact that the Lennard-Jones well depths in condensed phase are typically independent of temperature.31 Although limited experimental data precludes a further test of the CG model, the current results still show that the CG model can capture the critical properties and structures of PFC molecules and the corresponding PFC/CO2 mixtures within relatively wide temperature and pressure ranges. To further evaluate this CG model, the high-pressure phase equilibria for several long-chain PFCs in dense CO2 have been simulated. Figure 10 gives the predicting phase diagrams from the CG simulations for C12F26 and C13F28 in CO2 fluid at 323.15 K. For comparison, the results for C6F14/CO2, C8F18/CO2, and C9F20/CO2 systems are also provided. Presently, as far as we know, no experimental phase equilibrium data is reported for the longer chain PFCs in scCO2, and thus a comparison between relevant simulation and experiment is not possible at this time.

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As shown in Figure 10, the obtained qualitative behavior for the phase equilibria is similar with those observed for the shortchain PFCs (Figures 5-7). In the two-phase region, a very low solubility is found for the PFCs in the CO2 phase, whereas a definite solubility for CO2 molecules occurs in the PFC phase. It can be observed that the solubility of CO2 in different PFC molecules is very similar, which is qualitatively consistent with the experimental observation.51 A careful examination may suggest that, with the carbon atom number increasing, the equilibrium mole fraction of CO2 in the liquid phase branch increases. This is reasonable by considering the fact that the larger PFC molecule has more free space within its interior structure, promoting the solution of CO2 molecules. The gasphase branch in the phase diagram may represent the cloud point of the linear-perfluoroalkanes in the CO2 fluid. The PFC molecules always possess a very similar cloud point, and the expanded result (inset of Figure 10) shows that the solubility of PFC in the CO2 gas phase decreases with the PFC chain increasing, which suggests that larger PFC molecules have higher cloud point pressures. The results from the CG simulations are consistent with the previous experimental cloud point observations.53 4. Conclusions In this study, a CG model for PFCs has been developed. In the CG model, three consecutive backbone carbon atoms along with their associated fluorine atoms are mapped into one CG site. For perfluoroalkanes C3n(1F6n(2+2, the extra atoms are uniformly spread to each site, and a scaling relationship is introduced to extend the CG model to PFCs with arbitrary chain length. The intramolecular parameters were obtained by reproducing the intramolecular bond and angle distributions from atomic simulations. The intermolecular parameters were determined by fitting the experimental values of bulk densities and surface tensions for PFCs. Moreover, the vapor-liquid phase behavior for C6F14/CO2 mixture at 314.65 K was fitted by the GEMC simulation to obtain the interaction parameters between PFCs and CO2. The obtained CG model has been extensively tested by a series of molecular simulations. The RDFs of bulk PFCs from the CG simulations agree well with those from the AA simulations. Furthermore, the CG simulations reasonably reproduce the solvation structure of CO2 molecules around the PFC molecule by comparison with the AA simulations. A comparison of the vapor-liquid phase equilibria for PFCs/CO2 mixtures between the experimental data and the CG simulation has also been carried out, which shows that our CG model can reasonably describe the mixture phase behavior. Although there is no experimental phase equilibria data for long-chain PFCs, the predicted phase diagrams from the CG simulations give a reasonable trend. These results above confirm that the current CG model can be applied to fluorinated surfactants/polymers in scCO2 fluid in future work. Acknowledgment This study was supported by the National Natural Science Foundation of China under Grants 20776066 and 20976079, and the Natural Science Foundation from Jiangsu Province (BK2009359). Literature Cited (1) Dias, A. M. A.; Caco, A. I.; Coutinho, J. A. P.; Santos, L. M. N. B. F.; Pineiro, M. M.; Vega, L. F.; Gomes, M. F. C.; Marrucho, I. M. Thermodynamic Properties of Perfluoro-N-Octane. Fluid Phase Equilib. 2004, 225, 39.

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ReceiVed for reView April 21, 2010 ReVised manuscript receiVed June 27, 2010 Accepted July 15, 2010 IE100935U