Characteristics of the Johari-Goldstein process in rigid asymmetric molecules

Molecular dynamics simulations were carried out on a Lennard-Jones binary mixture of rigid (fixed bond length) diatomic molecules. The translational and rotational correlation functions, and the corresponding susceptibilities, exhibit two relaxation processes: the slow structural relaxation (α dynamics) and a higher frequency secondary relaxation. The latter is a Johari-Goldstein (JG) process, by its definition of involving all parts of the molecule. It shows several properties characteristic of the JG relaxation: (1) merging with the α relaxation at high temperature; (2) a change in temperature dependence of its relaxation strength on vitrification; (3) a separation in frequency from the α peak that correlates with the breadth of the α dispersion; and (4) sensitivity to volume, pressure, and physical aging. These properties can be used to determine whether a secondary relaxation in a real material is an authentic JG process, rather than more trivial motion involving intramolecular degrees of freedom. The latter has no connection to the glass transition, whereas the JG relaxation is closely related to structural relaxation, and thus can provide new insights into the phenomenon.

Figure 1

(a) First-order rotational correlation function and (b) imaginary part of the associated susceptibility, for the AB molecules in the system with $d$ $=$ 0.5. Temperatures (short to long times, high to low frequencies) are $T$ $=$ 1, 0.7, 0.6, 0.55, 0.52, 0.49 in the liquid state (solid lines) and $T$ $=$ 0.4, 0.33, 0.25 in the glass (dashed lines). In this and all subsequent figures units of length σ${}_{\mathrm{AA}}$, temperature ε${}_{\mathrm{AA}}$/$k_B$, and time ${(m{\sigma }_{\mathrm{AA}}^2/{\varepsilon }_{\mathrm{AA}})}^{1/2}$ are used.

Figure 2

(a) First-order rotational correlation function and (b) imaginary part of the associated susceptibility, for the AB molecules in the system with $d$ $=$ 0.7. Temperatures (short to long times, high to low frequencies) are $T$ $=$ 1, 0.6, 0.5, 0.45, 0.40, 0.38.

Figure 3

(a) Translational and rotational correlation functions for the AB molecules in the system with bond length $d$ $=$ 0.55. Self-intermediate scattering function for the center of mass (solid line), first-order (dashes), and second-order (dots) rotational correlation function. (b) Imaginary part of the associated susceptibilities.

Figure 4

α and β relaxation times for $d$ $=$ 0.55 (short) and $d$ $=$ 0.7 (long) molecules, obtained by fitting using the Williams ansatz [Eq. (5), filled symbols] and additive combination [Eq. (4), open symbols].

Figure 5

Temperature dependence of the rotational relaxation times of the α process (solid symbols) and β process (hollow symbols: glass; dotted symbols: liquid) for the systems with bond lengths $d$ $=$ 0.45, 0.5, 0.55, and 0.6.

Figure 6

Temperature dependence of the intensities of α (solid symbols) and β (hollow symbols: glass; dotted symbols: liquid) processes for the systems with bond lengths $d$ $=$ 0.45, 0.5, 0.55, and 0.6.

Figure 7

α-process stretch exponent as a function of the separation of α and β time constants for systems with bond lengths $d$ $=$ 0.45, 0.5, 0.55, and 0.6. Inset: Stretch exponent as a function of β relaxation time for the four systems at a constant α relaxation time of 10${}^5$.

Figure 8

Relaxation times for α and β processes as a function of pressure for $T$ $=$ 1.0, for the systems with bond lengths $d$ $=$ 0.5 and 0.6.

Figure 9

Physical aging in the glassy state, for bond length $d$ $=$ 0.5: Potential energy per molecule (top), β relaxation time (middle) and β relaxation strength (bottom) as a function of aging time following a temperature jump from $T$ $=$ 0.5 to temperatures $T$ $=$ 0.45, 0.40, 0.35, under constant pressure $P$ $=$ 1.

Figure 10

Relaxation strength vs relaxation time during aging for bond length $d$ $=$ 0.5. Lines are power law fits with a common exponent.