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Related Concept Videos

Chirality02:25

Chirality

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Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
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In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
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Chirality in Nature02:30

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Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.
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Molecules with Multiple Chiral Centers02:25

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Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
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The concept of prochirality leads to the nomenclature of the individual faces of a molecule and plays a crucial role in the enantioselective reaction. It is a concept where two or more achiral molecules react to produce chiral products. A typical process is the reaction of an achiral ketone to generate a chiral alcohol. Here, the achiral reactant reacts with an achiral reducing agent, sodium borohydride, to generate an equimolar mixture of the chiral enantiomers of the product. For example, an...
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Stereoisomers02:32

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On the basis of mirror symmetry, stereoisomers of an organic molecule can be further classified into diastereomers and enantiomers. Diastereomers are stereoisomers that are not mirror images of each other. Substituted alkenes, such as the cis and trans isomers of 2-butene, are diastereomers, as these molecules exhibit different spatial orientations of their constituent atoms, are not mirror images of each other, and do not interconvert. Here, the interconversion is suppressed due to...
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A Micropatterning Assay for Measuring Cell Chirality
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A Micropatterning Assay for Measuring Cell Chirality

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Chiral spiral cyclic twins.

Wolfgang Hornfeck1

  • 1Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic.

Acta Crystallographica. Section A, Foundations and Advances
|December 30, 2021
PubMed
Summary

A new formula generates chiral multiply twinned point sets for quasicrystals. This method applies to octagonal, decagonal, and dodecagonal symmetries, advancing aperiodic crystallography research.

Area of Science:

  • Crystallography
  • Materials Science
  • Mathematical Physics

Background:

  • Aperiodic crystals, such as quasicrystals, exhibit long-range orientational order without translational periodicity.
  • Multiply twinned structures present complex geometric arrangements that are challenging to model and generate.
  • Understanding the formation rules for these structures is crucial for their synthesis and application.

Purpose of the Study:

  • To present a novel formula for generating chiral m-fold multiply twinned two-dimensional point sets.
  • To explore the application of this formula for specific cases of even twin modulus m > 6, focusing on m = 8, 10, and 12.
  • To connect the generated point sets to the crystallographic properties of axial quasicrystals.

Main Methods:

  • Development of a formula based on an integer inclination sequence.
Keywords:
chiralcyclic twinsspiral

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  • Application of the formula to generate point sets for m = 8 (octagonal), m = 10 (decagonal), and m = 12 (dodecagonal) symmetries.
  • Analysis of the resulting point sets for chirality and multiply twinned characteristics.

    • Main Results:

    • A general formula for generating chiral m-fold multiply twinned point sets is successfully derived.
    • The formula effectively produces point sets corresponding to octagonal, decagonal, and dodecagonal quasicrystal symmetries.
    • The generated structures demonstrate a clear connection to the aperiodic crystallography of these quasicrystal systems.

    Conclusions:

    • The presented formula provides a systematic method for constructing complex chiral quasicrystal structures.
    • This work elucidates the relationship between mathematical generation rules and the physical properties of aperiodic materials.
    • The findings contribute to the fundamental understanding of quasicrystal formation and symmetry.