Characteristic times in the nanometer-picosecond translational collective dynamics of molecular liquids

Molecular-dynamics calculations of the translational dynamic structure factor in liquid ${\text{CO}}_2$ and ${\text{CD}}_4$ are analyzed by means of the generalized Langevin equation for the intermediate scattering function in the second-order memory function approximation. We give a rigorous general relation among the decay times of the memory and the lifetimes of the modes of the density-density correlation function. The comparison of the various characteristic times among them and with the collision time, carried out as a function of the wave vector, reveals strong relationships between the memory relaxation and the density-density correlation modes, some of which have purely “collisional” and other “collective” character. We show that essential information about the life time of structural properties in a molecular liquid at nanometer dimensions can be obtained if the time behavior of the correlation function is considered in addition to that of the memory function.

Figure 1

MD simulated center-of-mass $S\left(Q,\omega \right)$ of ${\text{CD}}_4$ at $Q=8.2{\text{nm}}^{-1}$ (error bars). The thin line is the VE best fit, and the thick line is the best fit obtained with a hydrodynamiclike memory model (see text).

Figure 2

Parameters of the damped harmonic oscillator representing the propagating modes. (a) $\Omega$ (open circles) and $z_s$ (full circles), with the respective lowest-order hydrodynamic behaviors $c_{s}Q$ (solid line) and $\left[\left({\gamma }_0-1\right)D_T+\nu \right]Q^2/2$ (dotted line). Data refer to ${\text{CO}}_2$. (b) The same as in (a) for ${\text{CD}}_4$. (c) Dispersion curve ${\omega }_s$ for ${\text{CO}}_2$ (full squares) and ${\text{CD}}_4$ (open squares) with the respective lowest-order hydrodynamic behavior $c_{s}Q$ (dotted line for ${\text{CO}}_2$, solid line for ${\text{CD}}_4$). For the values of $c_s$, ${\gamma }_0$, $D_T$, and $\nu$ see Refs. [5, 11].

Figure 3

Characteristic times of $M\left(Q,t\right)$ and $F\left(Q,t\right)$. (a) ${\tau }_T$ (dots with error bars) and ${\tau }_1/\gamma$ (open circles). ${\text{CO}}_2$ data are the upper curves; ${\text{CD}}_4$ plots are shifted downwards by one decade for graphical convenience. Solid lines give the lowest-order hydrodynamic behavior $1/\left({\gamma }_0{D}_T{Q}^2\right)$. (b) ${\tau }_1$ (full squares), ${\tau }_2$ (stars), ${\tau }_s/2$ (open circles), and $\tau$ (dots) for ${\text{CO}}_2$. Solid lines give the lowest-order hydrodynamic behavior $1/\left(D_T{Q}^2\right)$ of ${\tau }_1$ and $1/\left[\left({\gamma }_0-1\right)D_T+\nu \right]Q^2$ of ${\tau }_s/2$. The short line on the right side marks the value of $t_E$. (c) The same as in (b) for ${\text{CD}}_4$.