Effective structure of a system with continuous polydispersity - Patel, Palak; Nandi, Manoj Kumar; Nandi, Ujjwal Kumar; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2021)
In a system of N particles, with continuous size polydispersity, there exists an 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 pseudospecies 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 then define the maximum width of polydispersity, Delta sigma (0), that 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 polydispersity but shows a stronger dependence on the type of interaction potential. Systems with a 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.

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: a comparative study using two different methods of entropy calculation - Nandi, Ujjwal Kumar; Patel, Palak; Moid, Mohd; Nandi, Manoj Kumar; Sengupta, Shiladitya; Karmakar, Smarajit; Maiti, Prabal K.; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2022)
A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.

Dynamic heterogeneity in polydisperse systems: a comparative study of the role of local structural order parameter and particle size - Patel, Palak; Sharma, Mohit; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2023)
In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M-0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, s, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on s. Since the coupling between the SOP and s is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with s. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and s will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Effect of the presence of pinned particles on the structural parameters of a liquid and correlation between structure and dynamics at the local level - Patel, Palak; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2024)
Pinning particles at the equilibrium configuration of the liquid is expected not to affect the structure and any property that depends on the structure while slowing down the dynamics. This leads to a breakdown of the structure dynamics correlation. Here, we calculate two structural quantities: the pair excess entropy, S-2, and the mean field caging potential, the inverse of which is our structural order parameter (SOP). We show that when the pinned particles are treated the same way as the mobile particles, both S-2 and SOP of the mobile particles remain the same as those of the unpinned system, and the structure dynamics correlation decreases with an increase in pinning density, ``c.'' However, when we treat the pinned particles as a different species, even if we consider that the structure does not change, the expression of S-2 and SOP changes. The microscopic expressions show that the interaction between a pinned particle and a mobile particle affects S-2 and SOP more than the interaction between two mobile particles. We show that a similar effect is also present in the calculation of the excess entropy and is the primary reason for the well-known vanishing of the configurational entropy at high temperatures. We further show that, contrary to the common belief, the pinning process does change the structure. When these two effects are considered, both S-2 and SOP decrease with an increase in ``c,'' and the correlation between the structural parameters and the dynamics continues even for higher values of ``c.''

Exploring the soft pinning effect in the dynamics and the structure-dynamics correlation in multicomponent supercooled liquids - Anwar, Ehtesham; Patel, Palak; Sharma, Mohit; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2024)
We study multicomponent liquids by increasing the mass of 15% of the particles in a binary Kob-Andersen model. We find that the heavy particles have dual effects on the lighter particles. At higher temperatures, there is a significant decoupling of the dynamics between heavier and lighter particles, with the former resembling a pinned particle to the latter. The dynamics of the lighter particles slow down due to the excluded volume around the nearly immobile heavier particles. Conversely, at lower temperatures, there is a coupling between the dynamics of the heavier and lighter particles. The heavier particles' mass slows down the dynamics of both types of particles. This makes the soft pinning effect of the heavy particles questionable in this regime. We demonstrate that as the mass of the heavy particles increases, the coupling of the dynamics between the lighter and heavier particles weakens. Consequently, the heavier the mass of the heavy particles, the more effectively they act as soft pinning centers in both high and low-temperature regimes. A key finding is that akin to the pinned system, the self-dynamics and collective dynamics of the lighter particles decouple from each other as the mass of the heavy particles has a more pronounced impact on the latter. We analyze the structure-dynamics correlation by considering the system under the binary and modified quaternary framework, the latter describing the pinned system. Our findings indicate that whenever the heavy mass particles function as soft pinning centers, the modified quaternary framework predicts a higher correlation.

Dynamic signature of the thermodynamic transition in a novel mean field system - Anwar, Ehtesham; Nandi, Ujjwal Kumar; Patel, Palak; Kumawat, Sanket; Maitra Bhattacharyya, Sarika (Journal of Chemical Physics, 2025)
Understanding the connection between thermodynamics and dynamics in glass-forming liquids remains a central challenge in condensed matter physics. In this study, we investigate a novel model system that enables a continuous crossover from a standard three dimensional liquid to a fully connected mean field like system by introducing pseudo neighbors. These pseudo neighbors enhance the effective connectivity of the system without altering its local structure. While their presence slows down the dynamics, they influence thermodynamic properties even more significantly. In particular, the configurational entropy obtained via thermodynamic integration vanishes at a temperature much higher than the temperature where the dynamics begin to slow down, leading to a clear breakdown of the Adam-Gibbs relation. To uncover a possible dynamical signature of this thermodynamic transition, we analyze bond breakage dynamics. Unlike real-real bonds, which decay similarly in both the parent Kob-Andersen model and its mean field variant, real-pseudo bonds exhibit long lived, persistent behavior with strong temperature dependence. These bonds do not fully decay over time, leading to a finite saturation value of the bond breakage correlation function. Remarkably, we show that the number of surviving pseudo bonds can be analytically estimated and correlates directly with the thermodynamic transition temperature T-K. We propose a phenomenological relation between T-K and the number of surviving pseudo-bonds, establishing a novel link between thermodynamic and dynamic observables. Our results suggest that these persistent pseudo bonds serve as a robust dynamical signature of the thermodynamic transition, and the system might have properties analogous to those of randomly bonded ultrastable glasses.