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Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation
Accepted Manuscript Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation
Jia Wang, Cheng-Lin Liu PII: DOI: Reference:
S0167-7322(18)33521-9 doi:10.1016/j.molliq.2018.10.062 MOLLIQ 9807
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
9 July 2018 11 October 2018 12 October 2018
Please cite this article as: Jia Wang, Cheng-Lin Liu , Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation. Molliq (2018), doi:10.1016/j.molliq.2018.10.062
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ACCEPTED MANUSCRIPT Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation Jia Wang1,2, Cheng-Lin Liu2*
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1 Department of Precision Manufacturing Engineering, Suzhou Vocational Institute of
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Industrial Technology, Suzhou, 215104, China
2 National Engineering Research Center for Integrated Utilization of Salt Lake
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Resources Resource, East China University of Science and Technology, Shanghai,
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200237, China
*Corresponding authors
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E-mail address: [email protected] (C.L. Liu)
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Tel/Fax numbers: +86-21-64250981
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ACCEPTED MANUSCRIPT Abstract Structures and properties of molten alkali chlorides is the foundation of electrolyte process. In the paper, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaCl-CsCl in temperature range of near melting point to 1200 K within full composition range have been calculated intensively using
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equilibrium molecular dynamics (EMD) method. The calculated values are in good
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agreement with available experimental results. Simple databases for melt shear
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viscosity have been built based on the verified algorithm. Shear viscosities of these melts exhibit negative dependences on temperature and more complicated variation
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trends on compositions. Under the effects of local structure and interatomic force simultaneously, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-
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CsCl, NaCl-RbCl and NaCl-CsCl decrease firstly and then fluctuate slightly as the contents of LiCl or NaCl are increased. However, addition of NaCl into molten KCl
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deteriorates the melt fluidity. Expressions of melt shear viscosity vs. temperature &
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composition have also been obtained according to the calculated data finally. Keywords
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Molecular Dynamics Simulation; Molten alkali metal chlorides; Shear Viscosity
2
ACCEPTED MANUSCRIPT 1.
Introduction Due to the excellent performances of high temperature & chemical stability, fine
conductivity, good liquidity and high heat capacity 1, inorganic molten salts have many technological applications, such as energy storage devices 2, molten salt reactors 3, metal production electrolytes 4, nuclear reactor coolants 5, nuclear waste treatment
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agents 6, and so on. It is significant to reveal the nature of inorganic molten salts
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systematically and integrally for improving theoretical research and enhancing practical
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applications. Investigation on inorganic molten salts has long been the interests of many researchers around the world. Benefiting from the rapid developments of science &
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technology and computer technology, molten salts can be studied through not only experimental measuring but also computer simulation 7.
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Given extremely high temperature and corrosive conditions of molten salts, experimental measurements on molten salts are always influenced and even inhibited
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by costly and demanding experiment. It is not surprising, therefore, that there are
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substantial deficiencies and even disparities among the reported experimental results for molten salts. Computer simulation has been a less costly alternative than experiment,
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for example, Molecular Dynamics (MD) method, which can successfully predicted local structures and dynamics properties (such as diffusion coefficients, viscosity, ionic
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conductivity and so on) of pure molten salts and their mixtures
8–11
. Computer
simulation can also explore the performance of molten salts at different temperatures and salt compositions efficiently 12. Consisting of monatomic and single charged ions, alkali chloride melts have relatively simple structure and excellent transport performance, and have been main components or additives in many industries, such as molten salt electrolysis processing, high-temperature heat storage technology, and so on. It is significant to fully explore 3
ACCEPTED MANUSCRIPT the properties of molten alkali chlorides from both scientific and industrial viewpoints, among which shear viscosity is a very important property. In the production of magnesium and lithium electrolysis, with the commonly used electrolyte systems of MgCl2-NaCl-KCl/MgCl2-NaCl-CaCl2-KCl and LiCl-KCl respectively, the shear viscosity of electrolyte affects the separating effect between liquid metal, solid slag, gas
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and electrolyte. However, due to difficulty and high cost of molten salt investigations,
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before investigating complicated ternary/quarternary molten chloride systems, shear
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viscosities of more commonly used molten alkali binary chlorides have first been the focus of the research in this work.
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Shear viscosity of inorganic molten salt can be calculated through equilibrium molecular dynamics (EMD) simulations or non-equilibrium molecular dynamics
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(NEMD) simulations. Using EMD method to calculate shear viscosity of molten alkali metal chlorides is becoming increasingly sophisticated. Galamba
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had attempted to
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compute shear viscosities of molten KCl and NaCl with both NEMD and EMD methods.
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The values obtained from EMD method were found to be significantly lower than those predicted by NEMD method. Later, Nevins 14 explored calculation conditions through
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viscosity calculation of molten NaCl with EMD method to obtain a good compromise between calculation time and viscosity quality. Wang 15 calculated shear viscosities of
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the five pure molten alkali chlorides at different temperatures through EMD method. Shear viscosities of molten alkali halide mixtures have also been calculated through molecular dynamic simulations. Merlet 16 and Morgan 17 had calculated viscosities of molten LiF-KF and LiCl-KCl systems through Molecular Dynamics calculations. However, the research about viscosities of molten alkali chloride binary mixtures is discrete and far from comprehensive. There are quite a few experimental results about shear viscosities of molten alkali 4
ACCEPTED MANUSCRIPT metal chlorides. The existing data is discrete and far from consolidated. Most of them were just records for one melt at some discrete temperatures and compositions. Systematic investigations on shear viscosity of molten alkali metal chlorides is scarce owing to the rigorous experimental conditions and the tedious computational process. Therefore, the related fundamental data are sorely lacking. The effects of LiCl or NaCl
. Based on the previous work, shear viscosities of some more widely used molten
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18,19
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on shear viscosities of molten KCl, RbCl and CsCl at 1100K have been analyzed before
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alkali chloride binary systems at different temperatures and compositions have been calculated intensively through EMD method in this paper to supplement basic database
Methodology
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2.
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and meet practical engineering needs.
2.1. Simulation details
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Molecular dynamics simulations were performed to calculate shear viscosities of
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molten alkali metal chloride binary mixtures at different temperatures and components, i.e. LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaClCsCl. Calculated temperatures were within near melting point to 1200 K with an
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interval of 25 K. Lower limits of temperature were determined through corresponding
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equilibrium phase diagram. Calculated compositions ranged from 0 to 100% with an interval of 6.25%, in measuring of mole fraction of one component. For interaction between ions, following Born-Mayer-Huggins potential that had been successfully used in simulations of molten alkali halides was used: 𝑈𝑖𝑗 (𝑟) =
𝑞𝑖 𝑞𝑗 𝑟
𝜎𝑖𝑗 −𝑟
+ 𝐵𝑖𝑗 𝑒𝑥𝑝 (
𝜌
)−
𝐶𝑖𝑗 𝑟6
−
𝐷𝑖𝑗 𝑟8
(1)
In equation (1), the first term describes electrostatic interactions between ions, qi/qj is the ionic charge, and formal charge (+1 for alkali ions and -1 for chloride) was used. The second term represents Born-Huggins exponential short-range repulsion due to 5
ACCEPTED MANUSCRIPT overlap of electron clouds. Bij = Aij*b, in which b is a constant, being equal to 0.338×1019
𝑍
𝑍
J, Aij is Pauling factor 20,21, being equal to 1 + 𝑛i + 𝑛j , where Z denotes charge of ion i
j
and n denotes number of outer electrons, σ is crystal ionic "radii", and ρ is hardness parameter. The last two terms correspond to dipole-dipole and dipole-quadrupole
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dispersion interactions, and the dispersion constants Cij and Dij for alkali chloride systems were determined by Mayer 22.
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Potential parameters for the mixtures were determined as follows 18, and the detailed
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parameters used in this study were given in the Supporting Information. Taking LiClNaCl systems for example, in which the mole fraction of LiCl is x, the hardness
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parameter ρ for the mixtures obeys the rule of 1/ρmix = x/ρLiCl + (1-x)/ρNaCl. The
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dispersion parameters for Cl-Cl pair in the mixtures follow the formulas of Cmix(Cl-Cl) = xCLiCl(Cl-Cl) + (1-x)CNaCl(Cl-Cl) and Dmix(Cl-Cl) = xDLiCl(Cl-Cl) + (1-x)DNaCl(Cl-Cl). In the above expressions, ρLiCl, ρNaCl, CLiCl(Cl-Cl), CNaCl(Cl-Cl), DLiCl(Cl-Cl), and DNaCl(Cl-Cl) are the
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corresponding values of pure molten salts. For cationic pair Li-Na, σLi-Na =σLi+σNa, the parameters B, C, and D employ the geometric mean of the corresponding values for LiLi pair and Na-Na pair in the pure molten salts, i.e. BLi-Na = (BLi-Li·BNa-Na)1/2, CLi-Na =
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(CLi-Li·CNa-Na)1/2, DLi-Na = (DLi-Li·DNa-Na)1/2. The remaining parameters adopt the
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corresponding values of pure molten salts. The LAMMPS code was used to perform MD simulations. All the simulations were performed for a cubic box consisting of 1024 ions (512 cations and 512 anions respectively, and the numbers of each cation were determined according to mole fractions). Initial ionic configurations were random distribution. Initial velocities of ions were also random allocation and obeyed the Gaussian distribution. Periodic Boundary Condition was used to keep particle numbers constant and to eliminate boundary effect. Long-range interactions were handled using Ewald 6
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summation
ACCEPTED MANUSCRIPT method to eliminate truncation errors. In the Ewald summation, the precise that determined the relative root mean square (RMS) error in per-atom forces calculated by the method was set to be 1.0×10-6, meaning that the RMS error will be a factor of 1000000 smaller than the reference force that two unit point charges exert on each other at a distance of 1 Å. The cutoff radius rc for the short-range potential and the real space
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part of the Ewald summation was set to be L/2, where L is side length of simulation cell.
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Verlet algorithm 24 was used to solve Newton's equations of motion.
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For all the simulation, the systems were first equilibrated in isothermal-isobaric ensemble (NPT) with pressure fixed at 0 GPa around the desired temperature using 25,26
. Production runs were performed in
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Nose-Hoover thermostat and barostat
canonical ensemble (NVT) with Nose-Hoover thermostat method
27,28
at equilibrated
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cell volume. Damping parameters that determined relaxation rates of temperature and pressure were set to be 0.1 ps. To control initial oscillations, Nose-Hoover chains were
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used for the thermostat and barostat, and the chain numbers were 3 in this work 29. The
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relaxation time was set to be 500 ps and the production time was 10 ns, with a time step of 1 fs.
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2.2. Evaluated properties
MD simulations can be used to compute dynamic properties of molten salts using the
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equilibrium methods described below 24,30. Shear viscosity η measures the resistance of a fluid deformed by shear stress. Here, shear viscosity is calculated from time integral of off-diagonal stress tensor autocorrelation function (SACF) with steady-state EMD simulation through GreenKubo relationship 13,30: 𝜂=𝑘
1 𝐵
∞
∫ 〈𝑆𝑥𝑦 (0)𝑆𝑥𝑦 (𝑡)〉 𝑑𝑡 𝑇𝑉 0
(2)
where kB is Boltzmann constant, T is temperature, V is volume of simulation cell, and 7
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𝑆𝑥𝑦 = ∑𝑁 𝑖=1 [𝑚𝑖 𝑣𝑥𝑖 𝑣𝑦𝑖 + 2 ∑𝑗≠𝑖 𝑥𝑖𝑗 𝑓𝑦 (𝑟𝑖𝑗 )]
(3)
where mi is mass of ion i, vxi and vyi are x-component and y-component of vi (velocity of ion i) respectively, xij is x-component of rij = ri-rj and fy(rij) is y-component of force
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fij of ion i due to ion j. Each of the three independent off-diagonal components of stress tensor (i.e. Sxy, Sxz and Syz) provides an independent estimate of shear viscosity, and the
Results and discussions
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3.
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averaged value will be taken as the final viscosity value.
Shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl,
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NaCl-RbCl and NaCl-CsCl at different temperatures and components have been
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calculated from time integral of stress tensor autocorrelation function (SACF). Considering the computation cost and the fact that molten alkali chloride is mainly used
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below 800 °C, upper limit of computed temperature was set to be 1200 K. Lower limit
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was the near melting point, determined through corresponding equilibrium phase diagram.
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3.1. Decay and running integral behaviors of stress tensor autocorrelation function
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Decay and integral behaviors of SACF need to be tested before the viscosity calculation. The time for SACF calculation should be long enough to capture the whole decay process and to ensure the running integral of SACF reach a steady plateau. In this paper, the calculated components are evenly distributed between 0-100 for mole percentage of one salt. Therefore, pure salts at both ends, LiCl and CsCl, are selected in the test. Fig.1 gives the normalized SCAFs and corresponding running integrals of molten LiCl and CsCl. As revealed in Fig.1, both SCAFs decay to zero quickly and
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ACCEPTED MANUSCRIPT corresponding integrals reach the plateau after about 3 ps. To ensure the data accuracy, 5 ps is adopted to calculate SACFs in this paper. The SACFs will be averaged for 10
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million steps to ensure good statistics that repeated runs give the same plateau value.
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Fig. 1 Time Evolutions of Normalized SACFs and Corresponding Running Integrals for Molten LiCl and CsCl
3.2. Model verification Due to costly and demanding test conditions, systematic viscosity measurement for molten alkali chlorides within full composition and temperature ranges is impracticable for the current reality. Experimental values for shear viscosity of high temperature molten salts are always scarce and dispersed. In this section, some calculated viscosities have been tested with available experimental results to verify accuracy of calculation 9
ACCEPTED MANUSCRIPT method. As shown in Fig.2, comparisons for molten LiCl-CsCl system at 1020 K and KCl-NaCl at 1100 K
31
reveal good agreements between calculated and experimental
results. In addition, calculated results for the first four pure salts at 1100 K, i.e. 0.861 mPa·s for LiCl, 1.090 mPa·s for NaCl, 0.844 mPa·s for KCl and 1.143 mPa·s for RbCl, also exhibit good agreements with experimental values of 0.843, 1.022, 0.881 and 1.025 32-35
, with the errors being less than 10%. In all, simulation
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mPa·s correspondingly
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method described above can bring reliable viscosity values, and massive calculations
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will be carried out.
Fig.2 Comparisons between Computed Values and Experimental Results for Shear Viscosity of Molten LiCl-CsCl and NaCl-KCl
The simulated shear viscosities of these mixed molten salts in the temperature range of near melting point-1200 K within the whole concentration scope are listed in Table 10
ACCEPTED MANUSCRIPT 1-7. In addition, the expressions of viscosity on temperature and component have been fitted according to calculated results through 1stOpt software with LevenbergMarquardt (LM) - Universal Global Optimization (UGO) algorithms and convergence criteria of 1.0×10-10. 3.3. Shear viscosity database for molten alkali chlorides Molten LiCl-NaCl
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3.3.1.
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Shear viscosities for molten LiCl-NaCl at different temperatures and compositions
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have been listed in Table 1. It is obvious that shear viscosities decrease with increasing temperature for all the components. At a certain temperature, along with gradual
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increasing of LiCl, shear viscosities of the system first decrease and then increase slightly or show slight oscillation tendency.
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As analyzed previously from the radial distribution functions 18, addition of Li+ into NaCl will weaken interactions between counter-ions, strengthen interactions between
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chlorine ions and promote closed pack between cations. Structural loosening between
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counter-ions resulting from interactions weakening dominants, thus giving rise to improvement of melt fluidity and decrease of shear viscosity. With continuous addition
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of LiCl, strengthening of Cl-Cl interactions and promotion of closed packs between
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cations deteriorate melt fluidity to a certain extent, resulting in slightly increase of shear viscosity. On a whole, melt fluidity is always improved with the addition of LiCl, the difference just lies in the extent of improvement. Shear viscosity expression for molten LiCl-NaCl system at 850-1200 K within full component range has been fitted from data in Table 1, as follows: η(LiCl-NaCl) = 17.6142-3.1445×10-3 x+1.9166×10-5 x2 -1.3484×10-7 x3 -3.9976×10-2 T+3.3223×10-5 T2 -9.6073×10-9 T3 In equation (4), x denotes the mole fraction of LiCl, T denotes temperature. 11
(4)
ACCEPTED MANUSCRIPT Table 1 Shear Viscosities of Molten LiCl-NaCl at Different Temperatures (Units: mPa∙s) LiCl% 50.00 56.25
Temp (K)
0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
850
-
-
-
-
-
-
-
-
-
875
-
-
-
-
-
-
-
-
-
900
-
-
-
-
-
-
-
-
925
-
-
-
-
-
-
-
-
950
-
-
-
-
-
-
-
1.396
975
-
-
-
-
-
-
1.251
1.272
1000
-
-
-
-
-
1.187
1.251
1025
-
-
-
-
1.146
1.168
1.130
1050
-
-
-
1.098
1.083
1.095
1075
-
1.138
1.086
1.073
1.045
1.035
1100
1.090
1.031
0.994
1.015
0.947
1125
1.050
0.983
0.958
0.939
0.939
1150
1.026
0.878
0.969
0.859
1175
0.926
0.892
0.807
1200
0.882
0.829
0.822
75.00
87.50
93.75
100.00
-
-
1.648
1.557
-
-
1.524
1.568
-
-
-
-
1.400
1.414
-
-
-
1.374
1.292
1.365
1.371
1.314
1.393
1.257
1.348
1.324
1.275
1.225
1.212
1.218
1.215
1.227
1.247
1.269
1.225
1.201
1.293
1.160
1.165
1.217
1.113
1.056
1.178
1.169
1.147
1.181
1.097
1.075
1.114
1.039
1.062
1.034
1.183
1.157
1.107
1.168
1.118
1.099
1.043
1.044
1.040
1.018
1.049 0.981
1.099
1.005
0.990
1.010
0.985
0.999
0.986
0.924
1.048
1.061
1.039
0.963
0.978
0.964
0.993
0.955
0.930
0.935
0.896
0.948
1.006
0.950
0.924
0.890
0.816
0.950
0.857
0.914
0.859
0.881
0.987
0.907
0.884
0.987
0.906
0.918
0.864
0.900
0.926
0.859
0.843
0.869
0.838
0.876
0.866
0.888
0.835
0.806
0.766
0.797
0.850
0.772
0.813
0.807
0.736
0.791
0.773
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68.75
81.25
0.889
0.884
0.859
0.838
0.799
0.861
0.818
0.870
0.864
0.761
0.730
0.790
0.746
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0.888
0.839
0.828
0.761
0.760
0.774
0.694
0.766
0.751
0.800
0.774
0.730
0.691
0.757
0.758
0.709
0.659
0.751
0.736
0.757
0.707
0.670
0.773
0.674
0.715
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3.3.2.
62.50
LiCl-KCl
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Shear viscosities for molten LiCl-KCl at different temperatures and compositions have been listed in Table 2. Shear viscosities decrease with increasing temperature for
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all the components. At a certain temperature, along with gradual increase of LiCl, shear
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viscosities of molten LiCl-KCl system first decrease and then increase slightly or show slight oscillation tendency for different components under the effects of both interionic
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interactions and local atomic arrangements. As analyzed previously 18, addition of Li+ into KCl will weaken interactions between counter-ions, strengthen interactions
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between chlorine ions and promote closed pack between cations. In addition, viscosity of molten KCl is lower than that of molten NaCl at the same temperature. Similarly, viscosity of molten LiCl-KCl is also lower than that of molten LiCl-NaCl at the same temperature and LiCl content. Molten LiCl-KCl should be a better choice in some industrial applications of molten salts. Shear viscosity expression for molten LiCl-KCl system at 700-1200 K within full component range has been fitted from data in Table 2, as follows: 12
ACCEPTED MANUSCRIPT η(LiCl-KCl) = 30.1146+5.0115×10-4 x-6.3339×10-5 x2 +5.4347×10-7 x3
(5)
-7.6162×10-2 T+6.7268×10-5 T2 -2.0198×10-8 T3 In equation (5), x denotes the mole fraction of LiCl, T denotes temperature. Table 2 Shear Viscosities of Molten LiCl-KCl at Different Temperatures (Units: mPa∙s)
6.25
12.50
18.75
25.00
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
-
-
-
-
-
-
-
-
-
2.921
2.822
-
-
-
-
-
-
725
-
-
-
-
-
-
-
-
-
2.554
2.418
2.271
-
-
-
-
-
750
-
-
-
-
-
-
-
-
-
2.237
2.264
2.272
-
-
-
-
775
-
-
-
-
-
-
-
-
2.219
1.969
2.079
1.965
1.879
-
-
-
800
-
-
-
-
-
-
-
-
1.725
1.794
1.840
1.700
1.781
-
-
-
825
-
-
-
-
-
-
-
1.632
1.679
1.611
1.536
1.540
1.639
1.502
-
-
850
-
-
-
-
-
-
-
1.531
1.530
1.560
1.452
1.434
1.332
1.432
1.575
875
-
-
-
-
-
-
1.405
1.357
1.482
900
-
-
-
-
-
-
1.402
1.257
1.318
925
-
-
-
-
-
1.355
1.179
1.164
1.234
950
-
-
-
-
-
1.135
1.104
1.081
1.041
975
-
-
-
-
1.075
1.044
1.110
1.019
1000
-
-
-
1.092
1.061
1.019
0.986
1025
-
-
1.018
0.932
0.951
0.948
0.911
1050
-
0.923
0.850
0.867
0.871
0.895
0.834
0.861
0.888
1075
0.973
0.858
0.868
0.884
0.918
0.814
0.859
0.813
1100
0.844
0.841
0.851
0.822
0.846
0.806
0.780
1125
0.769
0.774
0.823
0.856
0.807
0.754
1150
0.765
0.775
0.717
0.699
0.745
0.723
1175
0.818
0.693
0.710
0.678
0.654
0.706
1200
0.695
0.721
0.679
0.662
0.597
0.668
LiCl-RbCl
93.75
100.00
-
1.459
1.394
1.329
1.395
1.337
-
-
1.281
1.254
1.271
1.253
1.221
1.244
1.198
1.218
1.070
1.203
1.218
1.111
1.173
1.151
1.215
1.269
1.051
1.120
1.062
1.113
1.079
1.059
1.061
1.097
1.073
1.011
0.953
0.957
1.056
1.066
1.047
1.030
1.034
0.995
0.897
0.933
0.934
0.928
0.935
0.925
0.984
0.991
1.010
0.868
0.941
0.930
0.855
0.850
0.852
0.955
0.869
0.819
0.924
0.882
0.789
0.878
0.863
0.855
0.891
0.795
0.816
0.849
0.750
0.787
0.810
0.811
0.784
0.912
0.841
0.881
0.775
0.755
0.687
0.725
0.772
0.711
0.761
0.713
0.733
0.861
0.789
0.709
0.827
0.720
0.725
0.755
0.694
0.702
0.757
0.755
0.746
0.723
0.697
0.744
0.689
0.688
0.658
0.693
0.685
0.680
0.777
0.751
0.623
0.612
0.656
0.618
0.724
0.699
0.633
0.655
0.665
0.685
0.659
0.583
0.699
0.631
0.606
0.620
0.656
0.590
0.633
0.653
0.652
0.715
NU
MA
D
SC
-
1.471
PT E
3.3.3.
RI
0.00
700
PT
LiCl%
Temp (K)
CE
Table 3 lists shear viscosities for molten LiCl-RbCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the
AC
components. At a certain temperature, along with gradual increase of LiCl, shear viscosities of molten LiCl-RbCl system exhibit an overall downward trend but some slight oscillation for different components. The addition of Li+ into RbCl weakens the interactions of Li-Cl and Rb-Cl pairs, strengthens interactions between Cl-Cl pairs and promotes closed pack between Li-Li, Rb-Rb and Li-Rb pairs. In the beginning, interaction weakening of Li-Cl and Rb-Cl pairs results in structural loosening between counter-ions, thus giving rise to improvement of melt fluidity and decrease of shear 13
ACCEPTED MANUSCRIPT viscosity. With continuous addition of LiCl, strengthening of Cl-Cl interactions and promotion of closed packs between cations become more and more significant and then deteriorate melt fluidity to a certain extent, resulting in slightly increase of shear viscosity. Shear viscosity expression for molten LiCl-RbCl system at 625-1200 K within full
PT
component range has been fitted from data in Table 3, as follows:
η(LiCl-RbCl) = 71.0297+7.3551×10-3 x-3.0849×10-4 x2 +2.0435×10-6 x3
RI
(6)
-19.5183×10-2 T+1.8326×10-4 T2 -5.7798×10-8 T3
SC
In equation (6), x denotes the mole fraction of LiCl, T denotes temperature.
NU
Table 3 Shear Viscosities of Molten LiCl-RbCl at Different Temperatures (Units: mPa∙s) LiCl%
Temp (K)
0.00
625
-
-
-
-
-
-
-
650
-
-
-
-
-
-
18.75
25.00
31.25
37.50
43.75 -
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00 -
-
6.856
-
-
-
-
-
-
6.057
5.321
-
-
-
-
-
-
MA
12.50
5.914
-
-
5.007
4.619
4.584
-
-
-
-
-
--
-
-
4.399
4.208
3.391
-
-
-
-
-
-
-
-
3.909
3.374
3.251
3.025
-
-
-
-
-
-
3.283
3.297
3.078
2.908
2.666
-
-
-
-
-
-
2.885
2.969
2.663
2.509
2.419
2.274
-
-
-
-
2.650
2.402
2.388
2.405
2.197
2.159
2.081
-
-
-
-
-
2.501
2.418
2.176
2.221
1.862
1.869
1.848
1.682
-
-
-
2.284
2.027
2.106
2.137
1.929
1.755
1.652
1.629
1.539
1.514
-
-
2.098
1.906
1.822
1.694
1.608
1.536
1.477
1.446
1.451
1.408
1.405
-
1.859
1.894
1.744
1.579
1.692
1.487
1.494
1.465
1.274
1.405
1.231
1.225
1.218
1.746
1.645
1.529
1.391
1.513
1.296
1.408
1.342
1.276
1.345
1.141
1.170
1.269
1.503
1.606
1.505
1.452
1.392
1.345
1.395
1.233
1.243
1.187
1.245
1.105
1.165
1.097
1.387
1.381
1.366
1.397
1.295
1.283
1.166
1.164
1.140
1.135
1.140
1.066
1.091
1.034
1.336
1.376
1.265
1.237
1.281
1.150
1.134
1.099
1.043
1.039
1.006
0.978
0.928
1.010
-
-
-
-
-
-
-
700
-
-
-
-
-
-
725
-
-
-
-
-
-
750
-
-
-
-
-
-
775
-
-
-
-
-
-
800
-
-
-
-
-
-
825
-
-
-
-
-
850
-
-
-
-
-
875
-
-
-
-
-
900
-
-
-
-
925
-
-
-
1.624
950
-
-
-
975
-
-
1.692
1000
-
1.423
1.413
1025
1.412
1.421
1050
1.321
1.260
1075
1.266
1.072
1100
1.143
1.065
1125
1.121
1150
AC
CE
PT E
675
D
6.25
-
1.324
1.242
1.212
1.179
1.119
1.101
1.079
1.014
1.031
1.062
0.905
1.014
0.889
0.946
0.924
1.192
1.234
1.187
1.074
1.069
1.043
0.945
1.072
0.944
0.883
0.996
0.931
0.864
0.880
0.816
1.185
1.034
1.098
1.093
0.967
0.982
0.973
0.894
0.892
0.935
0.825
0.904
0.845
0.854
0.881
1.098
1.031
1.018
1.023
0.929
0.973
0.963
0.968
0.861
0.893
0.870
0.797
0.779
0.753
0.861
1.021
0.976
0.953
0.993
0.960
0.925
0.951
0.880
0.853
0.848
0.793
0.772
0.826
0.714
0.740
0.746
1.008
1.008
1.076
0.925
0.924
0.912
0.874
0.789
0.765
0.751
0.785
0.788
0.701
0.736
0.654
0.677
0.751
1175
0.970
0.968
0.942
0.869
0.938
0.844
0.819
0.781
0.811
0.747
0.745
0.733
0.724
0.661
0.663
0.719
0.659
1200
0.873
0.927
0.879
0.832
0.791
0.810
0.733
0.736
0.748
0.680
0.758
0.700
0.665
0.664
0.695
0.694
0.715
3.3.4.
LiCl-CsCl
Table 4 lists shear viscosities for molten LiCl-CsCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the 14
ACCEPTED MANUSCRIPT components. At a certain temperature, along with gradual increase of LiCl, shear viscosities of molten LiCl-CsCl system exhibit an overall downward trend but some slight oscillation for different components. Similar with LiCl-RbCl system, the addition of LiCl into CsCl weakens the interactions of Li-Cl and Cs-Cl pairs, strengthens interactions between Cl-Cl pairs and promotes closed pack between Li-Li, Cs-Cs and
PT
Li-Cs pairs 19. On the one hand, with the interaction weakening of Li-Cl and Cs-Cl pairs,
RI
the counter-ions hold on to each other less tightly, resulting in the improvement of melt
SC
fluidity and decrease of shear viscosity. On the other hand, strengthening of Cl-Cl interactions and promotion of closed packs between cations will deteriorate melt
NU
fluidity and lead to the increase of shear viscosity. The shear viscosities of the melts present complicated trends under both effects.
MA
Table 4 Shear Viscosities of Molten LiCl-CsCl at Different Temperatures (Units: mPa∙s) LiCl% 50.00 56.25
0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
625
-
-
-
-
-
-
-
-
-
650
-
-
-
-
-
-
-
675
-
-
-
-
-
-
-
700
-
-
-
-
-
-
725
-
-
-
-
-
750
-
-
-
-
775
-
-
-
-
800
-
-
-
-
825
-
-
-
850
-
-
-
875
-
-
-
900
-
-
925
-
1.971
950
1.889
1.772
68.75
75.00
81.25
87.50
93.75
100.00
6.657
-
-
-
-
-
-
-
-
-
5.673
-
-
-
-
-
-
-
-
5.037
5.513
4.765
-
-
-
-
-
-
-
4.574
4.196
4.320
3.821
-
-
-
-
-
-
-
-
4.026
3.567
3.218
3.044
3.027
-
-
-
-
-
-
-
3.331
3.466
3.402
3.104
2.854
2.769
-
-
-
-
-
-
-
3.171
2.837
2.953
2.551
2.704
2.434
2.097
-
-
-
-
PT E
62.50
D
Temp (K)
2.552
2.608
2.594
2.486
2.301
1.928
2.058
-
-
-
-
-
2.408
2.082
2.141
1.864
2.342
1.952
1.797
1.847
1.566
-
-
-
-
2.112
1.954
1.848
1.946
2.044
1.748
1.831
1.711
1.577
1.591
1.406
-
-
2.068
1.804
1.946
1.863
1.928
1.714
1.579
1.566
1.584
1.472
1.458
1.390
1.287
-
2.934
1.993
1.802
1.883
1.635
1.560
1.610
1.552
1.365
1.369
1.326
1.444
1.326
1.273
1.243
1.218
1.683
1.820
1.674
1.764
1.447
1.476
1.449
1.416
1.288
1.404
1.292
1.245
1.226
1.197
1.269
1.611
1.546
1.463
1.458
1.327
1.377
1.282
1.371
1.132
1.215
1.284
1.060
1.096
1.069
1.097
AC
CE
-
-
975
1.610
1.517
1.470
1.320
1.443
1.340
1.378
1.252
1.221
1.187
1.161
1.177
1.075
1.103
1.073
1.068
1.034
1000
1.595
1.462
1.334
1.436
1.267
1.241
1.273
1.229
1.084
1.110
1.127
1.041
0.950
0.982
0.973
0.977
1.010
1025
1.516
1.327
1.269
1.432
1.114
1.177
1.132
1.088
1.029
1.012
0.997
0.982
0.888
0.927
0.918
0.962
0.924
1050
1.421
1.316
1.160
1.210
1.264
1.098
1.080
1.000
1.033
0.955
0.973
0.955
0.810
0.855
0.832
0.955
0.816
1075
1.267
1.202
1.156
1.112
1.072
1.028
0.983
1.018
0.892
0.929
0.914
0.859
0.914
0.873
0.896
0.825
0.881
1100
1.148
1.111
1.118
1.100
1.065
0.992
0.916
0.945
0.917
0.868
0.851
0.777
0.812
0.826
0.827
0.780
0.861
1125
1.028
0.980
0.980
0.985
0.975
1.003
0.899
0.891
0.827
0.791
0.715
0.729
0.736
0.772
0.766
0.769
0.746
1150
1.024
1.052
0.923
0.964
0.943
0.847
0.780
0.856
0.817
0.751
0.717
0.725
0.708
0.671
0.703
0.747
0.751
1175
0.974
0.961
0.925
0.900
0.868
0.786
0.811
0.806
0.712
0.736
0.745
0.651
0.750
0.642
0.709
0.617
0.659
1200
1.018
0.919
0.868
0.866
0.781
0.772
0.758
0.762
0.667
0.679
0.684
0.688
0.691
0.612
0.676
0.681
0.715
Shear viscosity expression for molten LiCl-CsCl system at 625-1200 K within full 15
ACCEPTED MANUSCRIPT component range has been fitted from data in Table 4, as follows: η(LiCl-CsCl) = 71.7276+5.9854×10-5 x-2.0148×10-4 x2 +1.5859×10-6 x3
(7)
-19.6375×10-2 T+1.8399×10-4 T2 -5.7930×10-8 T3 In equation (7), x denotes the mole fraction of LiCl, T denotes temperature. 3.3.5.
NaCl-KCl
PT
Table 5 lists shear viscosities for molten NaCl-KCl at different temperatures and
RI
compositions. Shear viscosities decrease with increasing temperature for all the components. At a certain temperature, along with gradual increase of NaCl content,
SC
shear viscosities of molten NaCl-KCl system exhibit an upward trend with some slight
NU
oscillation for different components. The addition of NaCl into KCl weakens the interactions of Na-Cl and K-Cl pairs 18, which will improve the fluidities of the melts.
MA
However, NaCl also strengthens interactions between Cl-Cl pairs and promotes closed pack between Na-Na, K-K and Na-K pairs
18
, which will deteriorate melt fluidity.
D
Compared with LiCl-XCl (X denotes Na, K, Rb, Cs) systems, the weakening of
PT E
interactions between counter-ions is weaker, so the corresponding improvement effects of melt fluidity is weak too. The deteriorate effect results from closed pack between
CE
cations is then in the leading position. Altogether, addition of NaCl into molten KCl will deteriorate its fluidity.
AC
Shear viscosity expression for molten NaCl-KCl system at 950-1200 K within full component range has been fitted from data in Table 5, as follows: η(NaCl-KCl) = 28.0759+8.2895×10-4 x-4.0774×10-6 x2 +1.8438×10-7 x3
(8)
-6.5903×10-2 T+5.4169×10-5 T2 -1.5221×10-8 T3 In equation (8), x denotes the mole fraction of NaCl, T denotes temperature.
Table 5 Shear Viscosities of Molten NaCl-KCl at Different Temperatures (Units: mPa∙s) Temp
NaCl%
16
ACCEPTED MANUSCRIPT (K)
0.00
6.25
12.50
18.75
25.00
31.25
950
-
-
-
-
-
-
975
-
-
-
-
-
-
1000
-
-
-
-
1.102
1.118
1.16
1025
-
-
-
1.111
0.986
1.016
1050
-
0.902
0.964
1.049
0.999
0.971
1075
0.973
0.874
0.920
0.914
0.924
1100
0.844
0.889
0.872
0.871
0.924
1125
0.769
0.819
0.785
0.869
1150
0.765
0.778
0.811
1175
0.818
0.758
0.779
1200
0.695
0.707
0.738
50.00
-
-
1.333
1.181
1.197
1.408
1.215
1.181
1.067
1.01
1.106
1.061
0.973
0.918
0.845
0.892
0.863
0.853
0.863
0.747
0.767
0.762
0.715
0.749
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
-
-
-
-
-
-
-
-
1.331
1.18
-
-
-
-
-
-
1.228
1.272
1.224
-
-
-
-
-
1.091
1.181
1.199
1.163
1.218
-
-
-
-
1.023
1.006
1.096
1.064
1.039
1.109
-
-
-
1.037
1.063
0.968
0.952
1.023
1.006
1.063
1.097
1.091
-
0.927
0.912
0.914
0.922
0.982
0.943
0.980
1.076
1.023
1.090
0.929
0.904
0.861
0.832
0.870
0.947
0.970
0.946
1.008
1.091
1.050
0.756
0.856
0.825
0.834
0.812
0.784
0.868
0.977
0.884
0.879
1.061
1.026
0.767
0.843
0.799
0.757
0.765
0.793
0.768
0.836
0.865
0.880
0.978
0.926
0.674
0.681
0.741
0.713
0.736
0.792
0.838
0.875
0.785
0.867
0.856
0.882
NaCl-RbCl
PT
43.75
RI
3.3.6.
37.50
SC
Table 6 lists shear viscosities for molten NaCl-RbCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the
NU
components. At a certain temperature, along with gradual increase of NaCl, shear
MA
viscosities of molten NaCl-RbCl system first decrease and then increase slightly or show slight oscillation tendency for different components under the effects of both
D
interionic interactions and local atomic arrangements. Similar with LiCl-RbCl system,
PT E
the interactions of Na-Cl and Rb-Cl pairs are weakened by the additive NaCl, resulting in the improvement of melt fluidity and decrease of shear viscosity. In the meantime,
CE
with the gradual addition of NaCl, interactions between Cl-Cl pairs are strengthened and closed packs between cations are promoted, leading to the deterioration of melt
AC
fluidity and the increase of shear viscosity. Shear viscosity expression for molten NaCl-RbCl system at 850-1200 K within full component range has been fitted from data in Table 6, as follows: η(NaCl-RbCl) = 34.9576-1.3531×10-3 x-3.1783×10-5 x2 +3.8871×10-7 x3
(9)
-8.1746×10-2 T+6.6960×10-5 T2 -1.8713×10-8 T3 In equation (9), x denotes the mole fraction of NaCl, T denotes temperature. Table 6 Shear Viscosities of Molten NaCl-RbCl at Different Temperatures (Units: mPa∙s) Temp
NaCl%
17
ACCEPTED MANUSCRIPT (K)
0.00
850 875
-
-
-
900 925
-
-
950 975
-
1000 1025
-
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
-
-
-
2.099
2.281 2.040
2.093
-
-
-
-
-
-
-
-
-
-
1.727
1.765 1.786
2.095 1.736
1.864 1.770
1.917 1.779
1.576
-
-
-
-
-
-
-
-
1.601
1.722 1.553
1.684 1.611
1.597 1.466
1.589 1.569
1.689 1.431
1.694 1.455
1.431 1.480
1.481 1.334
1.403
-
-
-
-
-
1.508 1.479
1.347 1.249
1.384 1.390
1.278 1.433
1.412 1.334
1.322 1.253
1.344 1.300
1.394 1.311
1.336 1.287
1.333 1.261
1.325 1.401
1.273 1.276
1.197
-
-
-
1.298 1.214
1.241 1.174
1.167 1.149
1.234 1.287
1.331 1.085
1.247 1.199
1.166 1.036
1.119 1.101
1.188 1.068
1.159 1.118
1.138 1.084
1.171 1.140
1.215 1.073
1.169 1.095
1.100
-
1.178 1.042
1.097 1.137
1.169 1.015
1.125 0.947
1.123 1.047
1.075 1.006
1.069 0.990
1.074 0.973
1.025 0.936
0.996 1.018
1.064 1.003
1.006 0.991
1.063 1.043
1.000 1.024
1.042 1.003
1.090
1.047 0.933
0.965 0.956
0.998 0.955
0.973 0.981
0.970 0.906
0.892 0.964
0.928 0.890
0.914 0.912
0.936 0.899
0.986 0.949
0.949 0.898
0.885 0.870
0.882 0.927
0.926 0.925
1.026
0.969
0.929
0.843
0.869
0.904
0.796
0.831
0.933
0.900
0.850
0.850
0.871
0.854
0.862
0.882
1100 1125
1.143
1150 1175
1.008 0.970
0.966 0.989
1200
0.873
0.845
3.3.7.
NaCl-CsCl
NU
Table 7 lists shear viscosities for molten NaCl-CsCl at different temperatures and
MA
compositions. Shear viscosities decrease with increasing temperature for all the components. The evolution rules of molten NaCl-CsCl systems are similar with those
D
of NaCl-RbCl systems. Similar with NaCl-RbCl system, the interactions of Na-Cl and
PT E
Cs-Cl pairs are weakened by the additive NaCl, resulting in the improvement of melt fluidity and decrease of shear viscosity. In the meantime, with the gradual addition of NaCl, interactions between Cl-Cl pairs are strengthened and closed packs between
CE
1.121
cations are promoted, leading to the deterioration of melt fluidity and the increase of shear viscosity. Under the effects of both interionic interactions and local atomic
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1.266
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1.321
18.75
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25.00
1050 1075
12.50
SC
1.412
6.25
arrangements, shear viscosities of molten NaCl-CsCl system first decrease and then increase slightly or show slight oscillation tendency for different components with the increase of NaCl content. Shear viscosity expression for molten NaCl-CsCl system at 800-1200 K within full component range has been fitted from data in Table 7, as follows: η(NaCl-CsCl) = 44.0431-3.1839×10-3 x-2.9839×10-5 x2 +5.1291×10-7 x3 18
(10)
1.050 0.926
ACCEPTED MANUSCRIPT -10.7021×10-2 T+9.0581×10-5 T2 -2.6081×10-8 T3 In equation (10), x denotes the mole fraction of NaCl, T denotes temperature. Table 7 Shear Viscosities of Molten NaCl-CsCl at Different Temperatures (Units: mPa∙s) NaCl% 0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
800
-
-
-
-
-
3.040
3.071
-
-
-
-
-
-
-
-
-
-
825 850
-
-
-
2.553
2.752 2.295
2.338 2.199
2.291
-
-
-
-
-
-
-
-
-
-
-
875 900
-
-
2.115
2.101 2.155
2.213 2.129
2.092 1.966
2.133 1.950
2.177 1.959
2.166 1.768
1.759
-
-
-
-
-
-
-
-
2.041 1.807
1.794 1.728
1.860 1.728
1.879 1.671
1.720 1.614
1.656 1.611
1.780 1.632
1.670 1.548
1.666 1.596
1.614 1.526
-
-
-
-
-
-
1.607 1.541
1.587 1.514
1.626 1.469
1.605 1.404
1.506 1.434
1.443 1.409
1.585 1.375
1.418 1.363
1.467 1.258
1.449 1.379
1.471 1.386
1.227
-
-
-
-
1.396 1.315
1.295 1.331
1.446 1.365
1.366 1.254
1.278 1.216
1.222 1.333
1.263 1.333
1.263 1.255
1.262 1.125
1.209 1.170
1.135 1.103
1.264 1.167
1.214 1.153
1.252
-
-
1.174 1.200
1.244 1.070
1.173 1.090
1.209 1.145
1.166 1.115
1.156 1.054
1.104 1.033
1.126 1.051
1.015 0.997
1.196 1.028
1.077 0.994
1.104 1.011
1.108 1.056
1.088 1.041
1.058 1.103
1.076 1.046
1.031 1.005
1.061 0.968
1.109 0.996
0.959 0.925
1.029 0.968
1.001 0.983
0.958 0.927
0.953 0.999
1.045 0.943
0.959 0.989
0.945 0.893
1.000 0.947
0.922 0.972
0.984 0.960
1.050
1.040 0.890
0.893 0.994
0.953 0.840
0.945 0.894
0.916 0.930
0.880 0.843
0.949 0.891
0.920 0.881
0.930 0.810
0.837 0.808
0.820 0.800
0.897 0.856
0.825 0.839
0.881 0.780
0.931 0.876
0.926
1.028
1175 1200
0.974
1.024 1.018
4.
Conclusions
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1125 1150
1.148
SC
1.267
1.421
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1075 1100
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1.516
1.595
Shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl,
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1025 1050
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975 1000
1.610
NaCl-RbCl and NaCl-CsCl in temperature range of near melting point-1200 K within full composition range have been calculated using MD simulation, to reveal the effects of temperature and composition on melt fluidity.
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1.889
With the gradual increase of temperature, shear viscosities of all these systems
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925 950
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Temp (K)
decrease monotonically. Melt shear viscosities exhibit a little complicated variation trends with the varying compositions under the effects of both interionic interactions and local atomic arrangements. With gradual increase of LiCl content, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl and LiCl-CsCl first decrease and then increase slightly or present slight oscillation tendency. However, the subsequent increase is small. With the increase of NaCl content, shear viscosities of molten NaClRbCl and NaCl-CsCl first decrease and then fluctuate slightly, while those of molten 19
-
1.090 1.026 0.882
ACCEPTED MANUSCRIPT NaCl-KCl show an overall increase trend. To summarize, LiCl can improve the fluidity of molten NaCl, KCl, RbCl and CsCl, while NaCl can improve the fluidity of molten RbCl and CsCl, but deteriorate that of molten KCl. Finally, simple databases for shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiClRbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaCl-CsCl have been built and
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corresponding temperature & composition - dependent equations for shear viscosities
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of these systems have been fitted according to the calculated results.
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Acknowledgments
We acknowledge the financial support provided by the National Natural Science
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Foundation Project of China Youth Found (51504099).
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References
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ACCEPTED MANUSCRIPT Mixtures of LiCl and KCl. J. Nucl. Mater. 2012, 2012, 17-22. (7) Rollet, A.-L.; Salanne, M. Studies of the Local Structures of Molten Metal Halides. Annu. Rep. Prog. Chem., Sect. C. 2011, 201, 88-123. (8) Trullàs, J.; Alcaraz, O.; González, L. E.; Silbert, M. Structure and Dynamics of Molten AgCl. The Inclusion of Induced Polarization. J. Phys. Chem. B. 2003, 107,
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(11) Luo, H.; Xiao, S.; Wang, S.; Huai, P.; Deng, H.; Hu, W. Molecular Dynamics Simulation of Diffusion and Viscosity of Liquid Lithium Fluoride. Comput. Mater.
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Mater. Sci. 2014, 83, 362–370. (13) Galamba, N.; Nieto De Castro, C. A.; Ely, J. F. Shear Viscosity of Molten Alkali
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Halides from Equilibrium and Nonequilibrium Molecular-Dynamics Simulations. J. Chem. Phys. 2005, 120, 224501. (14) Nevins, D.; Spera, F. J. Accurate Computation of Shear Viscosity from Equilibrium Molecular Dynamics Simulations. Mol. Simul. 2007, 33, 1261-1266. (15) Wang, J.; Sun, Z.; Lu, G.; Yu, J. Molecular Dynamics Simulations of the Local Structures and Transport Coefficients of Molten Alkali Chlorides. J. Phys. Chem. B, 2014, 118, 10196-10206. 21
ACCEPTED MANUSCRIPT (16) Merlet, C.; Madden, P. A.; Salanne, M. Internal mobilities and diffusion in an ionic liquid mixture, Phys. Chem. Chem. Phys. 2010, 12, 14109-14114. (17) Morgan, B.; Madden, P. A. Ionmobilities and microscopic dynamics in liquid (Li, K) Cl, J. Chem. Phys. 2004, 120, 1402-1413. (18) Wang, J.; Wu, J.; Sun, Z.; Lu, G.; Yu, J. Molecular Dynamics Study of the
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(19) Wang, J.; Wu, J.; Lu, G.; Yu, J. Molecular Dynamics Study of the Transport Properties and Local Structures of Molten Alkali Metal Chlorides. Part III. Four
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Binary Systems LiCl-RbCl, LiCl-CsCl, NaCl-RbCl and NaCl-CsCl. J. Mol. Liq. 2017, 238, 236-247.
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Compounds. J. Am. Chem. Soc. 1928, 50, 1036–1045. (22) Mayer, J. E. Dispersion and Polarizability and the van Der Waals Potential in the
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Alkali Halides. J. Chem. Phys. 1933, 1, 270–279. (23) Toukmaji, A. Y.; Board, J. A. Ewald Summation Techniques in Perspective: A
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Survey. Comput. Phys. Commun. 1996, 95, 73-92. (24) Allen, M. P.; Tlldesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1987. (25) Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant Pressure Molecular Dynamics Algorithms. J. Chem. Phys. 1994, 101, 4177-4189. (26) Melchionna, S.; Ciccotti, G.; Holian, B. L. Hoover Npt Dynamics for Systems Varying in Shape and Size. Mol. Phys. 1993, 78, 533-544. 22
ACCEPTED MANUSCRIPT (27) Nosé, S. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Mol. Phys. 2002, 100, 191-198. (28) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1696-1697. (29) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé-Hoover Chains: The Canonical
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S.K. Singer. Molten salts: chlorides and mixtures - electrical conductance, density, viscosity, and surface tension data, J. Phys. Chem. Ref. Data 4. 1975, 871-1178.
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(33) Janz, G. J. NIST Properties of Molten Salts Databases, NIST SRD 27; National
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Bureau of Standards: Boulder, CO, 1992. (34) Galamba, N.; Castro, C. A. N.; F. Ely, J. Molecular Dynamics Simulation of the
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(35) E. Veliyulin, A. Voronel, H.A. Oye. Universal features in the viscosity behavior of salt melts and their mixtures, J. Phys. Condens. Matter 7. 1995, 4821-4828.
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ACCEPTED MANUSCRIPT Highlights •
Shear viscosities present negative dependences on temperature.
•
Shear viscosities first decrease and then slightly fluctuate with the increase of LiCl content.
•
NaCl improves the fluidity of molten RbCl and CsCl, but deteriorates that
•
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of molten KCl. Simple databases for melt shear viscosity have been built based on the
Expressions of melt shear viscosity vs. temperature & composition have
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been fitted according to the calculated data.
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•
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verified algorithm.
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Jia Wang, Cheng-Lin Liu PII: DOI: Reference:
S0167-7322(18)33521-9 doi:10.1016/j.molliq.2018.10.062 MOLLIQ 9807
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
9 July 2018 11 October 2018 12 October 2018
Please cite this article as: Jia Wang, Cheng-Lin Liu , Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation. Molliq (2018), doi:10.1016/j.molliq.2018.10.062
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ACCEPTED MANUSCRIPT Temperature and composition dependences of shear viscosities for molten alkali metal chloride binary systems by molecular dynamics simulation Jia Wang1,2, Cheng-Lin Liu2*
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1 Department of Precision Manufacturing Engineering, Suzhou Vocational Institute of
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Industrial Technology, Suzhou, 215104, China
2 National Engineering Research Center for Integrated Utilization of Salt Lake
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Resources Resource, East China University of Science and Technology, Shanghai,
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NU
200237, China
*Corresponding authors
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E-mail address: [email protected] (C.L. Liu)
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Tel/Fax numbers: +86-21-64250981
1
ACCEPTED MANUSCRIPT Abstract Structures and properties of molten alkali chlorides is the foundation of electrolyte process. In the paper, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaCl-CsCl in temperature range of near melting point to 1200 K within full composition range have been calculated intensively using
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equilibrium molecular dynamics (EMD) method. The calculated values are in good
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agreement with available experimental results. Simple databases for melt shear
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viscosity have been built based on the verified algorithm. Shear viscosities of these melts exhibit negative dependences on temperature and more complicated variation
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trends on compositions. Under the effects of local structure and interatomic force simultaneously, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-
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CsCl, NaCl-RbCl and NaCl-CsCl decrease firstly and then fluctuate slightly as the contents of LiCl or NaCl are increased. However, addition of NaCl into molten KCl
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deteriorates the melt fluidity. Expressions of melt shear viscosity vs. temperature &
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composition have also been obtained according to the calculated data finally. Keywords
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Molecular Dynamics Simulation; Molten alkali metal chlorides; Shear Viscosity
2
ACCEPTED MANUSCRIPT 1.
Introduction Due to the excellent performances of high temperature & chemical stability, fine
conductivity, good liquidity and high heat capacity 1, inorganic molten salts have many technological applications, such as energy storage devices 2, molten salt reactors 3, metal production electrolytes 4, nuclear reactor coolants 5, nuclear waste treatment
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agents 6, and so on. It is significant to reveal the nature of inorganic molten salts
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systematically and integrally for improving theoretical research and enhancing practical
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applications. Investigation on inorganic molten salts has long been the interests of many researchers around the world. Benefiting from the rapid developments of science &
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technology and computer technology, molten salts can be studied through not only experimental measuring but also computer simulation 7.
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Given extremely high temperature and corrosive conditions of molten salts, experimental measurements on molten salts are always influenced and even inhibited
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by costly and demanding experiment. It is not surprising, therefore, that there are
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substantial deficiencies and even disparities among the reported experimental results for molten salts. Computer simulation has been a less costly alternative than experiment,
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for example, Molecular Dynamics (MD) method, which can successfully predicted local structures and dynamics properties (such as diffusion coefficients, viscosity, ionic
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conductivity and so on) of pure molten salts and their mixtures
8–11
. Computer
simulation can also explore the performance of molten salts at different temperatures and salt compositions efficiently 12. Consisting of monatomic and single charged ions, alkali chloride melts have relatively simple structure and excellent transport performance, and have been main components or additives in many industries, such as molten salt electrolysis processing, high-temperature heat storage technology, and so on. It is significant to fully explore 3
ACCEPTED MANUSCRIPT the properties of molten alkali chlorides from both scientific and industrial viewpoints, among which shear viscosity is a very important property. In the production of magnesium and lithium electrolysis, with the commonly used electrolyte systems of MgCl2-NaCl-KCl/MgCl2-NaCl-CaCl2-KCl and LiCl-KCl respectively, the shear viscosity of electrolyte affects the separating effect between liquid metal, solid slag, gas
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and electrolyte. However, due to difficulty and high cost of molten salt investigations,
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before investigating complicated ternary/quarternary molten chloride systems, shear
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viscosities of more commonly used molten alkali binary chlorides have first been the focus of the research in this work.
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Shear viscosity of inorganic molten salt can be calculated through equilibrium molecular dynamics (EMD) simulations or non-equilibrium molecular dynamics
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(NEMD) simulations. Using EMD method to calculate shear viscosity of molten alkali metal chlorides is becoming increasingly sophisticated. Galamba
13
had attempted to
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compute shear viscosities of molten KCl and NaCl with both NEMD and EMD methods.
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The values obtained from EMD method were found to be significantly lower than those predicted by NEMD method. Later, Nevins 14 explored calculation conditions through
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viscosity calculation of molten NaCl with EMD method to obtain a good compromise between calculation time and viscosity quality. Wang 15 calculated shear viscosities of
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the five pure molten alkali chlorides at different temperatures through EMD method. Shear viscosities of molten alkali halide mixtures have also been calculated through molecular dynamic simulations. Merlet 16 and Morgan 17 had calculated viscosities of molten LiF-KF and LiCl-KCl systems through Molecular Dynamics calculations. However, the research about viscosities of molten alkali chloride binary mixtures is discrete and far from comprehensive. There are quite a few experimental results about shear viscosities of molten alkali 4
ACCEPTED MANUSCRIPT metal chlorides. The existing data is discrete and far from consolidated. Most of them were just records for one melt at some discrete temperatures and compositions. Systematic investigations on shear viscosity of molten alkali metal chlorides is scarce owing to the rigorous experimental conditions and the tedious computational process. Therefore, the related fundamental data are sorely lacking. The effects of LiCl or NaCl
. Based on the previous work, shear viscosities of some more widely used molten
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18,19
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on shear viscosities of molten KCl, RbCl and CsCl at 1100K have been analyzed before
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alkali chloride binary systems at different temperatures and compositions have been calculated intensively through EMD method in this paper to supplement basic database
Methodology
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2.
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and meet practical engineering needs.
2.1. Simulation details
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Molecular dynamics simulations were performed to calculate shear viscosities of
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molten alkali metal chloride binary mixtures at different temperatures and components, i.e. LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaClCsCl. Calculated temperatures were within near melting point to 1200 K with an
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interval of 25 K. Lower limits of temperature were determined through corresponding
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equilibrium phase diagram. Calculated compositions ranged from 0 to 100% with an interval of 6.25%, in measuring of mole fraction of one component. For interaction between ions, following Born-Mayer-Huggins potential that had been successfully used in simulations of molten alkali halides was used: 𝑈𝑖𝑗 (𝑟) =
𝑞𝑖 𝑞𝑗 𝑟
𝜎𝑖𝑗 −𝑟
+ 𝐵𝑖𝑗 𝑒𝑥𝑝 (
𝜌
)−
𝐶𝑖𝑗 𝑟6
−
𝐷𝑖𝑗 𝑟8
(1)
In equation (1), the first term describes electrostatic interactions between ions, qi/qj is the ionic charge, and formal charge (+1 for alkali ions and -1 for chloride) was used. The second term represents Born-Huggins exponential short-range repulsion due to 5
ACCEPTED MANUSCRIPT overlap of electron clouds. Bij = Aij*b, in which b is a constant, being equal to 0.338×1019
𝑍
𝑍
J, Aij is Pauling factor 20,21, being equal to 1 + 𝑛i + 𝑛j , where Z denotes charge of ion i
j
and n denotes number of outer electrons, σ is crystal ionic "radii", and ρ is hardness parameter. The last two terms correspond to dipole-dipole and dipole-quadrupole
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dispersion interactions, and the dispersion constants Cij and Dij for alkali chloride systems were determined by Mayer 22.
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Potential parameters for the mixtures were determined as follows 18, and the detailed
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parameters used in this study were given in the Supporting Information. Taking LiClNaCl systems for example, in which the mole fraction of LiCl is x, the hardness
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parameter ρ for the mixtures obeys the rule of 1/ρmix = x/ρLiCl + (1-x)/ρNaCl. The
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dispersion parameters for Cl-Cl pair in the mixtures follow the formulas of Cmix(Cl-Cl) = xCLiCl(Cl-Cl) + (1-x)CNaCl(Cl-Cl) and Dmix(Cl-Cl) = xDLiCl(Cl-Cl) + (1-x)DNaCl(Cl-Cl). In the above expressions, ρLiCl, ρNaCl, CLiCl(Cl-Cl), CNaCl(Cl-Cl), DLiCl(Cl-Cl), and DNaCl(Cl-Cl) are the
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corresponding values of pure molten salts. For cationic pair Li-Na, σLi-Na =σLi+σNa, the parameters B, C, and D employ the geometric mean of the corresponding values for LiLi pair and Na-Na pair in the pure molten salts, i.e. BLi-Na = (BLi-Li·BNa-Na)1/2, CLi-Na =
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(CLi-Li·CNa-Na)1/2, DLi-Na = (DLi-Li·DNa-Na)1/2. The remaining parameters adopt the
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corresponding values of pure molten salts. The LAMMPS code was used to perform MD simulations. All the simulations were performed for a cubic box consisting of 1024 ions (512 cations and 512 anions respectively, and the numbers of each cation were determined according to mole fractions). Initial ionic configurations were random distribution. Initial velocities of ions were also random allocation and obeyed the Gaussian distribution. Periodic Boundary Condition was used to keep particle numbers constant and to eliminate boundary effect. Long-range interactions were handled using Ewald 6
23
summation
ACCEPTED MANUSCRIPT method to eliminate truncation errors. In the Ewald summation, the precise that determined the relative root mean square (RMS) error in per-atom forces calculated by the method was set to be 1.0×10-6, meaning that the RMS error will be a factor of 1000000 smaller than the reference force that two unit point charges exert on each other at a distance of 1 Å. The cutoff radius rc for the short-range potential and the real space
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part of the Ewald summation was set to be L/2, where L is side length of simulation cell.
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Verlet algorithm 24 was used to solve Newton's equations of motion.
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For all the simulation, the systems were first equilibrated in isothermal-isobaric ensemble (NPT) with pressure fixed at 0 GPa around the desired temperature using 25,26
. Production runs were performed in
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Nose-Hoover thermostat and barostat
canonical ensemble (NVT) with Nose-Hoover thermostat method
27,28
at equilibrated
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cell volume. Damping parameters that determined relaxation rates of temperature and pressure were set to be 0.1 ps. To control initial oscillations, Nose-Hoover chains were
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used for the thermostat and barostat, and the chain numbers were 3 in this work 29. The
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relaxation time was set to be 500 ps and the production time was 10 ns, with a time step of 1 fs.
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2.2. Evaluated properties
MD simulations can be used to compute dynamic properties of molten salts using the
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equilibrium methods described below 24,30. Shear viscosity η measures the resistance of a fluid deformed by shear stress. Here, shear viscosity is calculated from time integral of off-diagonal stress tensor autocorrelation function (SACF) with steady-state EMD simulation through GreenKubo relationship 13,30: 𝜂=𝑘
1 𝐵
∞
∫ 〈𝑆𝑥𝑦 (0)𝑆𝑥𝑦 (𝑡)〉 𝑑𝑡 𝑇𝑉 0
(2)
where kB is Boltzmann constant, T is temperature, V is volume of simulation cell, and 7
ACCEPTED MANUSCRIPT Sxy is xy-component of stress tensor. Sxy is defined as: 1
𝑆𝑥𝑦 = ∑𝑁 𝑖=1 [𝑚𝑖 𝑣𝑥𝑖 𝑣𝑦𝑖 + 2 ∑𝑗≠𝑖 𝑥𝑖𝑗 𝑓𝑦 (𝑟𝑖𝑗 )]
(3)
where mi is mass of ion i, vxi and vyi are x-component and y-component of vi (velocity of ion i) respectively, xij is x-component of rij = ri-rj and fy(rij) is y-component of force
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fij of ion i due to ion j. Each of the three independent off-diagonal components of stress tensor (i.e. Sxy, Sxz and Syz) provides an independent estimate of shear viscosity, and the
Results and discussions
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3.
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averaged value will be taken as the final viscosity value.
Shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl,
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NaCl-RbCl and NaCl-CsCl at different temperatures and components have been
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calculated from time integral of stress tensor autocorrelation function (SACF). Considering the computation cost and the fact that molten alkali chloride is mainly used
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below 800 °C, upper limit of computed temperature was set to be 1200 K. Lower limit
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was the near melting point, determined through corresponding equilibrium phase diagram.
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3.1. Decay and running integral behaviors of stress tensor autocorrelation function
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Decay and integral behaviors of SACF need to be tested before the viscosity calculation. The time for SACF calculation should be long enough to capture the whole decay process and to ensure the running integral of SACF reach a steady plateau. In this paper, the calculated components are evenly distributed between 0-100 for mole percentage of one salt. Therefore, pure salts at both ends, LiCl and CsCl, are selected in the test. Fig.1 gives the normalized SCAFs and corresponding running integrals of molten LiCl and CsCl. As revealed in Fig.1, both SCAFs decay to zero quickly and
8
ACCEPTED MANUSCRIPT corresponding integrals reach the plateau after about 3 ps. To ensure the data accuracy, 5 ps is adopted to calculate SACFs in this paper. The SACFs will be averaged for 10
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RI
PT
million steps to ensure good statistics that repeated runs give the same plateau value.
AC
Fig. 1 Time Evolutions of Normalized SACFs and Corresponding Running Integrals for Molten LiCl and CsCl
3.2. Model verification Due to costly and demanding test conditions, systematic viscosity measurement for molten alkali chlorides within full composition and temperature ranges is impracticable for the current reality. Experimental values for shear viscosity of high temperature molten salts are always scarce and dispersed. In this section, some calculated viscosities have been tested with available experimental results to verify accuracy of calculation 9
ACCEPTED MANUSCRIPT method. As shown in Fig.2, comparisons for molten LiCl-CsCl system at 1020 K and KCl-NaCl at 1100 K
31
reveal good agreements between calculated and experimental
results. In addition, calculated results for the first four pure salts at 1100 K, i.e. 0.861 mPa·s for LiCl, 1.090 mPa·s for NaCl, 0.844 mPa·s for KCl and 1.143 mPa·s for RbCl, also exhibit good agreements with experimental values of 0.843, 1.022, 0.881 and 1.025 32-35
, with the errors being less than 10%. In all, simulation
PT
mPa·s correspondingly
RI
method described above can bring reliable viscosity values, and massive calculations
AC
CE
PT E
D
MA
NU
SC
will be carried out.
Fig.2 Comparisons between Computed Values and Experimental Results for Shear Viscosity of Molten LiCl-CsCl and NaCl-KCl
The simulated shear viscosities of these mixed molten salts in the temperature range of near melting point-1200 K within the whole concentration scope are listed in Table 10
ACCEPTED MANUSCRIPT 1-7. In addition, the expressions of viscosity on temperature and component have been fitted according to calculated results through 1stOpt software with LevenbergMarquardt (LM) - Universal Global Optimization (UGO) algorithms and convergence criteria of 1.0×10-10. 3.3. Shear viscosity database for molten alkali chlorides Molten LiCl-NaCl
PT
3.3.1.
RI
Shear viscosities for molten LiCl-NaCl at different temperatures and compositions
SC
have been listed in Table 1. It is obvious that shear viscosities decrease with increasing temperature for all the components. At a certain temperature, along with gradual
NU
increasing of LiCl, shear viscosities of the system first decrease and then increase slightly or show slight oscillation tendency.
MA
As analyzed previously from the radial distribution functions 18, addition of Li+ into NaCl will weaken interactions between counter-ions, strengthen interactions between
D
chlorine ions and promote closed pack between cations. Structural loosening between
PT E
counter-ions resulting from interactions weakening dominants, thus giving rise to improvement of melt fluidity and decrease of shear viscosity. With continuous addition
CE
of LiCl, strengthening of Cl-Cl interactions and promotion of closed packs between
AC
cations deteriorate melt fluidity to a certain extent, resulting in slightly increase of shear viscosity. On a whole, melt fluidity is always improved with the addition of LiCl, the difference just lies in the extent of improvement. Shear viscosity expression for molten LiCl-NaCl system at 850-1200 K within full component range has been fitted from data in Table 1, as follows: η(LiCl-NaCl) = 17.6142-3.1445×10-3 x+1.9166×10-5 x2 -1.3484×10-7 x3 -3.9976×10-2 T+3.3223×10-5 T2 -9.6073×10-9 T3 In equation (4), x denotes the mole fraction of LiCl, T denotes temperature. 11
(4)
ACCEPTED MANUSCRIPT Table 1 Shear Viscosities of Molten LiCl-NaCl at Different Temperatures (Units: mPa∙s) LiCl% 50.00 56.25
Temp (K)
0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
850
-
-
-
-
-
-
-
-
-
875
-
-
-
-
-
-
-
-
-
900
-
-
-
-
-
-
-
-
925
-
-
-
-
-
-
-
-
950
-
-
-
-
-
-
-
1.396
975
-
-
-
-
-
-
1.251
1.272
1000
-
-
-
-
-
1.187
1.251
1025
-
-
-
-
1.146
1.168
1.130
1050
-
-
-
1.098
1.083
1.095
1075
-
1.138
1.086
1.073
1.045
1.035
1100
1.090
1.031
0.994
1.015
0.947
1125
1.050
0.983
0.958
0.939
0.939
1150
1.026
0.878
0.969
0.859
1175
0.926
0.892
0.807
1200
0.882
0.829
0.822
75.00
87.50
93.75
100.00
-
-
1.648
1.557
-
-
1.524
1.568
-
-
-
-
1.400
1.414
-
-
-
1.374
1.292
1.365
1.371
1.314
1.393
1.257
1.348
1.324
1.275
1.225
1.212
1.218
1.215
1.227
1.247
1.269
1.225
1.201
1.293
1.160
1.165
1.217
1.113
1.056
1.178
1.169
1.147
1.181
1.097
1.075
1.114
1.039
1.062
1.034
1.183
1.157
1.107
1.168
1.118
1.099
1.043
1.044
1.040
1.018
1.049 0.981
1.099
1.005
0.990
1.010
0.985
0.999
0.986
0.924
1.048
1.061
1.039
0.963
0.978
0.964
0.993
0.955
0.930
0.935
0.896
0.948
1.006
0.950
0.924
0.890
0.816
0.950
0.857
0.914
0.859
0.881
0.987
0.907
0.884
0.987
0.906
0.918
0.864
0.900
0.926
0.859
0.843
0.869
0.838
0.876
0.866
0.888
0.835
0.806
0.766
0.797
0.850
0.772
0.813
0.807
0.736
0.791
0.773
RI
PT
68.75
81.25
0.889
0.884
0.859
0.838
0.799
0.861
0.818
0.870
0.864
0.761
0.730
0.790
0.746
SC
0.888
0.839
0.828
0.761
0.760
0.774
0.694
0.766
0.751
0.800
0.774
0.730
0.691
0.757
0.758
0.709
0.659
0.751
0.736
0.757
0.707
0.670
0.773
0.674
0.715
NU
3.3.2.
62.50
LiCl-KCl
MA
Shear viscosities for molten LiCl-KCl at different temperatures and compositions have been listed in Table 2. Shear viscosities decrease with increasing temperature for
D
all the components. At a certain temperature, along with gradual increase of LiCl, shear
PT E
viscosities of molten LiCl-KCl system first decrease and then increase slightly or show slight oscillation tendency for different components under the effects of both interionic
CE
interactions and local atomic arrangements. As analyzed previously 18, addition of Li+ into KCl will weaken interactions between counter-ions, strengthen interactions
AC
between chlorine ions and promote closed pack between cations. In addition, viscosity of molten KCl is lower than that of molten NaCl at the same temperature. Similarly, viscosity of molten LiCl-KCl is also lower than that of molten LiCl-NaCl at the same temperature and LiCl content. Molten LiCl-KCl should be a better choice in some industrial applications of molten salts. Shear viscosity expression for molten LiCl-KCl system at 700-1200 K within full component range has been fitted from data in Table 2, as follows: 12
ACCEPTED MANUSCRIPT η(LiCl-KCl) = 30.1146+5.0115×10-4 x-6.3339×10-5 x2 +5.4347×10-7 x3
(5)
-7.6162×10-2 T+6.7268×10-5 T2 -2.0198×10-8 T3 In equation (5), x denotes the mole fraction of LiCl, T denotes temperature. Table 2 Shear Viscosities of Molten LiCl-KCl at Different Temperatures (Units: mPa∙s)
6.25
12.50
18.75
25.00
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
-
-
-
-
-
-
-
-
-
2.921
2.822
-
-
-
-
-
-
725
-
-
-
-
-
-
-
-
-
2.554
2.418
2.271
-
-
-
-
-
750
-
-
-
-
-
-
-
-
-
2.237
2.264
2.272
-
-
-
-
775
-
-
-
-
-
-
-
-
2.219
1.969
2.079
1.965
1.879
-
-
-
800
-
-
-
-
-
-
-
-
1.725
1.794
1.840
1.700
1.781
-
-
-
825
-
-
-
-
-
-
-
1.632
1.679
1.611
1.536
1.540
1.639
1.502
-
-
850
-
-
-
-
-
-
-
1.531
1.530
1.560
1.452
1.434
1.332
1.432
1.575
875
-
-
-
-
-
-
1.405
1.357
1.482
900
-
-
-
-
-
-
1.402
1.257
1.318
925
-
-
-
-
-
1.355
1.179
1.164
1.234
950
-
-
-
-
-
1.135
1.104
1.081
1.041
975
-
-
-
-
1.075
1.044
1.110
1.019
1000
-
-
-
1.092
1.061
1.019
0.986
1025
-
-
1.018
0.932
0.951
0.948
0.911
1050
-
0.923
0.850
0.867
0.871
0.895
0.834
0.861
0.888
1075
0.973
0.858
0.868
0.884
0.918
0.814
0.859
0.813
1100
0.844
0.841
0.851
0.822
0.846
0.806
0.780
1125
0.769
0.774
0.823
0.856
0.807
0.754
1150
0.765
0.775
0.717
0.699
0.745
0.723
1175
0.818
0.693
0.710
0.678
0.654
0.706
1200
0.695
0.721
0.679
0.662
0.597
0.668
LiCl-RbCl
93.75
100.00
-
1.459
1.394
1.329
1.395
1.337
-
-
1.281
1.254
1.271
1.253
1.221
1.244
1.198
1.218
1.070
1.203
1.218
1.111
1.173
1.151
1.215
1.269
1.051
1.120
1.062
1.113
1.079
1.059
1.061
1.097
1.073
1.011
0.953
0.957
1.056
1.066
1.047
1.030
1.034
0.995
0.897
0.933
0.934
0.928
0.935
0.925
0.984
0.991
1.010
0.868
0.941
0.930
0.855
0.850
0.852
0.955
0.869
0.819
0.924
0.882
0.789
0.878
0.863
0.855
0.891
0.795
0.816
0.849
0.750
0.787
0.810
0.811
0.784
0.912
0.841
0.881
0.775
0.755
0.687
0.725
0.772
0.711
0.761
0.713
0.733
0.861
0.789
0.709
0.827
0.720
0.725
0.755
0.694
0.702
0.757
0.755
0.746
0.723
0.697
0.744
0.689
0.688
0.658
0.693
0.685
0.680
0.777
0.751
0.623
0.612
0.656
0.618
0.724
0.699
0.633
0.655
0.665
0.685
0.659
0.583
0.699
0.631
0.606
0.620
0.656
0.590
0.633
0.653
0.652
0.715
NU
MA
D
SC
-
1.471
PT E
3.3.3.
RI
0.00
700
PT
LiCl%
Temp (K)
CE
Table 3 lists shear viscosities for molten LiCl-RbCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the
AC
components. At a certain temperature, along with gradual increase of LiCl, shear viscosities of molten LiCl-RbCl system exhibit an overall downward trend but some slight oscillation for different components. The addition of Li+ into RbCl weakens the interactions of Li-Cl and Rb-Cl pairs, strengthens interactions between Cl-Cl pairs and promotes closed pack between Li-Li, Rb-Rb and Li-Rb pairs. In the beginning, interaction weakening of Li-Cl and Rb-Cl pairs results in structural loosening between counter-ions, thus giving rise to improvement of melt fluidity and decrease of shear 13
ACCEPTED MANUSCRIPT viscosity. With continuous addition of LiCl, strengthening of Cl-Cl interactions and promotion of closed packs between cations become more and more significant and then deteriorate melt fluidity to a certain extent, resulting in slightly increase of shear viscosity. Shear viscosity expression for molten LiCl-RbCl system at 625-1200 K within full
PT
component range has been fitted from data in Table 3, as follows:
η(LiCl-RbCl) = 71.0297+7.3551×10-3 x-3.0849×10-4 x2 +2.0435×10-6 x3
RI
(6)
-19.5183×10-2 T+1.8326×10-4 T2 -5.7798×10-8 T3
SC
In equation (6), x denotes the mole fraction of LiCl, T denotes temperature.
NU
Table 3 Shear Viscosities of Molten LiCl-RbCl at Different Temperatures (Units: mPa∙s) LiCl%
Temp (K)
0.00
625
-
-
-
-
-
-
-
650
-
-
-
-
-
-
18.75
25.00
31.25
37.50
43.75 -
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00 -
-
6.856
-
-
-
-
-
-
6.057
5.321
-
-
-
-
-
-
MA
12.50
5.914
-
-
5.007
4.619
4.584
-
-
-
-
-
--
-
-
4.399
4.208
3.391
-
-
-
-
-
-
-
-
3.909
3.374
3.251
3.025
-
-
-
-
-
-
3.283
3.297
3.078
2.908
2.666
-
-
-
-
-
-
2.885
2.969
2.663
2.509
2.419
2.274
-
-
-
-
2.650
2.402
2.388
2.405
2.197
2.159
2.081
-
-
-
-
-
2.501
2.418
2.176
2.221
1.862
1.869
1.848
1.682
-
-
-
2.284
2.027
2.106
2.137
1.929
1.755
1.652
1.629
1.539
1.514
-
-
2.098
1.906
1.822
1.694
1.608
1.536
1.477
1.446
1.451
1.408
1.405
-
1.859
1.894
1.744
1.579
1.692
1.487
1.494
1.465
1.274
1.405
1.231
1.225
1.218
1.746
1.645
1.529
1.391
1.513
1.296
1.408
1.342
1.276
1.345
1.141
1.170
1.269
1.503
1.606
1.505
1.452
1.392
1.345
1.395
1.233
1.243
1.187
1.245
1.105
1.165
1.097
1.387
1.381
1.366
1.397
1.295
1.283
1.166
1.164
1.140
1.135
1.140
1.066
1.091
1.034
1.336
1.376
1.265
1.237
1.281
1.150
1.134
1.099
1.043
1.039
1.006
0.978
0.928
1.010
-
-
-
-
-
-
-
700
-
-
-
-
-
-
725
-
-
-
-
-
-
750
-
-
-
-
-
-
775
-
-
-
-
-
-
800
-
-
-
-
-
-
825
-
-
-
-
-
850
-
-
-
-
-
875
-
-
-
-
-
900
-
-
-
-
925
-
-
-
1.624
950
-
-
-
975
-
-
1.692
1000
-
1.423
1.413
1025
1.412
1.421
1050
1.321
1.260
1075
1.266
1.072
1100
1.143
1.065
1125
1.121
1150
AC
CE
PT E
675
D
6.25
-
1.324
1.242
1.212
1.179
1.119
1.101
1.079
1.014
1.031
1.062
0.905
1.014
0.889
0.946
0.924
1.192
1.234
1.187
1.074
1.069
1.043
0.945
1.072
0.944
0.883
0.996
0.931
0.864
0.880
0.816
1.185
1.034
1.098
1.093
0.967
0.982
0.973
0.894
0.892
0.935
0.825
0.904
0.845
0.854
0.881
1.098
1.031
1.018
1.023
0.929
0.973
0.963
0.968
0.861
0.893
0.870
0.797
0.779
0.753
0.861
1.021
0.976
0.953
0.993
0.960
0.925
0.951
0.880
0.853
0.848
0.793
0.772
0.826
0.714
0.740
0.746
1.008
1.008
1.076
0.925
0.924
0.912
0.874
0.789
0.765
0.751
0.785
0.788
0.701
0.736
0.654
0.677
0.751
1175
0.970
0.968
0.942
0.869
0.938
0.844
0.819
0.781
0.811
0.747
0.745
0.733
0.724
0.661
0.663
0.719
0.659
1200
0.873
0.927
0.879
0.832
0.791
0.810
0.733
0.736
0.748
0.680
0.758
0.700
0.665
0.664
0.695
0.694
0.715
3.3.4.
LiCl-CsCl
Table 4 lists shear viscosities for molten LiCl-CsCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the 14
ACCEPTED MANUSCRIPT components. At a certain temperature, along with gradual increase of LiCl, shear viscosities of molten LiCl-CsCl system exhibit an overall downward trend but some slight oscillation for different components. Similar with LiCl-RbCl system, the addition of LiCl into CsCl weakens the interactions of Li-Cl and Cs-Cl pairs, strengthens interactions between Cl-Cl pairs and promotes closed pack between Li-Li, Cs-Cs and
PT
Li-Cs pairs 19. On the one hand, with the interaction weakening of Li-Cl and Cs-Cl pairs,
RI
the counter-ions hold on to each other less tightly, resulting in the improvement of melt
SC
fluidity and decrease of shear viscosity. On the other hand, strengthening of Cl-Cl interactions and promotion of closed packs between cations will deteriorate melt
NU
fluidity and lead to the increase of shear viscosity. The shear viscosities of the melts present complicated trends under both effects.
MA
Table 4 Shear Viscosities of Molten LiCl-CsCl at Different Temperatures (Units: mPa∙s) LiCl% 50.00 56.25
0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
625
-
-
-
-
-
-
-
-
-
650
-
-
-
-
-
-
-
675
-
-
-
-
-
-
-
700
-
-
-
-
-
-
725
-
-
-
-
-
750
-
-
-
-
775
-
-
-
-
800
-
-
-
-
825
-
-
-
850
-
-
-
875
-
-
-
900
-
-
925
-
1.971
950
1.889
1.772
68.75
75.00
81.25
87.50
93.75
100.00
6.657
-
-
-
-
-
-
-
-
-
5.673
-
-
-
-
-
-
-
-
5.037
5.513
4.765
-
-
-
-
-
-
-
4.574
4.196
4.320
3.821
-
-
-
-
-
-
-
-
4.026
3.567
3.218
3.044
3.027
-
-
-
-
-
-
-
3.331
3.466
3.402
3.104
2.854
2.769
-
-
-
-
-
-
-
3.171
2.837
2.953
2.551
2.704
2.434
2.097
-
-
-
-
PT E
62.50
D
Temp (K)
2.552
2.608
2.594
2.486
2.301
1.928
2.058
-
-
-
-
-
2.408
2.082
2.141
1.864
2.342
1.952
1.797
1.847
1.566
-
-
-
-
2.112
1.954
1.848
1.946
2.044
1.748
1.831
1.711
1.577
1.591
1.406
-
-
2.068
1.804
1.946
1.863
1.928
1.714
1.579
1.566
1.584
1.472
1.458
1.390
1.287
-
2.934
1.993
1.802
1.883
1.635
1.560
1.610
1.552
1.365
1.369
1.326
1.444
1.326
1.273
1.243
1.218
1.683
1.820
1.674
1.764
1.447
1.476
1.449
1.416
1.288
1.404
1.292
1.245
1.226
1.197
1.269
1.611
1.546
1.463
1.458
1.327
1.377
1.282
1.371
1.132
1.215
1.284
1.060
1.096
1.069
1.097
AC
CE
-
-
975
1.610
1.517
1.470
1.320
1.443
1.340
1.378
1.252
1.221
1.187
1.161
1.177
1.075
1.103
1.073
1.068
1.034
1000
1.595
1.462
1.334
1.436
1.267
1.241
1.273
1.229
1.084
1.110
1.127
1.041
0.950
0.982
0.973
0.977
1.010
1025
1.516
1.327
1.269
1.432
1.114
1.177
1.132
1.088
1.029
1.012
0.997
0.982
0.888
0.927
0.918
0.962
0.924
1050
1.421
1.316
1.160
1.210
1.264
1.098
1.080
1.000
1.033
0.955
0.973
0.955
0.810
0.855
0.832
0.955
0.816
1075
1.267
1.202
1.156
1.112
1.072
1.028
0.983
1.018
0.892
0.929
0.914
0.859
0.914
0.873
0.896
0.825
0.881
1100
1.148
1.111
1.118
1.100
1.065
0.992
0.916
0.945
0.917
0.868
0.851
0.777
0.812
0.826
0.827
0.780
0.861
1125
1.028
0.980
0.980
0.985
0.975
1.003
0.899
0.891
0.827
0.791
0.715
0.729
0.736
0.772
0.766
0.769
0.746
1150
1.024
1.052
0.923
0.964
0.943
0.847
0.780
0.856
0.817
0.751
0.717
0.725
0.708
0.671
0.703
0.747
0.751
1175
0.974
0.961
0.925
0.900
0.868
0.786
0.811
0.806
0.712
0.736
0.745
0.651
0.750
0.642
0.709
0.617
0.659
1200
1.018
0.919
0.868
0.866
0.781
0.772
0.758
0.762
0.667
0.679
0.684
0.688
0.691
0.612
0.676
0.681
0.715
Shear viscosity expression for molten LiCl-CsCl system at 625-1200 K within full 15
ACCEPTED MANUSCRIPT component range has been fitted from data in Table 4, as follows: η(LiCl-CsCl) = 71.7276+5.9854×10-5 x-2.0148×10-4 x2 +1.5859×10-6 x3
(7)
-19.6375×10-2 T+1.8399×10-4 T2 -5.7930×10-8 T3 In equation (7), x denotes the mole fraction of LiCl, T denotes temperature. 3.3.5.
NaCl-KCl
PT
Table 5 lists shear viscosities for molten NaCl-KCl at different temperatures and
RI
compositions. Shear viscosities decrease with increasing temperature for all the components. At a certain temperature, along with gradual increase of NaCl content,
SC
shear viscosities of molten NaCl-KCl system exhibit an upward trend with some slight
NU
oscillation for different components. The addition of NaCl into KCl weakens the interactions of Na-Cl and K-Cl pairs 18, which will improve the fluidities of the melts.
MA
However, NaCl also strengthens interactions between Cl-Cl pairs and promotes closed pack between Na-Na, K-K and Na-K pairs
18
, which will deteriorate melt fluidity.
D
Compared with LiCl-XCl (X denotes Na, K, Rb, Cs) systems, the weakening of
PT E
interactions between counter-ions is weaker, so the corresponding improvement effects of melt fluidity is weak too. The deteriorate effect results from closed pack between
CE
cations is then in the leading position. Altogether, addition of NaCl into molten KCl will deteriorate its fluidity.
AC
Shear viscosity expression for molten NaCl-KCl system at 950-1200 K within full component range has been fitted from data in Table 5, as follows: η(NaCl-KCl) = 28.0759+8.2895×10-4 x-4.0774×10-6 x2 +1.8438×10-7 x3
(8)
-6.5903×10-2 T+5.4169×10-5 T2 -1.5221×10-8 T3 In equation (8), x denotes the mole fraction of NaCl, T denotes temperature.
Table 5 Shear Viscosities of Molten NaCl-KCl at Different Temperatures (Units: mPa∙s) Temp
NaCl%
16
ACCEPTED MANUSCRIPT (K)
0.00
6.25
12.50
18.75
25.00
31.25
950
-
-
-
-
-
-
975
-
-
-
-
-
-
1000
-
-
-
-
1.102
1.118
1.16
1025
-
-
-
1.111
0.986
1.016
1050
-
0.902
0.964
1.049
0.999
0.971
1075
0.973
0.874
0.920
0.914
0.924
1100
0.844
0.889
0.872
0.871
0.924
1125
0.769
0.819
0.785
0.869
1150
0.765
0.778
0.811
1175
0.818
0.758
0.779
1200
0.695
0.707
0.738
50.00
-
-
1.333
1.181
1.197
1.408
1.215
1.181
1.067
1.01
1.106
1.061
0.973
0.918
0.845
0.892
0.863
0.853
0.863
0.747
0.767
0.762
0.715
0.749
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
-
-
-
-
-
-
-
-
1.331
1.18
-
-
-
-
-
-
1.228
1.272
1.224
-
-
-
-
-
1.091
1.181
1.199
1.163
1.218
-
-
-
-
1.023
1.006
1.096
1.064
1.039
1.109
-
-
-
1.037
1.063
0.968
0.952
1.023
1.006
1.063
1.097
1.091
-
0.927
0.912
0.914
0.922
0.982
0.943
0.980
1.076
1.023
1.090
0.929
0.904
0.861
0.832
0.870
0.947
0.970
0.946
1.008
1.091
1.050
0.756
0.856
0.825
0.834
0.812
0.784
0.868
0.977
0.884
0.879
1.061
1.026
0.767
0.843
0.799
0.757
0.765
0.793
0.768
0.836
0.865
0.880
0.978
0.926
0.674
0.681
0.741
0.713
0.736
0.792
0.838
0.875
0.785
0.867
0.856
0.882
NaCl-RbCl
PT
43.75
RI
3.3.6.
37.50
SC
Table 6 lists shear viscosities for molten NaCl-RbCl at different temperatures and compositions. Shear viscosities decrease with increasing temperature for all the
NU
components. At a certain temperature, along with gradual increase of NaCl, shear
MA
viscosities of molten NaCl-RbCl system first decrease and then increase slightly or show slight oscillation tendency for different components under the effects of both
D
interionic interactions and local atomic arrangements. Similar with LiCl-RbCl system,
PT E
the interactions of Na-Cl and Rb-Cl pairs are weakened by the additive NaCl, resulting in the improvement of melt fluidity and decrease of shear viscosity. In the meantime,
CE
with the gradual addition of NaCl, interactions between Cl-Cl pairs are strengthened and closed packs between cations are promoted, leading to the deterioration of melt
AC
fluidity and the increase of shear viscosity. Shear viscosity expression for molten NaCl-RbCl system at 850-1200 K within full component range has been fitted from data in Table 6, as follows: η(NaCl-RbCl) = 34.9576-1.3531×10-3 x-3.1783×10-5 x2 +3.8871×10-7 x3
(9)
-8.1746×10-2 T+6.6960×10-5 T2 -1.8713×10-8 T3 In equation (9), x denotes the mole fraction of NaCl, T denotes temperature. Table 6 Shear Viscosities of Molten NaCl-RbCl at Different Temperatures (Units: mPa∙s) Temp
NaCl%
17
ACCEPTED MANUSCRIPT (K)
0.00
850 875
-
-
-
900 925
-
-
950 975
-
1000 1025
-
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
-
-
-
2.099
2.281 2.040
2.093
-
-
-
-
-
-
-
-
-
-
1.727
1.765 1.786
2.095 1.736
1.864 1.770
1.917 1.779
1.576
-
-
-
-
-
-
-
-
1.601
1.722 1.553
1.684 1.611
1.597 1.466
1.589 1.569
1.689 1.431
1.694 1.455
1.431 1.480
1.481 1.334
1.403
-
-
-
-
-
1.508 1.479
1.347 1.249
1.384 1.390
1.278 1.433
1.412 1.334
1.322 1.253
1.344 1.300
1.394 1.311
1.336 1.287
1.333 1.261
1.325 1.401
1.273 1.276
1.197
-
-
-
1.298 1.214
1.241 1.174
1.167 1.149
1.234 1.287
1.331 1.085
1.247 1.199
1.166 1.036
1.119 1.101
1.188 1.068
1.159 1.118
1.138 1.084
1.171 1.140
1.215 1.073
1.169 1.095
1.100
-
1.178 1.042
1.097 1.137
1.169 1.015
1.125 0.947
1.123 1.047
1.075 1.006
1.069 0.990
1.074 0.973
1.025 0.936
0.996 1.018
1.064 1.003
1.006 0.991
1.063 1.043
1.000 1.024
1.042 1.003
1.090
1.047 0.933
0.965 0.956
0.998 0.955
0.973 0.981
0.970 0.906
0.892 0.964
0.928 0.890
0.914 0.912
0.936 0.899
0.986 0.949
0.949 0.898
0.885 0.870
0.882 0.927
0.926 0.925
1.026
0.969
0.929
0.843
0.869
0.904
0.796
0.831
0.933
0.900
0.850
0.850
0.871
0.854
0.862
0.882
1100 1125
1.143
1150 1175
1.008 0.970
0.966 0.989
1200
0.873
0.845
3.3.7.
NaCl-CsCl
NU
Table 7 lists shear viscosities for molten NaCl-CsCl at different temperatures and
MA
compositions. Shear viscosities decrease with increasing temperature for all the components. The evolution rules of molten NaCl-CsCl systems are similar with those
D
of NaCl-RbCl systems. Similar with NaCl-RbCl system, the interactions of Na-Cl and
PT E
Cs-Cl pairs are weakened by the additive NaCl, resulting in the improvement of melt fluidity and decrease of shear viscosity. In the meantime, with the gradual addition of NaCl, interactions between Cl-Cl pairs are strengthened and closed packs between
CE
1.121
cations are promoted, leading to the deterioration of melt fluidity and the increase of shear viscosity. Under the effects of both interionic interactions and local atomic
AC
1.266
RI
1.321
18.75
PT
25.00
1050 1075
12.50
SC
1.412
6.25
arrangements, shear viscosities of molten NaCl-CsCl system first decrease and then increase slightly or show slight oscillation tendency for different components with the increase of NaCl content. Shear viscosity expression for molten NaCl-CsCl system at 800-1200 K within full component range has been fitted from data in Table 7, as follows: η(NaCl-CsCl) = 44.0431-3.1839×10-3 x-2.9839×10-5 x2 +5.1291×10-7 x3 18
(10)
1.050 0.926
ACCEPTED MANUSCRIPT -10.7021×10-2 T+9.0581×10-5 T2 -2.6081×10-8 T3 In equation (10), x denotes the mole fraction of NaCl, T denotes temperature. Table 7 Shear Viscosities of Molten NaCl-CsCl at Different Temperatures (Units: mPa∙s) NaCl% 0.00
6.25
12.50
18.75
25.00
31.25
37.50
43.75
50.00
56.25
62.50
68.75
75.00
81.25
87.50
93.75
100.00
800
-
-
-
-
-
3.040
3.071
-
-
-
-
-
-
-
-
-
-
825 850
-
-
-
2.553
2.752 2.295
2.338 2.199
2.291
-
-
-
-
-
-
-
-
-
-
-
875 900
-
-
2.115
2.101 2.155
2.213 2.129
2.092 1.966
2.133 1.950
2.177 1.959
2.166 1.768
1.759
-
-
-
-
-
-
-
-
2.041 1.807
1.794 1.728
1.860 1.728
1.879 1.671
1.720 1.614
1.656 1.611
1.780 1.632
1.670 1.548
1.666 1.596
1.614 1.526
-
-
-
-
-
-
1.607 1.541
1.587 1.514
1.626 1.469
1.605 1.404
1.506 1.434
1.443 1.409
1.585 1.375
1.418 1.363
1.467 1.258
1.449 1.379
1.471 1.386
1.227
-
-
-
-
1.396 1.315
1.295 1.331
1.446 1.365
1.366 1.254
1.278 1.216
1.222 1.333
1.263 1.333
1.263 1.255
1.262 1.125
1.209 1.170
1.135 1.103
1.264 1.167
1.214 1.153
1.252
-
-
1.174 1.200
1.244 1.070
1.173 1.090
1.209 1.145
1.166 1.115
1.156 1.054
1.104 1.033
1.126 1.051
1.015 0.997
1.196 1.028
1.077 0.994
1.104 1.011
1.108 1.056
1.088 1.041
1.058 1.103
1.076 1.046
1.031 1.005
1.061 0.968
1.109 0.996
0.959 0.925
1.029 0.968
1.001 0.983
0.958 0.927
0.953 0.999
1.045 0.943
0.959 0.989
0.945 0.893
1.000 0.947
0.922 0.972
0.984 0.960
1.050
1.040 0.890
0.893 0.994
0.953 0.840
0.945 0.894
0.916 0.930
0.880 0.843
0.949 0.891
0.920 0.881
0.930 0.810
0.837 0.808
0.820 0.800
0.897 0.856
0.825 0.839
0.881 0.780
0.931 0.876
0.926
1.028
1175 1200
0.974
1.024 1.018
4.
Conclusions
RI
1125 1150
1.148
SC
1.267
1.421
NU
1075 1100
MA
1.516
1.595
Shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl, LiCl-CsCl, NaCl-KCl,
D
1025 1050
PT E
975 1000
1.610
NaCl-RbCl and NaCl-CsCl in temperature range of near melting point-1200 K within full composition range have been calculated using MD simulation, to reveal the effects of temperature and composition on melt fluidity.
CE
1.889
With the gradual increase of temperature, shear viscosities of all these systems
AC
925 950
PT
Temp (K)
decrease monotonically. Melt shear viscosities exhibit a little complicated variation trends with the varying compositions under the effects of both interionic interactions and local atomic arrangements. With gradual increase of LiCl content, shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiCl-RbCl and LiCl-CsCl first decrease and then increase slightly or present slight oscillation tendency. However, the subsequent increase is small. With the increase of NaCl content, shear viscosities of molten NaClRbCl and NaCl-CsCl first decrease and then fluctuate slightly, while those of molten 19
-
1.090 1.026 0.882
ACCEPTED MANUSCRIPT NaCl-KCl show an overall increase trend. To summarize, LiCl can improve the fluidity of molten NaCl, KCl, RbCl and CsCl, while NaCl can improve the fluidity of molten RbCl and CsCl, but deteriorate that of molten KCl. Finally, simple databases for shear viscosities of molten LiCl-NaCl, LiCl-KCl, LiClRbCl, LiCl-CsCl, NaCl-KCl, NaCl-RbCl and NaCl-CsCl have been built and
PT
corresponding temperature & composition - dependent equations for shear viscosities
RI
of these systems have been fitted according to the calculated results.
SC
Acknowledgments
We acknowledge the financial support provided by the National Natural Science
NU
Foundation Project of China Youth Found (51504099).
MA
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PT E
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PT E
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23
ACCEPTED MANUSCRIPT Highlights •
Shear viscosities present negative dependences on temperature.
•
Shear viscosities first decrease and then slightly fluctuate with the increase of LiCl content.
•
NaCl improves the fluidity of molten RbCl and CsCl, but deteriorates that
•
PT
of molten KCl. Simple databases for melt shear viscosity have been built based on the
Expressions of melt shear viscosity vs. temperature & composition have
CE
PT E
D
MA
NU
SC
been fitted according to the calculated data.
AC
•
RI
verified algorithm.
24