CHME 498 Undergraduate Research Final Report New Mexico State University Gibbs Ensemble Computer Simulations of Vapor Liquid Equilibrium of Hydrazine Summer 2017 Gustav Barraza Faculty Adviser: Dr. Martha C. Mitchell P.E. July 31, 2017
The focus of this research is to develop an accurate representation of the vapor-liquid equilibrium region of hydrazine through Gibbs Ensemble computer simulations. Hydrazine is a highly reactive base and is often used as rocket propellant, this makes wet laboratory data collection dangerous. Computer simulations provide a safe method to gain understanding of this molecule s properties. To accomplish this long-term goal, baseline student objectives were set including: developing an understanding of thermodynamic elements of the vapor-liquid equilibrium region, developing basic understanding of statistical mechanics, developing understanding of molecular Monte-Carlo simulations, apply concepts to computer simulation software (MCCCS Towhee), and to extrapolate statistical thermodynamic data collected from computer simulations to develop a comprehensive vapor-liquid equilibrium region. The vapor-liquid equilibrium region, in its most general form, is where liquid and vapor states coexist with equal Gibbs energy. This information gives engineers access to many thermodynamic properties through equations of state such as, vapor pressure, triple and critical points and a more accurate notion of how a material may behave in application. The vapor liquid equilibrium region is bound by the triple and critical point. Modeling the vapor-liquid equilibrium region requires a vast amount of data collection. Empirical data for mapping an accurate depiction of the state equilibrium is not available for hydrazine. This leads us to run molecular simulations to acquire the data. Molecular simulations use statistical mechanics along with computer and statistical sciences to apply the laws of physics to comprehensively examine a system. The use of statistical mechanics is vital to this process. Statistical mechanics is a study that invokes classical and quantum mechanics assessing a system with theoretical probabilities yielding a proposed average behavior of a system (Frenkel & Smit, 2002). Though these means
data can be extrapolated to develop an accurate vapor-liquid equilibrium region for hydrazine that will be used by engineering and scientists to use in the field in many applications. The Monte Carlo method were first introduced by Ulam, Neumann, and Metropolis (Allen & Tildesley, 1996). The method is now widely used in many different sectors, including molecular simulations. The basis of the Monte Carlo method is a random input (fitting the set parameter) representative of the system, yields a probable output (Dizikes, 2010). After a multitude of runs the data is sufficient to compute an accurate average of the outputs. Due to its accuracy and principle of randomness it is a good choice for conduction molecular simulations, and evaluating thermodynamic properties. Monte Carlo simulations can handle the complex natural of molecular movements, and the functions used to describe the system such as the partition functions given by the Gibbs ensemble for example. Monte Carlo simulations demonstrates that it is adequate for the application of this research topic and maintains the integrity of its averages in complex situations. The statistical mechanics ensemble chosen, to assess hydrazine, is the Gibbs Ensemble. The Gibbs Ensemble is often chosen because of is simplicity, and accuracy in studying fluid phase equilibria. The Gibbs Ensemble, originally proposed by Panagiotopoulos, is an ensemble in which two theoretical boxes exist one in the vapor state and the other in the liquid state of the bulk (Panagiotopoulos, 1995). For simplicity, the boxes do not encompass the equilibrium region itself because this drastically increases the complexity of the simulation, and therefore increasing the computation difficulty (Frenkel & Smit, 2002). This ensemble holds pressure, temperature, and chemical potential constant across the boxes with respect to each other, while maintaining a fixed temperature (T) and fixed number of molecules (N). This means the individual boxes are
allowed to change if the net values stay constant (e.g. N = Nbox1+Nbox2, V= V1+V2) (Panagiotopoulos, 1995). A partition function describes the average energy of the system at a given temperature. The Gibbs ensemble used the QG (N, V, T) partition function shown below. N, V, T Λ!! exp exp Equation 1 (Frenkel & Smit, 2002) Λ is defined as the thermal de Broglie wavelength (Frenkel & Smit, 2002). N are the particles distributed over two volumes V1 and V2 = V V1 From the preceding expression, it follows that the probability of finding a configuration with n1 particles in box 1 with a volume V1 and positions (in scaled coordinates) and is given by the expression below.,,, exp!! Equation 2 (Frenkel & Smit, 2002) In the Gibbs Ensemble, the change in the system simulation comes from three Monte Carlo moves to develop understanding of fluid phase equilibria: displacement of a molecule within the box, a change volume of the box, or a movement of a molecule from one box to other. The listed moves have a way in which they uniquely satisfy the overall equilibrium of the two test regions. Displacement of a molecule within a box accounts for the equality of internal equilibrium. The change in box volumes accounts for pressure equality. The transfer of molecules between boxes
accounts for equality of chemical potential. Pictured below is an illustration that aids in the comprehension of the Monte Carlo moves described. (Panagiotopoulos, 1995) These moves must meet acceptance criteria (derived from Equation 2) before being approved as valid moves. Through these moves an average is computed and used to draw a picture of valid thermodynamic properties. The vapor-liquid equilibrium region of hydrazine will be developed by data yielded from a computer simulation software called MCCCS Towhee. MCCCS (Monte Carlo for Complex
Chemical Systems) Towhee is an open source software project lead by Marcus G. Martin. Towhee is a Monte Carlo molecular simulation code originally designed for the prediction of fluid phase equilibria using atom-based force fields and the Gibbs ensemble with particular attention paid to algorithms addressing molecule conformation sampling. (Martin, 2014). The software runs via a Unix operating system or like environment. A large of amount of time was used learning how to navigate this type of operating system. A focus of mine was running examples simulations, given by MCCCS Towhee, and cross referencing output files to assure that the software was compiled correctly. I was determined that the software was operational. The software, from a user stand point, consists of developing a force field file, input file, and output file. A tailored force field file for hydrazine has written by Dr. Mitchell and will be used to run simulations. The force field file consists of developed parameters, such as bonding information, angles, torsion information, and other hydrazine related molecular components. The input file is where most of the editing for simulations is completed. Input files consist of in for information setting parameters for the simulation such as ensemble type, necessary set parameters (such as T, N, and paths to the force field file), and logical arguments. The information given in the input files is used by towhee to dictate the how the simulation should be executed. The output files are where results of a simulation can be viewed for interpretation. The output file outlines results including energy data, chemical potential, density, temperature, and pressure information. The results are a product of simulation averages. Towhee provides a comprehensive platform on which to run molecular simulations. In conclusion of this research experience, the outlined objectives were met. Including basic knowledge of vapor-liquid equilibrium region, statistical mechanics, molecular Monte- Carlo simulations, software MCCCS Towhee, and to extrapolate statistical thermodynamic data.
The development of hydrazine vapor-liquid equilibrium is ready for the next round of Gibbs Ensemble computer simulations.
Citations Allen, M. P., & Tildesley, D. J. (1996). Computer Simulations of Liquids. Oxford: Oxford University Press. Anderson, P. K. (2006). Just Enough Unix (5th ed.). McGraw-Hill. Dizikes, P. (2010). Explained: Monte Carlo simulations (Mathematical technique lets scientists make estimates in a probabilistic world). Retrieved July 30, 2017, from http://news.mit.edu/2010/exp-monte-carlo-0517 MIT News Frenkel, D., & Smit, B. (2002). Understanding Molecular Simulation: From Algorithms to Application (2nd ed.). San Diego, California: Academic Press. Marcus G. Martin. (2014). Retrieved July 30, 2017, from http://towhee.sourceforge.net Panagiotopoulos A.Z. (1995). in M. Baus, L.R. Rull and J.P. Ryckaert, Observation, prediction and simulation of phase transitions in complex fluids, NATO ASI Series C, vol 460, pp. 463-501, Kluwer Academic Publishers, Dordrecht, The Netherlands.