Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory

Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, S. K.

doi:10.1103/physrevlett.119.265502

Cited by 26 publications

(46 citation statements)

References 48 publications

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“…It has also been suggested that the crossover temperature T c might be inferred from the T variation of S ex . 304,306 It would be an invaluable advance to the GET to have an alternative thermodynamic-based approach for calculating T A , and we plan to test this proposal against independent estimates of T A for our polymer model in the future. Over time, we hope to see the various 'pieces' of the entropy theory of glass formation to grow together to form a highly predictive and validated framework from theoretical, computational, and experimental perspectives.…”

Section: Rosenfeld and Excess-entropy Scalingmentioning

confidence: 99%

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

Xu,

Douglas,

Sun

2021

Preprint

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We provide a perspective on polymer glass formation, with an emphasis on models in which the fluid entropy and collective particle motion dominate the theoretical description and data analysis. The entropy theory of glass formation has its origins in experimental observations relating to correlations between the fluid entropy and liquid dynamics going back nearly a century ago, and it has entered a new phase in recent years. We first discuss the dynamics of liquids in the high temperature Arrhenius regime, where transition state theory is formally applicable. We then summarize the evolution of the entropy theory from a qualitative framework for organizing and interpreting temperature-dependent viscosity data by Kauzmann to the formulation of a hypothetical 'ideal thermodynamic glass transition' by Gibbs and DiMarzio, followed by seminal measurements linking entropy and relaxation by Bestul and Chang and the Adam-Gibbs (AG) model of glass formation rationalizing the observations of Bestul and Chang. These developments laid the groundwork for the generalized entropy theory (GET), which merges an improved lattice model of polymer thermodynamics accounting for molecular structural details and enabling the analytic calculation of the configurational entropy with the AG model, giving rise to a highly predictive model of the segmental structural relaxation time of polymeric glass-forming liquids. The development of the GET has occurred in parallel with the string model of glass formation in which concrete realizations of the cooperatively rearranging regions are identified and quantified for a wide range of polymeric and other glass-forming materials. The string model has shown that many of the assumptions of AG are well supported by simulations, while others are certainly not, giving rise to an entropy theory of glass formation that is largely in accord with the GET. As the GET and string models continue to be refined, these models progressively grow into a more unified framework, and this Perspective reviews the present status of development of this promising approach to the dynamics of polymeric glass-forming liquids.

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Section: Rosenfeld and Excess-entropy Scalingmentioning

confidence: 99%

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

Xu,

Douglas,

Sun

2021

Preprint

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“…The two potentials, the LJ and WCA, have same repulsive core but different attractive part; the LJ has an attractive tail while the WCA has no attraction. These models therefore offer an ideal benchmark for evaluating the role of repulsive and attractive interactions on the local structural order and on slowing down of dynamics of glass-forming liquids, and have been studied extensively over last several years [5,6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21]. We compare results of the two systems and identify causes that give rise a large difference in their local structural order and dynamics at lower liquid-like densities but almost identical results at sufficiently large densities.…”

Section: Introductionmentioning

confidence: 99%

“…Local structure analysis using topological cluster classification [29] and Voronoi face analysis [12] also point to subtle structural difference. Using the configurational entropy as the thermodynamic maker via the Adam-Gibbs relation [30], Banerjee et al [16][17][18] showed that the difference in dynamics of the WCA and LJ systems is due to difference in their configurational entropy. These results prompt one to ask whether a unified physical framework exists to understand the structure and dynamics and their relationship for systems such as the LJ and WCA glass forming liquids.…”

Section: Introductionmentioning

confidence: 99%

How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids?

Singh,

Singh

2021

Preprint

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The theory developed in our previous papers is applied in this paper to investigate the dependence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts of intermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jones glass-forming liquid and that of its WCA reduction to a model with truncated pair potential without attractive tail, we demonstrate why the two systems exhibit very different dynamics despite having nearly identical pair correlation functions. In particular, we show that local structures characterized by number of mobile and immobile particles around a central particle markedly differ in the two systems at densities and temperatures where their dynamics show large difference and nearly identical where dynamics nearly overlap. We also show how the parameter ψ(T ) that measures the role of fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) and the crossover temperature Ta depend on the intermolecular interactions. These parameters stemming from the intermolecular interactions characterize the temperature and density dependence of structural relaxation time τα. The quantitative and qualitative agreements found with simulation results for the two systems suggest that our theory brings out the underlying features that determine dynamics of glass-forming liquids.

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“…This observation also justifies the findings that theories like the mode coupling theory (MCT) and dynamic density functional theory which requires structure as an input cannot predict the difference in the dynamics of two systems having similar structures 7 . However, following these studies, there has been further investigation involving some of us in analyzing the role of pair structure in the dynamics 8,9 . It was shown that although the structure of the system cannot predict the actual dynamics, it has the information of the dynamical transition temperature, often referred to as the mode coupling transition temperature, T c 8,9 .…”

Section: Introductionmentioning

confidence: 99%

“…However, following these studies, there has been further investigation involving some of us in analyzing the role of pair structure in the dynamics 8,9 . It was shown that although the structure of the system cannot predict the actual dynamics, it has the information of the dynamical transition temperature, often referred to as the mode coupling transition temperature, T c 8,9 . These studies further showed that the information of the difference in the dynamics of two systems having very similar structure is also embedded in the structure.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of a Class of Mean Field Theories of the Glass Transition

Saha,

Nandi,

Dasgupta

et al. 2019

Preprint

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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 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.

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Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory

Cited by 26 publications

References 48 publications

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids?

A Comparative Study of a Class of Mean Field Theories of the Glass Transition

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