(a) The diffusion constants of the proton, water, and TMU molecules. (b) The water and proton MSD as a function of the thermostat coupling parameter for W = 0.2. (c) The water and proton diffusion constants (W = 0.2) as functions of thermostat coupling time. (d) The water O–H rotational correlation at different concentrations.
The probability of hydrogen bond donor number at different concentrations: (a) water-TMU, (b) hydronium-TMU, (c) hydronium-water, and (d) hydronium-water when proton transfer takes place (solid) and the predicted numbers assuming that the transfer probability is equal for each hydrogen bonded proton.
(a) The average hydrogen bond donor number and (b) the average hydronium ion lifetime as a function of concentration.
(a) Illustration of a hydronium ion captured by two TMU molecules, (b) the water-wire like structure around a hydronium ion, and (c) a hydronium ion in a bulk like environment. Hydrogen bonds are shown as red lines.
Normalized radial distribution function of (a) TMU methyl-methyl group, (b) water oxygen-oxygen, and (c) hydronium oxygen-water oxygen. The dashed line represents the distance distribution of R DA when proton transfer takes place in the bulk water.
(a) The orientational order parameter N order (defined in Eq. (2)) as a function of cutoff radius (r c ) at different concentrations. (b) Illustration of the orientation of the surrounding water molecules near a hydronium ion (water oxygens: red circles; hydronium oxygen: yellow circle; hydrogens: white circles).
The composition of the nine different simulated mixtures. All simulation boxes further contain one hydronium ion.
Proton transfer rates, k PT , in bulk water are given by different experimental or simulation methods.
Fitting parameters of the rotational correlation function as shown in Fig. 1(d). The tri-exponential function is chosen as: A 1 × exp ( − t/τ1) + A 2 × exp ( − t/τ2) + A 3 × exp ( − t/τ3).
The orientational order parameter around the hydronium ion at different TMU concentrations taken at a cutoff distance of 1.5 nm and the same quantity normalized with the water density.
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