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Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations
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Figures

Image of FIG. 1.

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FIG. 1.

Temperature dependence of the integral rotational correlation time τR in H2O, derived from 17O R 1 data reported here (red circles) and previously (white triangles).28,30 Also shown are τR values derived (after a minor correction; see text) from previously reported74,82 intramolecular dipolar 1H–17O R 1 data (gray or white circles) or calculated (black squares) from Eq. (2.1) using the simulated 17O TCF. The solid curve resulted from a fit of Eq. (2.4) to our 17O data and the dashed line is an Arrhenius-law extrapolation from the higher temperatures. The residuals panel shows the deviations of each set of data points from the fit to that data set. The top panel shows deviations of all data points from the displayed fit to our 17O data.

Image of FIG. 2.

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FIG. 2.

Temperature dependence of the integral rotational correlation time τR in D2O, derived from 2H R 1 data reported here (blue circles) and previously (white triangles).27,29 The solid curve resulted from a fit of Eq. (2.4) to our 2H data and the dashed line is an Arrhenius-law extrapolation from the higher temperatures. The residuals panel shows the deviations of each set of data points from the fit to that data set. The top panel shows deviations of all data points from the displayed fit to our 2H data.

Image of FIG. 3.

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FIG. 3.

Temperature dependence of the ratio of the translational and rotational diffusion coefficients, derived from experimental data (see text), for H2O (red squares) and D2O (blue circles). For comparison, the D2O data are also shown down-shifted by 12 K (open circles).

Image of FIG. 4.

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FIG. 4.

The biaxial 17O TCF at 252.5 K (red curve) with bi-exponential fit (black curve, dotted outside fit range). The left-hand semilog plot includes the full τ range used for the fit, while the right-hand linear plot shows the initial part of the TCF. The dashed-dotted curve is the contribution from the last (jump) term in Eq. (3.2). The top panels show the fit residuals (curve) and the standard error (shaded band) in the TCF computed from the full 10 ns trajectory (left) or from the densely sampled 100 ps initial part of the trajectory (right).

Image of FIG. 5.

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FIG. 5.

The uniaxial O–H TCF at 252.5 K (red curve) with bi-exponential fit (black curve, dotted outside fit range). The left-hand semilog plot includes the full τ range used for the fit, while the right-hand linear plot shows the initial part of the TCF. The dashed-dotted curve is the contribution from the last (jump) term in Eq. (3.2). The top panels show the fit residuals (curve) and the standard error (shaded band) in the TCF computed from the full 10 ns trajectory (left) or from the densely sampled 100 ps initial part of the trajectory (right).

Image of FIG. 6.

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FIG. 6.

Temperature dependence of the squared librational order parameter , obtained from bi-exponential fits to the 17O (red squares) and O–H (blue circles) TCFs. The lines are linear fits.

Image of FIG. 7.

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FIG. 7.

Temperature dependence of the correlation times τJ and τL, obtained from bi-exponential fits to the 17O (red inverted triangles) and O–H (blue triangles) TCFs. The solid curves are fits of Eq. (2.4) to these data and the dashed lines are Arrhenius-law extrapolations from the higher temperatures. Also shown are τJ values obtained from the CTRW model (open circles).

Image of FIG. 8.

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FIG. 8.

A 75 ps MD trajectory at 252.5 K showing the orientation of one of the O–H bonds of a water molecule at 5 fs resolution. To enhance the field of view, a Robinson projection of the unit sphere has been used, where the horizontal boundaries correspond to the poles. The dynamical basins identified by the coarse-graining algorithm are color-coded (chronological sequence: red, blue, green, black, cyan). A small fraction of the configurations (gray dots) do not belong to any basin according to the minimum dwell time criterion (Secs. II E and S-IV of Ref. 72). For each basin, the circle (distorted by the projection) is centered at the mean orientation and the radius corresponds to one standard deviation in angle.

Image of FIG. 9.

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FIG. 9.

Jump angle distribution f(θ) computed from MD-derived CTRW trajectory at 252.5 K (blue curve) and 296.3 K (red curve). The dashed curve represents a random jump angle distribution.

Image of FIG. 10.

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FIG. 10.

Waiting time distribution ψ(τ) computed from MD-derived CTRW trajectory at 296.3 K (solid red curve). The single-exponential fit (dashed black curve) includes data from the maximum in ψ(τ) up to τ = 15 ps and yields a decay time of 2.05 ps. The semilog plot in the inset highlights the single-exponential character of the distribution.

Image of FIG. 11.

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FIG. 11.

Waiting time distribution ψ(τ) computed from MD-derived CTRW trajectory at 252.5 K (solid red curve). The single-exponential (dashed blue curve) and bi-exponential (dashed black curve) fits include data from the maximum in ψ(τ) up to τ = 50 ps. The bi-exponential fit yields decay times of 3.43 and 8.54 ps, with a relative weight of 0.502 for the faster component. The semilog plot in the inset highlights the bi-exponential character of the distribution.

Image of FIG. 12.

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FIG. 12.

Temperature dependence of the mean waiting time τw, computed from MD-derived CTRW trajectories of the O–H bond orientation (open circles) and of the molecular center-of-mass position (solid squares).

Image of FIG. 13.

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FIG. 13.

The conditional jump rates k(T, τ | R) (red) and k(R, τ | T) (black) at 252.5 K (solid) and 296.3 K (dashed), calculated with a bin size of 150 fs. The jump rates have been normalized by the mean waiting time, τw(T) or τw(R). The inset shows that the conditional jump rate has reached its long-time limit 1/τw already at τ′ = τw.

Tables

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Table I.

Effective temperature of MD simulations.

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Table II.

Results of fitting Eq. (2.4) to τR data.a

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Table III.

Results of analyzing MD data with the CTRW model.

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/content/aip/journal/jcp/136/20/10.1063/1.4720941
2012-05-24
2014-04-25

Abstract

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision 17O and 2H NMR relaxation data for H2O and D2O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τR is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ∼48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τRD T at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τR to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.

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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/20/10.1063/1.4720941
10.1063/1.4720941
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