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Related Concept Videos

Chair Conformation of Cyclohexane02:02

Chair Conformation of Cyclohexane

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The chair conformation is the most stable form of cyclohexane due to the absence of angle and torsional strain. The absence of angle strain is a result of cyclohexane’s bond angle being very close to the ideal tetrahedral bond angle of 109.5° in its chair conformer. Similarly, the torsional strain is also absent owing to the perfectly staggered arrangement of bonds.
The hydrogen atoms linked to carbons are arranged in two different axial and equatorial orientations to achieve this...
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Stereoisomerism of Cyclic Compounds02:33

Stereoisomerism of Cyclic Compounds

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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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Conformations of Cycloalkanes02:29

Conformations of Cycloalkanes

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Adolf von Baeyer attempted to explain the instabilities of small and large cycloalkane rings using the concept of angle strain — the strain caused by the deviation of bond angles from the ideal 109.5° tetrahedral value for sp3  hybridized carbons. However, while cyclopropane and cyclobutane are strained, as expected from their highly compressed bond angles, cyclopentane is more strained than predicted, and cyclohexane is virtually strain-free. Hence, Baeyer’s theory that...
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¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

¹H NMR of Conformationally Flexible Molecules: Temporal Resolution

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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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Conformations of Cyclohexane02:11

Conformations of Cyclohexane

16.3K
Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal...
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Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Configurational entropy of randomly double-folding ring polymers.

Pieter H W van der Hoek1, Angelo Rosa1, Elham Ghobadpour2

  • 1SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.

The Journal of Chemical Physics
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Summary
This summary is machine-generated.

We calculated the exact number of ways a ring polymer can form tree-like structures. This finding helps understand genome folding and polymer physics, crucial for topological polymer science.

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Area of Science:

  • Polymer Physics
  • Computational Biology
  • Statistical Mechanics

Background:

  • Genome-like polymers, when topologically constrained, frequently adopt tree-like configurations through double-folding.
  • Understanding these complex folding patterns is essential for deciphering genome organization and polymer behavior under topological constraints.

Purpose of the Study:

  • To determine the precise number of possible tightly double-folded configurations for a ring polymer under ideal conditions.
  • To develop a theoretical framework for quantifying the topological complexity of polymer folding.

Main Methods:

  • Introduction of a novel coding scheme to represent how a ring polymer wraps a branching tree structure.
  • Application of a variant of Bertrand's ballot theorem to enumerate the number of admissible wrapping codes.
  • Validation using Monte Carlo simulations of an elastic lattice model for double-folded rings.

Main Results:

  • Derived an exact expression for the number of admissible configurations (ring entropy) for tightly double-folded ring polymers.
  • Monte Carlo simulations confirmed the theoretical predictions for branch-node and tree size statistics.
  • Demonstrated excellent agreement between simulation data and exact theoretical expressions.

Conclusions:

  • The study provides an exact mathematical solution for the enumeration of topologically constrained ring polymer configurations.
  • The findings offer a fundamental contribution to understanding polymer folding, with implications for genome organization and topological polymer physics.