Thermodynamics and Kinetics of Multi-component Mixtures

by Filipe da Cunha Thewes
Doctoral thesis
Date of Examination:2024-09-03
Date of issue:2025-06-27
Advisor:Prof. Dr. Peter Sollich
Referee:Prof. Dr. Peter Sollich
Referee:Prof. Dr. Matthias Krüger
Persistent Address: http://dx.doi.org/10.53846/goediss-11347

 

 

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Abstract

English

This thesis investigates the interplay between thermodynamics and kinetics in multi-component mixtures. The complex free energy landscape of these systems usually leads to phase separation in equilibrium. However, crowding effects hinder interspecies diffusion, slowing the system's approach to such states. This work explores the competition between the thermodynamic driving forces and the kinetically determined timescales. The first part focuses on the thermodynamic aspects of mixtures. Chapter 2 establishes a framework to analyse phase separation via linear instabilities in mixtures with random interactions. We explore how composition and non-random interactions affect these instabilities. The framework reveals that a small number of dominant species can control the thermodynamic instability. Chapter 3 extends the analysis by demonstrating how elastic interactions lead to phase-separated domains with a characteristic length-scale. Chapter 4 tackles the problem of designing stable phases consistently with Gibbs' phase rule. We show that designing interactions alone is insufficient to achieve more coexisting phases than predicted by the rule, highlighting the importance of interface design. A graph-theoretical approach yields stability criteria based on surface tensions. The second part explores the kinetic aspects. Chapter 5 develops a systematic approach to kinetics using a generalized model B. We derive an expression for the mobility matrix, revealing two modes of motion: collective and interdiffusive. This is supported by simulations and compared to an independent expression for the mobility derived from the hydrodynamic description of a lattice gas. Chapter 6 explores the impact of these kinetic considerations on various processes, showcasing the intricate interplay between thermodynamics and kinetics in multi-component mixtures. The final chapter of the thesis discusses broader applications of our results and perspectives for future work.
Keywords: thermodynamics; kinetics; multicomponent; statistical physics
 
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