molecular simulation strategies for large scale thermodynamic … · 2017. 2. 6. · prof. dr.-ing....

PROF. DR.-ING. HABIL. JADRAN VRABEC ThET

Molecular Simulation Strategies for

Large Scale Thermodynamic Data

Generation Minneapolis, 18. Oct. 2011

Gábor Rutkai

Monika Thol

Roland Span

Rolf Lustig

Jadran Vrabec


R. Span, “Multiparameter Equations of State”, Springer, Berlin (2000)

complete thermodynamic knowledge : ~10 substances

For pure chemical substances…

satisfactory knowledge :


Equations of state for CO2 (Span and Wagner, 1996)

0 ResF , , ,R T

70 0 0 0 0

1 2 3 i i

i 4

, ln a a a ln a ln 1 exp n

i i i i i

7 34t d t d cRes

i i

i 1 i 8

, a a exp

i i

39t d 2 2

i i i i i

i 35

a exp ( ) ( )

Ideal part:

Residual part:

Helmholtz Energy: T = 216 … 1100 K, p = 0 … 800 MPa

i

42b 2 2

i i i

i 40

a exp C ( 1) D ( 1)

Total:

49 Parameters

153 Exponents

5 013 exp. Data

τ =Tc / T δ = ρ / ρc


Contribution of molecular simulation

• powerful predictive capabilities (thermodynamic data)

• works under any physical conditions

• low cost

Why is molecular simulation not a mainstream solution for

thermodynamic data retrieval?

• suitable molecular models

• today’s MS software: only a few independent properties

• new properties require implementation

• development is impossible for an inexperienced user


• Cv

Equilibrium thermodynamic properties

particular thermodynamic property

specific statistical mechanical ensembles or special techniques

NVT NpT • Cp


Approach

For any thermodynamic property the underlying statistical

mechanical ensemble is in principle irrelevant*.

* H.W. Graben, J.R. Ray, Mol. Phys., 80, 1183-1193 (1993)

NVT • Cp • Cv


Project with ms2*(www.ms-2.de):

• large set of thermodynamic properties from one NVT simulation

• truly independent thermodynamic information

• generation of an extensive dataset in an automatized fashion

* S. Deublein et al., Comp. Phys. Comm., 182, 2350-2367 (2011).


The fundamental equation

(Helmholtz representation) (Massieu-Planck representation)

dnpdVTdSdU dnT

dVT

pdU

TdS

1

Legendre transformation

dnpdVSdTdF dnT

dVT

p

TUdd

1

(Energy representation) (Entropy representation)

TF /


Derivatives of the Massieu-Planck potential

EV

E

2E2

2

V

E

3E3

3

V

E

…

TF / mn

nmmn

nmT

T/1

/1

2

2

V

EnE


......n

iajb

iajb

n

n

iajbn

n

r

er

V

E

K. Meier and S. Kabelac, J. Chem. Phys., 124, 064104 (2006)

How to Calculate ? nn VU /

iajbiajb re

2

)(

1

)(

11

1

13

1

iajb

ijiajb

iajb

iajb

iajb

jM

b

iM

a

N

ij

N

i

resrr

er

VV

Ep

rr



TF / mn

nmmn

nmT

T/1

/1



011Tp 10TU 10011TH

20vC

0201

2

110120

1

1pC

20

2

11010201

2 121Tw

2

1101

2

2002

110102

//

/

TT

TVJT


Cyclohexane

*T. Merker, J. Vrabec and H. Hasse, Fluid Phase Equilib., submitted (2011)

Rigid 6CLJ united-atom model*


Cyclohexane

EOSEOSsim HHH /100

EoS: R. Span, and W. Wagner, Int. J. Thermophys., 24, 41-109 (2003).


Cyclohexane

• ms2 (MD, MC)

• 20 h (8 “nehalem” core) per simulation

• automatized (no user interaction)

• T = 500 K and ρ = 6.35 – 8.0 mol L-1

• ρ = 7.0 mol L-1 and T = 470 – 590 K

• 2 x 40 state points


Cyclohexane

EoS1: R. Span, and W. Wagner, Int. J. Thermophys., 24, 41-109 (2003).

EoS2: S.G. Penoncello, et. al., Int. J. Thermophys., 16, 519-531 (1995).


EoS1: R. Span, and W. Wagner, Int. J. Thermophys., 24, 41-109 (2003).

EoS2: S.G. Penoncello, et. al., Int. J. Thermophys., 16, 519-531 (1995).

Cyclohexane


Cyclohexane

...,,,,/100 pvEOSEOSsim CCHXXXX

H %5.1

EoS: R. Span, and W. Wagner, Int. J. Thermophys., 24, 41-109 (2003).

U %6.1

VC %8.0

pC %8.2

w %3.5

p %0.2


Conclusion

• Good cyclohexane potential model

• Approach is feasible for EoS development

• Large set of independent thermodynamic properties

• From a single NVT simulation per state point

• Automatized execution for NVT simulations

• Computational cost is an additional pair potential evaluation

for each volume derivative order


Thank you for listening!

This project is funded by

molecular simulation strategies for large scale thermodynamic … · 2017. 2. 6. · prof. dr.-ing....

Documents