Post on 29-Dec-2015
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Effect of the Range of Interactionson the Properties of Fluids
Equilibria of CO2, Acetone, Methanol and Water
Ivo Nezbeda 1,2, Ariel A. Chialvo 3,2, and Peter T. Cummings 2,3
1 Institute of Chemical Process Fundamentals. Academic of
Sciences, 16502 Prague 6 - Suchdol, Czech Republic2 Departments of Chemical Engineering. University of
Tennessee, Knoxville, TN 37996-2200, U.S.A.3 Chemical Sciences Division. Oak Ridge National Laboratory,
Oak Ridge, TN 37881-6110, U.S.A.
2
Rationale Generally long-range forces have negligible effect on the microstructure of fluids
• the structure of realistic model fluids and their short-range counterpart are (for all practical purposes) identical
Thermodynamic properties of fluids are accurately estimated by those of the short-range model counterparts
• e.g., configurational energy of the short-range models account for 95% of the total property
Long-range forces affect only details of the orientational correlations
• however, the dielectric constant remains unaffected These findings support the development of fast converging perturbation expansions
about the short-range reference• i.e., long-range Coulombic interactions treated as a perturbation
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Goals
Determine the effect of the long-range Coulombic interactions on the vapor-liquid equilibria properties of polar and associating fluids
• most realistic intermolecular potential models available carbon dioxide, acetone, methanol, and water
Interpret simulation results and develop simple perturbation approaches for
rigorous modeling
• modeling of aqueous solutions without resorting to long-range interactions e.g., I. Nezbeda, Mol. Phys., 99, 1631-1639 (2001)
• truly molecular-based equation of state for engineering calculations e.g., recently proposed equation for water (Nezbeda & Weingerl, Mol. Phys., 99,
1595-1606 (2001))
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Range of Intermolecular Interactions
Basic definitions
• Separation between short- and long-range potential interaction
€
u(r12,ω1,ω2 ) ≡ u(1,2) = uLJ (rss ) +qiq j
riji∈1, j∈2∑ucoul (1,2)
1 2 4 3 4
€
ushort −range (1,2) = u(1,2) − S(rss,rL ,rU )ucoul (1,2)
= uLJ (rss )+ 1− S(rss,rL ,rU )[ ]ucoul (1,2)
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Range of Intermolecular Interactions
Basic definitions• Switching function for the range transition
(e.g., rss=rOO for the case of water and methanol)
€
S(rss ,rL ,rU ) =
0 for r < rL
(r − rL )2(3rU − rL − 2r)
(rU − rL )3 for rL < r < rU
1 for r > rU
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
€
rss ≡ distance between reference (LJ) sites
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Range of Intermolecular Interactions
Simulation details• VLE simulations by NVT-GEMC
• Isochoric simulations by NVT-MD 516<N<700 for GEMC N=500 for MD cutoff distance ~ 3.6-5.0 ss (i.e., ~12-19Å)
electrostatics via reaction field Nosé thermostat for MD quaternion dynamics [rL, rU] chosen according to the location of the first peak of the RDF
for the reference sites
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Vapor-Liquid Equilibrium of Model Carbon Dioxide
Harris-Yung’s EPM2 model (*)• Estimated critical conditions from Wegner expansion
Short-range potential: Tc=310.8K, c=458.6kg/m3
Full potential: Tc=310.9K, c=455.1kg/m3
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0220.0
240.0
260.0
280.0
300.0
320.0
short-range
full-range
density (kg/m3)
T(K) CO2
-14.0 -12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0
short-range
full-range
Uc (kJ/mole)
CO2
(*) Harris and Yung, JCP, 99 (1995)
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Vapor-Liquid Equilibrium of Model Acetone
Jedlovszky-Pálinkás model (*)• Estimated critical conditions from Wegner expansion
Short-range potential: Tc=505.5K, c=275.0kg/m3
Full potential: Tc=499.3K, c=273.3kg/m3
-30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0
short-range
full-range
Uc(kJ/mole)
ACETONE
0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0
short-range
full-range
280.0
300.0
320.0
340.0
360.0
380.0
400.0
420.0
440.0
density (kg/m3)
ACETONE
T (K)
(*) Jedlovszky and Pálinkás, Mol. Phys., 84 (1995)
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Vapor-Liquid Equilibrium of Model Methanol
OPLS model (*)• Estimated critical conditions from Wegner expansion
Short-range potential: Tc=483.4K, c=250.2kg/m3
Full potential: Tc=484.6K, c=258.2kg/m3
0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0300.0
350.0
400.0
450.0
500.0
short-range
full-range
density (kg/m3)
T(K)METHANOL
(*)Jorgensen et al., JACS, 106 (1984)
-35.0 -30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0
short-range
full-range
Uc (kJ/mole)
METHANOL
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Vapor-Liquid Equilibrium of Model Water
TIP4P model (*)• Estimated critical conditions from Wegner expansion
Short-range potential: Tc=564.9K, c=339.4kg/m3
Full potential: Tc=566.1K, c=321.8kg/m3
-40.0 -30.0 -20.0 -10.0 0.0
short-range
full-range
Uc (kJ/mole)
WATER
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0300.0
350.0
400.0
450.0
500.0
550.0
600.0
short-range
full-range
density (kg/m3)
T(K) WATER
(*) Jorgensen, JCP, 77 (1982)
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Vapor-Liquid Equilibrium
Effect of range on vapor pressure (*)
(*) Nezbeda et al., (2001)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
280.0 300.0 320.0 340.0 360.0 380.0 400.0 420.0 440.0
short-rangefull-rangepressure (MPa)
Temperature (K)
ACETONE
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
220.0 240.0 260.0 280.0 300.0 320.0
short-rangefull-rangepressure (MPa)
Temperature (K)
CO2
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
300.0 350.0 400.0 450.0 500.0
short-rangefull-rangepressure (MPa)
Temperature (K)
METHANOL
0.0
20.0
40.0
60.0
80.0
100.0
120.0
300.0 350.0 400.0 450.0 500.0 550.0 600.0
short-rangefull-range
Pressure (MPa)
Temperature (K)
WATER
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Structure and Thermodynamics of Model Methanol
Effect of range on properties along isochore =0.76g/cc (*)
-38.0
-36.0
-34.0
-32.0
-30.0
-28.0
-26.0
-24.0
250.0 300.0 350.0 400.0 450.0 500.0 550.0
short-rangefull-range
Configurational Energy (kJ/mole)
Temperature (K)
-50.0
0.0
50.0
100.0
150.0
200.0
250.0
300.0
250.0 300.0 350.0 400.0 450.0 500.0 550.0
short-rangefull-range
Pressure (MPa)
Temperature (K)
(*) Nezbeda et al. (2001)
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Structure and Thermodynamics of Model Methanol
Effect of range on structure along isochore =0.76g/cc (*)
T=298K
(*) Nezbeda et al. (2001)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0
short-rangefull-range
gOO
(r)
r (Å)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
short-rangefull-range
gOH
(r)
r (Å)
0.0
0.5
1.0
1.5
2.0
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
short-rangefull-range
gCC
(r)
r (Å)
0.0
0.5
1.0
1.5
2.0
2.5
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
short-rangefull-range
gCO
(r)
r (Å)
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Structure and Thermodynamics of Model Methanol
Effect of range on structure along isochore =0.76g/cc (*)
T=548K
(*) Nezbeda et al. (2001)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
short-rangefull-range
gCO
(r)
r (Å)
0.0
0.5
1.0
1.5
2.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0
short-rangefull-range
gOO
(r)
r (Å)
0.0
0.5
1.0
1.5
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
short-rangefull-range
gOH
(r)
r (Å)
0.0
0.5
1.0
1.5
2.0
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
short-rangefull-range
gCC
(r)
r (Å)
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Interpretation of Simulation Results
Gibbs-Duhem equations including force-field variables (*)• Define coupling parameter , i.e.,
• Apply equilibrium conditions
• Derive Clapeyron equation
€
ufull−range = ushort−range + λ upert
€
−Sl − Sυ( )dT + V l −V υ
( )dP = −N upert TP
l− upert TP
υ ⎛ ⎝
⎞ ⎠dλ
€
dP dλ( )σ T = − N upert TP
l− upert TP
υ ⎛ ⎝
⎞ ⎠ V l − V υ
( )
(*) Nezbeda et al. (2001)
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Interpretation of Simulation Results
Gibbs-Duhem equations including force-field variables (*)
• Particular cases can be derived depending on relative sizes of the
involved properties in each phase
typical case (water and acetone)
additional cases apply to carbon dioxide and methanol
€
upert TP
l>> upert TP
υ
€
V l << V υ ≈ NkT P
€
Pfull−range ≅ Pshort −range × exp − upert TP
lkT ⎛
⎝ ⎞ ⎠
(*) Nezbeda et al. (2001)
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Summary and Final Remarks
Spatial and orientational distributions of molecules are marginally affected by long-range forces
Long-range forces affect details of the orientational ordering at short-range distances.• orientational correlations in the short- and full-range systems are
qualitatively similar
• integrals over these correlations, e.g., dielectric constant, do not differ significantly
Similar behavior is found in the dependence of thermodynamic properties, i.e., energy and pressure, on the range of the potential
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Summary and Final Remarks
Critical conditions appear to be unaffected by the long-range forces
These findings lend support to the use of perturbation expansion in the development of truly molecular-based equations of state
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Acknowledgements Research Support
• Grant Agency of the Czech Republic (Grant No 203/99/0134)
• Division of Chemical Sciences, Geosciences, and Biosciences, Office of
Basic Energy Sciences, U.S. Department of Energy under contract
number DE-AC05-00OR22725 with Oak Ridge National Laboratory,
managed and operated by UT-Battelle, LLC
For more info visit our web_sites
• http://www.icpf.cas.cz/theory/IvoNez.html
• http://www.ornl.gov/divisions/casd
• http://flory.engr.utk.edu/~aac
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