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Markov-type evolution of materials into a polar state
1Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, 3012 Berne, Switzerland. juerg.hulliger@iac.unibe.ch
Chemistry (Weinheim an Der Bergstrasse, Germany)
|February 4, 2003
Summary
Materials can develop macroscopic polarity through a stochastic growth process. Differences in how polar building blocks attach to surfaces drive this self-assembly, creating ordered structures.
Area of Science:
- Materials Science
- Statistical Physics
- Biophysics
Background:
- Assembling polar building blocks can lead to metastable states with macroscopic polarity.
- Stochastic polarity formation is governed by attachment probabilities of building blocks to a surface.
Purpose of the Study:
- To describe the stochastic process of polarity formation in materials.
- To unify the concept of growth-induced macroscopic polarity across different scientific domains.
Main Methods:
- Utilizing a Markov-chain process to model unidirectional growth.
- Analyzing attachment probabilities of polar building blocks based on their symmetry.
- Developing a unified stochastic growth model.
Main Results:
- A difference in attachment probabilities (tip-first vs. back-first) drives vectorial property evolution via configurational entropy.
- Growth-induced macroscopic polarity is observed in mechanical, crystalline, and biological systems.
- Examples include twinned crystals with pyroelectric effects and self-assembly of collagen fibril segments.
Conclusions:
- A unified stochastic growth model provides a general concept for forming materials with polar properties.
- The Markov-chain mechanism explains polarity formation in biological self-assembly, such as in connective tissues.