Mode-coupling glass transition in a fluid confined by a periodic potential - Nandi, Saroj Kumar; Bhattacharyya, Sarika Maitra; Ramaswamy, Sriram (Physical Review E, 2011)
We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behavior expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S. H. Krishnan, Ph.D. thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J. Special Topics 189, 135 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack [Phys. Rev. E 75, 031503 (2007)] and Lang et al. [Phys. Rev. Lett. 105, 125701 (2010)].

Interplay between crystallization and glass transition in binary lennard-Jones mixtures (vol 139, 104501, 2013) - Banerjee, Atreyee; Chakraborty, Suman; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2013)

Interplay between crystallization and glass transition in binary Lennard-Jones mixtures - Banerjee, Atreyee; Chakrabarty, Suman; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2013)
In this work we explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger x(A) (x(A) = 0.6, where x(A) is the mole fraction of the bigger particles) is a mixed fcc + bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger xA is a mixed NaCl + fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this ``bcc zone'' is due to the frustration between the locally preferred structure (LPS) and the mixed bcc + fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When x(A) is further increased (0.70 <= x(A) < 0.90) the systems show a tendency towards mixed fcc crystal formation. However, the ``bcc zone'' even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization. (C) 2013 AIP Publishing LLC.

Non-monotonic size dependence of diffusion and levitation effect: a mode-coupling theory analysis - Nandi, Manoj Kumar; Banerjee, Atreyee; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2013)
We present a study of diffusion of small tagged particles in a solvent, using mode coupling theory (MCT) analysis and computer simulations. The study is carried out for various interaction potentials. For the first time, using MCT, it is shown that only for strongly attractive interaction potential with allowing interpenetration between the solute-solvent pair the diffusion exhibits a non-monotonic solute size dependence which has earlier been reported in simulation studies [P. K. Ghorai and S. Yashonath, J. Phys. Chem. B 109, 5824-5835 (2005)]. For weak attractive and repulsive potential the solute size dependence of diffusion shows monotonic behaviour. It is also found that for systems where the interaction potential does not allow solute-solvent interpenetration, the solute cannot explore the neck of the solvent cage. Thus these systems even with strong attractive interaction will never show any non-monotonic size dependence of diffusion. This non-monotonic size dependence of diffusion has earlier been connected to levitation effect [S. Yashonath and P. Santikary, J. Phys. Chem. 98, 6368 (1994)]. We also show that although levitation is a dynamic phenomena, the effect of levitation can be obtained in the static radial distribution function. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4796232]

Role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials - Banerjee, Atreyee; Sengupta, Shiladitya; Sastry, Srikanth; Bhattacharyya, Sarika Maitra (Physical Review Letters, 2014)
We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.

Diffusion of small solute particles in viscous liquids: cage diffusion, a result of decoupling of solute-solvent dynamics, leads to amplification of solute diffusion - Acharya, Sayantan; Nandi, Manoj K.; Mandal, Arkajit; Sarkar, Sucharita; Bhattacharyya, Sarika Maitra (Journal of Physical Chemistry B, 2015)
We study the diffusion of small solute particles through solvent by keeping the solute solvent interaction repulsive and varying the solvent properties. The study involves computer simulations, development of a new model to describe diffusion of small solutes in a solvent, and also mode coupling theory (MCT) calculations. In a viscous solvent, a small solute diffuses via coupling to the solvent hydrodynamic modes and also through the transient cages formed by the solvent. The model developed can estimate the independent contributions from these two different channels of diffusion. Although the solute diffusion in all the systems shows an amplification, the degree of it increases with solvent viscosity. The model correctly predicts that when the solvent viscosity is high, the solute primarily diffuses by exploiting the solvent cages. In such a scenario the MCT diffusion performed for a static solvent provides a correct estimation of the cage diffusion.

Unraveling the success and failure of mode coupling theory from consideration of entropy - Nandi, Manoj Kumar; Banerjee, Atreyee; Sengupta, Shiladitya; Sastry, Srikanth; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2015)
We analyze the dynamics of model supercooled liquids in a temperature regime where predictions of mode coupling theory (MCT) are known to be valid qualitatively. In this regime, the Adam-Gibbs (AG) relation, based on an activation picture of dynamics, also describes the dynamics satisfactorily, and we explore the mutual consistency and interrelation of these descriptions. Although entropy and dynamics are related via phenomenological theories, the connection between MCT and entropy has not been argued for. In this work, we explore this connection and provide a microscopic derivation of the phenomenological Rosenfeld theory. At low temperatures, the overlap between the MCT power law regime and AG relation implies that the AG relation predicts an avoided divergence at T-c, the origin of which can be related to the vanishing of pair configurational entropy, which we find occurring at the same temperature. We also show that the residual multiparticle entropy plays an important role in describing the relaxation time. (C) 2015 AIP Publishing LLC.

Composition dependence of the glass forming ability in binary mixtures: the role of demixing entropy - Nandi, Ujjwal Kumar; Banerjee, Atreyee; Chakrabarty, Suman; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2016)
We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger ``A'' particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the ``B'' particles make it a good glass former. The locally favoured structure around ``B'' particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon. Published by AIP Publishing.

Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities - Banerjee, Atreyee; Nandi, Manoj Kumar; Sastry, Srikanth; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2016)
In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in this paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density. Published by AIP Publishing.

Determination of onset temperature from the entropy for fragile to strong liquids - Banerjee, Atreyee; Nandi, Manoj Kumar; Sastry, Srikanth; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2017)
In this paper, we establish a connection between the onset temperature of glassy dynamics with the change in the entropy for a wide range of model systems. We identify the crossing temperature of pair and excess entropies as the onset temperature. Below the onset temperature, the residual multiparticle entropy, the difference between excess and pair entropies, becomes positive. The positive entropy can be viewed as equivalent to the larger phase space exploration of the system. The new method of onset temperature prediction from entropy is less ambiguous, as it does not depend on any fitting parameter like the existing methods. Published by AIP Publishing.

Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics - Acharya, Sayantan; Nandi, Ujjwal Kumar; Bhattacharyya, Sarika Maitra (Journal Of Chemical Physics, 2017)
We present a study of the dynamics of small solute particles in a solvent medium where the solute is much smaller in size, mimicking the diffusion of small particles in crowded environment. The solute exhibits Fickian diffusion arising from non-Gaussian Van Hove correlation function. Our study shows that there are at least two possible origins of this non-Gaussian behaviour: the decoupling of the solute-solvent dynamics and the intermittency in the solute motion, the latter playing a dominant role. In the former scenario when averaged over time long enough to explore different solvent environments, the dynamics recovers the Gaussian nature. In the case of intermittent dynamics the non-Gaussianity remains even after long averaging and the Gaussian behaviour is obtained at a much longer time. Our study further shows that only for an intermediate attractive solute-solvent interaction the dynamics of the solute is intermittent. The intermittency disappears for weaker or stronger attractions. Published by AIP Publishing.

Role of the pair correlation function in the dynamical transition predicted by mode coupling theory - Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Physical Review Letters, 2017)
In a recent study, we have found that for a large number of systems the configurational entropy at the pair level S-c2, which is primarily determined by the pair correlation function, vanishes at the dynamical transition temperature T-c. Thus, it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this, we describe the dynamics of the system at the mean field level and, using the concepts of the dynamical density functional theory, show that the dynamical transition temperature depends only on the pair correlation function. Thus, this theory is similar in spirit to the microscopic mode coupling theory (MCT). However, unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature that is similar to T-c. This implies that the information of the dynamical transition temperature is embedded in the pair correlation function.

Validity of the Rosenfeld relationship: a comparative study of the network forming NTW model and other simple liquids - Banerjee, Atreyee; Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Journal of Chemical Sciences, 2017)
In this paper we explore the validity of the Rosenfeld and the Dzugutov relation for the Lennard-Jones (LJ) system, its repulsive counterpart, the WCA system and a network forming liquid, the NTW model. We find that for all the systems both the relations are valid at high temperature regime with an universal exponent close to 0.8. Similar to that observed for the simple liquids, the LJ and the WCA systems show a breakdown of the scaling laws at the low temperature regime. However for the NTW model, which is a simple liquid, these scaling laws are valid even at lower temperature regime similar to that found for ionic melts. Thus we find that the NTW model has mixed characteristics of simple liquids and ionic melts. Our study further reveals a quantitative relationship between the Rosenfeld and the Arrhenius relations. For strong liquids, the validity of the Rosenfeld relation in the low temperature regime is connected to it following the Arrhenius behaviour in that regime. Finally we explore the role of pair entropy and residual multiparticle entropy in the dynamics as a function of fragility of the systems.

Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy - Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2018)
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (S-c) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of S-c. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow. Published by AIP Publishing.

Comparative study of a class of mean field theories of the glass transition - Saha, Indranil; Nandi, Manoj Kumar; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Journal of Statistical Mechanics-Theory and Experiment, 2019)
In a recently developed microscopic mean field theory, we have shown that the dynamics of a system, when described only in terms of its pair structure, can predict the correct dynamical transition temperature. Further, the theory predicted the difference in dynamics of two systems (the Lennard-Jones and the Weeks-Chandler-Andersen) despite them having quite similar structures. This is in contrast to the Schweizer-Saltzman (SS) formalism which predicted the dynamics of these two systems to be similar. The two theories although similar in spirit have certain differences. Here we present a comparative study of these two formalism to find the origin of the difference in their predictive power. We show that not only the dynamics in the potential energy surface, as described by our earlier study, but also that in the free energy surface, like in the SS theory, can predict the correct dynamical transition temperature. Even an approximate one component version of our theory, similar to the system used in the SS theory, can predict the transition temperature reasonably well. Interestingly, we show here that despite the above mentioned shortcomings the SS theory can actually predict the correct transition temperatures. Thus microscopic mean field theories of this class which express dynamics in terms of the pair structure of the liquid while being unable to predict the actual dynamics of the system are successful in predicting the correct dynamical transition temperature.
Keywords: aging; etc); glasses (colloidal; glassy dynamics; mode coupling theory; Polymer; slow relaxation

Comparative study of anomalous size dependence of charged and neutral solute diffusion in water - Acharya, Sayantan; Nandi, Ujjwal K.; Bhattacharyya, Sarika Maitra (Journal of Physical Chemistry B, 2019)
We present a comparative study of size dependence of diffusion for charged and neutral solutes in water. Although both show nonmonotonicity of the size dependence of diffusion, their nature and origin are quite different. For neutral solutes, the peak position and the value of diffusion at the maximum are both independent of the solute water interaction. Interestingly, for charged solutes, with an increase in solute water interaction strength, the peak position shifts to lower solute sizes and with an increase in charge, it shifts to higher solute sizes. The diffusion value at the peak reduces with an increase in both solute water interaction and solute charge. We show that all these features observed for charged solutes can be understood in terms of the interplay between ionic and nonionic interactions which is definitely absent for neutral solutes. Some of the earlier studies addressing the nonmonotonicity in diffusion did suggest the interplay between the two interactions to be the cause. However, this is the first time we show that such an interplay gives rise to the nonmonotonicity in the potential energy which is a prerequisite for obtaining the nonmonotonicity in the diffusion. Such nonmonotonicity in the potential energy is absent for neutral solutes.

Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics (vol 146, 134504, 2017) - Acharya, Sayantan; Nandi, Ujjwal Kumar; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2019)

Continuous time random walk concepts applied to extended mode coupling theory: a study of the Stokes? Einstein breakdown - Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Journal of Physics-Condensed Matter, 2020)
In an attempt to extend the mode coupling theory (MCT) to lower temperatures, some years back an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). The theory successfully showed that there is hopping induced diffusive dynamics and the modified MCT coupled to the activated motion continues till low temperatures. Here we show that the theory although successful in describing other properties of supercooled liquids is unable to capture the Stokes?Einstein breakdown. We then show using continuous time random work (CTRW) formalism that the Unified theory is equivalent to a CTRW dynamics in presence of two waiting time distributions. It is known from earlier work on CTRW that in such cases the total dynamics is dominated by the fast motion. This explains the failure of the Unified theory in predicting the SE breakdown as both the structural relaxation and the diffusion process are described by the comparatively fast MCT like dynamics. The study also predicts that other forms of extended MCT with Markovian hopping kernel will face a similar issue. We next modify the Unified theory by applying the concept of renewal theory, usually used in CTRW models where the distribution has a long tail. According to this theory the first jump given by the persistent time is slower than the subsequent jumps given by the exchange time. We first show that for systems with two waiting time distributions even when both the distributions are exponential the persistent time is larger than the exchange time. We also identify the persistent time with the slower activated process. The extended Unified theory can now explain the SE breakdown. In this extended theory at low temperatures the structural relaxation is described by the activated dynamics whereas the diffusion is primarily determined by the MCT like dynamics leading to a decoupling between them. We also calculate a dynamic lengthscale from the wavenumber dependence of the relaxation time. We find that this dynamic length scale grows faster than the static length scale.
Keywords: continuous time random walk; mode coupling theory; Stokes?Einstein breakdown

Connecting real glasses to mean-field models - Nandi, Ujjwal Kumar; Kob, Walter; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2021)
We propose a novel model for a glass-forming liquid, which allows us 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-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, 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.

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.

Emergence of cooperatively reorganizing cluster and super-Arrhenius dynamics of fragile supercooled liquids - Singh, Ankit; Bhattacharyya, Sarika Maitra; Singh, Yashwant (Physical Review E, 2021)
In this paper, we develop a theory to calculate the structural relaxation time tau(alpha) of fragile supercooled liquids. Using the information of the configurational entropy and structure, we calculate the number of dynamically free, metastable, and stable neighbors around a central particle. In supercooled liquids, the cooperatively reorganizing clusters (CRCs) in which the stable neighbors form ``stable'' nonchemical bonds with the central particle emerge. For an event of relaxation to take place, these bonds have to reorganize irreversibly; the energy involved in the processes is the effective activation energy of relaxation. The theory brings forth a temperature T-a and a temperature-dependent parameter psi(T) which characterize slowing down of dynamics on cooling. It is shown that the value of psi(T) is equal to 1 for T > T-a, indicating that the underlying microscopic mechanism of relaxation is dominated by the entropy-driven processes, while for T < T-a, psi(T ) decreases on cooling, indicating the emergence of the energy-driven processes. This crossover of psi(T) from high to low temperatures explains the crossover seen in tau(alpha). The dynamics of systems that may have similar static structure but very different dynamics can be understood in terms of psi(T). We present results for the Kob-Anderson model for three densities and show that the calculated values of tau(alpha) are in excellent agreement with simulation values for all densities. We also show that when psi(T), tau(alpha), and other quantities are plotted as a function of T/T-a, (or Ta/T), the data collapse on master curves.

Microscopic theory of softness in supercooled liquids - Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Physical Review Letters, 2021)
We introduce a new measure of the structure of a liquid which is the softness of the mean-field potential developed by us earlier. We find that this softness is sensitive to small changes in the structure. Then, we study its correlation with the supercooled liquid dynamics. The study involves a wide range of liquids (fragile, strong, attractive, repulsive, and active) and predicts some universal behaviors such as the softness being linearly proportional to the temperature and inversely proportional to the activation barrier of the dynamics with system dependent proportionality constants. We establish a master equation between the dynamics and the softness parameter and show that, indeed, the dynamics, when scaled by the temperature and system dependent parameters, show a data collapse when plotted against softness. The dynamics of fragile liquids show a strong softness dependence, whereas that of strong liquids show a much weaker softness dependence. We also connect the present study with the earlier studies of softness involving machine learning (ML), thus, providing a theoretical framework for understanding the ML results.

Identifying structural signature of dynamical heterogeneity via the local softness parameter - Sharma, Mohit; Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Physical Review E, 2022)
In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.

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.

Comparative study of the correlation between the structure and the dynamics for systems interacting via attractive and repulsive potentials - Sharma, Mohit; Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2023)
We present the study of the structure-dynamics correlation for systems interacting via attractive Lennard-Jones (LJ) and its repulsive counterpart, the Weeks-Chandler-Andersen (WCA) potentials. The structural order parameter (SOP) is related to the microscopic mean-field caging potential. At a particle level, the SOP shows a distribution. Although the two systems have similar pair structures, their average SOP differs. However, this difference alone is insufficient to explain the well known slowing down of the dynamics in the LJ system at low temperatures. The slowing down can be explained in terms of a stronger coupling between the SOP and the dynamics. To understand the origin of this system specific coupling, we study the difference in the microscopic structure between the hard and soft particles. We find that for the LJ system, the structural differences of the hard and soft particles are more significant and have a much stronger temperature dependence compared to the WCA system. Thus, the study suggests that attractive interaction creates more structurally different communities. This broader difference in the structural communities is probably responsible for stronger coupling between the structure and dynamics. Thus, the system specific structure-dynamics correlation, which also leads to a faster slowing down in the dynamics, appears to have a structural origin. A comparison of the predictive power of our SOP with the local energy and two body excess entropy in determining the dynamics shows that in the LJ system, the enthalpy plays a dominant role and in the WCA system, the entropy plays a dominant role, and our SOP can capture both these contributions.

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.

Structural origin of relaxation in dense colloidal suspensions - Sahu, Ratimanasee; Sharma, Mohit; Schall, Peter; Bhattacharyya, Sarika Maitra; Chikkadi, Vijayakumar (PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2024)
Keywords: DEFORMATION; flow; glass-transition; ORDER; SOFT

Growth of structural lengthscale in Kob-Andersen binary mixtures: Role of medium range order - Kumawat, Sanket; Sharma, Mohit; Nandi, Ujjwal Kumar; Tah, Indrajit; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2025)
A central and extensively debated question in glass physics concerns whether a single, growing lengthscale fundamentally controls glassy dynamics, particularly in systems lacking obvious structural motifs such as the Kob-Andersen binary Lennard-Jones (KALJ) model. In this work, we investigate structural and dynamical lengthscales in supercooled liquids using the KALJ model in two compositions: 80:20 and 60:40. We compute the dynamical lengthscale from displacement-displacement correlation functions and observe a consistent growth as temperature decreases. To explore the static counterpart, we use a structural order parameter (SOP) based on the mean field caging potential. While this SOP is known to predict short time dynamics effectively, its bare correlation function reveals minimal spatial growth. Motivated by recent findings that long time dynamics reflect collective rearrangements, we perform spatial coarse-graining of the SOP and identify an optimal lengthscale L-max that maximizes structure-dynamics correlation. We show that the structural correlation length derived from SOP coarse-grained over L-max exhibits clear growth with cooling and closely tracks the dynamical lengthscale, especially for A particles in the 80:20 mixture and for both A and B particles in the 60:40 system. Our results reconcile the previously observed absence of static length growth in the KALJ model by highlighting the necessity of intermediate range structural descriptors. Furthermore, we find that the particles with larger structural length growth also correspond to species with latent crystallization tendencies, suggesting a possible link between structural order, dynamics, and incipient crystallization.