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Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions
A Ayadim1, Ph Germain, S Amokrane
1Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est, Créteil, 61 Avenue du Général de Gaulle, FR-94010 Créteil Cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
We reexamine the convolution approximation in mode-coupling theory (MCT) for fluid dynamics. Our findings suggest three-body correlations significantly impact the glass transition and nonergodicity parameter.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Mode-coupling theory (MCT) is a key tool for understanding nonergodic states in classical fluids.
- The convolution approximation is commonly used in MCT for static correlation functions, simplifying dynamic calculations.
Purpose of the Study:
- To reexamine the validity and impact of the convolution approximation in MCT.
- To investigate the role of three-body direct correlations beyond simple models.
Main Methods:
- Utilized accurate static correlation functions derived from fundamental measures functional.
- Extended analysis to include interaction potentials with short-range tails (attractive/repulsive).
Main Results:
- The convolution approximation may underestimate the significance of three-body direct correlations.
- Accurate static correlations reveal a potentially larger role for three-body effects than previously assumed.
Conclusions:
- The accuracy of static correlation functions is crucial for reliable MCT predictions.
- Three-body correlations can substantially influence the predicted glass transition line and nonergodicity parameter in fluids.
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