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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Conformations of Cyclohexane02:11

Conformations of Cyclohexane

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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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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...
14.6K
Conformations of Cycloalkanes02:29

Conformations of Cycloalkanes

13.9K
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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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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Network Covalent Solids02:18

Network Covalent Solids

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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
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Quantitative Hardness Measurement by Instrumented AFM-indentation
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Quantifying the rigidity of 2D carbides (MXenes).

Tao Hu1, Jinxing Yang2, Wu Li3

  • 1Institute of Materials Science and Devices, Suzhou University of Science and Technology, Suzhou 215009, China and Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China. wang@imr.ac.cn.

Physical Chemistry Chemical Physics : PCCP
|January 7, 2020
PubMed
Summary

MXenes are strong, flexible 2D materials for electronics. Their stiffness and rigidity increase with thickness and surface functionalization, making them ideal for bendable devices.

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Area of Science:

  • Materials Science
  • Nanotechnology
  • Condensed Matter Physics

Background:

  • MXenes are 2D carbides and nitrides with potential in flexible electronics.
  • Their mechanical properties, specifically elasticity and flexibility, are not well understood.

Purpose of the Study:

  • To evaluate the in-plane stiffness and out-of-plane rigidity of typical MXenes at the nanoscale.
  • To understand the influence of functional groups, chemical components, and thickness on MXene mechanical properties.

Main Methods:

  • First-principles calculations were used to investigate four typical MXenes (Ti2CTx, Ti3C2Tx, Nb2CTx, Nb4C3Tx).
  • Analysis focused on in-plane stiffness (C), out-of-plane bending rigidity (D), and Foppl-von Karman numbers (C/D).

Main Results:

  • Both stiffness (C) and bending rigidity (D) significantly increase with MXene thickness and surface functionalization.
  • MXenes exhibit Foppl-von Karman numbers comparable to MoS2 monolayers, indicating a balance of strength and flexibility.
  • The effective thickness of MXenes was found to be two-thirds of their average layer spacing.

Conclusions:

  • MXenes are robust yet flexible materials suitable for flexible electronics.
  • Thickness and surface functionalization are key factors in tuning MXene mechanical performance.
  • This study provides a quantitative basis for understanding MXene nanoscale rigidity.