Fig. 3: Characterization of the LLPT in molecular water by identifying links and knots.
From: Topological nature of the liquid–liquid phase transition in tetrahedral liquids
a,b, Illustrative snapshots of the LDL (a) and HDL (b) hydrogen-bond networks of molecular water, simulated using the TIP4P/Ice potential, at T = 188K and P = 1,100 bar and P = 2,000 bar, respectively. This temperature is slightly below the critical temperature (Tc = 188.8 K (ref. 9)), and the pressures are below and above the critical pressure (Pc = 1,725 bar (ref. 9)). In the LDL, only a few links are present (one is highlighted in a). In the HDL, both linked and knotted motifs are present (highlighted in b). c, The frequency distribution of the writhe (Wr) of the knotted paths found in the HDL network (essentially all being trefoil knots) at T = 188 K and P = 2,000 bar. The inset shows the idealized configuration of a trefoil knot, and the dotted vertical line indicates the value of the writhe for the idealized trefoil knot57. d, Dependence of \({{{{\mathcal{L}}}}}_{\mathrm{n}}\) and \({{{{\mathcal{W}}}}}_{\mathrm{n}}\), computed using rings of sizes up to \({l}_{\max }=13\), divided by \({{{{\mathcal{N}}}}}_{{{{\rm{R}}}}}\), as a function of P at T = 188 K for N = 1,000 molecules. Error bars represent the standard deviation as calculated along the corresponding molecular dynamics trajectory. e, The fluctuations in the density (ρ) and \({{{{\mathcal{L}}}}}_{\mathrm{n}}\) (computed using \({l}_{\max }=13\)) with time (t) along an isobaric–isothermal molecular dynamics trajectory for N = 300 molecules of TIP4P/Ice water at a temperature of T = 188 K for P = 1,100 bar, P = 1,725 bar and P = 2,000 bar.
