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, Chelyabinsk reg. Russia, Russian Federal Nuclear Centre – Institute of Technical Physics

INTRODUCTION Russian Federal Nuclear Centre – Institute of Technical Physics 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 Russian Federal Nuclear Centre – Institute of Technical Physics 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 Russian Federal Nuclear Centre – Institute of Technical Physics

An example of sewing together two physical models Before sewing togetherAfter sewing together Russian Federal Nuclear Centre – Institute of Technical Physics

Total EOS’ surface as a result of sewing together different physical models. Russian Federal Nuclear Centre – Institute of Technical Physics

Tabulation of theEOS

Scheme of the physical models sewed together in the frame of the wide range equation of state of WATER Russian Federal Nuclear Centre – Institute of Technical Physics

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. Russian Federal Nuclear Centre – Institute of Technical Physics Model of Water at T<10 000K and 0.1<  <4.0 g/cm 3

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 A 0 and g 0 -excess free energy and pair distribution function of a reference system,  -particle density, F id -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. Variational Perturbation Theory Russian Federal Nuclear Centre – Institute of Technical Physics

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)). Russian Federal Nuclear Centre – Institute of Technical Physics 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)). Russian Federal Nuclear Centre – Institute of Technical Physics 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 , (1999)). Data for liquid water are shifted by +0.5 g/cm 3. P(GPa)  (g/cm 3 ) Hugoniots of water and porous ice Russian Federal Nuclear Centre – Institute of Technical Physics

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) Approximation of interatomic potential for water Russian Federal Nuclear Centre – Institute of Technical Physics

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 , (1999)), Initial densities are indicated above the curves. Data for liquid water are shifted by +0.5 g/cm 3. Hugoniots of water and porous ice Russian Federal Nuclear Centre – Institute of Technical Physics

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 Russian Federal Nuclear Centre – Institute of Technical Physics

Scheme of the physical models sewed together in the frame of the wide range equation of state of WATER Russian Federal Nuclear Centre – Institute of Technical Physics ?