1
Effect of the Range of Interactions
on 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 Republic
2
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
3
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))
4
Range of Intermolecular Interactions
 Basic definitions
•
Separation between short- and long-range potential interaction

u(r12 , 1, 2 )  u(1,2)  uLJ (rss ) 

i1, j2
qi q j
rij
ucoul (1,2)

ushortrange (1, 2)  u(1, 2)  S(rss , rL , rU )ucoul (1, 2)
 uLJ (rss )  1 S(rss , rL ,rU )ucoul (1, 2)
5
Range of Intermolecular Interactions
 Basic definitions
•
Switching function for the range transition

for r  rL
0

(r  rL ) 2 (3rU  rL  2r)
S(rss ,rL ,rU )  
for rL  r  rU
3
(rU  rL )


for r  rU
1

rss  distance between reference (LJ) sites
(e.g., rss=rOO for the case of water and methanol)
6
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 sss (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
7
Vapor-Liquid Equilibrium of Model
Carbon Dioxide
 Harris-Yung’s EPM2 model (*)
•
Estimated critical conditions from Wegner expansion
 Short-range potential: Tc=310.8K, rc=458.6kg/m3
 Full potential: Tc=310.9K, rc=455.1kg/m3
32 0.0
30 0.0
T(K)
28 0.0
CO2
CO2
26 0.0
short-range
short-range
full-range
full-range
24 0.0
22 0.0
0.0
20 0.0
40 0.0
60 0.0
80 0.0
10 00.0
12 00.0
-14 .0
-12 .0
-10 .0
3
density (kg/m )
(*) Harris and Yung, JCP, 99 (1995)
-8.0
-6.0
U (kJ/mole)
c
-4.0
-2.0
0.0
8
Vapor-Liquid Equilibrium of Model
Acetone
 Jedlovszky-Pálinkás model (*)
•
Estimated critical conditions from Wegner expansion
 Short-range potential: Tc=505.5K, rc=275.0kg/m3
 Full potential: Tc=499.3K, rc=273.3kg/m3
44 0.0
42 0.0
40 0.0
ACETONE
T (K)
38 0.0
ACETONE
36 0.0
short-range
short-range
34 0.0
full-range
full-range
32 0.0
30 0.0
28 0.0
0.0
10 0.0
20 0.0
30 0.0
40 0.0
50 0.0
3
density (kg/m )
60 0.0
70 0.0
80 0.0
-30 .0
-25 .0
-20 .0
-15 .0
U (kJ/mole)
c
(*) Jedlovszky and Pálinkás, Mol. Phys., 84 (1995)
-10 .0
-5.0
0.0
9
Vapor-Liquid Equilibrium of Model
Methanol
 OPLS model (*)
•
Estimated critical conditions from Wegner expansion
 Short-range potential: Tc=483.4K, rc=250.2kg/m3
 Full potential: Tc=484.6K, rc=258.2kg/m3
50 0.0
T(K)
45 0.0
METHANOL
METHANOL
40 0.0
short-range
short-range
full-range
full-range
35 0.0
30 0.0
0.0
10 0.0
20 0.0
30 0.0
40 0.0
50 0.0
60 0.0
70 0.0
80 0.0
-35 .0
-30 .0
-25 .0
density (kg/m 3)
(*)Jorgensen et al., JACS, 106 (1984)
-20 .0
-15 .0
U (kJ/mole)
c
-10 .0
-5.0
0.0
10
Vapor-Liquid Equilibrium of Model
Water
 TIP4P model (*)
•
Estimated critical conditions from Wegner expansion
 Short-range potential: Tc=564.9K, rc=339.4kg/m3
 Full potential: Tc=566.1K, rc=321.8kg/m3
60 0.0
55 0.0
T(K)
50 0.0
WATER
WATER
45 0.0
short-range
short-range
full-range
40 0.0
full-range
35 0.0
30 0.0
0.0
20 0.0
40 0.0
60 0.0
80 0.0
10 00.0
12 00.0
-40 .0
3
density (kg/m )
(*) Jorgensen, JCP, 77 (1982)
-30 .0
-20 .0
U (kJ/mole)
c
-10 .0
0.0
11
Vapor-Liquid Equilibrium
80.0
16.0
70.0
14.0
60.0
pressure (MPa)
pressure (MPa)
 Effect of range on vapor pressure (*)
CO2
50.0
short-range
ful l-range
40.0
30.0
20.0
ACE T ONE
10.0
short-range
ful l-range
8.0
6.0
4.0
2.0
10.0
0.0
220. 0
12.0
240. 0
260. 0
280. 0
300. 0
0.0
280. 0
320. 0
300. 0
Temperature (K)
320. 0
340. 0
360. 0
380. 0
400. 0
420. 0
440. 0
Temperature (K)
70.0
120. 0
60.0
100. 0
Pressure (MPa)
pressure (MPa)
WAT E R
50.0
M ET HANOL
short-range
ful l-range
40.0
30.0
20.0
60.0
40.0
20.0
10.0
0.0
300. 0
short-range
ful l-range
80.0
350. 0
400. 0
Temperature (K)
450. 0
500. 0
0.0
300. 0
350. 0
(*) Nezbeda et al., (2001)
400. 0
450. 0
500. 0
Temperature (K)
550. 0
600. 0
12
Structure and Thermodynamics of Model
Methanol
 Effect of range on properties along isochore r=0.76g/cc (*)
-24.0
Configurational Energy (kJ/mole)
300.0
Pressure (MPa)
250.0
sh ort-range
full-ran ge
200.0
150.0
100.0
50.0
0.0
-50.0
250.0
300.0
350.0
400.0
450.0
500.0
550.0
-26.0
sh ort-range
full-ran ge
-28.0
-30.0
-32.0
-34.0
-36.0
-38.0
250.0
Temperature (K)
300.0
350.0
400.0
450.0
Temperature (K)
(*) Nezbeda et al. (2001)
500.0
550.0
13
Structure and Thermodynamics of Model
Methanol
 Effect of range on structure along isochore r=0.76g/cc (*)
4.0
4.0
3.5
3.5
3.0
2.5
g (r)
OO
3.0
short-range
ful l-range
short-range
ful l-range
2.5
g (r) 2.0
2.0
OH
1.5
1.5
1.0
1.0
0.5
0.5
0.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
T=298K
0.0
1.0
2.0
3.0
4.0
r (Å)
5.0
6.0
7.0
8.0
8.0
9.0
r (Å)
2.0
2.5
short-range
ful l-range
1.5
short-range
ful l-range
2.0
1.5
g (r) 1.0
g (r)
CC
CO
0.5
1.0
0.5
0.0
0.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
2.0
3.0
4.0
5.0
6.0
r (Å)
r (Å)
(*) Nezbeda et al. (2001)
7.0
14
Structure and Thermodynamics of Model
Methanol
 Effect of range on structure along isochore r=0.76g/cc (*)
1.5
2.0
short-range
ful l-range
short-range
ful l-range
1.5
1.0
g (r)
OO
g (r)
1.0
OH
0.5
0.5
0.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
T=548K
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
r (Å)
r (Å)
1.6
2.0
1.4
short-range
ful l-range
1.5
short-range
ful l-range
1.2
1.0
g (r)
CC
g (r)
CO
1.0
0.8
0.6
0.4
0.5
0.2
0.0
0.0
3.0
4.0
5.0
6.0
7.0
r (Å)
8.0
9.0
10.0
2.0
3.0
4.0
5.0
6.0
r (Å)
(*) Nezbeda et al. (2001)
7.0
8.0
9.0
15
Interpretation of Simulation Results
 Gibbs-Duhem equations including force-field variables (*)
•
Define coupling parameter l, i.e.,

•
Apply equilibrium conditions

•
u fullrange  ushortrange  l u pert


 
 S  S dT  V  V
l
l


dP   N 
 u pert
l
TP
 u pert
Derive Clapeyron equation

dP dl sT
  N 
 u pert
l
TP
 u pert
(*) Nezbeda et al. (2001)


 V l  V 
TP 


dl
TP 
16
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)




V l  V   NkT P
u pert
l
TP
Pfullrange
 u pert

TP
 Pshort range  exp 
 u pert
l
TP
additional cases apply to carbon dioxide and methanol
(*) Nezbeda et al. (2001)
kT

17
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
18
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
19
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
20
For those who wish to receive reprints
and/or more details, please write down:
Name
complete address
email