Related Experiment Video
Updated: Nov 27, 2025

Optical Tweezers to Study RNA-Protein Interactions in Translation Regulation
Published on: February 12, 2022
A Legendre-Fenchel Transform for Molecular Stretching Energies
Eivind Bering1, Dick Bedeaux2, Signe Kjelstrup2
1PoreLab, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway.
Abstract:
Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill's sense.
More Related Videos
07:11ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Related Concept Videos
IR Spectroscopy: Molecular Vibration Overview
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
According to Hooke's law, the vibrational frequency is directly proportional to...
IR Frequency Region: X–H Stretching
IR Frequency Region: Alkene and Carbonyl Stretching
Stretching frequencies are affected by several factors, such as resonance, inductive effects, ring strain, dipole moment, and hydrogen bonding. Consequently, the stretching frequency of the carbonyl double bond...
IR Frequency Region: Alkyne and Nitrile Stretching
Comparing the stretching vibrational frequency of C≡C triple bonds with that of double and single bonds, it is evident that C≡C triple bonds exhibit a higher stretching frequency than C=C double and C–C single bonds. Similarly, the C≡N triple bond...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations