ivo nezbeda 1,2 , ariel a. chialvo 3,2 , and peter t. cummings 2,3

1

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

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,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)

5


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

6


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

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, 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)

8

Vapor-Liquid Equilibrium of Model Acetone

Jedlovszky-Pálinkás model (*)• Estimated critical conditions from Wegner expansion



-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)

9

Vapor-Liquid Equilibrium of Model Methanol

OPLS model (*)• Estimated critical conditions from Wegner expansion



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

10

Vapor-Liquid Equilibrium of Model Water

TIP4P model (*)• Estimated critical conditions from Wegner expansion



-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


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


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

12

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


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


Pressure (MPa)

Temperature (K)

(*) Nezbeda et al. (2001)

13


Effect of range on structure along isochore =0.76g/cc (*)

T=298K


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


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


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


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


gCO

(r)

r (Å)

14


Effect of range on structure along isochore =0.76g/cc (*)

T=548K


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


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


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


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


gCC

(r)

r (Å)

15

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

( )


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)

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 ⎛

⎝ ⎞ ⎠


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

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ivo nezbeda 1,2 , ariel a. chialvo 3,2 , and peter t. cummings 2,3

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