Dynamical and orientational structural crossovers in low-temperature glycerol

Mean-square displacements of hydrogen atoms in glass-forming materials and proteins, as reported by incoherent elastic neutron scattering, show kinks in their temperature dependence. This crossover, known as the dynamical transition, connects two approximately linear regimes. It is often assigned to the dynamical freezing of subsets of molecular modes at the point of equality between their corresponding relaxation times and the instrumental observation window. The origin of the dynamical transition in glass-forming glycerol is studied here by extensive molecular dynamics simulations. We find the dynamical transition to occur for both the center-of-mass translations and the molecular rotations at the same temperature, insensitive to changes of the observation window. Both the translational and rotational dynamics of glycerol show a dynamic crossover from the structural to a secondary relaxation at the temperature of the dynamical transition. A significant and discontinuous increase in the orientational Kirkwood factor and in the dielectric constant is observed in the same range of temperatures. No indication is found of a true thermodynamic transition to an ordered low-temperature phase. We therefore suggest that all observed crossovers are dynamic in character. The increase in the dielectric constant is related to the dynamic freezing of dipolar domains on the time scale of simulations.

Figure 1

$\langle x^2\rangle =\langle \mathrm{\Delta }x{\left(t_r\right)}^2\rangle$ for g-d5 (upper panel) and g-d3 (lower panel) deuterated glycerol. The experimental data obtained from IN13 spectrometer for correspondingly deuterated glycerol [17] are compared to MD simulations. The simulated MSDs are separated into displacement of the glycerol center of mass (“Trans”) and the displacements of hydrogens relative to the center of mass (“Rot”). The dashed lines are the linear regressions drawn through the corresponding points from MD simulations.

Figure 2

$\langle \mathrm{\Delta }x{\left(t\right)}^2\rangle$ vs. time at $T=250$ K. The overall MSD (long-dashed line) is separated into the center of mass (solid line), rotational (dash-dotted line), and cross (dashed line) components (Eq. (4)).

Figure 3

Center-of-mass MSD, $\langle \mathrm{\Delta }{x}_c{\left(t\right)}^2\rangle$, of glycerol at different temperatures indicated in the plot.

Figure 4

$\langle x^2\rangle =\langle \mathrm{\Delta }x{\left(t_r\right)}^2\rangle$ for g-d5 measured on $t_r=25$ ps (open points) and $t_r=135$ ps (closed points). The center-of-mass $\langle \mathrm{\Delta }{x}_c^2\rangle$ (“T,” squares) and rotational $\langle \mathrm{\Delta }{x}_R^2\rangle$ (“R,” circles) contributions are shown separately. The dashed and dash-dotted lines are linear regressions drawn through the low-temperature and high-temperature points.

Figure 5

Average relaxation time $\langle \tau \rangle$ obtained from rotational correlation function (“rot”) and from the electric field correlation function (“field”) (analysis of 2.5 ns of NVE MD simulations, Appendix). The solid line refers to the average relaxation time [49] obtained by fitting the dielectric loss spectrum to the Cole-Davidson function [50]. The dashed line is a regression drawn through the MD points obtained from the electric field correlation function. $T_c$ (dotted line) indicates the crossover temperature.

Figure 6

Diffusion coefficients recorded experimentally by NMR (“Exp,” [39]) and obtained from the simulations (“MD”). The dashed line is a regression drawn through the MD points.

Figure 7

The Kirkwood factor (a) and dielectric constant (b) of glycerol calculated from MD (circles) and measured in bulk samples experimentally [54] (squares). The dashed lines are linear fits to the corresponding subsets of data to guide the eye. The Kirkwood factors in (a) were obtained both in NVE and NVT separate simulation runs.

Figure 8

Projection of the pair distribution function of glycerol on the orientational invariant $\mathrm{\Delta }(1,2)=({\widehat{\mathbf{e}}}_1·{\widehat{\mathbf{e}}}_2)$ calculated from MD simulations at different temperatures.

Figure 9

Orientational order parameters $p_1$ and $p_2$ in Eq. (11) calculated from MD trajectories at different temperatures.

Figure 10

Pair distribution functions $g\left(r\right)$ of the center of mass of glycerol calculated at the temperatures indicated in the plot. The calculated functions nearly coincide on the scale of the plot.

Figure 11

$C(r,t)$ at $t=2.5$ ps (black lines) and $t=2.5$ ns (blue lines) calculated from NVT simulations of glycerol at different temperatures indicated in the plot. The red line indicates NVE simulation at 270 K.