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Mesoscopic theory for systems with competing interactions near a confining wall
1Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland.
Physical Review. E
|January 23, 2020
Summary
A new mesoscopic theory describes self-assembling systems near surfaces. It reveals oscillatory decay in volume fraction and correlations, influenced by system boundaries.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Materials Science
Background:
- Self-assembly is crucial for materials science.
- Understanding behavior near surfaces is key for applications.
- Existing theories may lack microscopic grounding.
Purpose of the Study:
- Develop a mesoscopic theory for self-assembling systems near a planar surface.
- Derive Euler-Lagrange equations and boundary conditions from density functional theory.
- Provide a framework for systematic improvement of theoretical accuracy.
Main Methods:
- Utilized density functional theory for the grand thermodynamic potential.
- Derived mesoscopic equations and boundary conditions.
- Employed a generic model (GM) approximation, akin to Landau-Brazovskii theory.
- Solved linearized equations analytically, including for a double-Yukawa potential.
Main Results:
- Developed a mesoscopic theory applicable to semi-infinite systems.
- Expressed all coefficients in terms of interaction potentials and thermodynamic state.
- Observed exponentially damped oscillations in volume fraction and correlation functions perpendicular to the surface.
- Found oscillatory decay parallel to the surface, with increasing correlation length near boundaries.
Conclusions:
- The developed theory offers a microscopic basis for mesoscopic phenomena.
- Boundary effects significantly influence correlation functions.
- The framework allows for quantitative predictions and further theoretical refinement.
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