Development of an Intermolecular Potential Model for the n-Alkane Homologous Series

Overview

Hydrocarbons are used as feedstock for the production of natural gas, petrochemicals, gasoline, kerosene, oil, and paraffin wax. Recently, a considerable amount of effort has been spent trying to develop intermolecular potential models that adequately describe the complete n-alkane homologous series with a limited number of parameters. A typical approach has been to use a "united-atom" description to separate the molecules into methyl and methylene groups and assign intermolecular potential parameters to each group. Two recently proposed models, TraPPE¹ and NERD², use a Lennard-Jones potential to describe the interaction between non-bonded methyl and methylene groups. Both of the models were developed to reproduce the critical parameters and saturated liquid densities of the n-alkanes. The potentials do a reasonably good job in describing the critical parameters and saturated liquid densities, however the models do not predict the saturated vapor densities and vapor pressures with comparable accuracy.

Our approach has been to use a united-atom description of the molecules with the non-bonded interactions described by the Buckingham exponential-6 potential. The added flexibility of the exponential-6 potential has allowed us to get a good description of the critical parameters and saturated liquid densities in addition to the saturated vapor densities and vapor pressures. The development of the new potential started with ethane. Ethane contains two methyl groups and no methylene groups, thus allowing us to directly find suitable parameters for the methyl group. Hamiltonian scaling grand canonical Monte Carlo was used to find the phase behavior of a series of diatomic exponential-6 potentials. The reduced thermodynamic behavior was then compared to find the optimum parameters for the methyl group. The parameters for the methylene group were optimized with hexane and propane. The parameters were adjusted until a set of parameters was found that adequately described both propane and hexane.

Grand canonical Monte Carlo simulations have been combined with histogram reweighting techniques to determine the phase behavior of select n-alkanes. In addition, a mixed-field finite-size scaling analysis has been used to calculate the critical parameters. The NERD, TraPPE, and new models were used to determine the thermodynamic behavior of ethane, pentane, and octane. The phase behavior was also determined for propane, butane, hexane, and dodecane with the new model. Additionally, the critical parameters of the new model were determined for hexadecane, tetracosane, and octatetracontane. The details of the models follows below.

Potential Models

• Nonbonded interactions

  The nonbonded interactions between groups separated by more than three bonds are described by a pairwise additive intermolecular potential. The NERD and TraPPE models utilize the Lennard-Jones 12-6 intermolecular potential, whereas the new model employs the Buckingham exponential-6 intermolecular potential. The parameters for the models are given below.

  • NERD
    
    
    • Ethane
      

      Group	e	s
      CH3	100.6	3.825

      
      
    • Propane
      

      Group	e	s
      CH3	102.6	3.857
      CH2	45.8	3.93

      
      
    • Butane and longer
      

      Group	e	s
      CH3	104.0	3.91
      CH2	45.8	3.93

      
      
  • TraPPE
    
    

    Group	e	s
    CH3	98.0	3.75
    CH2	46.0	3.95

    
    
  • New Model
    
    

    Group	e	s	a
    CH3	129.63	3.679	16.0
    CH2	73.50	4.000	22.0

  
  
• bonded interactions
  
  
  • Bond Stretching
    
    
    • NERD

      The bond lengths are generated according to the stretching potential:

      V(r) = K_r (r-b_eq)² / 2

      with K_r = 96500 K/A² and b_eq = 1.54 A.

      
      
    • TraPPE

      All bond lengths are held fixed at a distance of 1.54 A.

      
      
    • New model

      The bond lengths are fixed. The length of the bond depends on the groups being connected.

      Bond	Length (A)
      CH3 - CH3	1.839
      CH3 - CH2	1.687
      CH2 - CH2	1.535

    
    
  • Bond Bending

    The bond angles for all of the models are generated according to the bending potential:

    V(q) = K_q (q-q_eq)² / 2

    with K_q = 62500 K/rad² and q_eq = 114.0^o.

    
    
  • Torsion Angles

    The torsion angles for all of the models are generated according to the torsion potential:

    V(f) = V₀ + V₁ (1+cos(f)) + V₂ (1-cos(2f)) + V₃ (1+cos(3f))

    with V₀ = 0 K, V₁ = 355.04 K, V₂ = -68.19 K, V₃ = 701.32 K.