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The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations
Paul Hopkins1, Andrea Fortini, Andrew J Archer
1H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.
The Journal of Chemical Physics
|December 22, 2010
Summary
We introduce a new dynamical density functional theory (DDFT) method to study fluid particle evolution. This approach accurately calculates the van Hove function, offering insights into slow dynamics in dense fluids.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Computational Fluid Dynamics
Background:
- Understanding the time evolution of particles in fluids is crucial for explaining macroscopic properties.
- The van Hove distribution function provides insights into particle correlations and dynamics.
- Dynamical Density Functional Theory (DDFT) offers a framework for studying time-dependent density profiles.
Purpose of the Study:
- To develop and validate a novel test particle approach using DDFT for analyzing the correlated time evolution of fluid particles.
- To calculate the van Hove distribution function by modeling the fluid as a binary mixture of self and distinct components.
- To investigate the free energy landscape underlying fluid dynamics and its relation to density.
Main Methods:
- A test particle approach based on dynamical density functional theory (DDFT).
- Treating the self and distinct parts of the van Hove function as components of a binary fluid mixture.
- Calculating time evolution of density profiles for these components.
- Application to a bulk fluid of Brownian hard spheres and comparison with Brownian dynamics simulations.
Main Results:
- Good agreement between the DDFT approach and Brownian dynamics simulations for the van Hove and intermediate scattering functions at low and intermediate densities.
- Validation of the Ramakrishnan-Yussouff approximation for the excess free energy functional.
- Observation of a developing minimum in the free energy landscape at increasing particle density under mean-field approximation.
- Monotonic free energy landscape for an ergodic fluid in an exact treatment of a confined model.
Conclusions:
- The DDFT-based test particle approach is a viable method for studying fluid dynamics and calculating the van Hove function.
- The study reveals insights into the free energy landscape's role in fluid behavior, particularly at high densities.
- Findings suggest implications for understanding slow, glassy, and arrested dynamics in dense systems.
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