Collineations of particles in the Kob-Andersen system

Numerous indications suggest that subtle changes occurring in the structures of liquids on supercooling are connected to the phenomenon of the glass transition and that detailed understanding of these changes is crucial for the development of new glasses with desired properties. J. D. Bernal in his 1962 Bakerian lecture in particular reported about an observation of approximately linear chains of several particles, referred to as collineations. He found that in the studied hard sphere system, these collineations can contain up to eight particles. Since then the collineations of three particles have been discussed in many papers in the context of the splitting of the second peak in pair density functions of supercooled liquids and glasses. However, it appears that longer collineations involving more that three particles have not been systematically studied. Here we report on our study of such collineations for the Kob-Andersen system of particles on cooling for the parent and inherent structures. Contrary to intuition, our findings reveal that below the potential energy landscape crossover temperature, the number of collineations in the parent structures can exceed that of the corresponding inherent structures. We also introduce a model that connects long collineations with the pair density and angular density distribution functions and demonstrate that this model describes long collineations quite well. We also studied the diffusion of the particles forming collineations and demonstrated that these particles are slightly slower than the randomly chosen average particle. Preliminary investigation of the collineations' lifetimes suggests that there are vibrational and structural relaxation regimes in the decay of the considered correlation function. The second part of the paper explores potential connections between collineations and (1) the disclination lines associated with the geometric frustration approach, (2) low-energy clusters from the topological cluster classification approach, and (3) chainlike cooperative motion of particles in low-temperature supercooled liquids. For the studied system, according to the used methods, no clear connection was found between collineations and these phenomena.