<p>Supporting information for:</p><p>Viscosity of heptane-toluene mixtures. Comparison of molecular dynamics and group contribution methods</p><p>Ana Milena Velásquez1, 2 and Bibian A. Hoyos1</p><p>1Universidad Nacional de Colombia, Sede Medellín, Facultad de Minas, Departamento de </p><p>Procesos y Energía, Carrera 80 No. 65-223, 050041 Medellín, Colombia</p><p>[email protected],(+574) 425-5285</p><p>UNIFAC–VISCO method</p><p>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].</p><p>Group k Rk Qk</p><p>CH2, CH2cy 0.6744 0.540</p><p>CH3 0.9011 0.848</p><p>CHar 0.5313 0.400</p><p>* The interaction parameter, ψ nm, is calculated using:</p><p>(S1)</p><p>For toluene and n-heptane groups, values of αnm are given in Table S2.</p><p>Table S2. Interaction parameters (αnm) used in the UNIFAC–VISCO method for toluene and n-heptane groups</p><p>[1].</p><p> n/m CH2 CH3 CH2cy CHar</p><p>CH2 0 66.53 224,9 406.7</p><p>CH3 -709.5 0 -130.7 -119.5</p><p>CH2cy -538.1 187.3 0 8.958</p><p>CHar -623.7 237.2 50.89 0</p><p>Grunberg–Nissan (G–N) method</p><p>Table S3. Group contribution parameters used in the G–N method for toluene and n-heptane (at 298 K) [2].</p><p>Group</p><p>- CH3 -0.100</p><p>> CH2 0.096 >CH- 0.204 >C< 0.433 Benzene ring 0.766 Consistent Valence Force Field (CVFF) potential</p><p>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): </p><p>(S2)</p><p> 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.</p><p>The energy contribution due to dihedral angle interactions, or sites separated by three bonds, was calculated using harmonic potential:</p><p>(S3)</p><p> where k , d and n are constants. 𝜙</p><p>The full list of the interaction parameters for the different molecules can be found in [3] </p><p>3 References</p><p>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</p><p>2. Poling BE, Prausnitz JM, O’Connell JP (2001) The properties of gases and liquids, Fifth Edit. McGraw-Hill, United States of America</p><p>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 </p><p>4</p>