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Predicting Products: SN1 vs. SN202:27

Predicting Products: SN1 vs. SN2

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Nucleophilic substitution reactions of alkyl halides can proceed via an SN1 or an SN2 mechanism. While in SN2 reactions, the nucleophile attacks the substrate simultaneously as the leaving group departs, in SN1 reactions, the substrate first dissociates to give the carbocation intermediate. Various factors such as the structure of the substrate, the strength of the nucleophile, and the nature of the solvent promote one mechanism over the other.
With increased substitution on the alkyl halide,...
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Resonance02:52

Resonance

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The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O bonds.
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Internal Energy02:00

Internal Energy

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The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with initial internal energy, Uinitial, undergoes a change in energy (transfer of work or heat), and the final internal energy of the system is Ufinal. Change in internal energy equals the difference between Ufinal and Uinitial.
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Internal Energy01:29

Internal Energy

7.0K
The internal energy of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules or entities in the system. The kinetic energy of an individual molecule includes contributions due to its rotation and vibration, as well as its translational energy. The potential energy is associated only with the interactions between one molecule and the other molecules of the system. Neither the system's location nor its motion is of any consequence as far as the internal...
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Internal Receptors01:31

Internal Receptors

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Many cellular signals are hydrophilic and therefore cannot pass through the plasma membrane. However, small or hydrophobic signaling molecules can cross the hydrophobic core of the plasma membrane and bind to internal, or intracellular, receptors that reside within the cell. Many mammalian steroid hormones use this mechanism of cell signaling, as does nitric oxide (NO) gas.
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1° Amines to Diazonium or Aryldiazonium Salts: Diazotization with NaNO2 Overview01:26

1° Amines to Diazonium or Aryldiazonium Salts: Diazotization with NaNO2 Overview

3.9K
Nitrous acid and nitric acids are two types of acids containing nitrogen, among which nitrous acid is weaker than nitric acid. Nitrous acid with a pKa value of 3.37 ionizes in water to give a nitrite ion and the hydronium ion.
The nitrous acid is unstable. Hence, it is formed in situ from a solution of sodium nitrite and cold aqueous acids such as hydrochloric or sulfuric acid. In an acidic solution, the –OH group of nitrous acid undergoes protonation to give oxonium ion, followed by...
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Related Experiment Video

Updated: Feb 2, 2026

Monitoring Dendritic Cell Migration using 19F / 1H Magnetic Resonance Imaging
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Utilization of 2:1 Internal Resonance in Microsystems.

Navid Noori1, Atabak Sarrafan2, Farid Golnaraghi3

  • 1School of Mechatronic Systems Engineering, Simon Fraser University, Surrey, BC V5A 1S6, Canada. nnoori@sfu.ca.

Micromachines
|November 15, 2018
PubMed
Summary
This summary is machine-generated.

This study explores nonlinear mode coupling in micro-beam resonators using a 2:1 internal resonance. Researchers found that the low-frequency mode can be autoparametrically excited, with damping affecting system performance.

Keywords:
2:1 internal resonanceenergy transfermicromachined resonatorsnonlinear modal interactionsperturbation method

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Area of Science:

  • Nonlinear Dynamics
  • Micro-Electro-Mechanical Systems (MEMS)
  • Resonant Systems

Background:

  • Nonlinear mode coupling is crucial in micro-resonator design.
  • Internal resonances can lead to complex system behaviors.
  • Understanding these phenomena is key for advanced MEMS applications.

Purpose of the Study:

  • To investigate nonlinear mode coupling at 2:1 internal resonance.
  • To analyze the autoparametric excitation of low-frequency modes.
  • To examine the influence of damping on micro-resonator performance.

Main Methods:

  • Analytical and experimental investigation.
  • Development of equations of motion using Lagrange's energy method.
  • Application of a two-variable expansion perturbation method.

Main Results:

  • A modified micro T-beam structure was proposed and analyzed.
  • Autoparametric excitation of the low-frequency mode was observed above a specific excitation amplitude threshold.
  • The impact of damping on the system's dynamic behavior was quantified.

Conclusions:

  • The study demonstrates controllable nonlinear dynamics in micro-resonators via 2:1 internal resonance.
  • Autoparametric excitation offers a mechanism for energy transfer and amplification.
  • Damping plays a significant role in modulating the observed nonlinear phenomena.