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Molecular Dynamics Simulation of Diffusion and Structure of Some nalkanes in Near Critical and Supercritical Carbon Dioxide at Infinite Dilution Huajie Feng, Wei Gao, Zhenfan Sun, Bingxin Lei, Gaonan Li, and Liuping Chen J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp401824d • Publication Date (Web): 23 Sep 2013 Downloaded from http://pubs.acs.org on September 30, 2013

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The Journal of Physical Chemistry

Molecular dynamics simulation of diffusion and structure of some n-alkanes in near critical and supercritical carbon dioxide at infinite dilution Huajie Feng,† Wei Gao,‡ Zhenfan Sun,*† Bingxin Lei,† Gaonan Li,† Liuping Chen*‡ † School of Chemistry and Chemical Engineering, Hainan Normal University, Haikou 571158, P. R. China ‡ KLGHEI of Environment and Energy Chemistry, School of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China KEYWORDS diffusion coefficient at infinite dilution; near critical and supercritical carbon dioxide; flexibility; alkane; molecular dynamics simulation ABSTRACT The diffusion coefficients of n-alkanes (from CH4 to C14H30) in near critical and supercritical carbon dioxide at infinite dilution have been studied by molecular dynamics simulation. The simulation results agree well with experiment, which suggests that the simulation method is a powerful tool to obtain diffusion coefficients of solutes in fluids at high pressures. The local structures of such fluids are further investigated by calculating radial distribution functions and coordination numbers. Meanwhile, the dihedral, end-to-end distance and radius of gyration, which are calculated to characterize the flexibility of n-alkanes, are used

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to explain reasonably the abnormal trends on radial distribution functions and coordination numbers. Moreover, it is found that the flexibility effects on diffusion in pure n-alkanes and infinitely dilute n-alkane/CO2 system are different. The differences in MD simulation results of molecular diffusion in such systems could be qualitatively explained by the flexibility. 1. Introduction The diffusion coefficient at high pressures is very important for estimating the separation rate and designing separation processes. However, it is very difficult and expensive to determine diffusion data experimentally because of rigorous experimental condition required.1-3 The Taylor dispersion method was applied to determinate diffusion coefficients of various organic compounds in supercritical carbon dioxide (scCO2) and which were correlated with molecular parameters and viscosity of fluids by several empirical equations.4-10 At present, computer simulation has already become one of the most important methods for obtaining diffusion coefficients of fluids.11-14 Moreover, such simulations can provide detailed and valuable characteristic pictures of molecular structure at the atomic level.15-18 In recent years, there are lots of researches on the diffusion coefficient and local structures of supercritical fluids by molecular dynamics (MD) simulations. Iwai and Higashi et al.19-21 used MD simulation to calculate diffusion coefficients of several aromatic compounds in scCO2 at infinite dilution. Skarmoutsos and Samios22 studied the behavior of the binary supercritical mixture of methane and carbon dioxide with the mole fraction x=0.2 of methane using the pair radial distribution functions, local coordination numbers, mole fractions and time correlation functions by MD simulation. Zabala et al.23 computed diffusion coefficient in CO2/n-alkane(nC10, nC16, nC22, nC28, nC44) binary liquid mixtures by MD simulation.


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Additionally, scCO2 has unique properties24 and was applied in various fields, for example, as extraction solvent for natural plants, as reaction medium for organic synthesis and preparation of advanced materials,25-27 etc. The solubility of scCO2 could be drastically altered by slightly changing the density of the solvent.28,29 The solute-solvent interactions in scCO2 have been investigated by means of UV, vibrational spectroscopy, NMR spectroscopy and MD simulation.30-33 However, to the best of our knowledge, there are few studies on diffusion of n-alkanes in near critical and supercritical carbon dioxide at infinite dilution. In this work, a series of MD simulations were performed to achieve information of the diffusion and structures for n-alkane in CO2 at infinite dilution. The simulation results are compared with the known experimental data measured by Umezawa and Nagashima34 to validate our theoretical predictions. Finally, this work strives to clarify the correlations between flexibility and local structures, diffusion in those fluids based on the analysis of adequate data obtained from this study, and investigate the solvent effect of scCO2 on n-alkane solute over a wide density range of the solvent. 2. Methods Simulations were performed with the GROMACS 4.0.7 software.35 We applied OPLS-UA (Optimized Potentials for Liquid Simulation-United Atoms)36 for n-alkanes, and EPM2 (elementary physical model)37 force field for CO2. To achieve the infinite dilution concentration, the mass fraction of n-alkane does not exceed 1%. The molecular numbers of CO2 in the cubic simulation box were 4000, and the corresponding molecular numbers and concentrations of nalkanes were listed in Table 1. The cutoff distance of potential function was taken to be 1.4 nm. The long range electrostatic interactions were taken into account by means of the Particle-mesh Ewald summation. The periodic boundary conditions were employed for all the simulations. The


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time step was set to be 1 fs. Initially, runs of 3×106 time steps were taken to re-equilibrate the system, and then runs of 3×106 time steps were used to calculate the diffusion coefficients and structural properties. The MD simulation was performed in the NVT ensemble for calculating the diffusion coefficients and structural properties. The density is needed to determine the box size when conducting NVT ensemble simulation. Because the mass fraction of n-alkanes does not exceed 1%, the density of the simulated system almost equals to the density of pure CO2. Hence, we used the density of pure CO2 instead of the density of the simulated system, and the density data of CO2 used in the simulation were taken from NIST Chemistry WebBook.38 At 10.5 MPa, the densities of CO2 at 299 K, 308 K and 323 K are 0.81860 g/ml, 0.73153 g/ml and 0.44859 g/ml, respectively. 3. Results and discussion 3.1. Diffusion coefficients. The diffusion coefficient of a molecule in the fluid system is calculated from the long-time limit of the mean-square displacement (MSD) by the following equation. D = lim t →∞

[r (t ) − r (0)]2 6t

(1)

where r(t) is the position of a molecule at time t, and the average is carried out over the time origin for autocorrelation and over all the molecules as usual. The diffusion coefficients of n-alkanes (from CH4 to C14H30) in CO2 at 10.5 MPa obtained from MD simulation and the measured values34 are collected in Table 2, along with the relative deviations between the experimentally determined and simulated diffusion coefficients, and the average relative deviations is 7.5%. Generally, the simulation results agree well with experiment


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of diffusion. Thus, we can use this simulation method to get diffusion coefficients at high pressures, under which it is rather difficult to measure experimentally. In present work, we predict diffusion coefficients of CH4 to C4H10 and C13H28 in CO2 at 299 K and 308 K, along with those of CH4 to C14H30 in CO2 at 323 K, and the results are also listed in Table 2. In general, the diffusion coefficient of n-alkanes decreases fast with the increasing carbon chain for short-chain n-alkanes (n7 the coordination number of CnH2n+2 rapidly decreases possibly means that long-chain n-alkane (which possibly start to exhibit a “polymer-like” nature) prefer to interact with themselves rather than with CO2, and the solvent effect of scCO2 on long-chain nalkane solute is smaller than that on short-chain n-alkane solute. We believe this observation is caused by the flexibility of long-chain n-alkanes. The flexibility of a chain molecule is essentially determined by the rotational behaviors of the skeletal bonds and the intersegmental interactions. Free bond-rotation and weak intersegmental interactions would lead to greater flexibility. The flexibility varies markedly with carbon-chain


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length and temperature. Moreover, the flexibility is also affected by the solvent. First, we study the flexibility by calculating the distribution of dihedrals, which is plotted in Figure 3. From Figure 3, for short-chain n-alkanes, the largest peak heights are around -50° and 50°, while for long-chain n-alkane, the largest peak heights are around -180° and 180° at different temperatures. In other words, the dihedrals of short-chain n-alkanes mainly vary around -50° and 50°, while the dihedrals of long-chain n-alkane not only mainly vary around -50° and 50°, but also significantly extend to mainly vary around -180° and 180°. On the other hand, generally, the peak heights of an n-alkane at low temperature are higher than that of the corresponding n-alkane at high temperature. That is, the variation of the dihedrals of longer n-alkane at higher temperature is greater. Therefore, this variation trend shows that the flexibility increases with increasing carbon-chain length and increasing temperature, and it is similar to the trend that the flexibility of the polymer molecules increases with increasing temperature. 42,43 It is well known that the mean-square end-to-end distance and radius of gyration are usually adopted to evaluate the flexibility of the polymer molecule.42,44,45 Similarly, in this work, we use the end-to-end distance and the radius of gyration to characterize the flexibility of n-alkane molecules. The mean end-to-end distance and the mean radius of gyration of n-alkanes are calculated and plotted in Figure 4 and Figure 5, respectively. Obviously, the mean end-to-end distance and the mean radius of gyration both increase significantly with increasing carbon chain. Then, the distribution of the end-to-end distance is plotted in Figure 6. It is clear that the variation of the end-to-end distance of longer n-alkane is larger. That is, longer n-alkane has larger flexibility. On the other hand, the peak height generally decreases with increasing carbon chain. However, the peak height of n-C8H18 is higher than that of n-C7H16. In addition, the peak height of an n-alkane at low temperature is higher than that of the corresponding n-alkane at high


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temperature, and it means that n-alkane at higher temperature has larger flexibility. Similarly, the distribution of the mean radius of gyration is calculated and plotted in Figure 7. Obviously, the variation of the mean radius of gyration of longer n-alkane is larger, and it means that longer nalkane has larger flexibility. Generally, the peak height also decreases with increasing carbon chain. However, the peak height of n-C8H18 is lower than that of n-C9H20 at 299 K. At 308 K and 323 K, this abnormal phenomenon does not appear and it may be because the disparity of the flexibility of different n-alkanes reduces at high temperatures. Additionally, the peak height of an n-alkane at low temperature is higher than that of the corresponding n-alkane at high temperature, and it means that n-alkane at higher temperature has larger flexibility. In summary, the discontinuities around n-C8H18 observed in the distributions of the end-to-end distance and in the distributions of the mean radius of gyration could support the discontinuities in the coordination numbers. Furthermore, the time dependence of the mean end-to-end distance and the mean radius of gyration of n-alkanes are calculated and plotted in Figure 8 and Figure 9, respectively. In Figure 8, it is obviously that from C2H6 to n-C6H14, the fluctuation is very small, while for n-C7H16, the fluctuation suddenly becomes strong, and from n-C7H16 to n-C14H30, the mean end-to-end distance of n-alkanes fluctuates more and more strongly with increasing carbon chain. And the similar variation can be seen in Figure 9 for the mean radius of gyration. Also, in order to see the fluctuation of n-alkane molecules around the corresponding equilibrium state, the time correlation functions of the end-to-end distance and its corresponding correlation times for n-alkanes from n-C6H14 to n-C14H30 are calculated. The time correlation function is calculated using the relation: C (t ) =

< δα ( 0 ) ⋅ δα ( t ) > < δα ( 0 ) > 2


(3)

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where δα ( t ) = α ( t ) − < α > ( < α > is the mean value), the time correlation functions are calculated from 0 ps to 6000 ps, and the data are sampled once every 1 ps. The corresponding correlation time is given by the relation: ∞

τ = ∫ C (t )dt 0

(4)

We approximate the integral by the rectangle rule. In Figure 10, the correlation times of the end-to-end distance for n-C6H14 to n-C14H30 are plotted. Generally, the correlation time shows a trend of increase in twists and turns with increasing carbon chain, and it is similar to the increase trend of the coordination numbers for n-C6H14 to n-C14H30, so it could further support the abnormal trend of the coordination numbers. Although the flexibility increases with increasing carbon chain, the correlation time which characterizes the fluctuation of n-alkane molecules around the equilibrium state does not progressively increase with increasing carbon chain, and some other features of n-alkane molecules do as well. When the flexibility increases to a certain level, n-alkane molecules could show different features. Overall, the dihedral, end-to-end distance and radius of gyration show that the n-alkanes with longer chain at higher temperature has larger flexibility, then the center of mass of longer chain n-alkane molecules become more unstable, and it affects the local structure of first solvation shell. More importantly, for long-chain n-alkanes, the large flexibility causes abnormal trends on RDFs and coordination numbers. Usually, the amplitude for the first maximum of RDFs decreases with increasing temperature. However, the long-chain n-alkanes have large flexibility, hence it leads to the abnormality that the amplitudes for the first maximum of RDFs at 308 K are larger than that at 299 K for C6H14/CO2 to C14H30/CO2, and the amplitudes for the first maximum of RDFs at 323 K are larger than that at 308 K for C3H8/CO2 to C14H30/CO2, and the increment rate becomes larger and larger. On the other hand, the flexibility of long-chain n-alkanes affects


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the local structure of first solvation shell, so it affects the coordination numbers. In order to explain the abnormal trend of the coordination numbers, the diagram of the coordination numbers in the first solvation shell of n-alkanes is plotted in Figure 11. In Figure 11a, the nalkane molecules represent short-chain n-alkanes from CH4 to n-C7H16, while the n-alkane molecules represent long-chain n-alkanes from n-C8H18 to n-C14H30 in Figure 11b. As shown in Figure 11a, there are many CO2 molecules around the short-chain n-alkane. In Figure 11b, the flexibility of long-chain n-alkane is very large, and the long-chain n-alkane molecule is much curved. Therefore, the steric hindrance around the center of mass of molecule is large, and it makes the CO2 molecules move from the first solvation shell to the second solvation shell, then the coordination numbers in the first solvation shell of long-chain n-alkanes decreases, and it leads to the abnormality that the average coordination numbers of n-C8H18 to n-C14H30 are smaller. Conversely, the abnormal trends on RDFs and coordination numbers just reflect the flexibility effect. As mentioned above, the flexibility effects on diffusion behaviour in pure n-alkanes and nalkanes in CO2 at infinite dilution are different. For example, the relative deviations between the measured and simulated self-diffusion coefficients are 28.0% for n-C7H16 at 315 K and saturation vapor pressure,41 46.2% for n-C10H22 at 314 K and 5 MPa,41 respectively, while the relative deviations between the observed and simulated diffusion coefficients of n-C7H16 and n-C10H22 in CO2 at infinite dilution are −8.2% and −11.8% at 308 K and 10.5 MPa (Table 2). These differences in MD simulation results of molecular diffusion in such systems could be qualitatively explained by Figure 12. For pure long-chain n-alkane systems shown in Figure 12a, the flexibility of carbon chain is large, and the carbon chain tends to become curved and coiled together. So the long-chain n-alkanes exist actually in the coiled and aggregated state, which are


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greatly affected by temperature. Compared with low temperature, the simulated self-diffusion coefficients at high temperatures are more accurately, this indicated that increase in temperature can weaken these coiling and aggregating effects.41 Unfortunately, these effects result in complicated interactions among molecules on self-diffusion behavior of long-chain molecules, which can not be simulated exactly by the classical force field. Thus, how to simulate accurately self-diffusion in long-chain n-alkanes systems at high pressures is still a challenge. In Figure 12b, for n-alkane/CO2 systems at infinite dilution, each n-alkane molecule is surrounded with many CO2 molecules, namely, the long-chain n-alkane molecule exists as curved and isolated state rather than coiled and aggregated one, thus the solvent CO2 changes the local structure of n-alkanes by its flexibility. This work confirms that the OPLS force field is reliable to be used in MD simulation of n-alkanes in CO2 at infinite dilution, and its results agree well with experiment of diffusion. Moreover, it is concluded that the OPLS force field is valid to calculate diffusion coefficients for other long-chain molecules without coiling and aggregating effect. 4. Conclusions We have carried out MD simulations of n-alkanes (from CH4 to C14H30) in CO2 at infinite dilution. In general, the results of MD simulation agree well with experiment of diffusion, so it provides a simple method to get diffusion coefficients of solutes in near critical and supercritical condition, under which experimental determinations of diffusion data are rather difficult and time-consuming. In present work, we explored the local structures of n-alkane/CO2 systems. The dihedral, endto-end distance and radius of gyration show that the n-alkane with longer chain at higher temperature has greater flexibility. In addition, the discontinuities around n-C8H18 observed in


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the distributions of the end-to-end distance and in the distributions of the mean radius of gyration, along with the tortuous increase trend of the correlation time, could support the abnormal trend of the coordination numbers. The large flexibility leads to the abnormality that the amplitudes for the first maximum of RDFs at 308 K are larger than that at 299 K for n-C6H14/CO2 to nC14H30/CO2, and the amplitudes for the first maximum of RDFs at 323 K are larger than that at 308 K for C3H8/CO2 to n-C14H30/CO2, and the increment rate becomes larger and larger. On the other hand, the flexibility affects the local structure of first solvation shell, thus it leads to the abnormality that the average coordination numbers of n-C8H18 to n-C14H30 are smaller. In summary, although the flexibility increases with increasing carbon chain, some features of nalkanes does not progressively increase with increasing carbon chain. When the flexibility increases to a certain level, n-alkane molecules could show different features. It is found that the flexibility effects on diffusion behaviour in pure n-alkanes and n-alkanes in CO2 at infinite dilution are different. These differences in MD simulation results of molecular diffusion in such systems could be qualitatively explained by the flexibility. For pure long-chain n-alkane systems, it exist actually in the coiled and aggregated state that is yet affected by temperature, which can reduce these coiling and aggregating effects. However, for n-alkane/CO2 systems at infinite dilution, the long-chain n-alkane molecule exists as curved and isolated state, thus the solvent CO2 changes the local structure of n-alkanes by its flexibility. Just these coiling and aggregating effects lead larger errors in simulated self-diffusion coefficients for pure longchain n-alkanes. As for n-alkanes in CO2 at infinite dilution, the simulated diffusion coefficients agree well with measured values. In addition, this study also confirms that the OPLS force field is valid to calculate diffusion coefficients for other long-chain molecules without coiling and aggregating effect. And the present results provide deep insight into local structure and


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corresponding diffusion behavior of long-chain molecules, and are helpful for obtaining exact diffusion coefficients by MD method.

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Figure 1. The carbon chain dependence of RDFs between center of mass (alkane)-center of mass (CO2) at 10.5 MPa. (a) to (n) for CH4 to C14H30, respectively.

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C oordination num bers

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Figure 2. The average coordination numbers of n-alkanes in CO2 at 10.5 MPa.


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0.40

Mean radius of gyration / nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 32

0.35 0.30 0.25 0.20 0.15 0.10 0.05 2

4

6

8

10

12

14

CnH2n+2

Figure 5. The mean radius of gyration of n-alkanes at 10.5 MPa.


18

Page 19 of 32

70

(a) 299 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14


60 50 40 30 20 10 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

End-to-end distance / nm 70

(b) 308 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

60


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50 40 30 20 10 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

End-to-end distance / nm


19


70

(c) 323 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14


60 50 40 30 20 10 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

End-to-end distance / nm

Figure 6. The distribution of the end-to-end distance of n-alkanes at 10.5 MPa.

(a) 299 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

40


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

30

20

10

0 0.10

0.15

0.20

0.25

0.30

0.35

0.40



20

Page 21 of 32

(b) 308 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14


40

30

20

10

0 0.10

0.15

0.20

0.25

0.30

0.35

0.40

Mean radius of gyration / nm (c) 323 K

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

40


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30

20

10

0 0.10

0.15

0.20

0.25

0.30

0.35

0.40


Figure 7. The distribution of the mean radius of gyration of n-alkanes at 10.5 MPa.


21


mean end-to-end distance / nm

1.2

(a)

299 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

1.0

0.8

0.6

0.4

0.2 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns

1.2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

(b)

308 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

1.0

0.8

0.6

0.4

0.2 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns


22

Page 23 of 32


1.2

(c)

323 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

1.0

0.8

0.6

0.4

0.2 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns

Figure 8. The time dependence of the mean end-to-end distance of n-alkanes at 10.5 MPa.

0.40

mean radius of gyration / nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

299 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

0.35 0.30 0.25 0.20 0.15 0.10 0.05 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns


23



0.40

(b)

308 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

0.35 0.30 0.25 0.20 0.15 0.10 0.05 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns

0.40


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 32

(c)

323 K C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

0.35 0.30 0.25 0.20 0.15 0.10 0.05 3.0

3.5

4.0

4.5

5.0

5.5

6.0

t / ns

Figure 9. The time dependence of the mean radius of gyration of n-alkanes at 10.5 MPa.


24

Page 25 of 32

650

299K 308K 323K

600

The correlation time / ps

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


550 500 450 400 350 300 250 6

8

10

12

14

CnH2n+2

Figure 10. The correlation time of the end-to-end distance for n-alkanes at 10.5 MPa.

Figure 11. The diagram of the coordination numbers in the first solvation shell of n-alkanes. (a) the n-alkane molecules represent short-chain n-alkanes from CH4 to n-C7H16; (b) the n-alkane molecules represent long-chain n-alkanes from n-C8H18 to n-C14H30.


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

Figure 12. The diagram of the flexibility effect for long-chain n-alkanes. (a) pure n-alkanes; (b) n-alkanes in carbon dioxide at infinite dilution

Table 1. Molecular numbers n and concentrations c of n-alkane in different n-alkane/CO2 systems

Solute

n

c / %(wt)

CH4

110

1.00

C 2H 6

58

0.99

C 3H 8

40

1.00

C4H10

30

0.99

C5H12

24

0.98

C6H14

20

0.98

C7H16

17

0.97

C8H18

15

0.97

C9H20

13

0.95

C10H22

12

0.97

C11H24

11

0.98

C12H26

10

0.97

C13H28

9

0.94

C14H30

8

0.90


26

Page 27 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Comparison of measured and simulated diffusion coefficients of n-alkanes in CO2 at infinite dilution at 10.5 MPa (number (CO2)=4000) in 10−9m2·s−1a

299 K

308 K

323 K

n-alkane

a

Exp.

MD

Error/%

Exp.

MD

Error/%

MD

CH4

-

27.2

-

-

32.8

-

69.1

C 2H 6

-

21.9

-

-

26.0

-

59.7

C 3H 8

-

19.7

-

-

21.8

-

46.7

C4H10

-

15.8

-

-

19.0

-

38.9

C5H12

13.0

14.1

8.5

17.6

17.8

1.1

35.7

C6H14

13.0

13.5

3.8

17.6

16.2

-8.0

32.1

C7H16

12.6

13.1

4.0

17.1

15.7

-8.2

30.6

C8H18

12.4

11.8

-4.8

17.1

15.6

-8.8

28.1

C9H20

12.1

11.4

-5.8

16.7

15.2

-9.0

27.8

C10H22

11.8

11.3

-4.2

16.1

14.2

-11.8

26.5

C11H24

11.5

10.1

-12.2

16.1

14.0

-13.0

25.3

C12H26

11.0

10.3

-6.4

15.7

13.4

-14.6

23.9

C13H28

-

9.85

-

-

13.5

-

23.5

C14H30

9.41

9.70

3.1

14.1

12.9

-8.5

22.0

The measured diffusion coefficients are taken from ref 34.

Table 3. The simulated diffusion coefficients of CO2 in n-alkane/CO2 systems at 10.5 MPa in 10−9m2·s−1

system

299 K

308 K

323 K

CH4-CO2

21.1

26.4

55.5

C2H6-CO2

20.7

26.6

55.5

C3H8-CO2

21.0

26.2

55.6

C4H10-CO2

20.8

26.6

55.7

C5H12-CO2

21.1

27.0

55.3

C6H14-CO2

21.1

26.6

55.3


27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C7H16-CO2

21.0

27.0

55.8

C8H18-CO2

21.0

27.1

55.9

C9H20-CO2

21.2

27.2

55.3

C10H22-CO2

21.0

26.4

55.7

C11H24-CO2

20.9

26.6

55.9

C12H26-CO2

21.1

25.9

55.9

C13H28-CO2

21.3

26.7

55.0

C14H30-CO2

21.2

26.6

55.7

Page 28 of 32

AUTHOR INFORMATION Corresponding Author Email: [email protected] (Zhenfan Sun), [email protected] (Liuping Chen) ACKNOWLEDGMENT The authors acknowledge Dr. Xin Liu and Dr. Li Zhang working at the Zhejiang Sci-Tech University for helpful discussion about MD simulation. This work was supported by the Natural Science Foundation of Hainan Province (no. 212014) and the Scientific Research Foundation of Hainan Normal University (no. 00203020218). REFERENCES (1)

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