Monte Carlo Calculations for Alcohols
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Transcript of Monte Carlo Calculations for Alcohols
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MONTE CARLO CALCULATIONS FOR
ALCOHOLS
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ABSTRACT
Trappe-UA force-field for hydrocarbons has been extended to primary, secondary
alcohols.
Coupled-decoupled configurational bias Monte-Carlo Simulations in the Gibbs ensemble
has been carried to calculate the 1 component vapor-liquid coexistence curves for
Alcohols.
Phase equilibria of the pure alcohols are accurately described by the Trappe-UA Force
fields.
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IMPORTANCE OF VLE
VLE gives the nature of intermolecular interactions present in
the liquid and vapor phases.
Useful in developing equations of state and corresponding state
theories Knowledge of critical points and VLE are key to achieving
fundamental understanding of these fluids.
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ALCOHOLS UNDER STUDY
Methanol
Ethanol
Propan-1-ol
Propan-2-ol
Butan-2-ol
Pentan-1-ol
Octan-1-ol
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ALCOHOLS
They are amphiphilic molecules composed of a f lexible, non-polar alkyl tail and a polar
hydroxyl head that is capable of acting as hydrogen donor and acceptor
Alcohols have desirable solvent characteristics due to their amphiphil ic nature.
They are readily available
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NEED FOR MOLECULAR SIMULATION
Knowledge of fluid phase diagrams and related thermo-physical properties is
essential in process design and process optimization.
Reliable Experimental data are only available for relatively low molecular
weight alcohols and only over a limited temperature range because of their
thermal instability above 600K. Molecular simulation is an alternative approach to obtain the thermo-physical
properties of alcohols
Accuracy of the prediction depends largely on the quality of the force-field
used and how well it describes the system.
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TRAPPE MODEL
Trappe Model was developed to
Reproduce Thermo-Physical Properties over a wide range of physical Conditions
Keep the models as transferable as possible by minimizing the number of (Pseudo)
atoms needed for any particular molecule and by using the same parameters for a
given (Pseudo) atom in all types of molecules
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TRAPPE MODEL
A Pseudo Atom mimics the interactions of its core electrons plus a share of the valence
electron that make its bonds to the neighboring atoms.
The Contribution of the valence electrons far outweighs the contribution of the core
electrons towards molecular polarizability.
Example: Pseudo atom for methyl group that is connected to another Carbon atom,
accounts for 3 C-H bonds and a share of the C-C bond. The same Pseudo atom can be
used for the methyl group in ethane, propane etc.
However the pseudo atom for the methyl group connected by a single bond to an Oxygen
atom is different due to the differences in the electronegativity between C and O atoms
which leads to intramolecular charge transfer and requires the use of a partial charge
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FORCE FIELD DEVELOPMENT
In Trappe-UA model, CHx groups are treated as pseudo atoms located at the sites of the
carbon atoms whereas all other atoms(e.g O and H) are modeled explicitly.
Non-bonded interactions are described by
Non-Bonded potentials of the above equation are used only for interactions of pseudo-
atoms belonging to different molecules or belonging to the same molecule but whose
interactions are not accounted for by any of the intramolecular, bonded potentials.
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FORCE-FIELD DEVELOPMENT
In TRAPPE-UA force-fields, all bond-lengths are fixed
A harmonic potential is used to control bond angle bending
Where , o and K are the measured bending angle, equilibrium bending angle and the
force constant
The Torsional potentials used to restrict the dihedral rotations is as shown above
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SIMULATION DETAILS
Combination of the Gibbs Ensemble Monte Carlo Method and the Configurational Bias
Monte Carlo method was employed to calculate the Vapor-Liquid Coexistence curves
Combined volume of the simulation boxes was adjusted to yield liquid-phase simulation
boxes with linear dimension of 30 A and larger vapor -phase simulation box containing
atleast 10 molecules
For the LJ part of the potential, a cut -off distance of 14 A was set and analytic tail
corrections were enforced.
An Ewald sum with thin-foil boundary conditions was used for the long-range electrostatic
interactions
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SIMULATION DETAILS
5 different Monte-Carlo moves were used to sample phase space in the Gibbs ensemble
simulations. The moves are
Translational
Rotational
Conformational
Volume Exchanges
Particle Swaps between boxes
Moves were selected randomly with fixed probabilities that were adjusted to yield about
one volume exchange or particle swap move per 10 MC Cycles and the remainder of the
moves were equally divided among the other moves
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SIMULATION DETAILS
Coupled decoupled Configurational Bias Monte-Carlo algorithm was used for
conformational and particle swap moves.
Computational efficiency was increased by utilizing a
Biased insertion
Additional center of mass based cut-off which avoids computing unnecessarydistances.
Coupled-decoupled CBMC particle swap proceeds as follows
(i) The hydroxyl O is inserted(using multiple insertions)
(ii) The Hydroxyl H and -carbons are added as a consequence
(iii) Then, the remainder of the alkyl tail is grown
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RESULTS
Methanol(Dashed lines and Squares), Ethanol(Solid lines and circles)
Pentan-1-ol(dotted lines and diamonds), octan-1-ol (dash-dotted lines and triangles up)
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RESULTS
Propan-1-ol(solid lines and circles), Propan-2-ol ( dashed lines and squares)
Butan-2-ol (dash-dotted lines and tr iangles down)
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RESULTS
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RESULTS
Experimental Saturated liquid densities are very well reproduced with average deviations
of about 1%.
However, larger deviations were observed for the saturated vapor densities and
pressures.
Vapor pressures are overestimated at higher reduced temperatures but underestimated at
lower reduced temperatures which is more pronounced for lower molecular weight
alcohols. TRAPPE force-field predicted high saturated vapor-pressures for unsaturated
alkanes too.
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CRITICAL CONSTANTS
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RESULTS
Agreement for the critical constants are satisfactory
Critical Temperatures of most alcohols are slightly underestimated with an average
deviation of about 1.5%
Critical densities are overestimated on average by about 3%
Critical Density disagreement can be due to
Law of rectilinear diameters has a negative slope, an underestimation of the
critical temperatures results in an overestimation of the critical densities
Vapor densities at elevated temperatures are too high, which results in a shift of
the mean saturated densities to higher values
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OUR GCN AND NPT RESULTS
T p rVap rLiq(K) (MPa) (kg/m3) (kg/m3)
470 1.64303 34.44982 591.996500 3.017061 70.74142 521.8192510 3.618617 91.18393 488.4794515 3.948885 106.3667 468.5673
470 1.626919 33.83991 591.4571500 3.02532 74.36615 515.2263510 3.616337 91.72798 485.3918515 3.923665 105.7948 472.4864
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CONCLUSION
The performance of the TRAPPE-UA Force field for the prediction of thermo-physical
properties is in general very satisfactory with mean errors of about
1% for the saturated liquid densities
1.5% for the critical temperature
3% for the critical density
As observed for alkanes, alkenes, this force field tends to over-predict the saturated
vapor densities.
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REFERENCES
Bin chen,Jeffrey J. Potoff, and J. Iija Siepmann. Monte Carlo Calculations for Alcohols.
Transferable Potentials for Phase equilibria. 5. United-Atom Description of Alcohols
Frenkel D and Smit B. Understanding Molecular Simulations.
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THANK YOU