Schematic picture of a simple homogeneous model of a coarse-grained PEN. Green and red spheres are potential minima in solidlike and liquidlike states, respectively. All potential minima in a solidlike state are connected to a potential minimum in a liquidlike state. Some configurations of solidlike and liquidlike states for (H2O)12 are shown for reference.
Time series of potential energy E(t) with its coarse-grained one E MA(t) for (a) (H2O)6 at T = 60 K and (b) (H2O)12 at T = 135 K. Dashed line represents a boundary between the solidlike and liquidlike state (E s = −31.2 and −37 kJ/mol for (a) and (b), respectively).
Configurations of water molecules for local potential minima in the solidlike state. (a) Two different configurations of local potential minima in the solidlike state in (H2O)6. (b) Two different configurations of local potential minima in the solidlike state in (H2O)12, while there are many different local potential minima in it. These configurations are obtained by minimizing the potential energy of a water cluster in the solidlike state using the steepest descent method.
Probability of the number of trials. (a) (H2O)6 at T = 60 K. (b) (H2O)12 at T = 149 K. Triangular symbols are the results of the MD simulations. Histogram represents the probability of p(1 − p) k−1 with p = 0.55 and 0.22 for (a) and (b), respectively.
Weibull plot, i.e., (a) ln |ln [1 − F(τα)]| vs. ln τα and (b) ln |ln [1 − F(τβ)]| vs. ln τβ. Symbols are the results of the MD simulations. Lines are the fitting lines. The slopes of the fitting lines indicate the exponent γ of the Weibull distribution (9) . The Weibull exponents for the trapping-time distribution of τα are almost γ = 1, which implies the exponential distribution.
Schematic picture of a generalized SHN model. Potential minima within solidlike states (green spheres) are not directly connected to those within solidlike states.
Probability density functions for τα and τβ in a semi-log scale for T = 135 K. Histograms are the results of the MD simulations. The value of E s is set to be −36.5 kJ/mol. The dashed line is a fitting curve of the Weibull distribution (9) obtained by the Weibull plot. The dotted line is a fitting curve of a superposition of the exponential distribution (11) for n = 2. The fitting parameters are p 1 = 0.4 and p 2 = 0.6. The two relaxation times are obtained by the mean trapping times for E MA < −37 kJ/mol and −37 < E MA < −36.5 kJ/mol (τ1 = 5 ns and τ2 = 0.5 ns).
The mean trapping times ⟨τα⟩ and ⟨τβ⟩ vs. 1000/T in (H2O)12 water cluster. The values of E s are set to be −37, −37, −36.9, −36.5, and −36.5 kJ/mol for T = 135, 138, 142, 149, and 155 K, respectively. Circles and triangles are the results for ⟨τα⟩ and ⟨τβ⟩, respectively. Solid lines are the linear fitting lines: ⟨τα⟩ = τ0 exp (1000A/T) and ⟨τβ⟩ = τ1 exp (1000B/T) (τ0 = 5.6 × 10−6, A = 1.86, τ1 = 2.9 × 10−6, and B = 1.74). Dashed line represents τ0 exp (1000B/T)/p.
The probability p, the Weibull exponent γ, the mean trapping time ⟨τβ⟩, ⟨τβ⟩/p, the mean trapping time ⟨τα⟩, and the relaxation time a for (H2O)12.
Article metrics loading...
Full text loading...