Theoretical study of the role of Ti nanoparticles on the reactivity reduction of sodium water reaction

Abstract

High reactivity of liquid sodium (Na) with water has been a significant problem for the Sodium Fast Cooled Reactor (SFR), which uses liquid Na as a coolant. Dispersing titanium (Ti) nanoparticles (NPs) in liquid Na represses the reactivity of the sodium-water reaction (SWR); cohesion of Na onto Ti NPs surface has been suggested as a mechanism for this reduction. However this hypothesis should be tested by precise calculation or experiment. Still, only a few studies have focused on the mechanism, because the reactivity and opacity of liquid Na limit precise experimental observations. In this study, Na and Ti atom interaction and Ti NP concentration near the reaction surface were evaluated using ab-initio calculation and molecular dynamics (MD) simulation. Based on the calculation results, the effect of cohesive interaction between Na and Ti NPs effect on the initial stage of SWR reactivity was modeled. To investigate atomic interaction between Na and Ti NPs surface, ab-initio calculation based on density functional theory was performed. The adsorption energy of Na on a Ti(0001) surface was evaluated with respect to various adsorption coverages (0.25, 0.5 , 1ML) and sites (top, bridge, fcc hollow, hcp hollow). Adsorption energy was inversely proportional to the coverage, and the hcp hollow site was the most favorable adsorption site for every coverage. The most stable adsorption state for the Na was 0.25ML at the hcp hollow site; in this configuration, adsorption energy was 1.6 eV. Projected density of states of the electrons and adsorption energy revealed a strong chemical adsorption; it is induced by covalent-like metallic bonds between adsorbed Na and Ti atoms on the Ti(0001) surface. To determine the effects of temperature and pressure on the adsorption, atomistic thermodynamics was used with some assumptions. To investigate Ti NP concentration near the reaction surface, the free energy profile with respect to the NPs immersion depth was investigated using MD simulation. To reduce computational cost, the system was represented using 83972 Na atoms and a 5-nm coarse grained Ti NP. The embedded atomic model (EAM) and ab-initio based potential model were used to model Na-Na and Na-NP interactions respectively. To evaluate free energy by means of potential of mean force, the Umbrella Sampling (US) and Weighted Histogram Analysis Method (WHAM) were used with the constrained force 2 eV/Å. No free energy barrier was found near the liquid Na/vacuum interface while the NP was pulled 5 Å from its full-immersion state. Results of MD simulations of 5-nm Ti NPs agreed with experimental results that used 10 nm Ti NPs. Therefore, Ti NP concentration at the reaction surface is almost same as the Ti NP concentration in the liquid bulk before SWR perturbs the reaction surface significantly. Based on the previous studies on the kinetics of SWR, Ab-initio and MD simulation results, the reactivity regression model due to the cohesion between Na and Ti NPs is proposed. The model predict SWR reactivity regression ratio at t <1s within relative error=8% for 10nm Ti NPs case, however the model shows large difference with 50nm Ti NPs experiment case. The cause of the large discrepancy is assumed to be the error of the prediction of the concentration of the NPs at the reaction surface; If NP is pecked denser than BCC lattice structure, so the concentration of the 50nm Ti NPs at the reaction surface is 23.4mM, χ discrepancy becomes 0. In order to validate the model, precise experiment results with visualization should be conducted further.