Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids

We formulate a microscopic, no adjustable parameter, theory of activated relaxation in supercooled liquids directly in terms of the repulsive and attractive forces within the framework of pair correlations. Under isochoric conditions, attractive forces can nonperturbatively modify slow dynamics, but at high enough density their influence vanishes. Under isobaric conditions, attractive forces play a minor role. High temperature apparent Arrhenius behavior and density-temperature scaling are predicted. Our results are consistent with recent isochoric simulations and isobaric experiments on a deeply supercooled molecular liquid. The approach can be generalized to treat colloidal gelation and glass melting, and other soft matter slow dynamics problems.

Figure 1

Nondimensionalized alpha relaxation times for the LJ (orange, solid) and WCA (purple, dashed) fluids at two packing fractions as a function of dimensionless inverse temperature. For thermal systems, ${\tau }_0\equiv {(24\rho {\sigma }^2)}^{-1}\sqrt{M/\pi k_{B}T}$, where $M$ is the particle mass [33]. The black points denote the predicted emergence of a barrier (ideal NMCT crossover), while the green dashed line shows the high temperature Arrhenius behavior. (Inset) The average effective attractive (orange, solid) and repulsive (purple, top curve at small $\beta \epsilon$) contributions to the force vertex, in arbitrary units, for the same packing fractions.

Figure 2

Collapse of the nondimensionalized alpha times for the isochoric LJ systems at different packing fractions. Temperature is scaled by the apparent Arrhenius barrier, $E_{\infty }(\eta )$. (Inset) $\beta E_{\infty }$ for LJ (blue, stars) and WCA (red, crosses) fluids (almost indistinguishable), compared to the onset temperature $k_B{T}_{\text{onset}}$ (LJ, purple, closed squares; WCA, orange, open squares). The black dashed line is the power law $\beta E_{\infty }\propto {\eta }^{9.3}$.

Figure 3

Dimensionless mean alpha times for LJ (solid) and WCA (dashed) fluids as a function of scaled inverse temperature at reduced pressures (right to left) of $\tilde{P}=0$, 2, 4, 6, 8, 10. The horizontal line illustrates the kinetic vitrification based on ${\tau }_{\alpha }(T_g)=100\mathrm{s}$ and ${\tau }_0=0.1\mathrm{ps}$. (Inset) Model equation of state results (curves; see the Supplemental Material [28]) for $\tilde{P}=0$, 2, 4, 6 (right to left). The black hashed curve shows the fit to simulation data [39] of the one-component LJ fluid and should be compared to the $\tilde{P}=0$ (red) curve.

Figure 4

Logarithm of the mean alpha time (in seconds) vs reduced inverse temperature for the LJ (orange, solid) and WCA (purple, dashed) fluids at $\tilde{P}=0$, compared to experimental OTP data (green stars) [23]. The theory curves are shifted vertically to match the high temperature experimental relaxation times. (Inset) Collapse of the dimensionless alpha times for $\tilde{P}=0$, 2, 4, 6, 8, 10 (curves) and isochoric $\eta =0.50$, 0.52, 0.54, 0.56, 0.58 (points) conditions with the reduced variable $\beta \epsilon {\eta }^{10}$. The horizontal line has the same meaning as in Fig. 3.