Related Experiment Video
Updated: Jul 11, 2026
11:27
X-Ray Crystallography to Study the Oligomeric State Transition of the Thermotoga maritima M42 Aminopeptidase TmPep1050
Published on: May 13, 2020
Conformational transitions in single polymer molecules modeled with a complete energy landscape: continuous two-state
1Department of Physics and Atmospheric Science, Dalhousie University, B3H 3J5 Halifax, NS, Canada. hanke@fhi-berlin.mpg.de
The European Physical Journal. E, Soft Matter
|March 23, 2007
Summary
This study introduces a continuous model for polymer chains, extending the Freely Jointed Chain (FJC) model. This new approach accurately predicts polymer behavior, including thermal fluctuations, matching experimental data for Dextran.
Area of Science:
- Polymer Physics
- Statistical Mechanics
- Biophysics
Background:
- The Freely Jointed Chain (FJC) model is a fundamental tool for polymer physics.
- Existing FJC models often use discrete energy states, limiting their accuracy for continuous conformational changes.
- Accurate modeling of polymer elasticity and fluctuations is crucial for understanding biological and synthetic materials.
Purpose of the Study:
- To extend the Freely Jointed Chain (FJC) model by replacing discrete conformational energies with continuous functions.
- To develop a statistical mechanics framework for this continuous model in both Gibbs and Helmholtz ensembles.
- To validate the model's predictive power by fitting experimental force-extension data for polymers like Dextran.
Main Methods:
- Developed a continuous energy function for polymer conformers based on their length.
- Applied statistical mechanics in the Gibbs ensemble to derive a conformational multi-state model.
- Utilized Transfer Matrix methods in the Helmholtz ensemble to calculate statistical properties, including thermal fluctuations.
- Fitted the model to experimental equilibrium force-extension curves.
Main Results:
- The continuous model successfully fits the equilibrium force-extension curve for Dextran.
- The model accurately predicts thermal fluctuations, showing near-perfect agreement with experimental results.
- The developed statistical mechanics framework provides a comprehensive description of polymer behavior.
Conclusions:
- The continuous Freely Jointed Chain (FJC) model offers a more accurate and versatile approach to polymer physics.
- This model enhances the understanding of polymer elasticity and thermal fluctuations.
- The methodology is applicable to various polymers and can be extended to other statistical mechanics problems.
Related Concept Videos
02:13Energy Diagrams, Transition States, and Intermediates
Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products. Peaks on the energy diagram represent stable structures with measurable lifetimes, while other...
02:18Conformations of Ethane and Propane
In an organic molecule, free rotation about the carbon-carbon single bond results in energetically different conformers of the molecule. Due to this rotation, called the internal rotation, ethane has two major conformations — staggered and eclipsed.
Staggered conformation is a low energy and more stable conformation with the C-H bonds on the front carbon placed at 60°dihedral angles relative to the C-H bonds on the back carbon, leading to a reduced torsional strain. In staggered ethane, the...
Staggered conformation is a low energy and more stable conformation with the C-H bonds on the front carbon placed at 60°dihedral angles relative to the C-H bonds on the back carbon, leading to a reduced torsional strain. In staggered ethane, the...
02:20Conformations of Butane
Unlike ethane and propane that have only two major conformations, butane has more than two conformers. The staggered form of butane in which the bulky methyl groups on the two carbons are placed on opposite sides, that is, at a dihedral angle of 180°, is the lowest energy, most stable form — called the anti conformer. This conformation is stabilized due to the absence of steric repulsion between the largely spaced out methyl groups. The other two staggered conformations are degenerate and have...
02:11Conformations of Cyclohexane
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 tetrahedral value,...
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 tetrahedral value,...
00:52¹H NMR of Conformationally Flexible Molecules: Temporal Resolution
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...
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...