Microscopic origin of liquid viscosity from unstable localized modes (2408.07937v2)

Abstract: Viscosity is the resistance of a liquid to flow, governed by atomic-scale friction between its constituent atoms. While viscosity can be directly computed using the Green-Kubo formalism, its microscopic origin remains poorly understood. In this work, we calculate the viscosity of a $\mathrm{Cu_{50}Zr_{50}}$ metallic liquid and a Kob-Andersen model in a large range of temperatures and compare the results with a theoretical formula based on nonaffine linear response and instantaneous normal mode theory. This analysis reveals that, above approximately the mode-coupling temperature ($T_{\text{MC}}$), unstable localized instantaneous normal modes (ULINMs) control the viscosity, suggesting a microscopic definition of it as diffusive momentum transport facilitated by local structural excitations mediated by ULINMs as precursors. On the other hand, at $ \approx T_{\text{MC}}$, we observe a dynamical crossover below which the viscosity is governed by stable modes. This behavior is compatible with the topological transition that emerges in the potential energy landscape between minima dominated dynamics ($T<T_{\text{MC}}$), corresponding to stable modes, and saddles dominated dynamics ($T>T_{\text{MC}}$), related to unstable ones. Finally, leveraging on the concept of configurational entropy, a quantitative model to connect viscosity with ULINMs is also proposed and validated in both the Arrhenius and non-Arrhenius regimes. In summary, our work provides a microscopic definition of liquid viscosity and highlights the fundamental role of ULINMs as its building blocks, ultimately opening the path to an atomic-scale prediction of viscosity in liquids and glasses.

• The paper identifies unstable localized instantaneous normal modes (ULINMs) as the primary microscopic contributors to liquid viscosity via diffusive momentum transport.
• It proposes a novel quantitative model that links viscosity directly to configurational entropy, validated across different liquid regimes.
• The study provides atomic-scale insights useful for predicting liquid properties and designing materials with tailored transport characteristics.

Analyzing the Microscopic Origins of Liquid Viscosity through Unstable Localized Modes

The paper "Microscopic Origin of Liquid Viscosity from Unstable Localized Modes" offers an innovative exploration of the factors contributing to liquid viscosity, extending our understanding from a simplistic macroscopic viewpoint to a more nuanced atomic-scale perspective. The authors conduct an in-depth investigation into the Cu$_{50}$Zr$_{50}$ metallic liquid and a Kob-Andersen (KA) model, deploying theoretical and computational analysis to elucidate the fundamental mechanisms underlying liquid viscosity.

The research leverages two theoretical approaches: the nonaffine linear response framework and the instantaneous normal mode (INM) theory, culminating in the identification of unstable localized instantaneous normal modes (ULINMs) as the pivotal contributors to viscosity. This identification leads to a novel conception of viscosity as a manifestation of diffusive momentum transport, primarily driven by local structural excitations mediated by ULINMs.

Key Findings and Methodological Insights

1. Theory and Simulation Models:
   • The authors calculate viscosity across various temperatures in two distinct models: a $\mathrm{Cu}_{50}\mathrm{Zr}_{50}$ metallic liquid and a Kob-Andersen binary Lennard-Jones mixture.
   • Comparisons are made with traditional methods such as the Green-Kubo formalism and the Einstein-Stokes relation, demonstrating that these do not fully capture the microscopic mechanisms at play.
2. The Role of Unstable Localized Modes:
   • Analysis indicates that only ULINMs contribute significantly to viscosity. This insight allows the authors to derive a viscosity prediction formula reliant on ULINM parameters, representing a methodological leap in predicting liquid properties at an atomic level.
   • The paper underscores the inability of stable modes and unstable delocalized modes to influence viscosity significantly, thereby providing a refined focus on ULINMs as essential elements.
3. Configurational Entropy and Viscosity Linkage:
   • The authors propose a model correlating viscosity with the configurational entropy of the system. This quantitative model is validated across both Arrhenius and non-Arrhenius regimes, offering a new predictive capability.
   • Their findings suggest a direct relationship between the fraction of ULINMs and the configurational entropy, reinforcing the model's robustness.
4. Empirical Validation:
   • Viscosity measurements derived from ULINM-based theoretical predictions align well with empirical measurements and traditional computational methods (Green-Kubo formula), particularly at higher temperatures.

Implications and Future Directions

The results of this paper not only enhance our theoretical understanding of liquid viscosity but also pave the way for practical applications in designing materials with tailored transport properties. By focusing on a microscopic scale, the paper suggests pathways for developing atomic-scale predictions for complex liquids and glassy materials, which can have substantial implications for material science and related engineering disciplines.

The interaction between viscosity and ULINMs offers potential insights into the broader disciplines of soft matter physics and complex fluid dynamics, offering avenues for exploring the role of microscopic excitations in diverse dynamical processes. Furthermore, these findings can guide future experimental work, where validation of theoretical predictions at the atomic scale remains a critical endeavor.

Future research could further explore the transformation of localized modes near the glass transition and their implications for the mechanical properties of amorphous solids. This research invites further theoretical advancements and the creation of more refined computational models to capture the full spectrum of interactions in fluid viscosity dynamics, potentially leading to new paradigms in understanding liquid behavior at the molecular level.