How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids

The theory developed in our previous papers [Phys. Rev. E 99, 030101(R) (2019); Phys. Rev. E 103, 032611 (2021)] is applied in this paper to investigate the dependence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts of intermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jones glass-forming liquid and that of its WCA reduction to a model with truncated pair potential without attractive tail, we demonstrate why the two systems exhibit very different dynamics despite having nearly identical pair correlation functions. In particular, we show that local structures characterized by the number of mobile and immobile particles around a central particle markedly differ in the two systems at densities and temperatures where their dynamics show large difference and nearly identical where dynamics nearly overlap. We also show how the parameter $\psi \left(T\right)$ that measures the role of fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) and the crossover temperature $T_a$ depend on the intermolecular interactions. These parameters stemming from the intermolecular interactions characterize the temperature and density dependence of structural relaxation time ${\tau }_{\alpha }$. The quantitative and qualitative agreements found with simulation results for the two systems suggest that our theory brings out the underlying features that determine the dynamics of glass-forming liquids.

Figure 1

The reduced effective potential $\beta w_{aa}\left(r\right)$ between a pair of particles of species $\alpha$ and $\gamma$ separated by distance $r$ (expressed in unit of ${\sigma }_{aa}$) in a system of WCA at a density $\rho =1.2$ and temperature $T=0.3$. $\beta w_{aa}^{\left(iu\right)}$, $r_{ih}$ are, respectively, value and location of $i\mathrm{th}$ maximum and $r_{il}$ is the location on the left-hand side of the shell where $\beta w_{aa}^{\left(i\right)}\left(r\right)=\beta w_{aa}^{\left(iu\right)}$ (shown by dashed line). The location $r_{il}^{″}$ and $r_{ih}^{″}$ are values of $r$ on the left- and right-hand side of the shell where $\beta w_{aa}^{\left(i\right)}\left(r\right)=[\beta w_{aa}^{\left(iu\right)}-\psi ]$ (shown by full line). $\beta w_{aa}^{\left(id\right)}$ is the depth of the $i\mathrm{th}$ shell.

Figure 2

Comparison of values of $K$ for the LJ and WCA systems. These values were found when value of $\psi$ was fixed to 1 at all temperatures. In both cases, $K$ is constant above a density-dependent temperature $T_a$ and decreases from its constant value upon cooling below $T_a$. Values of $T_a$ of the two systems at different densities are given in Table 1. Symbols represent calculated values and curves are least square fit.

Figure 3

Comparison of values of $\psi (T,\rho )$ of the two systems at different temperatures and densities. Symbols are calculated values and curves are least square fit. A large difference in values of $\psi (T,\rho )$ of the two systems for $\rho =1.2$ below $T=0.68$ is seen whereas for $\rho =1.6$ values of $\psi \left(T\right)$ almost overlap at all temperatures.

Figure 4

Comparison of values of $g_{\alpha \gamma \left(r\right)}$ and its different parts $g_{\alpha \gamma }^{\left(f\right)}\left(r\right)$, $g_{\alpha \gamma }^{\left(m\right)}\left(r\right)$, and $g_{\alpha \gamma }^{\left(s\right)}\left(r\right)$ of the LJ (full lines) and WCA (dashed lines) for $\rho =1.2$ and $T=0.5$. In panel (a), $\alpha ,\gamma =a,a$ and in panel (b), $\alpha ,\gamma =a,b$. A large difference can be seen between the values of $g_{\alpha \gamma }^{\left(s\right)}\left(r\right)$ and of $g_{\alpha \gamma }^{\left(m\right)}\left(r\right)$ of the two systems, while values of $g_{\alpha \gamma }\left(r\right)$ are nearly identical.

Figure 5

Same as in Fig. 4 but for $\rho =1.4$ and $T=1.0$. A relatively small difference is seen between values of $g_{\alpha \gamma }^{\left(s\right)}\left(r\right)$ and of $g_{\alpha \gamma }^{\left(m\right)}\left(r\right)$ of the two systems compared with $\rho =1.2$.

Figure 6

Same as in Fig. 4 but for $\rho =1.6$ and $T=2.0$. Values of $g_{\alpha \gamma }\left(r\right)$ and of its components, $g_{\alpha \gamma }^{\left(f\right)}\left(r\right)$, $g_{\alpha \gamma }^{\left(m\right)}\left(r\right)$, and $g_{\alpha \gamma }^{\left(s\right)}\left(r\right)$ of the two systems are nearly identical.

Figure 7

Comparison of values of $n_1^{\left(f\right)}$, $n_1^{\left(m\right)}$, and $n_1^{\left(s\right)}$ as a function of $1/T$ for the two systems. Letters $f$, $m$, and $s$ stand, respectively, for free, metastable, and stable and the subscript 1 stands for the first shell. Full lines represent values of the LJ system and dashed lines of the WCA system.

Figure 8

Comparison of values of fraction of mobile, $p_m$, and immobile, $p_l$ (defined in the text), particles in the first shell around the central particle of the two systems. Line symbols are the same as in Fig. 7. The dotted part of each line represents extrapolated values. The two curves of $p_m$ and $p_l$ meet at $T=T_{ml}$ where half of particles of the first neighbor become immobile.

Figure 9

Comparison of values of activation energy $\beta E^{\left(s\right)}$ for the relaxation in column (a) and the relaxation time in column (b) as a function of $1/T$ at three densities of the two systems. Curves (full for the LJ and dashed for the WCA) represent calculated values and circles (full for the LJ and open for the WCA) in column (b) represent simulation values.

Figure 10

Comparison of density dependence of the temperature $T_a$ of the two systems. Circles (full for the LJ and open for the WCA systems) represent calculated values (given in Table 1) and curves (full for the LJ and dashed for the WCA) represent fit $T_a=a_0{\rho }^{\gamma }$ with $\gamma =4.757$ and 5.821, respectively for the LJ and WCA systems.

Figure 11

Comparison of collapse of calculated (lines) and simulation (symbols) data of ${\tau }_{\alpha }$ of the two systems as a function of $T_a/T$. (b) While in the case of LJ system, good collapse takes place. (a) In case of the WCA, both the calculated as well as simulation values fail to collapse on one curve.