Fig. 4: Thermodiffusive behaviour in alkali halide solutions with different anions.

a Measured T₀ for NaF, NaCl, and NaI aqueous solutions. The error bars are estimated for a 95% confidence interval based on at least three replicates. The left plot is for C ∈ [0.02, 0.50]m with C on a logarithmic scale. Linear fits were obtained with an R² value of 0.99, 0.98, and 0.95 for NaF, NaCl, and NaI, respectively. On the right is for C ∈ [0.02, 3.00]m with C on a linear scale, with the yellow box indicating the \(\log (C)\) plot range. Literature data is plotted in the same colour with asterisks: I.⁷⁷, II.³⁷, III.³⁸. All ions are thermophobic above T₀ and thermophilic below T₀. On the left, linear fits are applied while on the right, the lines are visual guides. FEP results are shown in the inset for lone anions (1 ion per 883 water molecules equating to a concentration of 0.063 m). b, c ΔΔG and ΔS_hyd from FEP results for Na⁺, I⁻  (σ = 0.488 nm), free-roaming NaI, a forced NaI pair, and I⁻  re-parameterised to be larger (σ = 0.600 nm) or smaller (σ = 0.350 nm). With the presence of the Na ⁺  counterion, ΔΔG decreases monotonically with decreasing temperature for both free-roaming and paired NaI. Further parameter investigations are in Supplementary Fig. 9. More results on the counterion and ion pairing effects is in Supplementary Fig. 13. In c, the presence of small ions, such as Na⁺ or “Small I⁻”, results in a markedly negative hydration entropy S_hyd, while larger ions such as I⁻  or “Large I⁻ ” has positive S_hyd values.