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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

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Condensation transition in polydisperse hard rods.

M R Evans¹, S N Majumdar, I Pagonabarraga

¹SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom. m.evans@ed.ac.uk

The Journal of Chemical Physics

|January 19, 2010

Summary

This study introduces a mass transport model for polydisperse hard rods, revealing a factorized steady state distribution that minimizes free energy. The model predicts a condensation transition for particles with variable sizes (p>1).

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Area of Science:

Statistical Mechanics
Soft Matter Physics
Thermodynamics

Background:

Studying polydispersity in physical systems is crucial for understanding complex fluid behavior.
Previous work focused on hard sphere fluids, but lacked a dynamic mass transport perspective.
The interplay between particle size distribution and phase transitions requires further investigation.

Purpose of the Study:

To develop and analyze a mass transport model for polydisperse hard rods with variable diameters.
To identify the steady-state size distribution and its relation to free energy minimization.
To investigate the emergence of phase transitions, specifically condensation, in this system.

Main Methods:

Stochastic mass transport simulations on a ring.
Analytical derivation of the steady-state distribution.
Application of density functional theory (DFT).

Main Results:

A factorized steady-state distribution was found, minimizing free energy for polydisperse hard rods.
The model accurately describes systems where particle size scales as v(i)^(1/p).
A real-space condensation transition occurs for p>1, forming macroscopic aggregates coexisting with a fluid phase.

Conclusions:

The study bridges stochastic mass transport and polydispersity in hard sphere fluids.
The derived distribution represents an optimal polydispersity for minimizing free energy.
The findings provide insights into condensation phenomena in systems with variable particle sizes.