Molecular dynamics simulation of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glassy state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the nonergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the intensity of the JG process increases significantly, eventually subsuming the slower α relaxation. This evolution of the JG motion into structural relaxation underlies the correlation of many properties of the JG and α dynamics.

Figure 1

First-order rotational correlation function for the $AB$ molecules at $P$ = 1 and the indicated temperatures (temperature decreases bottom to top).

Figure 2

Imaginary part of the susceptibility associated with the first-order rotational correlation function of the $AB$ molecules.

Figure 3

Temperature dependence of the α and JG relaxation times and intensities. The temperatures associated with the respective appearance and disappearance of the α process are indicated.

Figure 4

Top: Angular position as a function of time for the four molecules denoted by the symbols in the lower panel. The curves have been shifted vertically for clarity. Bottom: Rotational correlation function for representative individual $AB$ molecules (gray lines). Inset: Single-molecule nonergodicity factor $Q$ against relaxation time ${\tau }_{\mathit{JG}}$ for each $AB$ molecule, along with the linear regression and correlation coefficient.

Figure 5

Distribution of (a) single-molecule JG relaxation times and (b) single-molecule nonergodicity parameters of the $AB$ molecules, for the indicated temperatures in the glassy state.

Figure 6

Single-molecule JG relaxation time (a) and nonergodicity parameter (b) for the $AB$ molecules plotted against local density (density in a sphere of radius 0.8 around the $B$ particle). The lines represent linear regressions having the indicated correlation coefficients.