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物理化学学报  2018, Vol. 34 Issue (10): 1124-1135    DOI: 10.3866/PKU.WHXB201801291
所属专题: 材料科学的分子模拟
论文     
Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study
WANG Lin1,2,XIN Liang2,ISHIYAMA Tatsuya3,PENG Qiling4,YE Shen1,2,MORITA Akihiro1,2,*()
1 Department of Chemistry, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan
2 Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
3 Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan
4 Institute for Catalysis, Hokkaido University, Kita-ku, Sapporo 001-0021, Japan
Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study
Lin WANG1,2,Liang XIN2,Tatsuya ISHIYAMA3,Qiling PENG4,Shen YE1,2,Akihiro MORITA1,2,*()
1 Department of Chemistry, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan
2 Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
3 Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan
4 Institute for Catalysis, Hokkaido University, Kita-ku, Sapporo 001-0021, Japan
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摘要:

Ethylene carbonate (EC) liquid and its vapor-liquid interface were investigated using a combination of molecular dynamics (MD) simulation and vibrational IR, Raman and sum frequency generation (SFG) spectroscopies. The MD simulation was performed with a flexible and polarizable model of the EC molecule newly developed for the computation of vibrational spectra. The internal vibration of the model was described on the basis of the harmonic couplings of vibrational modes, including the anharmonicity and Fermi resonance coupling of C=O stretching. The polarizable model was represented by the charge response kernel (CRK), which is based on ab initio molecular orbital calculations and can be readily applied to other systems. The flexible and polarizable model can also accurately reproduce the structural and thermodynamic properties of EC liquid. Meanwhile, a comprehensive set of vibrational spectra of EC liquid, including the IR and Raman spectra of the bulk liquid as well as the SFG spectra of the liquid interface, were experimentally measured and reported. The set of experimental vibrational spectra provided valuable information for validating the model, and the MD simulation using the model comprehensively elucidates the observed vibrational IR, Raman, and SFG spectra of EC liquid. Further MD analysis of the interface region revealed that EC molecules tend to orientate themselves with the C=O bond parallel to the interface. The MD simulation explains the positive Im[$ \chi ^{(2)}$](ssp) band of the C=O stretching region in the SFG spectrum in terms of the preferential orientation of EC molecules at the interface. This work also elucidates the distinct lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra. The lineshapes of the C=O band are split by the Fermi resonance of the C=O fundamental and the overtone of skeletal stretching. The Fermi resonance of C=O stretching was fully analyzed using the empirical potential parameter shift analysis (EPSA) method. The apparently different lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra were attributed to the frequency shift of the C=O fundamental in different solvation environments in the bulk liquid and at the interface. This work proposes a systematic procedure for investigating the interface structure and SFG spectra, including general modeling procedure based on ab initio calculations, validation of the model using available experimental data, and simultaneous analysis of molecular orientation and SFG spectra through MD trajectories. The proposed procedure provides microscopic information on the EC interface in this study, and can be further applied to investigate other interface systems, such as liquid-liquid and solid-liquid interfaces.

关键词: Ethylene carbonateSFGFermi resonanceEPSA    
Abstract:

Ethylene carbonate (EC) liquid and its vapor-liquid interface were investigated using a combination of molecular dynamics (MD) simulation and vibrational IR, Raman and sum frequency generation (SFG) spectroscopies. The MD simulation was performed with a flexible and polarizable model of the EC molecule newly developed for the computation of vibrational spectra. The internal vibration of the model was described on the basis of the harmonic couplings of vibrational modes, including the anharmonicity and Fermi resonance coupling of C=O stretching. The polarizable model was represented by the charge response kernel (CRK), which is based on ab initio molecular orbital calculations and can be readily applied to other systems. The flexible and polarizable model can also accurately reproduce the structural and thermodynamic properties of EC liquid. Meanwhile, a comprehensive set of vibrational spectra of EC liquid, including the IR and Raman spectra of the bulk liquid as well as the SFG spectra of the liquid interface, were experimentally measured and reported. The set of experimental vibrational spectra provided valuable information for validating the model, and the MD simulation using the model comprehensively elucidates the observed vibrational IR, Raman, and SFG spectra of EC liquid. Further MD analysis of the interface region revealed that EC molecules tend to orientate themselves with the C=O bond parallel to the interface. The MD simulation explains the positive Im[$ \chi ^{(2)}$](ssp) band of the C=O stretching region in the SFG spectrum in terms of the preferential orientation of EC molecules at the interface. This work also elucidates the distinct lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra. The lineshapes of the C=O band are split by the Fermi resonance of the C=O fundamental and the overtone of skeletal stretching. The Fermi resonance of C=O stretching was fully analyzed using the empirical potential parameter shift analysis (EPSA) method. The apparently different lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra were attributed to the frequency shift of the C=O fundamental in different solvation environments in the bulk liquid and at the interface. This work proposes a systematic procedure for investigating the interface structure and SFG spectra, including general modeling procedure based on ab initio calculations, validation of the model using available experimental data, and simultaneous analysis of molecular orientation and SFG spectra through MD trajectories. The proposed procedure provides microscopic information on the EC interface in this study, and can be further applied to investigate other interface systems, such as liquid-liquid and solid-liquid interfaces.

Key words: Ethylene carbonate    SFG    Fermi resonance    EPSA
收稿日期: 2017-12-26 出版日期: 2018-01-29
基金资助: Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Cooperative Research Program of Institute for Catalysis, Hokkaido University, Japan and the Grants-in-Aids(JP25104003);Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Cooperative Research Program of Institute for Catalysis, Hokkaido University, Japan and the Grants-in-Aids(JP26288003);the Japan Society for the Promotion of Science (JSPS) and Ministry of Education, Culture, Sports and Technology (MEXT), Japan
通讯作者: MORITA Akihiro     E-mail: morita@tohoku.ac.jp
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WANG Lin,XIN Liang,ISHIYAMA Tatsuya,PENG Qiling,YE Shen,MORITA Akihiro. Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study[J]. 物理化学学报, 2018, 34(10): 1124-1135.

Lin WANG,Liang XIN,Tatsuya ISHIYAMA,Qiling PENG,Shen YE,Akihiro MORITA. Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study. Acta Physico-Chimica Sinca, 2018, 34(10): 1124-1135.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201801291        http://www.whxb.pku.edu.cn/CN/Y2018/V34/I10/1124

Fig 1  Molecular structure of EC. The red vectors illustrate the definition of molecule-fixed coordinates $(\xi, \eta, \zeta)$ .
NICDescription
Carbonyl group: $S_1 = r_{\text{C?O}}$ C=O str
$S_2 = \dfrac{1}{\sqrt{2}}(\theta_1 - \theta_2$ )C=O in-plane bend
$S_3 = \omega_1$ C=O out-of-plane bend
$\omega_1$ is the wagging angle of C=O bond from the O-C-O plane
Five-membered ring: $S_4 =\dfrac{1}{\sqrt{2}}(r_1 + r_5)$ skeletal(1)
$S_5 =\dfrac{1}{\sqrt{2}}(r_1 - r_5)$ skeletal(2)
$S_6 =\dfrac{1}{\sqrt{2}}(r_2 + r_4)$ skeletal(3)
$S_7 =\dfrac{1}{\sqrt{2}}(r_2 - r_4)$ skeletal(4)
$S_8 = r_3$ skeletal(5)
$S_9 = 0.6324[\alpha_1 + a(\alpha_2+\alpha_5)+b(\alpha_3+\alpha_4)]$ skeletal(6)
$S_{10} = 0.3325[(a-b)(\alpha_2-\alpha_5)+(1-a)(\alpha_3-\alpha_4)]$ skeletal(7)
$S_{11} = 0.6324[b(\tau_1+\tau_5)+a(\tau_2+\tau_4)+\tau_3]$ skeletal(8)
$S_{12} =0.3325[(a-b)(\tau_4-\tau_2)+(1-a)(\tau_5-\tau_1)]$ skeletal(9)
$r_1$ , e.g., is the bond 1-2. $\alpha_2$ , e.g., is the angle 1-2-3, and $\tau_2$ , e.g.,
is the dihedral angle 1-2-3-4. $a=\cos 144^\circ$ , $b=\cos 72^\circ$ .
Methylene group: $S_{13} (S_{14}) =\dfrac{1}{\sqrt{2}} (r_1 + r_2)$ C-H sym str
$S_{15} (S_{16}) =\dfrac{1}{\sqrt{2}} (r_1 - r_2)$ C-H asym str
$S_{17} (S_{18}) = \alpha$ ${\rm{CH_2}}$ bend
$S_{19} (S_{20}) = \dfrac{1}{2}(\beta_1 - \beta_2 + \beta_3 - \beta_4)$ ${\rm{CH_2}}$ rock
$S_{21} (S_{22}) = \dfrac{1}{2}(\beta_1 + \beta_2 - \beta_3 - \beta_4)$ ${\rm{CH_2}}$ wag
$S_{23} (S_{24}) = \dfrac{1}{2}(\beta_1 - \beta_2 - \beta_3 + \beta_4)$ ${\rm{CH_2}}$ twist
$r_1$ , $r_2$ are the bond of C- ${\rm{H_1}}$ and C- ${\rm{H_2}}$ , respectively.
Table 1  Natural internal coordinates $S_1 $- $ S_{24}$ of EC.
AtomCharge $\sigma$ $\varepsilon$
${\rm{C_1}}$ 0.7083.75439.32
${\rm{O_1}}$ -0.5092.96878.64
${\rm{O_2(O_3)}}$ $ -$0.3293.00711.28
${\rm{C_2(C_3)}}$ 0.1643.50276.14
${\rm{H_1(H_4)}}$ 0.0272.4262.76
${\rm{H_2(H_3)}}$ 0.0392.4262.76
Table 2  ESP charges and LJ parameters, $\sigma$ (?) and $\varepsilon$ (J $\cdot$mol$^{-1}$), of EC.
Fig 5  Calculated (a) and experimental (b) SFG intensity spectra of EC vapor-liquid interface under $ssp$ (red) and $sps$ (blue) polarizations. The main peak frequencies are labeled.
Cal.Exp.
$\rho$ /(g $\cdot$mL$^{-1}$)1.323 (0.002)1.322 64
$\Delta H_v$ /(kcal $\cdot$mol$^{-1}$)17.86 (0.14)14.36 65
$\gamma$ /(mN $\cdot$m$^{-1}$)68.8 (3.4)54.6 66
Table 3  Calculated and experimental results of density ($\rho$), heat of vaporization ($\Delta H_v$), and surface tension ($\gamma$) of EC liquid.
Fig 2  Calculated (a, c) and experimental (b, d) IR (a, b) and Raman (c, d) spectra of liquid EC.
Fig 3  Calculated (a, c) and experimental (b, d) IR (a, b) and Raman (c, d) spectra of liquid EC in the C=O stretching region. The peak frequencies are labeled in the panels.
Fig 4  (a) Calculated density profile of EC interface as a function of $\hat{z}$ . Blue line denotes the fitting result by Eq.(24). (b) Definition of the orientation angle $\theta_{{\rm{CO}}}$ of an EC molecule. (c) Product of density $\rho$ and $\cos _{{\rm{CO}}}$ by Eq.(25) as a function of $\hat{z}$ . (d) Probability density distributions $P(\cos _{{\rm{CO}}}, \{ z_1 < \hat{z} < z_2 \} )$ in the bulk and interface by Eq.(26).
Fig 6  (a) Calculated ${\rm{Im}} [\chi^{(2)}_{yyz}]$ spectra of EC interface. Different colors denote the calculated results from different interface regions. (b) Self part spectrum ${\rm{Im}} [\chi^{(2), {\rm{self}}}_{yyz}]$ by Eq.(18).
$\xi$ $\eta$ $\zeta$
$(\partial \mu_{r} / \partial q_\textrm{CO})^{\rm{mol}}$ 00-0.0193
$(\partial \alpha_{pq} / \partial q_\textrm{CO})^{\rm{mol}}$ $\xi$ 0.003400
$\eta$ 00.01140
$\zeta$ 000.0989
Table 4  Derivatives of dipole moment $(\partial \mu_r / \partial q_\textrm{CO})^{\rm{mol}}$ and polarizability $(\partial \alpha_{pq} / \partial q_\textrm{CO})^{\rm{mol}}$ with respect to the C=O stretching normal mode $q_\textrm{CO}$ of EC molecule.
Fig 7  Calculated IR (a), Raman (b), and ${\rm{Im}} [\chi^{(2), {\rm{self}}}_{yyz}]$ (c) spectra of liquid EC in the EPSA procedure. Different colors denote different scaling factors $s$ on the force constant $k_{4, 4}$ . (d) Fermi resonance mechanism of the the C=O stretching fundamental ( $\nu_\rm{C=O}$ ) and the overtone of skeletal stretching ( $2 \nu_\rm{skel}$ ). The upper and lower panels indicate the cases of $s=1.0$ and $s=1.12$ , respectively. Left panels illustrate the energy diagrams of split levels, while the right panels illustrate the consequent line shapes. The black and blue lines correspond to the cases of the bulk liquid (IR, Raman) and interface (SFG), respectively.
1 Aurbach D. ; Talyosef Y. ; Markovsky B. ; Markevich E. ; Zinigrad E. ; Asraf L. ; Gnanaraj J. S. ; Kim H.-J. Electrochim. Acta 2004, 50, 247.
doi: 10.1016/j.electacta.2004.01.090
2 Xu K. Chem. Rev. 2004, 104, 4303.
doi: 10.1021/cr030203g
3 Xu K. Chem. Rev. 2014, 114, 11503.
doi: 10.1021/cr500003w
4 Aurbach D. ; Markovsky B. ; Salitra G. ; Markevich E. ; Talyossef Y. ; Koltypin M. ; Nazar L. ; Ellis B. ; Kovacheva D. J. Power Sources 2007, 165, 491.
doi: 10.1016/j.jpowsour.2006.10.025
5 Xu K. ; von Cresce A. J. Mater. Chem. 2011, 21, 9849.
doi: 10.1039/C0JM04309E
6 Augustsson A. ; Herstedt M. ; Guo J.-H. ; Edstrom K. ; Zhuang G. V. ; Ross P. N., Jr. ; Rubensson J. -E. ; Nordgren J. Phys. Chem. Chem. Phys. 2004, 6, 4185.
doi: 10.1039/B313434B
7 Zhao L. ; Watanabe I. ; Doi T. ; Okada S. ; Yamaki J. J. Power Sources 2006, 161, 1275.
doi: 10.1016/j.jpowsour.2006.05.045
8 Liu N. ; Li H. ; Wang Z. ; Huang X. ; Chen L. Electrochem. Solid-State Lett. 2006, 9, A328.
doi: 10.1149/1.2200138
9 Zhuang G. V. ; Xu K. ; Yang H. ; Jow T. R. ; Ross P. N., Jr. J. Phys. Chem. B 2005, 109, 17567.
doi: 10.1021/jp052474w
10 Yamada Y. ; Koyama Y. ; Abe T. ; Ogumi Z. J. Phys. Chem. C 2009, 113, 8948.
doi: 10.1021/jp9022458
11 Jeong S. -K. ; Song H. -Y. ; Kim S. I. ; Abe T. ; Jeon W. S. ; Yin R. -Z. ; Kim Y. S. Electrochem. Commun. 2013, 31, 24.
doi: 10.1016/j.elecom.2013.02.019
12 Liu H. ; Tong Y. ; Kuwata N. ; Osawa M. ; Kawamura J. ; Ye S. J. Phys. Chem. C 2009, 113, 20531.
doi: 10.1021/jp907146n
13 Yu L. ; Liu H. ; Wang Y. ; Kuwata N. ; Osawa M. ; Kawamura J. ; Ye S. Angew. Chem. Int. Ed. 2013, 52, 5753.
doi: 10.1002/anie.201209976
14 Horowitz Y. ; Han H. -L. ; Ross P. N. ; Somorjai G. A. J. Am. Chem. Soc. 2016, 138, 726.
doi: 10.1021/jacs.5b10333
15 Nicolau B. G. ; Garca-Rey N. ; Dryzhakov B. ; Dlott D. D. J. Phys. Chem. C 2015, 119, 10227.
doi: 10.1021/acs.jpcc.5b01290
16 Mukherjee P. ; Lagutchev A. ; Dlott D. D. J. Electrochem. Soc. 2012, 159, A244.
doi: 10.1149/2.022203jes
17 Richmond G. L. Chem. Rev. 2002, 102, 2693.
doi: 10.1021/cr0006876
18 Tian C. ; Shen Y. Surf. Sci. Rep. 2014, 69, 105.
doi: 10.1016/j.surfrep.2014.05.001
19 Ishiyama T. ; Imamura T. ; Morita A. Chem. Rev. 2014, 114, 8447.
doi: 10.1021/cr4004133
20 Morita A. ; Hynes J. T. Chem. Phys. 2000, 258, 371.
doi: 10.1021/jp0133438
21 Morita A. ; Hynes J. T. J. Phys. Chem. B 2002, 106, 673.
doi: 10.1021/jp0133438
22 Perry A. ; Ahlborn H. ; Moore P. ; Space B. J. Chem. Phys. 2003, 118, 8411.
doi: 10.1063/1.1565994
23 Walker D. S. ; Hore D. K. ; Richmond G. L. J. Phys. Chem. B 2006, 110, 20451.
doi: 10.1021/jp063063y
24 Morita A. ; Ishiyama T. Phys. Chem. Chem. Phys. 2008, 10, 5801.
doi: 10.1039/B808110G
25 Auer B. M. ; Skinner J. L. J. Phys. Chem. B 2009, 113, 4125.
doi: 10.1021/jp806644x
26 Tainter C. ; Pieniazek P. ; Lin Y. ; Skinner J. J. Chem. Phys. 2011, 134, 184501.
doi: 10.1063/1.3587053
27 Nagata Y. ; Mukamel S. J. Am. Chem. Soc. 2010, 132, 6434.
doi: 10.1021/ja100508n
28 Hall S. A. ; Jena K. C. ; Trudeau T. G. ; Hore D. K. J. Phys. Chem. C 2011, 115, 11216.
doi: 10.1021/jp2025208
29 Nagata Y. ; Hsieh C. -S. ; Hasegawa T. ; Voll J. ; Backus E. H. G. ; Bonn M. J. Phys. Chem. Lett. 2013, 4, 1872.
doi: 10.1021/jz400683v
30 Medders G. R. ; Paesani F. J. Am. Chem. Soc. 2016, 138, 3912.
doi: 10.1021/jacs.6b00893
31 Ishiyama T. ; Sokolov V. V. ; Morita A. J. Chem. Phys. 2011, 134, 024510.
doi: 10.1063/1.3514146
32 Kawaguchi T. ; Shiratori K. ; Henmi Y. ; Ishiyama T. ; Morita A. J. Phys. Chem. C 2012, 116, 13169.
doi: 10.1021/jp302684q
33 Wang L. ; Peng Q. ; Ye S. ; Morita A. J. Phys. Chem. C 2016, 120, 15185.
doi: 10.1021/acs.jpcc.6b03935
34 Wang L. ; Ishiyama T. ; Morita A. J. Phys. Chem. A 2017, 121, 6701.
doi: 10.1021/acs.jpca.7b05378
35 Morita A. ; Kato S. J. Am. Chem. Soc. 1997, 119, 4021.
doi: 10.1021/ja9635342
36 Ishida T. ; Morita A. J. Chem. Phys. 2006, 125, 074112.
doi: 10.1063/1.2219746
37 Ishiyama T. ; Morita A. J. Chem. Phys. 2009, 131, 244714.
doi: 10.1063/1.3279126
38 Ishiyama T. ; Morita A. J. Phys. Chem. C 2011, 115, 13704.
doi: 10.1021/jp200269k
39 Ishiyama T. ; Sokolov V. V. ; Morita A. J. Chem. Phys. 2011, 134, 024509.
doi: 10.1063/1.3514139
40 Wang L. ; Ishiyama T. ; Morita A. J. Phys. Chem. A 2017, 121, 6687.
doi: 10.1021/acs.jpca.7b05320
41 Morita A. ; Kato S. J. Chem. Phys. 1998, 108, 6809.
doi: 10.1063/1.476096
42 Pulay P. ; Fogarasi G. ; Pang F. ; Boggs J. E. J. Am. Chem. Soc. 1979, 101, 2550.
doi: 10.1021/ja00504a009
43 Becke A. D. J. Chem. Phys. 1993, 98, 5648.
doi: 10.1063/1.464913
44 Lee C. ; Yang W. ; Parr R. G. Phys. Rev. B 1988, 37, 785.
doi: 10.1103/PhysRevB.37.785
45 Dunning T. H., Jr. J. Chem. Phys. 1989, 90, 1007.
doi: 10.1063/1.456153
46 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision C.01; Gaussian Inc.: Wallingford, CT, USA, 2010.
47 Heinz H. ; Suter U. W. J. Phys. Chem. B 2004, 108, 18341.
doi: 10.1021/jp048142t
48 Morita A. ; Kato S. J. Phys. Chem. A 2002, 106, 3909.
doi: 10.1021/jp014114o
49 Jorgensen W. L. ; Maxwell D. S. ; Tirado-Rives J. J. Am. Chem. Soc. 1996, 118, 11225.
doi: 10.1021/ja9621760
50 Martinez L. ; Andrade R. ; Birgin E. G. ; Martinez J. M. J. Comp. Chem. 2009, 30, 2157.
doi: 10.1002/jcc.21224
51 Nose S. J. Chem. Phys. 1984, 81, 511.
doi: 10.1063/1.447334
52 Hoover W. G. Phys. Rev. A 1985, 31, 1695.
doi: 10.1103/PhysRevA.31.1695
53 Kagaku Binran(Japanese), 4th ed.; The Chemical Society of Japan, Ed.; Maruzen: Tokyo, Japan, 1993.
54 Martyna G. J. ; Tobias D. J. ; Klein M. L. J. Chem. Phys. 1994, 101, 4177.
doi: 10.1063/1.467468
55 Allen M. P. ; Tildesley D. J. Computer Simulation of Liquids Oxford, UK: Clarendon Press, 1987.
56 Fincham D. Mol. Sim. 1994, 13, 1.
doi: 10.1080/08927029408022180
57 Yu Q. ; Ye S. J. Phys. Chem. C 2015, 119, 12236.
doi: 10.1021/acs.jpcc.5b03370
58 Ye S. ; Noda H. ; Morita S. ; Uosaki K. ; Osawa M. Langmuir 2003, 19, 2238.
doi: 10.1021/la0266233
59 Ye S. ; Kathiravan A. ; Hayashi H. ; Tong Y. ; Infahsaeng Y. ; Chabera P. ; Pascher T. ; Yartsev A. P. ; Isoda S. ; Imahori H. ; et al J. Phys. Chem. C 2013, 117, 6066.
doi: 10.1021/jp400336r
60 Ye S. ; Tong Y. ; Ge A. ; Qiao L. ; Davies P. B. Chem. Rec. 2014, 14, 791.
doi: 10.1002/tcr.201402039
61 Peng, Q.; Liu, H.; Ye, S. J. Electroanal. Chem. 2017, 800, 134. doi: 10.1016/j.jelechem.2016.09.006, Special Issue in honor of Masatoshi Osawa
62 McQuarrie, D. A. Statistical Mechanics; University Science Books: Sausalito, CA, USA, 2000.
63 Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, NY, USA, 1955.
64 Peppel W. J. Ind. Eng. Chem. 1958, 50, 767.
doi: 10.1021/ie50581a030
65 Verevkin S. P. ; Toktonov A. V. ; Chernyak Y. ; Schaffner B. ; Borner A. Fluid Phase Equilib. 2008, 268, 1.
doi: 10.1016/j.fluid.2008.03.013
66 Naejus R. ; Lemordant D. ; Coudert R. ; Willmann P. J. Chem. Thermodyn. 1997, 29, 1503.
doi: 10.1006/jcht.1997.0260
67 Walton J. ; Tildesley D. ; Rowlinson J. ; Henderson J. Mol. Phys. 1983, 48, 1357.
doi: 10.1080/00268978300100971
68 Matsumoto M. ; Kataoka Y. J. Chem. Phys. 1988, 88, 3233.
doi: 10.1063/1.453919
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