arXiv subjects

Ilian Pihlajamaa

Publications and source records attributed to Ilian Pihlajamaa.

14 recordsLinked to original sources

arXiv2026

Non-Monotonic Dynamical Correlations Across The Glass Crossover

The dramatic slowing down of structural relaxation in supercooled liquids is accompanied by the emergence of dynamic heterogeneity. A monotonically increasing dynamical correlation length, measured at the $α$-timescale, is one of the remarkable features of this phenomenon. Here we show that this picture is incomplete: the dynamical correlation length measured in the $β$-relaxation regime exhibits a striking non-monotonic temperature dependence, reaching a maximum near the mode-coupling crossover temperature $T_c$ and decreasing upon further cooling, even as local dynamical fluctuations continue to intensify. This behavior suggests a crossover from spatially extended, maximally cooperative motion near $T_c$ to increasingly compact and localized relaxation events below it. We demonstrate that this evolution is quantitatively captured by stochastic beta-relaxation theory, an extension of mode-coupling theory beyond mean-field that explicitly predicts an avoided dynamical transition in finite dimensions. Our results provide the first direct spatial evidence in favor of the avoided-transition picture of the mode-coupling crossover, and establish the peak of the $β$-regime correlation length as a robust indicator of the mode-coupling crossover.

cond-mat.soft↗

arXiv2025

Fundamental measure theory for predicting many-body correlation functions

We study many-body correlation functions within various Fundamental Measure Theory (FMT) formulations and compare their predictions to Monte Carlo simulations of hard-sphere fluids. FMT accurately captures the qualitative behavior of three- and four-body structure, particularly at low and intermediate wavevectors. At higher wavevectors, the predictions of FMT vary in quantitative accuracy. We show that the dominant contributions to the four-point structure factor arise from direct triplet correlations, allowing the evaluation of four-point correlations to be greatly simplified. In glass-forming liquids at high volume fractions, FMT correctly reproduces deviations from the convolution approximation, highlighting FMT's ability to capture growing structural multipoint correlations upon supercooling.

physics.chem-ph↗

arXiv2025

Polydispersity-driven dynamical differences between two- and three-dimensional supercooled liquids

Previous studies have suggested a conundrum in the relaxation dynamics of polydisperse supercooled liquids. It has been shown that in two dimensions, the relative relaxation times of particles of different sizes become more similar as the material is cooled, whereas the opposite happens in three dimensions: they decouple. Here we resolve this conundrum. First, we show that the coupling observed in two dimensions is an artifact of cage correction introduced to account for Mermin-Wagner fluctuations. Instead, the relative relaxation time of small and large particles in two dimensions remains constant or slightly decouples with temperature, as opposed to the substantial decoupling observed in three dimensions. Investigating these dimensional differences further, we find through mobile cluster analysis that small particles initiate relaxation in both dimensions. As the clusters grow larger, they remain dominated by small particles in three dimensions whereas in two cluster growth becomes particle-size agnostic. We explain these findings with a minimal model by studying the distributions of single-particle barrier heights in the system, showing there is a clear difference in the environments of small and large particles, depending on the dimensionality. These findings highlight the critical role of dimensionality in glass formation, providing new insights into the mechanisms underlying the glass transition in polydisperse supercooled liquids.

cond-mat.soft↗

arXiv2024

Dissecting mode-coupling theory for supercooled liquids

The mode-coupling theory (MCT) of the glass transition ranks among the most successful first-principles kinetic theories to describe glassy dynamics. However, MCT does not fully account for crucial aspects of the dynamics near the glass transition. To facilitate improving the theory, we critically test the approximations inherent in MCT for a supercooled mixture using Brownian dynamics simulations. Although each MCT approximation significantly impacts the predicted dynamics, our findings show that long-time cancellations of errors occur due to static and dynamic approximations of four-point correlation functions, with the validity of these approximations remaining relatively constant across different temperatures. Notably, the MCT form of the memory functional maintains remarkably high accuracy even in the supercooled regime when evaluated with the intermediate scattering function from simulations. The primary discrepancies between theoretical predictions and experimental results arise from the self-consistent nature of the MCT equations, which amplify minor errors in the memory kernel. This suggests that minor corrections to the memory functional could substantially enhance the theory's predictive accuracy.

cond-mat.soft↗

arXiv2024

Simple fluctuations in simple glass formers

Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways.

cond-mat.dis-nn↗

arXiv2024

Comparison of integral equation theories of the liquid state

The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce e.g. the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equations for a given closure and pair interaction potential.

cond-mat.soft↗

arXiv2023

Competing Relaxation Channels in Continuously Polydisperse Fluids: A Mode-Coupling Study

Systems with a high degree of size polydispersity are becoming standard in the computational study of deeply supercooled liquids. In this work we perform a systematic analysis of continuously polydisperse fluids as a function of the degree of polydispersity within the framework of the Mode-Coupling Theory of the glass transition (MCT). Our results show that a high degree of polydispersity tends to stabilize the liquid phase against vitrification, the magnitude of which depends on the shape of the polydispersity distribution. Further, we report on a separation between the localization lengths of the smallest and largest particles. A diameter-resolved analysis of the intermediate scattering functions reveals that this separation significantly stretches the relaxation patterns, which we quantitatively study by an analysis of the dynamical exponents predicted by the theory. Our observations have strong implications for our understanding of the nature of dynamical heterogeneities and localization lengths in continuously polydisperse systems. These results suggest that the dynamics of the smallest particles is of central importance to understand structural relaxation of continuously size polydisperse fluids, already in the mildly supercooled regime where MCT is usually applicable.

cond-mat.soft↗

arXiv2023

Influence of polydispersity on the relaxation mechanisms of glassy liquids

State-of-the-art techniques for simulating deeply supercooled liquids require a high degree of size polydispersity to be effective. While these techniques have enabled great insight into the microscopic dynamics near the glass transition, the effect of the large polydispersity on the dynamics has remained largely unstudied. Here we show that a particle's size not only has a strong correlation with its mobility, but we also observe that, as the mode-coupling temperature is crossed and the system becomes more deeply supercooled, a dynamic separation between small mobile and larger quiescent particles emerges at timescales corresponding to cage escape. Our results suggest that the cage escape of this population of mobile particles facilitates the later structural relaxation of the quiescent particles. In the deep supercooled regime, we show that particles of different sizes display varying degrees of breakdown of the Stokes-Einstein relation and have different activation energy barriers. Overall, this indicates that it is important to account for particle-size effects when generalizing results to other glass-forming systems.

cond-mat.soft↗

arXiv2023

A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics

Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalised Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown, and accurately predicting or measuring it via e.g. a numerical inverse Laplace transform remains a herculean task. Here we describe a novel method using deep neural networks (DNNs) to measure memory kernels from dynamical data. As proof-of-principle, we focus on the notoriously long-lived memory effects of glassy systems, which have proved a major challenge to existing methods. Specifically, we learn a training set generated with the Mode-Coupling Theory (MCT) of hard spheres. Our DNNs are remarkably robust against noise, in contrast to conventional techniques which require ensemble averaging over many independent trajectories. Finally, we demonstrate that a network trained on data generated from analytic theory (hard-sphere MCT) generalises well to data from simulations of a different system (Brownian Weeks-Chandler-Andersen particles). We provide a general pipeline, KernelLearner, for training networks to extract memory kernels from any non-Markovian system described by a GLE. The success of our DNN method applied to glassy systems suggests deep learning can play an important role in the study of dynamical systems that exhibit memory effects.

cond-mat.dis-nn↗

arXiv2023

Emergent structural correlations in dense liquids

The complete quantitative description of the structure of dense and supercooled liquids remains a notoriously difficult problem in statistical physics. Most studies to date focus solely on two-body structural correlations, and only a handful of papers have sought to consider additional three-body correlations. Here, we go beyond the state of the art by extracting many-body static structure factors from molecular dynamics simulations and by deriving accurate approximations up to the six-body structure factor via density functional theory. We find that supercooling manifestly increases four-body correlations, akin to the two- and three-body case. However, at small wave numbers, we observe that the four-point structure of a liquid drastically changes upon supercooling, both qualitatively and quantitatively, which is not the case in two-point structural correlations. This indicates that theories of the structure or dynamics of dense liquids should incorporate many-body correlations beyond the two-particle level to fully capture their intricate behaviour.

cond-mat.stat-mech↗

arXiv2022

Many-body correlations are non-negligible in both fragile and strong glassformers

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a non-trivial competition between static triplet correlations that work to stabilize the glass state, and dynamic higher-order correlations which destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are in fact non-negligible in both fragile and strong glassformers.

cond-mat.soft↗

arXiv2022

Geometric percolation of colloids in shear flow

We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.

cond-mat.soft↗

arXiv2021

Blunt-end driven re-entrant ordering in quasi two-dimensional dispersions of spherical DNA brushes

We investigate the effects of crowding on the conformations and assembly of confined, highly charged, and thick polyelectrolyte brushes in the osmotic regime. Particle tracking experiments on increasingly dense suspensions of colloids coated with ultra-long double stranded DNA (dsDNA) fragments reveal non-monotonic particle shrinking, aggregation and re-entrant ordering. Theory and simulations show that shrinking is induced by the osmotic pressure exerted by the counterions absorbed in neighbor brushes, while aggregation and re-entrant ordering are the effect of a short-range attraction competing with the electrostatic repulsion. Blunt-end interactions between dsDNA fragments of neighboring brushes are responsible for the attraction and can be tuned by inducing free-end backfolding through the addition of monovalent salt. Our results show that base stacking is a mode parallel to hybridization to steer colloidal assembly, in which attractions can be fine-tuned through salinity and, potentially, grafting density and temperature.

cond-mat.soft↗

arXiv2019

Geometric percolation of hard nanorods: the interplay of spontaneous and externally induced uniaxial particle alignment

We present a numerical study on geometric percolation in liquid dispersions of hard slender colloidal particles subjected to an external orienting field. In the formulation and liquid-state processing of nanocomposite materials, the alignment of particles by external fields such as electric, magnetic or flow fields is practically inevitable, and often works against the emergence of large nanoparticle networks. Using continuum percolation theory in conjunction with Onsager theory, we investigate how the interplay between externally induced alignment and the spontaneous symmetry breaking of the uniaxial nematic phase affects cluster formation within nanoparticle dispersions. It is known that the enhancement of particle alignment by means of a density increase or an external field may result in the breakdown of an already percolating network. As a result, percolation can be limited to a small region of the phase diagram only. Here, we demonstrate that the existence and shape of such a "percolation island" in the phase diagram crucially depends on the connectivity length -- a critical distance defining direct connections between neighbouring particles. Deformations of this percolation island can lead to peculiar re-entrance effects, in which a system-spanning network forms and breaks down multiple times with increasing particle density.

cond-mat.soft↗