Flexibility and Regularity of the Hydration Structures of Ions by an Example of Na⁺: Nonempirical Insight

Abstract

The stationary nonempirical simulations of [Na(H2O) n ]+ clusters with n in the range of 28–51 carried out at the density functional level with a hybrid B3LYP functional and the Born-Oppenheimer molecular dynamics modeling of the size-selected clusters reveal the interrelated structural and energetic peculiarities of the sodium ion hydration structures. Surface, bulk, and transient structures are distinguished by different locations of the sodium nucleus (close to either the spatial center of the structure or one of its side faces) and a consistently changing coordination number (which typically equals five or six). The differences and correlations between the stationary and averaged dynamically changing configurations are quantified. The ⟨r NaO⟩, mean Na–O distances for the first-shell water molecules, are found to depend both on the spatial character of the structure and the local coordination of sodium. The ⟨r NaO⟩ values are compared to different experimental estimates, and the virtual discrepancy of the latter is explained based on the results of cluster simulations. Different coordination neighborhoods of the sodium ion are predicted depending on its local fraction in actual specimens.

Tailoring the Self-Assembly of Steviol Glycoside Nanocarriers with Steroidal Amphiphiles

“…Namely, we calculated the change in the number of shell D 2 O molecules by subtracting the total expected number of D 2 O based on the solvation numbers of the pure micelles, N 1,s (SDS/SDC/SC) and N 2,s (Stevia-G), while taking into account the varying degree of ionization. Assuming that the relative change in hydration numbers is equal between the surfactants, i.e., Δ N s = N 1,ex,s / N 1,s = N 2,ex,s / N 2,s , the interpolated pure hydration number is given by N 0,s = N 1,s N 1,agg + N 2,s N 2,agg + C N N ion , where C N = 5 is the primary solvation shell coordination number of the counterion . The excess solvation is then given by N ex,s = N s – N 0,s = N 1,ex,s N 1,agg + N 2,ex,s N 2,agg , from which Δ N s can be calculated.…”

“…where N ion = N agg − z is the number of bound counterions, gives (N s − C N N ion )/N agg = 5 ± 1 as the number of associated D 2 O molecules per SDS headgroup given that the bound counterions retain their primary solvation shells with a D 2 O coordination number similar to that of water (C N ≈ 5). 56 We found the aforementioned results to be in the range expected for SDS micelles based on previous findings, 39,57−59 and we therefore used the estimated molecular volumes and SLDs to analyze the SDS/Stevia-G mixed micelles.…”

“…Assuming that the relative change in hydration numbers is equal between the surfactants, i.e., ΔN s = N 1,ex,s /N 1,s = N 2,ex,s /N 2,s , the interpolated pure hydration number is given by N 0,s = N 1,s N 1,agg + N 2,s N 2,agg + C N N ion , where C N = 5 is the primary solvation shell coordination number of the counterion. 56 The excess solvation is then given by N ex,s = N s − N 0,s = N 1,ex,s N 1,agg + N 2,ex,s N 2,agg , from which ΔN s can be calculated.…”