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Updated: Aug 11, 2026
10:37
Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Markov-type evolution of materials into a polar state
1Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, (Switzerland). juerg.hulliger@iac.unibe.ch
Chemistry (Weinheim an Der Bergstrasse, Germany)
|October 4, 2002
Summary
Materials can develop macroscopic polarity through a stochastic growth process. Differences in how polar building blocks attach to surfaces drive this evolution, observed in crystals and biological tissues.
Area of Science:
- Materials Science
- Physics
- Biophysics
Background:
- Assembling polar building blocks can lead to metastable states with macroscopic polarity.
- Stochastic polarity formation is influenced by attachment probabilities of building blocks to a surface.
- Polar building blocks exhibit asymmetric attachment probabilities ('tip-first' vs. 'back-first').
Purpose of the Study:
- To explain the formation of macroscopic polarity in materials through a unified stochastic growth model.
- To demonstrate how differences in attachment probabilities drive the evolution of vectorial properties.
- To illustrate growth-induced polarity with examples from various scientific domains.
Main Methods:
- Modeling material assembly as a Markov-chain process of unidirectional growth.
- Describing stochastic polarity formation using attachment probabilities.
- Analyzing the gain in configurational entropy driving vectorial property evolution.
Main Results:
- A difference in attachment probabilities fundamentally drives the evolution of macroscopic polarity.
- Growth upon centrosymmetric seeds can yield twinned crystals with pyroelectric effects.
- A Markov-chain mechanism explains polarity formation in connective tissues via collagen self-assembly.
Conclusions:
- A unified stochastic growth model provides a general concept for forming polar materials.
- Macroscopic polarity arises from the inherent asymmetry in polar building block attachment.
- The principles apply across mechanical, crystalline, and biological systems.
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