Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

Chakrabarty, Saurish; Das, Rajsekhar; Karmakar, Smarajit; Dasgupta, Chandan

doi:10.1063/1.4958632

Cited by 29 publications

(37 citation statements)

References 36 publications

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“…Its rationalization is considered fundamental to understanding the glass transition problem [20][21][22][23][24][25][26][27][28][29][30]. The AG relation can be written as X(T ) = X 0 exp A X T Sc(T ) , where X is an appropriate measure of dynamics i.e.…”

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confidence: 99%

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

2017

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The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its the thermodynamics via. the configurational entropy, and is of fundamental importance in descriptions of glassy behaviour. The breakdown of the Stokes-Einstein (SEB) relation between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.It is now clear from extensive research over the last two decades that, as a liquid is gradually (super)cooled, its dynamics becomes spatially heterogeneous ("dynamical heterogeneity") [1][2][3] and the collective nature of the underlying relaxation processes can be quantified by various growing correlation length scales [4, 5]. Dynamics can be described by different measures -the translational diffusion coefficient (D), the shear viscosity (η) or the α-relaxation time (τ α ). At high temperatures, where particle motions are diffusive, all these time scales are mutually coupled. D and η are related via the Stokes-Einstein (SE) relation [6, 7] : D = mk B cπ T Rη , (m, R are respectively mass and radius of a diffusing particle, T is the temperature of the liquid and the constant c depends on stick or slip boundary condition). At high temperatures, owing to exponential decay of self-intermediate scattering function F s (k, t) = exp(−Dk 2 t) at all probe wave vectors k, D also gets coupled to the relaxation time τ (k) measured from F s (k, t) : Dk 2 τ (k) = constant. Further, τ α is often used as a proxy for η (or η/T ) in the SE relation to save computational cost. At low temperatures in dense, viscous liquids, D becomes much bigger than the value estimated from τ α (η) using the SE relation. This phenomenon is known as the breakdown of the SE relation (SEB) [2,[8][9][10][11][12][13] [1, 2, 7, 8] interprets the SEB as a consequence of the dynamical heterogeneity (DH) developing in the liquid upon cooling. DH simply means that there are populations of slow and fast particles which form transient clusters, making the dynamics spatially heterogeneous. The existence of DH leads to the expectation of a distribution of diffusion coefficients and relaxation times [12,14] corresponding to populations of different mobility. The observed D is dominated by the fast population, while the observed τ (or η) is governed mainly by the slow population, leading to the decoupling and the SEB. The observed decoupling (SEB) is an average effect in such a picture, which however, does not clarify the role played by a heterogeneity length scale.The breakdown of the SE relation poses a puzzle...

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Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

2017

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“…Note that in the mean-field system, the breakdown of the AG relation and also the vanishing of the configurational entropy at a temperature where the dynamics show complete relaxation are similar to what has been observed for another family of models, namely, the pinned system. [33][34][35][36]45 In the pinned system, the relaxation time obtained from single-particle dynamics remains finite at temperatures for which the configurational entropy vanishes, and there is some evidence 54 that the relaxation time associated with the collective dynamics also remains finite at such temperatures. It has also been argued that the configurational entropy has a finite value when the vibrational entropy is calculated using an anharmonic approximation.…”

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confidence: 99%

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

Patel

Moid

et al. 2022

The Journal of Chemical Physics

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“…It has a peak at time scale close to τ α and the peak height grows with decreasing temperature. Scaling arguments presented later in the text show that the peak height of this newly defined "pinning susceptibility", χ p is directly proportional to ξ d p , where ξ p is the static length scale obtained using random pinning [35][36][37] and d is the number of spatial dimensions. This pinning length scale, ξ p is in turn related to the static length scale, ξ s associated with the amorphous order as ξ s ∼ ξ…”

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“…[32][33][34] that an ideal glass state can be obtained by introducing quenched disorder in the form of pinned particles in supercooled liquids. Although the existence of such an ideal glass state is still debated [35,36], random pinning has become a diagnostic tool to study the dynamics of the supercooled liquids and to test the validity of existing theories of glass transition [37]. Similar to χ T and χ φ , in the context of random pinning, we define the "pinning susceptibility" as…”

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Pinning susceptibility: a novel method to study growth of amorphous order in glass-forming liquids

2017

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Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. In this Letter, we propose an experimentally realizable yet simple correlation function to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results which are consistent with other conventional methods.Glasses are ubiquitous in nature and are of immense practical importance in our day-to-day lives as well as in modern technology. In spite of knowing their presence and usefulness from the early history of mankind, the nature of the glassy state and the glass transition, where the viscosity of a liquid increases by many orders of magnitude within a narrow temperature or density window, still puzzles the scientific community and is believed to be one of the major unsolved problems in condensed matter physics [1][2][3][4][5][6][7][8][9]. The viscosity of a glass forming liquid increases so dramatically that one is often tempted to believe that viscosity probably diverges at a certain critical temperature associated with a thermodynamic phase transition. Thus, not surprisingly, there are two types of theories on glass transition. The first type assumes that the (ideal) glass transition is a thermodynamic phase transition and glassy states are believed to be a thermodynamic state of matter. This approach is taken by the Random First Order Transition (RFOT) theory [10][11][12]. The other approach is to consider the glass transition to be a purely dynamic phenomenon and the slowdown of dynamics is thought to be a result of an ever increasing number of self-generated kinetic constraints with supercooling [13][14][15].In spite of all the differences in opinion about the existence of a true thermodynamic glass transition, there is a consensus about the existence and growth of correlation lengths along with the rapid increase in viscosity or relaxation time [2][3][4][5][7][8][9]. Recently there have been a lot of progress in identifying at least two different length scales -(a) a dynamic length scale akin to the length scale characterizing the heterogeneity present in the dynamics of supercooled liquids [4,5,8] and (b) a static length scale of the so called "amorphous order" [7,[16][17][18][19][20][21]. Simple two-point density correlation functions have been shown to be unsuitable for the identification of the build up of these correlations in the supercooled liquids. A ...

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Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

Cited by 29 publications

References 36 publications

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation

Pinning susceptibility: a novel method to study growth of amorphous order in glass-forming liquids

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