Brigham Young University BYU ScholarsArchive Faculty Publications 1997-06-22 Predicting the viscosity of alkanes using nonequilibrium molecular dynamics: Evaluation of intermolecular potential models Richard L. Rowley [email protected] William Allen Follow this and additional works at: https://scholarsarchive.byu.edu/facpub Part of the Chemical Engineering Commons BYU ScholarsArchive Citation Rowley, Richard L. and Allen, William, "Predicting the viscosity of alkanes using nonequilibrium molecular dynamics: Evaluation of intermolecular potential models" (1997). Faculty Publications. 665. https://scholarsarchive.byu.edu/facpub/665 This Peer-Reviewed Article is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Faculty Publications by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Predicting the viscosity of alkanes using nonequilibrium molecular dynamics: Evaluation of intermolecular potential models William Allen and Richard L. Rowley Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602 ~Received 28 January 1997; accepted 17 March 1997! Nonequilibrium molecular dynamics ~NEMD! viscosity simulations of branched and linear alkanes at liquid densities were performed using both united-atom ~UA! and all-atom ~AA! intermolecular potential models in order to study the relative efficacy of the models in predicting fluid viscosity. Both models were used in conjunction with fixed bond lengths and bond angles, but different torsional potentials were investigated. The commonly used Ryckaert–Bellemans intermolecular potential model, which accurately predicts viscosities for short straight-chain alkanes, produced values for branched and long-chain alkanes that were significantly below experimental values. Likewise, a more complex UA model that uses transferrable site potentials and is commonly used to simulate thermodynamic properties also under predicted viscosities for branched and long-chain molecules. The UA models were also found to be density dependent, substantially under predicting viscosity at high liquid densities for all model fluids tested. Predicted viscosities using AA intermolecular potential models were generally substantially too large compared to experiment when using model parameters from the literature, even though thermodynamic properties were adequately predicted. However, evidence suggests that accurately modeling the hydrogen interactions and the rotation potential of methyl groups is essential for accurate viscosity simulations. Therefore, a new set of parameters for the hydrogen interactions was regressed using viscosity simulations of 2-methylpropane and n-pentane. Like the UA model, the AA model with the new parameters is still somewhat density dependent, but gives reasonably accurate predictions of viscosity for most fluids. © 1997 American Institute of Physics. @S0021-9606~97!50224-8# I. INTRODUCTION n-butane, isobutane, n-hexane, and cyclohexane over a very wide range of liquid densities.1,12 However, in order to bring Liquid viscosity is an important design variable in many the isobutane simulations into agreement with experiment, industrial applications, yet it is often difficult to predict ac- adjustment of one model parameter was required. This sug- curately, especially for a fluid composed of branched gests that the homogeneous UA ~UA-RB! approach may be molecules.1 NEMD simulation provides a method for the cal- inadequate because different model parameters were required culation of viscosity, theoretically at any condition, from for branched and linear groups.13 Even with angle bending molecular interactions and rigorous physics. The accuracy of and bond stretching included in the UA-RB model, simula- the predictions can therefore be viewed as a direct probe of tions on n-hexadecane produced viscosities significantly the accuracy of the model used for the interactions. lower than the experimental value, even though the equilib- The majority of NEMD simulations of alkanes to date rium hydrostatic pressure was accurately predicted.14 This have used simplified molecular models to study the rheologi- suggests that the UA-RB model is too simple for accurate cal properties of alkanes at high shear rate.2–8 These simula- viscosity predictions for long straight-chain alkanes as well tions have in general used Lennard-Jones ~LJ!, site–site, united-atom ~UA! models, where each carbon atom with the as branched molecules. hydrogen atoms bonded to it are modeled as a single inter- Heterogeneous UA models that use different LJ interac- acting site. The most common model has been a homoge- tion parameters for the methyl and methylene groups have neous site model due to Ryckaert and Bellemans9 ~RB!,in also been used in NEMD simulations of viscosity. Cui et al. which all sites are equivalent regardless of the degree of used such a heterogeneous model for n-decane and found branching. Other simulations have focused on comparing good agreement with experimental data at low liquid 10 NEMD viscosities extrapolated to zero shear rate to viscosi- densities, but later simulations at higher densities produced ties obtained from equilibrium molecular dynamics ~EMD! viscosities that were significantly lower than the experimen- 7 and the Green–Kubo relation.6,10,11 Agreement between the tal values. Simulated viscosities for n-hexadecane and EMD and NEMD methods has provided verification of both n-tetracosane were again substantially below the experimen- methods independent of any inaccuracies in the molecular tal viscosity even though the experimental and simulated model. n-decane values were in reasonably good agreement. Only a few NEMD simulations have been performed The simulations outlined above seem to indicate that with the intent of comparing the simulated viscosity to the both the homogeneous and heterogeneous UA intermolecular experimental viscosity. Simulations with the RB model have potential models are inadequate for accurately simulating the been used to predict quite accurately the viscosity of viscosity of long-chain and branched alkanes, particularly at J. Chem. Phys. 106 (24), 22 June 1997 0021-9606/97/106(24)/10273/9/$10.00 © 1997 American Institute of Physics 10273 Downloaded¬16¬Sep¬2009¬to¬128.187.0.164.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://jcp.aip.org/jcp/copyright.jsp 10274 W. Allen and R. L. Rowley: The viscosity of alkanes higher densities. In the all-atom ~AA! intermolecular poten- TABLE I. Intermolecular site–site LJ parameters used in the simulations. tial model,15 more realistic asymmetry is provided to the Numbers in parentheses indicate the number of carbon atoms bonded to the adjacent carbon atom. overall intermolecular interactions by placing LJ interaction sites at each atomic center rather than at each carbon. The Model Site s/Å (e/k)/K interaction parameters for this model were regressed from UA-RB Ref. 9 All 3.923 72 equilibrium properties,14 but we know of no systematic study ~ ! UA-OPLS ~Ref. 11! CH (4) 3.96 72.97 of the use of this model to obtain viscosities from simula- 3 CH3(3) 3.91 80.52 tions. The objectives of this work were to systematically CH3(2) 3.905 88.07 study the efficacy of different intermolecular potential mod- CH2 3.905 59.38 els in obtaining accurate viscosity information from NEMD CH 3.85 40.26 C 3.80 25.16 simulations, to investigate the cause of any model inadequa- AA-OPLS ~Ref. 13! C 3.5 33.21 cies, and to improve on the models where possible. H 2.5 15.10 II. SIMULATION DETAILS A. Model fluids Fluids selected for simulation were chosen to represent a chosen because the UA and AA parameters were regressed variety of branched and linear alkanes. Models representing in essentially the same way and at the same conditions. n-butane, n-octane, and n-dodecane were simulated in order Simulations of the density and heat of vaporization for vari- to study model performance for various chain lengths; mod- ous fluids have been shown to be essentially equivalent when els for 2-methylpropane, 2,2-dimethylbutane, and 2,2- using the AA-OPLS or UA-OPLS model parameters.15 A dimethylpropane were studied to determine model effective- recent comparison showed that UA-OPLS parameters gave ness for branched alkanes. Simulations were also performed excellent predictions of bulk thermodynamic properties for using a model representing cyclopentane to see the structural the simple alkanes modeled.16 Although the original AA- dependence of site–site parameters between straight-chain OPLS parameters included small point charges on the hydro- and ring molecules. Simulations were run at two to three gen atoms, simulations using this model indicate that the conditions for each fluid in order to determine how the mo- point charges do not contribute noticeably to the calculation lecular models performed at different densities and tempera- of bulk properties,15,16 and they were not included in the tures. AA-OPLS model used in this study. Intramolecular interactions were modeled using a tor- B. Potential models sional potential, utors , assigned to each dihedral angle, f,in addition to LJ intramolecular interactions between sites sepa- Pairwise-additive, site–site, LJ interactions were used to rated by four or more carbon bonds. The RB intramolecular model the intermolecular potentials. LJ interaction sites were potential model located at carbon centers for the UA models and at all atomic centers for the AA models. Distances