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Related Concept Videos

Stability of Substituted Cyclohexanes02:30

Stability of Substituted Cyclohexanes

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This lesson discusses the stability of substituted cyclohexanes with a focus on energies of various conformers and the effect of 1,3-diaxial interactions.
The two chair conformations of cyclohexanes undergo rapid interconversion at room temperature. Both forms have identical energies and stabilities, each comprising equal amounts of the equilibrium mixture. Replacing a hydrogen atom with a functional group makes the two conformations energetically non-equivalent.
For example, in...
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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...
1.0K
Conformations of Cyclohexane02:11

Conformations of Cyclohexane

14.2K
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...
14.2K
Disubstituted Cyclohexanes: cis-trans Isomerism02:37

Disubstituted Cyclohexanes: cis-trans Isomerism

13.3K
Depending upon the different spatial orientation of the substituents, the disubstituted cycloalkanes exhibit two types of stereoisomers. The cis isomers have the substituents on the same side of the ring, whereas the trans isomers have the substituents on the opposite sides. These stereoisomers exhibit different physical properties and cannot be interconverted without breaking the carbon-carbon bonds.
In cyclohexane, the substituents can occupy different positions generating distinct isomers....
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Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

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Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
8.3K
Chair Conformation of Cyclohexane02:02

Chair Conformation of Cyclohexane

16.8K
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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Interactive Molecular Model Assembly with 3D Printing
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Criticality and conformality in the random dimer model.

S Caracciolo1, R Fabbricatore1, M Gherardi1

  • 1Dipartimento di Fisica dell'Università di Milano, and INFN, sez. di Milano, Via Celoria 16, 20100 Milan, Italy.

Physical Review. E
|May 19, 2021
PubMed
Summary
This summary is machine-generated.

Localized perturbations in 2D random dimer models create extensive excitations. These excitations exhibit conformal invariance, with properties depending on lattice bipartiteness, linking to spin glass domain walls or self-avoiding walks.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Critical systems exhibit long-range correlations where local perturbations have distant effects.
  • The random dimer problem is a fundamental model in statistical mechanics, relevant to understanding covering properties and phase transitions.

Purpose of the Study:

  • To investigate the impact of localized perturbations on the solution of the 2D random dimer problem.
  • To characterize the nature and statistical properties of induced excitations.
  • To explore the relationship between these excitations and established models like spin glasses and random walks.

Main Methods:

  • Accurate numerical analysis was employed to study the random dimer problem.
  • Calculation of fractal dimensions and scaling exponents for the induced excitations.
  • Comparison of excitation properties on bipartite and nonbipartite lattices.

Main Results:

  • Local perturbations can induce extensive excitations with finite probability.
  • Excitations on nonbipartite lattices share statistical properties with spin glass domain walls.
  • Excitations on bipartite lattices resemble loop-erased self-avoiding random walks.
  • Evidence of conformal invariance was found, consistent with Schramm-Loewner Evolution (SLE) with a parameter κ dependent on lattice bipartiteness.

Conclusions:

  • The study reveals universal behaviors in excitations of the 2D random dimer problem, influenced by lattice structure.
  • Conformal invariance and connections to SLE suggest deep underlying mathematical structures governing these systems.
  • Findings provide insights into critical phenomena and the nature of disorder in physical systems.