**Molecular
Simulation Study of n-Alkane Mixtures using Transition Matrix Monte Carlo
Methods**

Tamaghna
Chakraborti^{1}, Jhumpa Adhikari^{1}

^{1}Department
of Chemical Engineering, IIT Bombay,

Powai, Mumbai – 400076.

(E-mail : tamaghna.chakraborti@gmail,com, adhikari@che.iitb.ac.in )

*Abstract*
– Fluid phase equilibrium is one of the very important aspects of the chemical
industry. With the advent and improvement of computational resources molecular
simulation techniques have become an important means to obtain the desired
equilibrium properties. Pertinent to molecular simulation techniques is the
question of obtaining reliable and reproducible data in the least
computationally expensive way possible. Molecular simulation techniques require
as input a potential model which governs the way different molecules in a
system interact with one another. The accuracy and the reliability of data
obtained from molecular simulations depend to a considerable extent on the different
potential models which are available in literature like TraPPE^{1},
NERD^{2}
and COMPASS^{3}
with TraPPE being more successful than others in the realm of fluid phase
equilibrium. Different simulation techniques have been tried in order to obtain
macroscopic equilibrium properties in the least computationally expensive way
possible. One of the first techniques to compute equilibrium properties without
the use of an interface (which is computationally intensive due to the large
number of molecules involved) was by using the Gibbs ensemble Monte Carlo
technique^{4}
by Panagiotopoulos. With the advent of transition matrix Monte Carlo methods,
new methods for determination of fluid phase equilibria have evolved. Errington^{5}
had successfully incorporated the transition matrix technique to the grand
canonical and the isothermal-isobaric ensemble simulation algorithm and used it
to determine the phase diagram of Lennard-Jones fluid. Shen and Errington^{6}^{,}^{7}
had extended the technique to the determination of phase diagrams of monoatomic
mixtures. It is the endeavor of this work to extend the work of Shen and
Errington to molecular mixtures starting with the n-alkane homologous series.
The n-alkane series is probably the most widely studied of all molecular groups^{8}^{,}^{9}^{,}^{10}
mainly because of the simplicity of its implementation. The systems being studied
here are the methane-ethane, ethane-propane and propane-butane molecular
mixtures. The main reason for studying these binary mixture systems is that the
critical points of the respective components are close to one another the
molecules being adjacent in the same homologous series. All the systems are
well studied both using experiments as well as molecular simulations. This
makes it amenable to comparison with data available from literature. The whole
point of this exercise is to check the validity of the TraPPE forcefield as we
deal with molecular mixtures as well as extend the method of Shen and Errington^{7}
to molecular mixtures. The results indicate that TraPPE does well in accounting
for the equilibrium densities of the vapor and the liquid phases, it misses the
mark by a wide margin when it comes to calculation of pressure.

**References**

1. Martin, M. G. & Siepmann, J. I. Transferable Potentials for Phase Equilibria. 1.
United-Atom Description of n -Alkanes. **5647,** 2569–2577 (1998).

2. Nath, S. K.,
Escobedo, F. a. & de Pablo, J. J. On the simulation of vapor–liquid
equilibria for alkanes. *J. Chem. Phys.* **108,** 9905 (1998).

3. Martin, M. G. &
Thompson, A. P. Industrial property prediction using Towhee and LAMMPS. *Fluid
Phase Equilib.* **217,** 105–110 (2004).

4. Panagiotopoulos, A.
Z. Exact calculations of fluid-phase equilibria by Monte Carlo simulation in a
new statistical ensemble. *Int. J. Thermophys.* **10,** 447–457 (1989).

5. Errington, J. R.
Direct calculation of liquid–vapor phase equilibria from transition matrix
Monte Carlo simulation. *J. Chem. Phys.* **118,** 9915 (2003).

6. Shen, V. K. &
Errington, J. R. Determination of fluid-phase behavior using transition-matrix
Monte Carlo: binary Lennard-Jones mixtures. *J. Chem. Phys.* **122,**
064508 (2005).

7. Errington, J. R.
& Shen, V. K. Direct evaluation of multicomponent phase equilibria using
flat-histogram methods. *J. Chem. Phys.* **123,** 164103 (2005).

8. Smit, B.,
Karaborni, S. & Siepmann, J. I. Computer simulations of vapor–liquid phase
equilibria of n-alkanes. *J. Chem. Phys.* **102,** 2126 (1995).

9. Singh, J. K. &
Errington, J. R. Calculation of phase coexistence properties and surface
tensions of n-alkanes with grand-canonical transition-matrix monte carlo
simulation and finite-size scaling. *J. Phys. Chem. B* **110,** 1369–76
(2006).

10. Pàmies, J. C.,
McCabe, C., Cummings, P. T. & Vega, L. F. Coexistence Densities of Methane
and Propane by Canonical Molecular Dynamics and Gibbs Ensemble Monte Carlo
Simulations. *Mol. Simul.* **29,** 463–470 (2003).

** **

**Extended Abstract:**File Not Uploaded

See more of this Group/Topical: Engineering Sciences and Fundamentals