wide range equation of state of water smirnova m.s., dremov v.v., sapozhnikov a.t. russian...

Wide Range Equation of State of Water

Smirnova M.S., Dremov V.V., Sapozhnikov A.T.Russian Federation Nuclear Centre – Institute of Technical Physics

P.O. Box 245, Snezhinsk, 456770 Chelyabinsk reg. Russia,E-mail: [email protected]

Russian Federal Nuclear Centre – Institute of Technical Physics

mailto:[email protected]

INTRODUCTION


Up-to-date modeling of materials behavior when dynamic loading requires precise Equations of State (EOS)

During the shock wave loading and subsequent release the thermodynamic parameters may vary in a wide range and a material may undergo phase transitions, dissociation and ionization.

The EOS should have rather simple mathematical form to be efficiently used in the cintimuun dynamics computer codes.

The requirements are contradictory:

Precise

Wide-range

Simple mathematical form

INTRODUCTION


Examples of EOSs constructed in RFNC-VNIITF during the last few years:

•Multi-phase equation of state of Iron (three solid phases, liquid, vapour). AIP Conf. Proc. 620, 87 (2002)

•Wide range equation of state of water taking into account dissociation and ionization. AIP Conf. Proc. 706, 49 (2004)

•Muti-phase equation of state of quartz (two solid phases liquid, vapour). AIP Conf. Proc. 845, 119 (2006)

•Muti-phase equation of state of cerium (two solid phases and liquid). AIP Conf. Proc. 845, 77 (2006)

Scheme of the physical models sewed together in the frame of the wide range equation of state of WATER

p


An example of sewing together two physical models

Before sewing together After sewing together


Total EOS’ surface as a result of sewing together different physical models.



Tabulation of theEOS


p


In this region water is to be considered as a mixture of molecular fluids

To construct thermodynamic model describing properties of water in the region covered by shock data obtained in experiments with porous ice and snow the Variational Perturbation Theory has been applied.

Some peculiarities of intermolecular potential of water were investigated

Dissociation reactions have been introduced in the model.


Model of Water at T<10 000K and 0.1<<4.0 g/cm3

Helmholtz free energy in this approach can be written in the following form which is correct to the first order terms of intermolecular potential:

where A0 and g0 -excess free energy and pair distribution function of a reference system, -particle density, Fid -perfect gas free energy and U(r)=(r)- 0(r), (r), 0(r) -intermolecular potential for actual and reference system respectively. So called exp-6 potential has been taken as an actual intermolecular potential.

)(),(5.0 00 rUrdrgNAFF id

r

rrrr

*0*

0 6)/1(exp

6

6)(

Variational Perturbation Theory


When considering dissociation we take the following reactions into account

First of these reactions is responsible for appearance of the conduc-tivity of water when shock compression (See F.Ree J.Chem.Phys., v.76, p.5287, (1982)).

2 2 3

2

2

2

H O H O OH

H O OH H

OH O H

O O O

H H H


Chemical reaction taken into account

U (K)

r(A)Fig. 1 Averaged by various mutual orientations intermolecular potential

for water (F.Ree J.Chem.Phys., v.76, p.5287, (1982)).


Interatomic potential for water

Fig. 2 Hugoniots of water and porous ice. Solid line – calculation with potential (1), * - experimental data (R.F. Trunin, G.V. Simakov, M.V. Zhernokletov Thermophysics of high temperatures, v.37, pp.732-737, (1999)). Data for liquid water are shifted by +0.5 g/cm3.

P(GPa)

(g/cm3)

Hugoniots of water and porous ice


Two simple steps to improve the model

Step1 More accurate approximation of ab-inition data (*) requites

temperature dependence of r* parameter (characteristic molecular size)

Step 2 Ab-inition calculations (*) we refer to in this work did not take into account multiparticle interactions. To do this remaining in the frame of pair potential we suppose:

(*) F.Ree J.Chem.Phys., v.76, p.5287, (1982)

* * 00 1.0 exp

Tr r

T

0 000

1T T

Approximation of interatomic potential for water


1 1.5 2 2.5 30

10

20

30

40

50

60

70

80

ro (g/ccm)

P(G

Pa)

0.15

0.25

0.35

0.6

0.9

1.0

Fig. 5 Hugoniots of liquid water, porous ice and snow. Solid lines- calculations, characters – experimental data (R.F. Trunin, G.V. Simakov, M.V. Zhernokletov Thermophysics of high temperatures, v.37, pp.732-737, (1999)), Initial densities are indicated above the curves. Data for liquid water are shifted by +0.5 g/cm3.

Hugoniots of water and porous ice


Themodymanic model of water taking into account dissociation and peculiarities of interaction of water molecules depending on temperature and density have been constructed on the basis of Variational Perturbation Theory.

Good agreement between results of calculation and experimental data on shock compression of water, porous ice and snow has been achieved.

Ab-initio calculations being used when constructing intermolecular potential should take into account multiparticle interaction.

It would be interesting to compare multiparticle contribution to the potential effectively taken into account in this work with this obtained from ab-initio calculations.

Conclusions



p


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wide range equation of state of water smirnova m.s., dremov v.v., sapozhnikov a.t. russian...

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