Glass-transition asymptotics in two theories of glassy dynamics: Self-consistent generalized Langevin equation and mode-coupling theory

Elizondo-Aguilera, Luis Fernando; Voigtmann, Thomas

doi:10.1103/physreve.100.042601

Cited by 26 publications

(37 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present NE-SCGLE approach, whose equilibrium version is conceptually closer to MCT (see a recent and detailed discussion in ref. 30 ), provides a complementary kinetic perspective, predicting the two-stage aging of the dynamics without assuming a priori a two-level arrest scenario.…”

Section: Resultsmentioning

confidence: 99%

Interference between the glass, gel, and gas-liquid transitions

Olais-Govea

López-Flores

Zepeda-López

et al. 2019

Sci Rep

View full text Add to dashboard Cite

Recent experiments and computer simulations have revealed intriguing phenomenological fingerprints of the interference between the ordinary equilibrium gas-liquid phase transition and the non-equilibrium glass and gel transitions. We thus now know, for example, that the liquid-gas spinodal line and the glass transition loci intersect at a finite temperature and density, that when the gel and the glass transitions meet, mechanisms for multistep relaxation emerge, and that the formation of gels exhibits puzzling latency effects. In this work we demonstrate that the kinetic perspective of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory of irreversible processes in liquids provides a unifying first-principles microscopic theoretical framework to describe these and other phenomena associated with spinodal decomposition, gelation, glass transition, and their combinations. The resulting scenario is in reality the competition between two kinetically limiting behaviors, associated with the two distinct dynamic arrest transitions in which the liquid-glass line is predicted to bifurcate at low densities, below its intersection with the spinodal line.

show abstract

Section: Resultsmentioning

confidence: 99%

Interference between the glass, gel, and gas-liquid transitions

Olais-Govea

López-Flores

Zepeda-López

et al. 2019

Sci Rep

View full text Add to dashboard Cite

show abstract

“…For a single decay channel, the contraction is not needed and we recover the equations considered for the analysis in Ref. [41] for matrix-valued correlation functions.…”

Section: Equations Of Structural Relaxationmentioning

confidence: 99%

Scaling equations for mode-coupling theories with multiple decay channels

Jung,

Voigtmann,

Franosch

2020

Preprint

View full text Add to dashboard Cite

Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in lateral and longitudinal direction to the walls are very different, or fluids of nonspherical particles with distinct relaxation patterns for translational and rotational degrees of freedom. Here, we perform an asymptotic analysis of the slow structural relaxation close to kinetic arrest as described by mode-coupling theory (MCT) with several relaxation channels. Compared to standard MCT, the presence of multiple relaxation channels significantly changes the structure of the underlying equations of motion and leads to additional, non-trivial terms in the asymptotic solution. We show that the solution can be rescaled, and thus prove that the well-known β-scaling equation of MCT remains valid even in the presence of multiple relaxation channels. The asymptotic treatment is validated using a novel schematic model. We demonstrate that the numerical solution of this schematic model can indeed be described by the derived asymptotic scaling laws close to kinetic arrest. Additionally, clear traces of the existence of two distinct decay channels are found in the low-frequency susceptibility spectrum, suggesting that clear footprints of the additional relaxation channels can in principle be detected in simulations or experiments of confined or molecular liquids.Then the inverse of the memory kernel readsThe contraction C{. . .} of the preceeding expression yields then − K(z) to the desired order.In particular from the zeroth order N −1 c = C{F −1 c }. The inverse density correlation function follows from the equation of motion Ŝ(z) −1 = −zS −1 − S −1 K(z)S −1 . Since the structure factor varies as S = S c + σS (1) , additional terms are generated in the expansion. Collecting terms one arrives at

show abstract

“…Within MCT, the static structural properties of the supercooled fluid constitute the only external to the theory input that is required for the calculation of the glass transition line and the critical form factors. In the literature, such properties have been obtained either from computer simulations [59][60][61] or from IET calculations combined with elementary closures (when simulation input was unavailable) which include the aforementioned HNC approximation for soft long range interaction potentials [29,62] or the Percus-Yevick (PY) approximation for hard sphere short range interactions [16,17,33,[63][64][65]. More advanced IET closures which enforce thermodynamic consistency through free parameters or resemble the VMHNC approximation by featuring an optimized correspondence rule have also been considered [66][67][68].…”

Section: Combining Mct With Advanced Iet Approachesmentioning

confidence: 99%

Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas

Castello

Tolias

2021

Molecules

View full text Add to dashboard Cite

The mode coupling theory of supercooled liquids is combined with advanced closures to the integral equation theory of liquids in order to estimate the glass transition line of Yukawa one-component plasmas from the unscreened Coulomb limit up to the strong screening regime. The present predictions constitute a major improvement over the current literature predictions. The calculations confirm the validity of an existing analytical parameterization of the glass transition line. It is verified that the glass transition line is an approximate isomorphic curve and the value of the corresponding reduced excess entropy is estimated. Capitalizing on the isomorphic nature of the glass transition line, two structural vitrification indicators are identified that allow a rough estimate of the glass transition point only through simple curve metrics of the static properties of supercooled liquids. The vitrification indicators are demonstrated to be quasi-universal by an investigation of hard sphere and inverse power law supercooled liquids. The straightforward extension of the present results to bi-Yukawa systems is also discussed.

show abstract

Glass-transition asymptotics in two theories of glassy dynamics: Self-consistent generalized Langevin equation and mode-coupling theory

Cited by 26 publications

References 74 publications

Interference between the glass, gel, and gas-liquid transitions

Interference between the glass, gel, and gas-liquid transitions

Scaling equations for mode-coupling theories with multiple decay channels

Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas

Contact Info

Product

Resources

About