Search

Recently, some of us developed a novel model glass-forming liquid with k extra interactions with pseudo neighbours to each liquid particle over and above the regular interactions with its neighbours. Analysis of the structure and dynamics of these systems showed that with an increase in k the systems have more mean-field like properties. This work presents an extensive study of the thermodynamics of the above-mentioned model for several values of k and its correlation with the dynamics. We surprisingly find that the usual thermodynamic integration (TI) method of calculating the entropy provides unphysical results for this model. It predicts the vanishing of configurational entropy at state points at which both the collective and the single-particle dynamics of the system show complete relaxation. We then employ a new method known as the two-phase thermodynamics (2PT) method to calculate the entropy. We find that with an increase in k the difference in the entropy computed using the two methods (2PT and TI) increases. We also find that in the temperature range studied, the entropy calculated via the 2PT method satisfies the Adam-Gibbs (AG) relationship between the relaxation time and the configurational entropy, whereas the entropy calculated via the TI method shows a strong violation of the same. We then apply the 2PT method to calculate the entropy in another system where some fractions of particles are pinned randomly in their equilibrium positions. This system also shows a similar breakdown of the AG relationship as reported earlier. We show that the difference in entropy calculated via the 2PT and TI methods increases with an increase in pinning density. We also find that when the entropy is calculated using the 2PT method, the AG relationship between the dynamics and the entropy holds., Comment: 16 pages, 27 figures, 3 tables

In a system of N particles, with continuous size polydispersity there exists N(N-1) number of partial structure factors making it analytically less tractable. A common practice is to treat the system as an effective one component system which is known to exhibit an artificial softening of the structure. The aim of this study is to describe the system in terms of M pseudo species such that we can avoid this artificial softening but at the same time have a value of M << N. We use potential energy and pair excess entropy to estimate an optimum number of species, M_{0}. We find that systems with polydispersity width, {\Delta}{\sigma}_{0} can be treated as a monodisperse system. We show that M_{0} depends on the degree and type of polydispersity and also on the nature of the interaction potential, whereas, {\Delta}{\sigma}_{0} weakly depends on the type of the polydispersity, but shows a stronger dependence on the type of interaction potential. Systems with softer interaction potential have a higher tolerance with respect to polydispersity. Interestingly, M_{0} is independent of system size, making this study more relevant for bigger systems. Our study reveals that even 1% polydispersity cannot be treated as an effective monodisperse system. Thus while studying the role of polydispersity by using the structure of an effective one component system care must be taken in decoupling the role of polydispersity from that of the artificial softening of the structure., Comment: 12 pages, 15 figures, 2 tables

We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo neighbours and by means of analytical calculations, we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with increasing k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the MCT power law behaviour for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with increasing k whereas the non-Gaussian parameter is independent of it. Thus we conclude that with the increase in the number of pseudo neighbours the system becomes more mean-field like. By comparing our results with previous studies on mean-field like system we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit., Comment: 19 pages, 21 figures