Competition between vitrification and crystallization in lennard-jones binary mixture : a molecular dynamic simulation study (PhD)

Abstract

When a liquid is cooled slowly, it attains minimum energy by searching through all the possible configurations, consequently forming a crystal at the freezing point. When there is an increase in the cooling rate, the system visits a lesser number of probable configurations, which increases the disorder in the solid. The tendency to find equilibrium further reduces with an increase in the complexity of the constituent particles, that is, the shape or relative change in their concentrations in multicomponent systems. There is an increased tendency to settle in multiple local minima, which eventually leads to glass transition on further cooling. The state of glass is highly disordered, structurally similar to liquids, but mechanically similar to solids. Single component Lennard-Jones (LJ) liquid at lower temperatures crystallizes whereas, LJ binary mixture used in the study of Kob and Andersen (Phys. Rev. Lett. 73, 1376 (1994)) (KALJ) with 20% minority component (B particle) undergo glass transition on cooling. At compositions of the minority component (≤ 10%), the binary mixture crystallizes in the studies by Valdes et. al.(J. Chem. Phys. 130, 154505 (2009)). In this work, molecular dynamics simulations of the pure Lennard-Jones system and the Kob-Andersen model with the variations in the composition of the minority component B in the range 0%−15% are performed to see the effects of increment in B (impurity) on the structures and relaxation dynamics. The glass transition is characterized by the dynamics, while studies on crystallization focus on the structure. Therefore, both structural and dynamical studies are done to understand crystallization, vitrification, and the competition between them. To study glass transition, we have generated low-temperature state points by a fast quenching and looked at the structural variations for each composition at different temperatures. Pressure variations at B particle’s concentration as 0%,1%,5%,7.5%,10%,12.5%, and 15% show a linear decrease in pressure on cooling due to an increase in particles’ mutual affinity on the successive increment of B particles. We define a characteristic temperature called TLS for each composition studied, which is the lowest temperature where a system can stay supercooled in a typical long-time trajectory which is much longer than the α-relaxation time. It is considered as the temperature of the last supercooled state. We find that TLS reduces linearly with an increase in B concentration. Below this temperature, a system shows a sudden transition in the order identifiable from the global bond-order parameter Q6, which differs at different B concentrations. The typical Q6 value diminishes with an increase in the B concentration. The reduction of the order is also clearly visible from the radial distribution functions g(r), whose first peak gets taller; besides, the second peak gets broadened due to the formation of the multiple secondary structures on supercooling. We have analyzed the partial radial distribution function gAA(r), which shows that at all compositions, A component undergoes crystalline ordering below TLS. As temperature reduces, the first peak of the g(r) increases in height, showing enhancement in the caging that is quantified using ρloc, which is the local density at the first peak of g(r). When the local density increases as temperature reduce, it shows enhancement of the barrier height and reduction in free-volume available to the particles for relaxation. The crystalline state just below TLS serves as a free energy minimum of the configuration for a system. Comparison of the g(r) in this state shows that there is a difference in the positions and heights of various peaks, which vary non-monotonically with composition. The analysis of partial g(r) shows that the A−B interaction locally destabilizes the lattice by inducing local defects; hence, the lattice formation gets destabilized. Eventually, with more concentration of B, the crystallization suppressed to support the glass transition at deeper supercooling with stabilization of local structures. The hallmark of a glass-forming system is the cage formation and the associated dynamic heterogeneities. The mean square displacements at TLS show a prolonged sub-diffusive regime, which gets more prolonged as impurity increases; thus, give a qualitative comparison of the formation of dynamical cages that enhances collective relaxation. The comparison of the non-Gaussian parameter α2(t) near TLS shows that its peak height increases as B concentration increases, signifying deepening of the dynamic heterogeneity. This increase of height and peak position of α2(t) of B induces growth of α2(t) of A, thus, showing competition between both the species in establishing order and disorder at lower temperatures The overall or average α2(t) is largely influenced by the α2(t) of B particle. As temperature reduces at all compositions, the cage size reduces. Near a critical cage size, there is a trigger of crystallization, around rcage ∼ 0.23, at all compositions. Fs(q, t) at all the supercooled states show KWW-exponent β ∼ 0.9 signifying a nearly exponential relaxation. At 15% B, the variation of the Fs(q, t) shows a considerable slowdown of the relaxation process. By computing β of A and B, we find that as B composition increases, the heterogeneity in the relaxation of B component decreases, and that of A increases leading to the mixing of collective relaxation process in the supercooled state. This study shows that no sharp boundary exists from crystallization towards vitrification when the B concentration increases. The transition from a system that prefers crystallization to the one that prefers glass transition is gradual. Hence, we predict TLS for a couple of nearby higher B concentrations by linear extrapolation of B% versus TLS. We have computed the mode-coupling theory glass transition temperature Tc from the schematic mode-mode coupling theory and the dynamics divergence temperature T0 of Vogel-Fulcher-Tammann relation from the fit of the τα versus temperature. Tc is always between TLS and T0. The slope of variation of TLS with composition is the highest, therefore, it will cross variation in Tc and TLS at higher concentrations of ∼ 17% and ∼ 23% respectively. As the growth of the order parameter Q6 weakens with B, for higher concentrations of B, TLS may not be meaningful. We extrapolated the value of Tc at well-known composition 20% of B to be 0.47, which closer to the reported value 0.435 with an 8% deviation. The length and time scale of the dynamic heterogeneity is related to the variation of the 4-point correlator χ4(q, t). The peak height of χP 4 (q, t) quantifies the correlated motion between the particles. We have proposed a power-law fit χ4(q, t) = a (τα/τ0)d which works reasonably well. We have proposed and tested a power-law relation of the form connecting the peak height to excess density χP 4 (k, t) = A(ρ0−ρloc)k that relates the correlated motion with the stability of the cages.