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Organic Materials Properties: Densities, Cohesive Energies, and Heats of Vaporization
This application note describes the calculation of densities, cohesive energy densities (CED), and enthalpies of vaporization for a range of straight chain hydrocarbon fluids. The construction, simulation, and analysis methodologies employed are reviewed; and the accuracy of atomistic simulation for organic materials and polymers illustrated. Mean absolute errors are 0.23% and 0.28% for densities and heats of vaporization respectively for the PCFF+ forcefield.
Organic materials in their various forms are critically important technologically. Hence there is considerable interest in the accurate simulation of their properties. Here we provide an illustration of the simulation of organic fluids, employing straight chain hydrocarbon systems as the basis for the study. These simple hydrocarbon systems are of importance, given their uses as fuels and solvents, and their properties are well characterized experimentally, providing a sound basis for methodological validation.
The methods employed include model construction, making use of the MedeA PolymerBuilder, molecular dynamics calculation, using LAMMPS, and detailed analysis of simulation output managed by the MedeA JobServer.
Atomistic molecular dynamics calculations rely on rapidly calculated forces on component atoms followed integration of Newtonian equations of motion to yield a comprehensive description of the behavior of a given system as a function of time. The combinations of functional form and parameters, required to calculate system energies and forces are collectively termed forcefields 1, and forcefield accuracy governs the quality of simulated properties.
Experience with the simulation techniques illustrated here indicates that the simulation accuracies obtained for hydrocarbons are representative of those achievable for arbitrary organic systems. Modern forcefields for organic systems have been derived on the basis of broad coverage of common molecular components.
Where forcefield coverage is available, simulations may be undertaken and high levels of accuracy obtained in advance of experiment 23456. Forcefields for organic systems are constructed to be broadly applicable, and as the current example illustrates, the agreement between simulation and experiment is generally excellent, with simulated properties typically within a percentage point of observed values.
As noted, the simulations described here employ LAMMPS 7, the Sandia National Laboratories ‘Large-scale Atomic/Molecular Massively Parallel Simulator’, which yields highly optimized molecular dynamics performance, particularly when coupled with multiprocessor compute environments. The MedeA®framework provides a flexible environment to LAMMPS which allows facile model construction, forcefield assignment, simulation workflow construction, calculation management, and analysis capabilities.
Building Hydrocarbon Systems
Atomistic molecular dynamics simulations require a starting model. Here initial hydrocarbon models were constructed using the MedeA PolymerBuilder, where n-decane is treated as a 5-residue polyethylene oligomer. The MedeA PolymerBuilder constructs polymer models from a library of standard repeat units, and provides a comprehensive treatment of composition and stereochemistry.
If required, the repeat unit library can be readily extended by the user, such that any desired chain-like system can be constructed and simulated. The hydrocarbon models described here represent examples of the methodologies typically applied using MedeA®environment and LAMMPS to model polymeric system.
Creating Simulation Models
The simulation of the physical and energetic properties for a fluid requires a condensed model. Such a model may be readily constructed based on the isolated molecular description as shown above. MedeA®supports a variety of tools which can be used to create compact models. For example, the application of a translational symmetry rapidly leads to ‘supercell’ model.
This model can in turn be compacted to typical liquid density using a molecular dynamics simulation protocol which employs a progressively reduced external applied pressure, as shown schematically in flowchart form. Liquid models, and indeed condensed polymer models, can also be readily created using the MedeA Amorphous Cell Builder 8.
MedeA®provides flexible support for forcefields for use within LAMMPS. Atom type assignments are made automatically on the basis of standard template rules 9. Several popular forcefields are supplied with MedeA®for use with LAMMPS.
The present investigation employs the PCFF+ forcefield, which is based on the PCFF forcefield2 with extensions and refinements, in particular for non-bonded parameters, which have been derived as part of Materials Design’s R&D effort in a similar manner to that employed in the earlier development of the COMPASS forcefield3456.
The simulation strategy employed may be summarized as follows:
Construct n-hexane model employing the MedeA PolymerBuilder, and NPT molecular dynamics calculations using MedeA LAMMPS.
Assess the sensitivity of calculated properties to model size and simulation durations. Determine the optimum simulation size and duration.
For a range of hydrocarbons from n-pentane to n-icosane, employ the protocol developed in previous step, computing a range of properties.
Selecting Calculation Parameters
Variation in the calculated density of n-hexane, together with uncertainties estimated from the property’s fluctuations, at 25°C and 1 atmosphere as a function of: (a) system size, (where the number of molecules in the simulation is n³), and (b) simulation duration in picoseconds (ps).
For n-hexane, converged simulation results are obtained with systems of 216 hexane molecules (where the initial supercell dimension is 6) and simulation durations of 200ps.
Practical experience indicates that systems of 3,500 atoms and NPT trajectory durations of 200ps are more than adequate for most purposes. The experimental density of n-hexane at 298.15K is 0.6548 g/cm³ and the simulations yield a value of 0.6547 g/cm³, that is for hexane, the simulated density value (with PCFF+) is just 0.02% lower than the experimental value.
Computed Hydrocarbon Properties
The MedeA LAMMPS flowchart methodology enables the use of reuse of a simulation methodology with any desired system or set of systems. Hence applying this simulation protocol to a range of hydrocarbon systems is rapidly accomplished.
The resulting properties are summarized in the two tables. Densities, with PCFF+, are within 0.5% of experimental values. Cohesive energy densities are also tabulated. Heats of vaporization are closely related to cohesive energy density, and agreement between calculation and experiment is better than 1% (for PCFF+).
Mean absolute errors are 0.23% and 0.28% for densities and heats of vaporization respectively for PCFF+. For comparison, for COMPASS, these values are 0.36% and 1.8%.
These calculated properties are based on simple structural models constructed by using standard techniques within the MedeA®environment, atomistic molecular dynamics simulation, and the PCFF+ forcefield.
Computed densities, cohesive energy densities, and heats of vaporization for selected hydrocarbons at 25°C and 1 atm. The Δρ% and ΔΔHvap% values show the percentage discrepancy between experiment and calculation. Cohesive energy densities were obtained via modifications to LAMMPS made by Materials Design® 10. Experimental densities and heats of vaporization are taken from references 11 and 12 respectively.
|Material||ρ expt. (g/cm³)||ΔHvap expt. (kJ/mol)||ρ calc. PCFF+ (g/cm³)||Δρ PCFF+ (%)||CED calc. PCFF+ (J/cm³)||ΔHvap calc PCFF+ (kJ/mol)||ΔΔHvap PCFF+ (%)|
⁺Extrapolated value for the under-cooled liquid below the normal freezing point.
|Material||ρ expt. (g/cm³)||ΔHvap expt. (kJ/mol)||ρ calc. COMPASS (g/cm³)||Δρ COMPASS (%)||CED calc. COMPASS (J/cm³)||ΔHvap calc COMPASS (kJ/mol)||ΔΔHvap COMPASS (%)|
⁺Extrapolated value for the under-cooled liquid below the normal freezing point.
Additional Simulation Opportunities
As data from the two tables demonstrates, hydrocarbon properties can be simulated computationally with impressive agreement between calculated and experimental densities, cohesive energy densities, and heats of vaporization.
It should also be emphasized that a range of additional properties may also be obtained directly from such simulation procedures. Thermal conductivity, viscosity, the variation in density as a function of pressure, for example, are also accessible, and the agreement between simulation and experiment is also, in general, excellent.
This makes computational screening in advance of experiment or even synthesis practical for many systems. Additionally, diffusive properties are similarly accessible for relatively small molecules (for example those with fewer than approximately 15 carbon atoms) and self diffusion coefficients may be simulated directly using molecular dynamics methods (see 13, for example).
There are some limits on simulated properties. Simulations are typically currently limited to trajectories extending to nano-second timescales. Hence, intrinsically slow dynamical processes, as occur in long chain polymer systems, or diffusion of large molecules, present difficulties. Additionally, system sizes are typically limited to systems measured in the thousands of atoms.
However, LAMMPS is able to exploit parallel compute resources with ease and microsecond simulation durations are becoming more common 14, and million and billion atom simulations have been reported by several groups using LAMMPS 1516.
Given the sound methodological basis of the calculations, and the increasing affordability of computational resources, it is quite clear that molecular dynamics simulations will be of ongoing importance and impact in the prediction and rationalization of the properties of organic materials.
MedeA Modules Employed
The present calculations were performed with the MedeA®platform using the following integrated modules in the MedeA®software environment:
- The standard MedeA®framework
- MedeA PolymerBuilder
- MedeA LAMMPS interface
- MedeA JobServer
- MedeA TaskServers
References and Notes
Calculations based on empirical energy functions and parameters derive from early analysis of vibrational properties of molecular systems, leading the use of the term forcefield to describe functional form and its parameterization. ↩
H. Sun, S. J. Mumby, J.R. Maple, A. T. Hagler, J. Phys. Chem. 99, 5873 (1995) ↩
H. Sun and D. Rigby, Spectrochimica Acta A153, 1301 (1997) ↩
D. Rigby, H. Sun, B.E. Eichinger, Polymer International 44, 311 (1997) ↩
H. Sun, J. Phys. Chem. B102, 7338 (1998) ↩
H. Sun, P. Ren, J.R. Fried, Comput. Theor. Polymer Sci. 8, 229 (1998) ↩
The MedeA Amorphous Cell Builder is scheduled for release in January 2012. ↩
Forcefield assignment template rules employ a chemical pattern language which for the recognition of specific groups of atoms and the assignment of appropriate forcefield types. Partial charge assignments are also made automatically, on the basis of bond charge increments. ↩
Modification to LAMMPS for cohesive energy density calculation made by Materials Design®. The source code for these changes is available upon request. The results of the tables were obtained with 500ps trajectories with 1000 molecules in the simulation cell. ↩
F.D. Rossini, Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds, Carnegie Press, Pittsburgh (1953) ↩
Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation, Blackwell Scientific Publications, Oxford (1985) ↩
Y. Iwai, H. Higashi, H. Uchida, Y. Arai, Fluid Phase Equilibria 127, 251 (1997) ↩
M.L. Klein, W. Shinoda, Science 321, 798 (2008) ↩
M. Buehler, A. Hartmaier, M. Duchaineau, F. Abraham and H. Gao Acta Mech Sinica 21, 103 (2005) ↩
F. Abraham, R. Walkup, H. Gao, M. Duchaineau, T. D. De La Rubia, M. Seager Proc. Natl. Acad. Sci. 99, 5783 (2002) ↩