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A Monte Carlo discrete sum (MCDS) approach to energies of formation for small methanol clusters

A Monte Carlo discrete sum (MCDS) approach to energies of formation for small methanol clusters. Srivatsan Raman*, Barbara Hale and Gerald Wilemski. Physics Department, *Chemical Engineering Department University of Missouri-Rolla, Rolla, MO – 65409, USA.

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A Monte Carlo discrete sum (MCDS) approach to energies of formation for small methanol clusters

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  1. A Monte Carlo discrete sum (MCDS) approach to energies of formation for small methanol clusters Srivatsan Raman*, Barbara Hale and Gerald Wilemski Physics Department, *Chemical Engineering Department University of Missouri-Rolla, Rolla, MO – 65409, USA Supported by the Engineering Physics Program, U.S. DOE

  2. Experimental Nucleation rates JEXP vs Classical Theory Predictions JCLASSICAL

  3. MOTIVATION FOR THIS WORK • Classical Nucleation Model – Poor temperature dependence • To apply a molecular treatment of small Methanol clusters – Avoid use of bulk surface tension and describe cluster as discrete set of molecules • To build a foundation for treating binary systems comprising methanol and water

  4. MCDS nucleation rate model:(n*) = critical size cluster concentration from Monte CarloNucleation rate, JMCDS = classical steady state form J MCDS = Jo cl(n*)Monte Carlo Jo cl= monomer flux factor times Zeldovich factor Use sum of Monte Carlo free energy differences.

  5. Hydrogen CH3 Methyl group + + Oxygen THREE-SITE INTERMOLECULAR PAIR POTENTIAL FOR METHANOL* Atom/Func grp O 86.5 3.030 -0.700 CH3 105.2 3.740 +0.265 H 0.0 0.0 +0.435 rCO 1.4246 Å rOH 0.9451 Å 108.53o Uαβ = ULJ + UCOULOMB * Monica E. van Leeuwen and Berend Smit, J. Phys Chem, 99,1831 (1995)

  6. STATISTICAL MECHANICAL FORMALISM Law of Mass Action (Assuming non-interacting mixture of ideal gases with each cluster constituting an ideal gas system) Separating the kinetic energy contribution from the canonical partition function, Z, we have…. ‘Q’ is the configurational partition function

  7. After algebraic manipulations, we have where, ‘S1’ is the monomer supersaturation ratio

  8. The Two Canonical Ensembles Ensemble A n molecules Ensemble B (n-1) molecules in cluster + one monomer

  9. vs ANALYSIS OF -δFn We plot or,

  10. vs

  11. vs

  12. vs

  13. MOTIVATION FOR SCALING OF FREE ENERGY DIFFERENCES WITH (TC/T – 1) is the cluster excess surface entropy per molecule is a nearly universal constant. It is about ‘2’ for most substances, but for associated liquids, it is approximately ‘1.5’

  14. Experimental Nucleation rates JEXP vs Classical Theory Predictions JCLASSICAL

  15. Experimental Nucleation rates JEXP vs Monte Carlo calculated Nucleation rates JMCDS

  16. Results and Discussion • Potential model and free energy difference results: • -- slope agrees with σbulk in the limit of large cluster sizes • -- intercept indicates about the right vapor pressure • -- the free energies scale with [Tc/T -1] and permit • predictions of J over range of T • Prediction of nucleation rate: • -- no improvement over classical model in terms of magnitude -- improved temperature dependence for 255 K and 272 K data • Large discrepancy in magnitude of J: • Experimental data are corrected for small n-mer formation • (Strey et al). Can present model provide improved estimate of heat of association effect on final temperature?

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