Search

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 centres in both high and low-temperature regimes. A key finding is that akin to the pinned system, the self 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 centres, the modified quaternary framework predicts a higher correlation., Comment: 15 pages, 28 figures, 1 table

Amorphous solids relax via slow molecular rearrangement induced by thermal fluctuations or applied stress. Although microscopic structural signatures predicting these structural relaxations have long been sought, a physically motivated structural measure relevant to diverse systems remains elusive. Here, we introduce a structural order parameter derived from the mean-field caging potential experienced by the particles due to their neighbors, which reliably predicts the occurrence of structural relaxations. The parameter, derived from density functional theory, is a measure of susceptibility to particle rearrangements that can effectively identify weak or defect-like regions in disordered systems. Using experiments on dense colloidal suspensions, we demonstrate a causal relationship between this order parameter and the structural relaxations of the amorphous solid. In quiescent suspensions, increasing the density leads to stronger correlations between the structure and dynamics. Under applied shear, the mean structural order parameter increases with increasing strain, signaling shear-induced softening, which is accompanied by the proliferation of plastic events. In both cases, the order parameter reliably identifies weak regions where the plastic rearrangements due to thermal fluctuation or applied shear preferentially occur. Our study paves the way to a structural understanding of the relaxation of a wide range of amorphous solids, from suspensions to metallic glasses.

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 that 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 interaction between a pinned and 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 the primary reason for the well-known vanishing of the configurational entropy at high temperatures. We further show that contrary to 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"., Comment: 18 pages, 45 figures, 1 table

We present the study of the structure-dynamics correlation for systems interacting via attractive Lennard- Jones and its repulsive counterpart, the 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 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 shows that in the LJ system, the dynamics is driven by enthalpy, whereas in the WCA system, it is driven by entropy, and our SOP can capture both these contributions., Comment: 14 pages, 44 figures

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 = M0 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, {\sigma}, and this coupling increases with polydispersity and decreases with an increase in M . Careful analysis shows that at lower polydispersity the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on {\sigma}. Since the coupling between the SOP and {\sigma} is higher for M = 1 thus, 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 {\sigma}. Thus our study suggests that for systems with high polydispersity, the correlation of any order parameter and {\sigma} will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter., Comment: 14 pages, 41 figures, 1 table

In a recent study by some of us, we have proposed a new measure of the structure of a liquid, the softness of the mean-field caging potential, and shown that it can describe the temperature dependence of the dynamics. In this work, we put this parameter through a stringent test and study the causal relationship between this softness parameter at the local level and the local dynamics. We first extend the earlier study to describe the local softness. We find a distribution of the softness value where the distribution has reasonably strong temperature dependence. This shows that the parameter can identify the local structural heterogeneity. We then study the lifetime of the softness parameter and show that its lifetime is connected to the well-known cage structure in the 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. We find that at lower temperatures, the structural heterogeneity increases, and also, the structure becomes a better predictor of the dynamics, thus giving rise to dynamic 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 neighbourhood, confirming the well-known facilitation effect., Comment: 12 pages, 38 figures

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

In this paper we develop a theory to calculate the structural relaxation time {\tau} {\alpha} of fragile su percooled 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 temper ature 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 T a /T ) the data collapse on master curves., Comment: 10 pages, 12 figures

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. We then 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 behaviours like the softness is linearly proportional to the temperature and inversely proportional to the activation barrier of the dynamics with system dependent proportionality constants. We write down 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.

In an attempt to extend the mode coupling theory (MCT) to lower temperatures, an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). 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 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.

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 WCA) 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 formalisms 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. According to our analysis, the absence of the Vineyard approximation in the SS formalism led it to predict similar dynamics for the two systems. 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., Comment: 12 pages, 5 figures

In this work, we perform a comparative study of the size dependence of diffusion of charged and neutral solutes in water. The neutral solute in water shows a nonmonotonicity in the size dependence of diffusion. This is usually connected to the well known Levitation effect where it is found that when solute diffuses through the transient solvent cages then for attractive solute-solvent interaction and for a particular size of the solute there is a force balance which leads to the maximum in diffusion. Similar maximum in diffusion of charged solutes has also been observed and connected to Levitation effect. However, earlier studies of ionic diffusion connects this nonmonotonicity to the interplay between hard sphere repulsion and Coulombic attraction. In this work, we show that although the size dependence of both charged and neutral solutes have a nonmonotonicity, there is a stark difference in their behaviour. For charged solute with increase in attraction the maximum shifts to higher solute sizes and has a lower value whereas for neutral solute it remains at the same place and has a higher value. We show by studying the ionic and non-ionic part of the potential that for larger solutes it is the nonionic part which dominates and for smaller solutes the ionic part and the is a transition between them. As the charge on the solute increases, this transition takes place at larger solute sizes which leads to the shift in the diffusivity maxima and reduction of the peak value. We show that although the charged solutes also explore the solvent cage even before we reach the size which Levitates due to Coulombic attraction the diffusion value drops. Thus the origin of diffusivity maxima in charged and neutral solute diffusion is different.

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 ($S_{ex}$) 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 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 GCM suggesting suppression of activation. Interestingly despite suppression of activation the Adam-Gibbs (AG) relation which describes activated dynamics holds in GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG and mode coupling power law regime leading to a power law behaviour of $S_c$. From our analysis of this power law behaviour we predict that in 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 GCM is quite narrow.

In a recent study we have found that for a large number of systems the configuration entropy at pair level, $S_{c2}$, which is primarily determined by the structural information, vanishes at the mode coupling 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 function theory show that the dynamics depends only on the structure of the liquid. Thus this theory is similar in spirit to the microscopic MCT. However unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature which is similar to $T_{c}$. Thus our study reveals that the information of the mode coupling transition temperature is embedded in the structure of the liquid., Comment: 8 Pages, 3 Figs

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., Comment: 7 pages, 5 figures, accepted in J. Chem. Sci. (Special Issue on THEORETICAL CHEMISTRY/CHEMICAL DYNAMICS)

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(RMPE), 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. Our study also reveals the connection between fragility and the degree of breakdown of the Stokes Einstein (SE) relation., Comment: 8 pages, 4 figures

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., Comment: 10 pages, 7 figures and 2 tables

In this paper, we present a study of supercooled liquids interacting with the Lennard Jones (LJ) potential and the corresponding purely repulsive (Weeks-Chandler-Andersen or WCA) 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 (AG) 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 (rdf) of the B type of particles, the rdf of AA pairs and AB pairs give rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study (Phys. Rev. Lett.,\textbf {113}, 225701, 2014) and shows that they are generic in nature, independent of density., Comment: 12 pages,11 figures

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 shows that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles are decreased. We find that the 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 spontaneously when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behavior 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 structural frustration caused by the locally favored structure around the smaller "B" particles which make it a good glass former. 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 phenomena., Comment: 11pages,15 figures

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 MCT power law regime and AG relation implies that the AG relation predicts an avoided divergence at $T_c$, the origin of which is traced back to the vanishing of pair configurational entropy, which we find occurs at the same temperature. We also show that the residual multiparticle entropy plays an important role in describing the relaxation time, Comment: 25 pages ,8 figures

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.

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 $x_A$ 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 ($0.70\leq x_A < 0.90$) 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.

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 for strongly attractive interaction potential with soft core (allowing interpenetration between the solute-solvent pair) the diffusion exhibits a non-monotonic size dependence. This was earlier predicted in simulation and experimental studies and was connected to levitation effect [J. Phys. Chem. B 2005, 109, 5824-5835]. Our MCT analysis reveals that for weak or no attractive interactions, all the small solute particles studied here show levitation through the inter-solvent transient cage. However, for strong attractive interaction the levitation is not present for the smallest particle sizes. It is found that for systems where the interaction potential is hard, not allowing any interpenetration between the solute-solvent pair, the solute cannot explore the inter-solvent cage. Thus these systems will never show any non monotonic size dependence of diffusion. We also show that although levitation is a dynamic phenomena, the effect of levitation can be obtained in the radial distribution function., Comment: 19 pages, 7 figures

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory (MCT) 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 behaviour 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, PhD thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J-ST 189, 135-139 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack, PRE 75, 031503 (2007) and Lang et al., PRL 105, 125701 (2010)., Comment: This is the published version of the paper, minor modification, few more references added

As a liquid is progressively supercooled an intriguing weakening of the wavenumber ($q$) dependence of the structural relaxation time $\tau(q)$ in the large q limit is observed both in experiments and simulation studies. Neither the continuous Brownian diffusive dynamics nor the discontinuous activated events can alone explain the anomalous wavenumber dependence. Here we use our recently developed theory that unifies the mode coupling theory (MCT) for continuous dynamics and the random first order transition theory (RFOT) treatment of activated discontinuous motion as a nucleation (instanton) process, to understand the wavenumber dependence of density relaxation. The predicted smooth change in mechanism of relaxation from diffusive to activated, in the crossover regime, is wavevector dependent and is eventually responsible for sub-quadratic, almost linear, $q$ dependence of the relaxation time., Comment: 15 pages and 5 figures, minor changes in the content

In low temperature supercooled liquid, below the ideal mode coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. We present a theory which incorporates interaction between the two processes and shows that hopping can induce continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics (described here by the mode coupling theory (MCT)) and the activated hopping (described here by the random first order transition theory). We apply the theory to real systems (Salol) to show that the theory correctly predicts the temperature dependence of the non-exponential stretching parameter, $\beta$, and the primary $\alpha$ relaxation timescale, $\tau$. The study explains why, even below the ergodic to non-ergodic transition, the dynamics is well described by MCT. The non-linear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory explains the observed variation of the stretching exponent $\beta$ with the fragility parameter, $D$., Comment: 8 pages, 4 figures

We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from continuous diffusion, described using general two coupling parameter ($F_{12}$) mode coupling theory (MCT), and from the activated hopping, described using the random first order transition (RFOT) theory, incorporating the effect of dynamical heterogeneity. The theory is valid over the whole temperature plane and shows correct limiting MCT like behavior above $T_{c}$ and goes over to the RFOT theory near the glass transition temperature, $T_{g}$. Between $T_{c}$ and $T_{g}$, the theory predicts that neither the continuous diffusion, described by pure mode coupling theory, nor the hopping motion alone suffices but both contribute to the dynamics while interacting with each other. We show that the interplay between the two contributions conspires to modify the relaxation behavior of the DSF from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Close to $T_c$, coupling between the short time part of MCT dynamics and hopping reduces the stretching given by the F$_{12}$-MCT theory significantly and accelerates structural relaxation. As the temperature is progressively lowered below $T_c$, the equations yield a crossover from MCT dominated regime to the hopping dominated regime. In the combined theory the dynamical heterogeneity is modified because the low barrier components interact with the MCT dynamics to enhance the relaxation rate below $T_c$ and reduces the stretching that would otherwise arise from an input static barrier height distribution., Comment: 7 pages, 4 figures

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated events (called instantons) which lead to the spatial reorganization of molecules in the region where the instanton pops up. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event which can be derived from the random first order transition theory. The vertex is proportional to $exp(-A/s_{c})$ where $s_{c}$ is the configurational entropy. Close to the glass transition temperature, $T_{g}$, since $s_{c}$ is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor in deeply supercooled liquid fairly well, with a hopping dominated decay following the MCT plateau., Comment: 11 pages, 5 figures, 1 table