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Breaking the rules for topological defects: smectic order on conical substrates.

Ricardo A Mosna¹, Daniel A Beller, Randall D Kamien

¹Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

Crystals on curved surfaces face ordering challenges. This study uses cone-shaped substrates to reveal how localized curvature induces defects like cusps and singularities in two-dimensional smectic order.

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Area of Science:

Materials Science
Condensed Matter Physics
Surface Science

Background:

Ordered phases on curved substrates exhibit complex behavior due to the interplay between ordering and intrinsic curvature.
This is particularly relevant for nanoscale materials where surface imperfections approach lattice constant scales.
Understanding these phenomena is crucial for designing advanced materials and devices.

Purpose of the Study:

To investigate the impact of localized intrinsic curvature on two-dimensional smectic order.
To analyze the formation of frustration, cusps, and singularities in ordered phases on curved surfaces.
To provide insights into the general problem of crystal growth on real-world surfaces.

Main Methods:

Studying two-dimensional smectic order on substrates with localized intrinsic curvature.
Utilizing cone-shaped substrates and their intersections with planes.
Employing simplified "paper and tape" constructions for detailed analysis.

Main Results:

Localized curvature on cone-shaped substrates induces significant structural changes in smectic order.
The study details the formation of cusps and singularities as a direct consequence of substrate geometry.
The "paper and tape" models provide a clear visualization of defect formation mechanisms.

Conclusions:

Localized intrinsic curvature is a key factor driving defect formation in ordered phases on surfaces.
The findings offer a fundamental understanding of crystal behavior on non-ideal substrates.
This research contributes to the broader field of materials science concerning nanoscale ordering on curved surfaces.