Viscosity of Heptane-Toluene Mixtures. Comparison of Molecular Dynamics and Group Contribution
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Viscosity of heptane-toluene mixtures. Comparison of molecular dynamics and group contribution methods
Ana Milena Velásquez1, 2 and Bibian A. Hoyos1
1Universidad Nacional de Colombia, Sede Medellín, Facultad de Minas, Departamento de
Procesos y Energía, Carrera 80 No. 65-223, 050041 Medellín, Colombia
[email protected],(+574) 425-5285
UNIFAC–VISCO method
2Author to whom any correspondence should be addressed. 1 Table S1. Volume and surface area parameters used in the UNIFAC–VISCO method for toluene and n- heptane groups [1].
Group k Rk Qk
CH2, CH2cy 0.6744 0.540
CH3 0.9011 0.848
CHar 0.5313 0.400
* The interaction parameter, ψ nm, is calculated using:
(S1)
For toluene and n-heptane groups, values of αnm are given in Table S2.
Table S2. Interaction parameters (αnm) used in the UNIFAC–VISCO method for toluene and n-heptane groups
[1].
n/m CH2 CH3 CH2cy CHar
CH2 0 66.53 224,9 406.7
CH3 -709.5 0 -130.7 -119.5
CH2cy -538.1 187.3 0 8.958
CHar -623.7 237.2 50.89 0
Grunberg–Nissan (G–N) method
Table S3. Group contribution parameters used in the G–N method for toluene and n-heptane (at 298 K) [2].
Group
- CH3 -0.100
> CH2 0.096 >CH- 0.204 >C< 0.433 Benzene ring 0.766 Consistent Valence Force Field (CVFF) potential
2 To represent the toluene and n-heptane molecules, this study used the Consistent Valence Force Field (CVFF) potential, which is a function of the Van der Waals and electrostatic interactions, as well as the intramolecular bond, angle, and dihedral interactions, as shown in Eq. (S2):
(S2)
where ε and σ are the Lennard–Jones potential parameters; rij is the separation distance between atoms i and j; qi and qj are the atomic charges; kθ, θ and θeq are the angle constant, the angle among the three atoms and the equilibrium angle, respectively; kl, l and leq are the binding constant, the bond length between each pair of atoms and the equilibrium bond length, respectively.
The energy contribution due to dihedral angle interactions, or sites separated by three bonds, was calculated using harmonic potential:
(S3)
where k , d and n are constants. 𝜙
The full list of the interaction parameters for the different molecules can be found in [3]
3 References
1. Chevalier JL, Petrino P, Gaston-Bonhomme Y (1988) Estimation method for the kinematic viscosity of a liquid-phase mixture. Chem Eng Sci 43:1303–1309. doi: 10.1016/0009-2509(88)85104-2
2. Poling BE, Prausnitz JM, O’Connell JP (2001) The properties of gases and liquids, Fifth Edit. McGraw-Hill, United States of America
3. Levitt M, Hirshberg M (1995) Potential energy function and parameters for simulations of the molecular dynamics of proteins and nucleic acids in solution. Comput Phys Commun 91:215–231. doi: 10.1016/0010-4655(95)00049-L
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