(335b) Effects Of Attractive Forces On The Diffusivity Based On The Speadmd Model
When new molecules are synthesized, their target properties may be well known but their engineering properties may be completely unknown. For example, a small molecule drug candidate may be known to have high biological activity, but measuring its vapor pressure, bulk density, viscosity, and thermal conductivity would require gram quantities. Even the melting temperatures measured by millions of freshman chemistry students require purified quantities near 0.01g. Developing those quantities with that purity can be overwhelming for the large number of trial products that may be encountered in the early stages of development.
The Step Potential Equilibria And Discontinuous Molecular Dynamics (SPEADMD) model provides a basis for molecular modeling of thermodynamic and transport properties. It is based on Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic Perturbation Theory (TPT). DMD simulation is applied to the repulsive part of the potential, complete with molecular details like interpenetration of the interaction sites, 110?a bond angles, branching, and rings.1,2 The thermodynamic effects of disperse attractions and hydrogen bonding are treated by TPT. This approach accelerates the molecular simulations in general and the parameterization of the transferable potentials in particular. Transferable potentials have been developed and tested for over 200 components comprising 22 families.3,4
Unfortunately, there is no theory comparable to TPT when treating transport properties.5 Most theories of transport properties rely on empirical variations of correlations for spherical reference fluids. Furthermore, existing correlations are typically specific to a given range of conditions: gas, dense gas, or liquid, for example. To overcome this situation, we must leverage the dynamics from the reference fluid simulations while accurately correlating and predicting experimental data. We show how to achieve this combination of rigorous fundamentals and empirical accuracy and compare to the accuracy of existing engineering correlations for diffusivity, thermal conductivity, and viscosity.
Diffusivity is the simplest property to study by molecular simulation, but its treatment provides valuable insights into other transport properties. This work analyzes the diffusivity as a function of temperature at five packing fractions for n-alkane chains with 5, 10, 20, and 40 carbons. The attractive potentials are modeled as described by Elliott and Gray.6 We find that the attractive forces impart a steady frictional contribution that increases strongly with chain length. The increasing friction with chain length due to attractive forces is stronger than the increase due to repulsive forces for chains in this length range. These data provide a basis for a generalized correlation with comparison to the experimental data of von Meerwall and coworkers.7
(1) Cui, J.; Elliott Jr., J. R. Phase Diagrams for Multi-Step Potential Models of n-Alkanes by Discontinuous Molecular Dynamics/Thermodynamic Perturbation Theory.J. Chem. Phys. 2002, 116, 8625. (2) Unlu, O.; Gray, N. H.; Gerek, Z. N.; Elliott, J. R. Transferable Step Potentials for the Straight Chain Alkanes, Alkenes, Alkynes, Ethers, and Alcohols.Ind. Eng. Chem. Res. 2004, 43, 1788-1793. (3) Baskaya, F. S.; Gray, N. H.; Gerek, Z. N.; Elliott, J. R. Transferable Step Potentials for Amines, Amides, Acetates, and Ketones.Fluid Phase Eq. 2005, 236, 42-52. (4) Gray, N. H.; Gerek, Z. N.; Elliott, J. R. Molecular Modeling of Isomer Effects in Naphthenic and Aromatic Hydrocarbons.Fluid Phase Eq. 2005, Vol 228-229C, 147-153. (5) Alder, B. J.; Alley, W. E.; Rigby, M. Correction to the Van Der Waals Model for Mixtures and for the Diffusion Coefficient.Physica 1974, 73, 143-155. (6) Elliott, J. R.; Gray, N. H. Asymptotic Trends in Thermodynamic Perturbation Theory.J. Chem. Phys. 2005, 123, 184902. (7) Tao, H.; Lodge, T. P.; von Meerwall, E. D. Diffusivity and Viscosity of Concentrated Hydrogenated Polybutadiene Solutions.Macromolecules 2000, 33, 1747-1758.