Thermodynamic and dynamic properties in binary mixtures of propylene carbonate with dimethyl carbonate and ethylene carbonate

Journal of Molecular Liquids 175 (2012) 97–102

Contents lists available at SciVerse ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Thermodynamic and dynamic properties in binary mixtures of propylene carbonate with dimethyl carbonate and ethylene carbonate Sanghun Lee, Sung Soo Park ⁎ Corporate R&D Center, Samsung SDI Co. Ltd., Yongin, 446-577, South Korea

a r t i c l e

i n f o

Article history: Received 21 February 2012 Received in revised form 23 August 2012 Accepted 28 August 2012 Available online 8 September 2012 Keywords: Lithium ion battery Electrolyte Carbonate mixtures Molecular dynamics Dielectric constant Diffusion coefficient

a b s t r a c t Molecular dynamics simulations of binary mixtures of propylene carbonate (PC) + dimethyl carbonate (DMC) and PC + ethylene carbonate (EC) with various compositions were performed to study thermodynamic and dynamic properties such as density, dielectric constant and self-diffusion coefficient. For a better understanding of the thermodynamic behavior of the mixtures, the excess molar volume and excess dielectric constant with the various mole fractions were calculated. In addition, a computational approach of the Molecular Dynamics with Electronic Continuum (MDEC) model combined with density functional theory was used to determine the dielectric constants. Fair agreement was found between the results from our simulations and available experimental data. By comparison of the two mixtures observed in various mole fractions, the thermodynamic and dynamic behaviors of PC + DMC were highly asymmetrical whereas those of PC+ EC were nearly symmetrical. © 2012 Elsevier B.V. All rights reserved.

1. Introduction For the past two decades, non-aqueous compounds such as cyclic carbonates (e.g. ethylene carbonate (EC) and propylene carbonate (PC)) and linear carbonates (e.g. dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), diethyl carbonate (DEC)) have been typically used as primary solvents of electrolyte in lithium ion batteries (LIBs) [1,2]. Most electrolytes contain two or more cyclic and linear carbonates as a solvent whereas single compound solvents are rarely used because there are many benefits of carbonate mixtures. For example, when EC and DMC are mixed, it seems that a synergetic effect is achieved because the qualities of each individual solvent are imparted onto the resultant mixture: the high anodic stability of EC on cathode surfaces, the strong ability of EC to dissociate lithium salts, and low viscosity of DMC to promote ion transport [1]. Particularly, by balancing the mobility of ions (self-diffusion) and the degree of dissociation of ionic salts, the mixtures of cyclic and linear carbonates show higher ionic conductivity than the pure components. Therefore, it is important to characterize fundamental quantities of thermodynamic, dynamic and transport properties of the solvent mixtures. Multiple physical properties such as densities, mixing enthalpies, viscosities, dielectric constants, surface tensions and the excess quantities for binary mixtures of cyclic and linear carbonates with various compositions were characterized [3,4]. However, relying on experimental studies only, it is rather difficult to understand fundamental thermodynamic, dynamic and transport properties of the solvent mixtures at a ⁎ Corresponding author. E-mail address: [email protected] (S.S. Park). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2012.08.018

molecular level. For a rational design of solvents mixed in electrolytes, it is necessary to take into account of their intermolecular interactions between the different components. In that sense, a molecular dynamics (MD) simulation can be a powerful tool to investigate the structural, dynamic and thermodynamic properties of such mixed solvents. MD simulations have achieved considerable success on various mixture systems, such as mixtures of Lennard–Jones liquids [5–7], aqueous mixtures [8–11] and organic solvents [12–17]. The simulations have provided insight into the molecular mobility in mixed solvents such as solvation and diffusivity, although an essential validation leads to experimental data [12–15]. In particular, the MD studies on mixtures of carbonate solvents including lithium salts [16,17] have mainly focused on transportation and solvation of lithium ions but thermodynamic properties of solvents themselves have not been sufficiently explored. In the present work, our primary focus of study is binary carbonate mixtures without salts. The crucial point is the choice of force field for classical MD simulation which reliably describes the interactions between the components of mixtures. For this purpose, the COMPASS force field [18–21] was reasonably defined and successfully employed in pure solvents of carbonate series [22]. This study aims to estimate thermodynamic and dynamic properties of PC (C4H6O3), DMC (C3H6O3), EC (C3H4O3) (Fig. 1) and their binary mixtures (DMC+ PC and EC +PC) with various compositions. In addition, the excess thermodynamic properties such as molar volume and dielectric constant are determined for the mixtures as functions of a composition. As employed in our previous study [22], the MDEC model [23–25] is used to determine the dielectric constants. Therefore, the main effort of this study intends to assess the viability of simple nonpolarizable MD simulation by the comparison between experimental

98

S. Lee, S.S. Park / Journal of Molecular Liquids 175 (2012) 97–102

describe pure electronic polarization of the medium. In the MDEC (molecular dynamics with electronic continuum) model, there is a simple scaling relation between the total dielectric constant ε and εMD: ð2Þ

ε ¼ ε∞ ·εMD

Fig. 1. Structures of (a) PC, (b) DMC, and (c) EC. Red, gray and white spheres represent oxygen, carbon, and hydrogen atoms, respectively.

where ε∞ is the high frequency dielectric constant. The actual dipole moment μ, is related to the dipole moment obtained by the pffiffiffiffiffiffi 2 non-polarizable MD, μMD, as μ ¼ ε∞ μ MD ; therefore 〈M 2〉 = ε∞〈MMD 〉, 2 where 〈MMD〉 is the mean square fluctuation of the dipole moment obtained by the non-polarizable MD, and we find: εMD ¼ 1 þ

and calculated data and understanding the mixing behaviors of two distinctly different carbonate species: highly asymmetric DMC +PC – in terms of the molecular geometry as well as the mobility – and weakly asymmetric EC +PC. 2. Simulation details We performed MD simulations with the most recent version of the non-polarizable COMPASS force field which was originally developed by Sun [18] and used the FORCITE module in Materials Studio 5.5 package [26]. Various compositions of DMC + PC and EC + PC mixtures including each pure solvent were listed in Table 1. Each system contains 100 molecules in a cubic box with the periodic boundary condition. In order to obtain randomized initial coordinates, the systems were equilibrated for 1 ns with the NPT (fixed number of particles, pressure and temperature) ensemble at 298 K (DMC + PC) and 313 K (EC + PC) and 0.1 MPa employing Nose's thermostat [27] and Andersen's barostat [28]. After the equilibration, the properties of our interest were averaged for 40 ns. The standard errors were obtained by the block average method. The time step was set to 1 fs and the cut-off radius for the van der Waals interactions was 9 Å. The long-range corrections for density and pressure were applied. In order to account for the charge interactions, the Ewald sum technique was employed. To obtain dielectric constants, we used Neumann's dipole moment fluctuation formula [29,30], 4π D 2 E ε ¼ ε∞ þ M 3VkB T

ð1Þ

where 〈M 2〉 is the mean square fluctuation of the (actual) total dipole moment and V, kB and T are volume, the Boltzmann constant and temperature, respectively. However, as reported in recent literatures [23–25] the dielectric constant obtained with non-polarizable force fields, for example the COMPASS in this study, εMD, does not explicitly

4π D 2 E M MD : 3VkB T

Hence, if one has ε∞ of a material, its dielectric constant can be calculated by the non-polarizable MD simulation. In cases of pure DMC, PC, and EC compounds, we used the values of ε∞ obtained from our recent report [22] where we successfully determined ε∞s of various pure linear and cyclic carbonates with a high accuracy from a simple computational approach that we set up with DFT calculation [31]. For the mixture systems, the mixing rule of the Lorentz–Lorenz equation was used: ! ! ε∞;12 −1 ε∞;1 −1 ε∞;2 −1 ¼ ∅1 þ ∅2 ε∞;12 þ 2 ε∞;1 þ 2 ε∞;2 þ 2

Mole fraction of PC

0 (pure DMC or EC) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (pure PC)

Density (g/cm3) DMC + PC (298 K)

EC + PC (313 K)

1.0407 ± 0.0006 (1.0633) 1.0560 ± 0.0003 1.0712 ± 0.0003 1.0855 ± 0.0003 1.0999 ± 0.0004 1.1145 ± 0.0002 1.1282 ± 0.0004 1.1425 ± 0.0003 1.1562 ± 0.0002 1.1695 ± 0.0002 1.1826 ± 0.0002 (1.1995)

1.2643 ± 0.0007 (1.3220) 1.2516 ± 0.0002 1.2411 ± 0.0004 1.2298 ± 0.0002 1.2200 ± 0.0002 1.2102 ± 0.0002 1.2004 ± 0.0003 1.1922 ± 0.0002 1.1830 ± 0.0003 1.1746 ± 0.0003 1.1670 ± 0.0003 (1.1827)

ð4Þ

where ε∞,12, ε∞,1 and ε∞,2 are the high frequency dielectric constants of the mixture and the pure components respectively, and ∅ 1 and ∅ 2 are the volume fractions. Using the MDEC model in conjunction with the DFT calculation, we predicted the total dielectric constants of various pure organic solvents with moderate accuracy [22], and this work is an extension to mixture systems. The excess molar volumes were calculated by E

Vm ¼

ðx1 M 1 þ x2 M2 Þ − ρ12



x1 M 1 x2 M2 þ ρ1 ρ2

 ð5Þ

where x1 and x2 are the mole fractions of the pure components, M1 and M2 are the molar masses, and ρ12, ρ12 and ρ12 are the densities of the mixture and the pure components, respectively. The excess dielectric constants were determined by E

ε ¼ ε12 −ðθ1 ε1 þ θ2 ε2 Þ

ð6Þ

where θ1 and θ2 are the dielectric fractions of the pure components. θ1 is given by [4,32] θ1 ¼ fðx1 V 1 Þ=ðε1 þ 2Þg

Table 1 Density of DMC+PC and EC+PC obtained by MD simulation. The values in parentheses are experimental data of pure DMC, EC and PC [3,4].

ð3Þ

  ðx1 V 1 Þ ðx2 V 2 Þ þ = ε1 þ 2 ε2 þ 2

ð7Þ

where V1 and V2 are the molar volumes of the pure components. This model is more appropriate than the usual equation: E

ε ¼ ε12 −ðx1 ε2 þ x2 ε2 Þ

ð8Þ

which does not account for the components of mixtures having weak interactions in the solution [4]. In addition, the self-diffusion coefficients of the center of masses were obtained by the well-known Einstein relation: D¼

 E 1 d D 2 lim r ðt Þ−r ð0Þ 6 t→0 dt

where r(t) is the coordinate of the center of mass at time t.

ð9Þ

S. Lee, S.S. Park / Journal of Molecular Liquids 175 (2012) 97–102

3. Results and discussion In Table 1, compositions and densities of DMC + PC and EC + PC mixtures obtained by MD simulations in this work are listed. Compared with the experimental values, the calculated densities of pure DMC, PC, and EC are slightly underestimated within the relatively small differences (DMC: 2.1%, PC: 1.4% and EC: 4.4%), as also shown in Fig. 2(a). A decade ago, MD simulations were performed for several organic solvents with the early version of the COMPASS force field [33]. The calculated densities of PC and DMC were 1.03 ± 0.01 (15% underestimation) and 1.13± 0.01 g/cm 3 (6% overestimation), respectively. This large discrepancy has been notably improved by subsequent optimizations [19–21] which produced reliable results for various organic carbonates [22]. Even though Borodin and Smith developed many-body polarizable force fields for LIB electrolytes (e.g. ether, alkane and carbonate based solvents) which accurately predict structural, dynamic and transport properties [34], the non-polarizable MD simulation in this study has an advantage of the high computational efficiency. The excess molar volumes of DMC + PC and EC + PC mixtures determined by Eq. 5 are shown in Fig. 2(b). In general, the sign of excess molar volume (VE) depends upon the relative strengths of the intermolecular interactions between the different components such as hydrogen bonds, charge transfer interaction, weak physical forces (dipole–dipole, dipoleinduced dipole or dispersion forces), and geometrical (steric) factor. In this study, the calculated VEs of DMC + PC mixtures are negative whereas those of EC + PC mixtures are positive — both are nearly symmetric with respect to the composition of PC, i.e. the minimum of VE in DMC + PC (or maximum in EC + PC) occurs at x = 0.5. Francesconi and Comelli experimentally measured VEs of DMC + PC at 298 K [3]. As shown in Fig. 2(b), our results qualitatively agree with the experiments, however there is a quantitative difference (the negative maximum of

(a)

Excess molar volume (cm3/mol)

(b)

99

the excess molar volumes is −0.229 cm3/mol at x(PC)= 0.5 in the MD simulation whereas it is −0.377 cm3/mol at x(PC) = 0.42 in the experiment). In order to determine the dielectric constant as explained in the previous section, we accounted for the high frequency dielectric constant, ε∞, as a scaling factor. In our previous study, we calculated the ε∞s of various pure organic solvents for LIBs [22] and the values of DMC, PC and EC were re-used in this study. This simple methodology was proven to cover a wide range of small organic molecules [31]. The mixtures are obtained by the Lorentz–Lorenz equation and shown in Fig. 3. As expected from Eq. 4, the ε∞1/2 s shows a strong linearity over the entirety of compositions. By applying the total dipole moments to Eqs. 2 and 3 (the MDEC model) we calculated the dielectric constants. It is important to stress how fast the present calculations of the dielectric constants are converged. Because the dielectric properties are dependent upon longranged and collective fluctuations, the slow convergences of the dielectric constants are a well-known fact. As shown in our previous study [22], it is necessary to use a sampling time longer than at least 8 ns. In Fig. 4(a) and (b), the cumulative average values of the dielectric constants of DMC + PC and EC + PC mixtures are exhibited, respectively. They are the block average results of 5 blocks of 8 ns (i.e. total simulation time is 40 ns). As the mole fraction of PC increases, the mixtures of DMC + PC increase to a high dielectric constant but those of the EC + PC decrease. As a function of the mole fraction of PC, simulated and experimental values of the dielectric constants are exhibited in Fig. 5(a) and Table 2. The dielectric constant of the pure DMC is very accurately predicted by the MDEC model whereas those of the pure PC and EC are relatively underestimated to a large margin of about 30%. The discrepancy of the dielectric constants of the PC and EC may be partly attributed to the force field. In order to find out reasons for the relatively large disagreement, comparison with other non-polarizable force fields (CHARMM [35] or AMBER [36,37], for example) is required, which is out of the scope in this study. Nevertheless, it is noticeable that the simulation results become more comparable with the experimental values owing to the introduction of the MDEC concept. As long as the content of the PC in the DMC+ PC mixture increases, the discrepancy between the MDEC and experimental values increases as well, though the trend with the composition of calculated values compares fairly well with the experimental data. The excess dielectric constants of DMC + PC and EC + PC are shown in Fig. 5(b). For the DMC + PC, they show qualitative agreement with the experiment over the entire region. The relatively large and positive values of the excess dielectric constants indicate that mixing DMC and PC results in the increase of the effective number of aligned dipoles contributing to the dielectric polarization. In addition, the maximum at the PC-rich composition means that the DMC molecules with the small molecular dipole moment become aligned in

0.2 DMC + PC (MD, 298 K) DMC + PC (Exp., 298 K) EC + PC (MD, 313 K)

0.0

-0.2

-0.4 0.0

0.5

1.0

Mole fraction of PC Fig. 2. (a) Density and (b) excess molar volume of DMC + PC and EC + PC as functions of the mole fraction of PC. The experimental values are from Ref. [3]. Dotted lines are drawn as a guide for the eye.

Fig. 3. High frequency dielectric constant as a function of the mole fraction of PC. The values of pure DMC, EC and PC are obtained by DFT calculation (Ref. [22]) and those containing mixtures are calculated by the Lorentz–Lorenz equation (Eq. 4).

100

S. Lee, S.S. Park / Journal of Molecular Liquids 175 (2012) 97–102

Fig. 5. (a) Dielectric constant and (b) excess dielectric constant of DMC+PC and EC+PC obtained by MDEC and experiment. Dotted lines are drawn as a guide for the eye. Fig. 4. Cumulative average of the dielectric constant of (a) DMC + PC at 298 K and (b) EC + PC at 313 K obtained by MDEC.

the high PC environments. Contrastingly, due to the similarity of the dielectric properties of the constituents, the magnitude of the excess dielectric constants of the EC + PC mixtures is relatively small compared with those of the DMC + PC mixtures. In Fig. 6(a) and (b), the mean square displacements (MSDs) of DMC and PC in the DMC+ PC mixtures are shown, respectively. As the mole fraction of the PC increases, the mobility of both PC and DMC decreases because the PC is more viscous than the DMC. Because the asymmetry in mobility of the pure DMC and PC is very large, the variation of mobility with compositions is clearly observed for both components. Meanwhile, in the case of the EC + PC mixtures, this variation is not discernable due to the proximity of mobility of the pure EC and PC as shown in Fig. 6(c) and (d). From the beginning of the simulations, the MSDs of each component linearly increase with time; therefore, we can easily obtain selfdiffusion coefficients from Eq. 9 (Fig. 7). To our knowledge, the experimental diffusion coefficients of the PC, EC or DMC have not been published. However, Soetens et al. [38] showed that the diffusion coefficient can be estimated from experimental viscosity through the Wilke–Chang formula [39]:

D12

1 −6 1:17  10 T ðcM 2 Þ =2 ¼ η2 V 10:6

ð10Þ

where D12 is the diffusion coefficient of a solute 1 in a solvent 2, M2 the molecular mass of the solvent, T the temperature, η2 the viscosity of the solvent, V1 the molecular volume of the solute and c an association parameter (1.5 in this case). The ‘estimated’ experimental diffusion coefficients of the PC and DMC are 0.74 ×10−9 and 2.80× 10−9 m2 s−1

at 298 K, and that of the EC is 1.10 × 10 − 9 m 2 s − 1 at 313 K, respectively, which are in reasonable agreement with the values obtained by our MD simulations (PC: 0.68 (± 0.02) × 10 − 9 m 2 s − 1, DMC: 2.29 (± 0.08) × 10 − 9 m 2 s − 1 and EC: 0.95 (± 0.03) × 10 − 9 m 2 s − 1). Even though the DMC molecules are ~ 3.4 times faster than the PC molecules in the pure state, when they are in the mixed state, the difference in mobility is not so large at any composition (the former are only 1.2–1.5 times faster than the latter) because they exert mutual influence on each other. In addition, the diffusion coefficients of the DMC + PC mixtures are linearly varied with the composition; in contrast, those of the EC + PC mixtures are nearly constant because the diffusion coefficients of the two components are close to each other.

Table 2 Dielectric constants of DMC + PC and EC+ PC obtained by MDEC model. The values in parentheses are experimental data of pure DMC, EC and PC [4]. Mole fraction of PC

0 (pure DMC or EC) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (pure PC)

Dielectric constant DMC + PC (298 K)

EC + PC (313 K)

3.17 ± 0.02 (3.20) 6.07 ± 0.08 9.47 ± 0.16 13.07 ± 0.12 16.87 ± 0.36 20.85 ± 0.28 24.44 ± 0.43 29.23 ± 0.26 34.97 ± 0.74 38.97 ± 0.83 44.67 ± 0.69 (64.9)

59.66 ± 1.36 (89.8) 59.39 ± 0.91 56.55 ± 0.69 55.93 ± 1.35 54.06 ± 0.24 50.84 ± 0.63 50.90 ± 0.85 47.64 ± 0.74 47.15 ± 1.05 45.26 ± 0.83 44.19 ± 0.44

S. Lee, S.S. Park / Journal of Molecular Liquids 175 (2012) 97–102

101

Fig. 6. Mean square displacement of (a) DMC and (b) PC in DMC + PC at 298 K, and (c) EC and (d) PC in EC + PC at 313 K.

4. Conclusion Using MD simulations, we have simulated pure DMC, PC, EC and their binary mixtures (DMC + PC and EC+ PC) with various compositions. Calculated densities are in good agreement with the experimental values within 4%. The negative excess molar volumes in the DMC + PC mixtures are qualitatively in favor of Francesconi et al.'s experiments [3] and it indicates that more efficient packing or attractive interactions occur when the DMC and PC are mixed. Conversely, in the EC + PC mixtures, positive excess molar volumes are observed and it indicates that repulsive interactions occur between the components. From the calculated high frequency dielectric constants of the pure DMC, PC and EC [22] the high frequency dielectric constants of the mixtures are estimated by the Lorentz–Lorenz equation. Dielectric constants are calculated

with moderate accuracy from the dipole moment fluctuations of the MD simulations and the estimated high frequency dielectric constants. The MDEC model improves the comparison between the calculated and measured dielectric constants. From the calculated excess dielectric constants, we know that the DMC molecules become aligned in the high PC environments. In contrast, the excess dielectric constants of the EC + PC mixtures are relatively small due to their similarity of dielectric properties. Calculated diffusion coefficients of the DMC, EC and PC are in reasonable accord with the “estimated” experimental values from their viscosities. In the mixed state, the PC and DMC, which show highly asymmetric mobilities in the pure state, are mutually affecting each other; therefore, the difference in the mobilities becomes small. Meanwhile, the mobilities of EC and PC are nearly constant at any composition because they show similar diffusivities in the pure states. The current work suggests that a simple computational approach is promising for optimizing the mixed carbonate solvents in the electrolytes.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] Fig. 7. Diffusion coefficient of each component in DMC + PC at 298 K and EC + PC at 313 K as a function of the mole fraction of PC obtained by MD simulation.

[12]

K. Xu, Chemical Reviews 104 (2004) 4303 (and references therein). M.A. Pacheco, C.L. Marshall, Energy & Fuels 11 (1997) 2. R. Francesconi, F.J. Comelli, Chemical and Engineering Data 40 (1995) 811. R. Naejus, D. Lemordant, R. Coudert, P. Willmann, The Journal of Chemical Thermodynamics 29 (1997) 1503. M. Schoen, C. Hoheisel, Molecular Physics 52 (1984) 33. D.L. Jolly, R.J. Bearman, Molecular Physics 41 (1980) 137. M. Mecke, J. Winkelmann, J. Fischer, Journal of Chemical Physics 110 (1999) 1188. I.I. Vaisman, M.L. Berkowitz, Journal of the American Chemical Society 114 (1992) 7889. M. Ferrario, M. Haughney, I.R. McDonald, M.L. Klein, Journal of Chemical Physics 93 (1990) 5156. D.R. Wheeler, R.L. Rowley, Molecular Physics 94 (1998) 555. H. Yu, D.P. Geerke, H. Liu, W.F. van Gunsteren, Journal of Computational Chemistry 27 (2006) 1494. D.S. Venables, C.A. Schmuttenmaer, Journal of Chemical Physics 113 (2000) 3249.

102

S. Lee, S.S. Park / Journal of Molecular Liquids 175 (2012) 97–102

[13] H. Kovacs, J. Kowalewski, A. Laaksonen, Journal of Physical Chemistry 94 (1990) 7378. [14] V.A. Harmandaris, D. Angelopoulou, V.G. Marvantzas, D.N. Theodorou, Journal of Chemical Physics 116 (2002) 7656. [15] M. Zhang, F. Müller-Plathe, Journal of Chemical Physics 123 (2005) 124502. [16] T. Li, P.B. Balbuena, Journal of the Electrochemical Society 146 (1999) 3613. [17] O. Borodin, G.D. Smith, The Journal of Physical Chemistry. B 113 (2009) 1763. [18] H. Sun, The Journal of Physical Chemistry. B 102 (1998) 7338. [19] S.W. Bunte, H. Sun, The Journal of Physical Chemistry. B 104 (2000) 2477. [20] J. Yang, Y. Ren, A. Tian, H. Sun, The Journal of Physical Chemistry. B 104 (2000) 4951. [21] M.J. McQuaid, H. Sun, D. Rigby, Journal of Computational Chemistry 25 (2004) 61. [22] S. Lee, S.S. Park, The Journal of Physical Chemistry. B 115 (2011) 20271. [23] I.V. Leontyev, A.A. Stuchebrukhov, Journal of Chemical Physics 130 (2009) 085102. [24] I.V. Leontyev, A.A. Stuchebrukhov, Journal of Chemical Theory and Computation 6 (2010) 1498. [25] I.V. Leontyev, A.A. Stuchebrukhov, Physical Chemistry Chemical Physics 13 (2011) 2613. [26] http://accelrys.com/products/materials-studio. [27] S. Nose, Journal of Chemical Physics 81 (1984) 511. [28] H.C. Andersen, Journal of Chemical Physics 72 (1980) 2384. [29] M. Neumann, Molecular Physics 50 (1983) 841.

[30] [31] [32] [33] [34] [35]

[36]

[37] [38] [39]

M. Neumann, O. Steinhauser, Chemical Physics Letters 102 (1983) 508. S.S. Park, S. Lee, J.Y. Bae, F. Hagelberg, Chemical Physics Letters 511 (2011) 466. S.L. Oswal, M.V. Rathnam, Indian Journal of Chemistry 26A (1987) 29. K. Tasaki, Journal of the Electrochemical Society 149 (2002) A418. O. Borodin, G.D. Smith, The Journal of Physical Chemistry. B 110 (2006) 6279. A.D. MacKerell Jr., D. Bashford, M. Bellott, R. Dunbrack, J. Evanseck, M. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F.T.K. Lau, C. Mattos, S. Michnick, T. Ngo, D.T. Nguyen, B. Prodhom, W.E. Reiher III, B. Roux, M. Schlenkrich, J.C. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiorkiewicz-Kuczera, D. Yin, M. Karplus, The Journal of Physical Chemistry. B 102 (1998) 3586. W. Cornell, P. Cieplak, C. Bayly, I. Gould, K. Merz, D. Ferguson, D. Spellmeyer, T. Fox, J. Caldwell, P. Kollman, Journal of the American Chemical Society 117 (1995) 5179. J. Wang, P. Cieplak, P. Kollman, Journal of Computational Chemistry 21 (2000) 1049. J.-C. Soetens, C. Millot, B. Maigret, I. Bakó, Journal of Molecular Liquids 92 (2001) 201. R.S. Brodkey, H.C. Hershey, Transport Phenomena, McGraw-Hill International Edition, Columbus, 1988.