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Related Concept Videos

¹H NMR Chemical Shift Equivalence: Homotopic and Heterotopic Protons01:03

¹H NMR Chemical Shift Equivalence: Homotopic and Heterotopic Protons

Protons in identical electronic environments within a molecule are chemically equivalent and have the same chemical shift. The replacement test is a useful tool to identify chemical equivalence and predict NMR spectra. A substituent replaces each of the protons being examined and the resulting molecules are compared. If the same molecule is obtained, the protons are equivalent or homotopic. Replacement of any hydrogens in ethane by chlorine yields chloroethane because all six protons are...
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Replacing each alpha-hydrogen in chloroethane by bromine (or a different functional group) yields a pair of enantiomers. Such protons are called prochiral or enantiotopic and are related by a mirror plane. Enantiotopic protons are chemically equivalent in an achiral environment. Because most proton NMR spectra are recorded using achiral solvents, enantiotopic hydrogens yield a single signal.
In chiral compounds such as 2-butanol, replacing the methylene hydrogens at C3 produces a pair of...
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Bioequivalence studies are crucial in evaluating whether new drugs can match an approved one regarding pharmacological effects and clinical performance. These studies test if drugs, despite different dosage forms, share identical plasma concentration-time profiles. Three types of equivalence are central to these studies: chemical, pharmaceutical, and therapeutic. Chemical equivalence indicates that two or more drug products contain identical active ingredients in equal amounts. Pharmaceutical...
¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

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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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.

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Calibration-free In Vitro Quantification of Protein Homo-oligomerization Using Commercial Instrumentation and Free, Open Source Brightness Analysis Software
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Ensemble inequivalence in single-molecule experiments.

M Süzen1, M Sega, C Holm

  • 1Frankfurt Institute for Advanced Studies, Goethe-University, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

Statistical mechanics in bulk systems ensures ensemble equivalence. However, for single linear molecules, thermodynamic ensemble equivalence is not guaranteed, especially in low force regimes, but transitions to equivalence with increasing chain length and force.

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Area of Science:

  • Statistical Mechanics
  • Polymer Physics
  • Thermodynamics

Background:

  • In bulk systems, thermodynamic quantities yield consistent expectation values in the thermodynamic limit, irrespective of the chosen statistical ensemble.
  • Single linear molecules, analogous to statistical systems, approach their thermodynamic limit with increasing chain length.
  • The equivalence of statistical ensembles for such systems is complex, with existing literature presenting conflicting findings.

Purpose of the Study:

  • To investigate the ensemble equivalence for single linear molecules, specifically addressing the relationship between the isotensional (Gibbs) and isometric (Helmholtz) ensembles.
  • To analyze the scaling properties of the ensemble difference as a function of chain length (degree of polymerization).
  • To characterize the transition from ensemble inequivalence to equivalence under varying stretching conditions.

Main Methods:

  • Studied two distinct linear chain models.
  • Analyzed the scaling behavior of the difference between Gibbs and Helmholtz ensembles.
  • Examined the transition from low-stretching to high-stretching regimes as a function of the degree of polymerization.

Main Results:

  • Demonstrated that ensemble equivalence is not achieved for macroscopic chains in the low force regime.
  • Characterized the transition from ensemble inequivalence to equivalence.
  • The degree of polymerization significantly influences ensemble equivalence, particularly in relation to applied force.

Conclusions:

  • Ensemble equivalence for single linear molecules is dependent on the applied force and chain length.
  • Macroscopic chains do not exhibit ensemble equivalence at low forces, highlighting limitations in direct application of bulk system principles.
  • A transition regime exists where ensemble equivalence becomes achievable with increasing force and chain length.