molecular simulation strategies for large scale thermodynamic … · 2017. 2. 6. ·...

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

Molecular Simulation Strategies for

Large Scale Thermodynamic Data

Generation

Athens, 2. Sept. 2011

Gábor Rutkai

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

7

0 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 i7 34

t d t d cRes

i i

i 1 i 8

, a a exp

i i39

t 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

i42

b 2 2

i i i

i 40

a exp C ( 1) D ( 1)

Total:

49 Parameters

153 Exponents

5 013 exp. Data

TTc / c /


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 automatizable 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

UV

U

2U2

2

V

U

3U3

3

V

U

…

TF /

mn

nmmn

nmT

T

/1/1

2

2

V

U

nU


......n

iajb

iajb

n

n

iajbn

n

r

ur

V

U

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

How to Calculate ? nn VU /

iajbiajb ru

2

)(

1

)(

11

1

13

1

iajb

ijiajb

iajb

iajb

iajb

jM

b

iM

a

N

ij

N

i rr

ur

VV

Up

rr



TF /

mn

nmmn

nmT

T

/1/1



011 Tp 10TU 10011 TH

20vC

0201

2

110120

1

1

pC

20

2

11010201

2 121Tw

21101

2

2002

110102

//

/

TT

TVJT


Cyclohexane

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

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

• ρ = 6.35 – 8.0 mol L-1

• 40 state points


Cyclohexane T = 500 K



Cyclohexane


T = 500 K


Cyclohexane

...,,,,/100 pvEOSEOSsim CCHXXXX

H %5.1


U %6.1

VC %8.0

pC %2.3

w %7.5

p %8.2


Conclusion

• Good cyclohexane potential model

• Apporach is feasible for EoS development

• Large set of independent thermodynamic properties

• From a single NVT simulation per state point

• Execution of NVT simulations is well automatizable

• Computational cost is an additional pair potential evaluation

for each volume derivative order


Thank you for listening!


Derivative with respect to the Temperature

NVTZTF ln

V

NVT

NVT

NVT

V

NVT

V T

Z

ZTZ

T

ZT

T

FS

1ln

ln

2T

UTNVTZln



NVTZTTF ln NVTZln

V

NVT

NVTV

NVT

V

Z

Z

Z

1ln

NN

NN

V

NVT

NVTV dUVN

dUUVNZ

Zr

r

exp

!

1

exp!

1

1

NNNVT dUVN

Z r exp!1

NNNVT dUUVN

Zr

exp

!

1

U



NVTZTF ln NVTZln

V

NVT

VT

Z

T

)/1(

ln

)/1(

U

V

NVTNVT

V T

ZTZ

T

F

lnln

2T

U


Pair potentials

612

4iajbiajb

iajbrr

u

LJ LRC (site-site cutoff):

drr

ur

VN

V

U iajb

rc

3

LRC

3

12 .........

LRC

n

iajb

n

n

r

n

n

r

ur

V

U

c

3

RF

RF

12

11

c

iajb

iajb

jbia

iajbr

r

r

qqu

(Lennard-Jones potential) (reaction-field correction)

molecular simulation strategies for large scale thermodynamic … · 2017. 2. 6. ·...

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