Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures

Molecular friction is a crucial factor in fluid dynamics, influencing diffusion, dissipation, and the approach to equilibrium. The friction experienced by molecules in liquids exhibits a delayed response (non-Markovian dynamics), impacting processes like macromolecular transition rates and viscoelastic behavior. However, the origin of friction from the conservative forces between molecules and atoms remains a significant challenge. Stokes's friction law links friction to macroscopic shear viscosity, scaling remarkably well to single molecules. While Stokes's hydrodynamic treatment addresses slow oscillatory motions, the transition from the atomistic, frictionless picture (governed by Newton's laws) to the macroscopic, frictional picture remains unclear. Macroscopic friction has been linked to microscopic chaos and the Lyapunov spectrum, but the connection to dynamic friction ζ(ω) is still an open issue. First-principle theories are hindered by the strong interactions in liquids. While frequency-resolved friction data could bridge the atomistic and hydrodynamic regimes, obtaining accurate high-frequency data has been limited by technical challenges. This research aims to overcome these limitations to understand how friction emerges from the atomistic interactions.

Previous studies have explored non-Markovian dynamics in liquids, observing memory effects on various timescales. The Stokes-Einstein relation, linking single-molecule friction to macroscopic viscosity, has shown remarkable success, particularly in the low-frequency regime. However, the high-frequency behavior and the atomistic origins of friction remain poorly understood. Attempts to connect macroscopic transport coefficients to microscopic chaos through the Lyapunov spectrum have yielded limited success in explaining dynamic friction. Theoretical efforts, notably the works of Zwanzig and Mori, have provided formal connections between many-particle Liouville operators and dissipation spectra, but their application requires uncontrolled approximations. Studies on hard-sphere fluids have yielded insights into Markovian friction, but lack the flexibility to address the transition to a frictionless regime. Recent advancements in data analysis techniques have improved the acquisition of high-frequency information, but limitations still persist.

High-precision molecular dynamics simulations were conducted for three liquids: water, a dense Lennard-Jones (LJ) fluid, and a supercooled binary mixture. The simulations computed the mean-square displacement (MSD) to estimate dynamic friction ζ(ω) and the memory function γ(t). Two complementary routes were used to analyze the data: (1) a complex analysis approach based on the Fourier-Laplace transform of correlation functions, employing an adapted Filon algorithm for sparse time grids; and (2) a time-domain approach using stable deconvolution techniques for uniform time grids. These independent methods allowed for cross-validation. The velocity autocorrelation function (VACF) was obtained from numerical differentiation of the MSD. Theoretical considerations based on sum rules and the short-time behavior of the VACF were used to rationalize the observed high-frequency behavior of the friction. An analytically solvable model was used to support the theoretical findings. Control simulations of a single particle in a fixed cage were performed to investigate the physical mechanism behind the onset of friction. Frequency-dependent viscosity η(ω) was calculated from additional simulations to test the generalized Stokes-Einstein relation (GSER). The GSER links microscopic friction to macroscopic viscoelastic properties.

The simulations revealed that friction in all three liquids exhibits an exponentially fast suppression beyond a liquid-characteristic frequency ωc. This finding contrasts with typical algebraic peaks and demonstrates that liquids exhibit purely elastic behavior above ωc. The onset of friction is non-local in time; it cannot be predicted from the instantaneous behavior of molecular trajectories. The GSER, which links microscopic friction to macroscopic viscoelastic response, was found to be invalid for the Newtonian fluid but serves as a qualitative (water) or quantitative (supercooled liquid) description. Analysis of the VACF revealed that the short-time decay is parabolic, while long-time behavior showed liquid-specific features including power-law decays. The control simulations, with a single particle in a fixed cage, demonstrated that high-frequency friction is primarily driven by irreversible momentum transfer to neighboring molecules. The memory functions γ(t), representing the autocorrelation of Brownian forces, displayed complex behavior including a short-time parabolic decay, oscillatory behavior, and power-law tails. The long-lived nature and complexity of γ(t) precluded simple models. The study offers a robust and ansatz-free method for extracting dynamic friction and memory functions from simulation and experimental data. The high-frequency viscoelastic response of the liquids displayed an exponential decay, consistent with the behavior of an elastic solid.

The study's findings significantly advance our understanding of molecular friction in liquids. The rapid onset of friction at a characteristic frequency, driven by irreversible momentum transfer, resolves a long-standing challenge in fluid physics. The non-local nature of friction underscores the limitations of approaches that rely on local properties of molecular trajectories. The testing and validation (or invalidation) of the GSER across different liquids highlights the complex interplay between microscopic and macroscopic behavior. The significant differences in the high-frequency behavior and validity of GSER among the three liquids indicates the limitation of using GSER to describe highly viscous liquid. The results provide a framework for understanding vitrification mechanisms and the dynamics of soft materials, with implications for diverse applications, ranging from nanoscale processes to the behavior of biological systems. The study also extends our understanding of the Stokes-Einstein relation and its validity in different regimes. The observed deviation of the GSER emphasizes the complexities of linking microscopic and macroscopic response in liquids.

This research demonstrates the rapid onset of molecular friction in liquids at a characteristic frequency, driven by irreversible momentum transfer. The generalized Stokes-Einstein relation was found to hold only under certain conditions. The study provides a framework for understanding the interplay between atomistic and hydrodynamic behavior in liquids. Future research could explore the relationship between friction and the Lyapunov spectrum and investigate the frequency-dependent GSER violations near the glass transition.

While the simulations used a large number of particles, finite-size effects might still influence the results. The choice of interatomic potentials could influence the detailed dynamics, although the selection of prototypical liquids allows for generalizations. The analysis techniques, while robust, may be sensitive to noise in the data. The findings primarily focus on three specific liquids; further studies across a wider range of liquids are needed for complete generalization.