Fig. 4: Molecular dynamics modelling of thermodiffusive desalination.

a Molecular dynamics (MD) model of seawater brine under a non-uniform temperature profile spanning ca. 20–60 °C. The ion concentration (for all ions) decreases as the temperature increases, demonstrating thermophobic behaviour of seawater ions in silico. The simulation volume (top) contains water molecules (light grey), and seawater ions (multiple colours). A cold and hot thermostat of width 1 nm are placed at x = 5 nm and x = 15 nm (highlighted regions). The steady state temperature (solid line) and time-averaged ion concentration (markers) between \(\left[{t}_{0}=20,\,{t}_{{{{{{{{\rm{final}}}}}}}}}=280\right]\) ns of simulation time are plotted. The error bars are the standard deviations for the time-averaged temperature and concentration within the steady state simulation time. b Average ion concentration in simulated seawater brine and NaCl brine across temperature. The concentration drop for seawater brine (7000 ± 400 ppm) was larger than concentration drop for NaCl brine (3800 ±  600 ppm). The ion concentration for seawater brine (in orange) and NaCl brine (in blue) is averaged over four and three independent replicates, respectively, and shown with standard error in the mean of the local temperature (markers with error bars). The spread in the average ion concentration is shown at a 95% confidence interval (shaded regions) due to the small number of replicates. A linear line of best fit is reported with an R² value for seawater brine (solid line) as C(T) = (−176 ± 11)T + (78,600 ± 500) ppm and NaCl brine (dashed line) as C(T) = (−95 ± 14)T + (73,600 ± 600) ppm. c Comparison of Soret coefficients obtained from MD simulations and experiments (both from this work and literature). (i) The Soret coefficient calculated for seawater brine is 1.8 times larger than that of NaCl brine. The errors arise from the S_T calculation process. When applying different possible fits to the results (with a confidence interval of 95%), they result in different ΔC. Details of the error derivation are available in Supplementary Method 5. The double asterisk annotation (**) indicates that the increase in the Soret coefficient is statistically significant with p = 0.003 (i.e. p < 0.01), reported by a one-sided t-test. (ii) The Soret coefficient for NaCl brine obtained from MD simulations is comparable to that from experiments. (iii) The experimental Soret coefficient for NaCl in this work is lower than that of ref. ³⁷.