Related Experiment Video
Updated: Dec 29, 2025
08:00
DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
Published on: October 25, 2017
7.2K
Statistical ensemble inequivalence for flexible polymers under confinement in various geometries
Sandipan Dutta1, Panayotis Benetatos2
1Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Korea.
Soft Matter
|February 5, 2020
Summary
Confinement of single polymers, like Gaussian chains, to surfaces causes statistical ensemble inequivalence. This effect, driven by fluctuations, is observed across various geometries and is crucial for interpreting single-molecule experiments.
Area of Science:
- Statistical mechanics
- Polymer physics
- Soft matter
Background:
- Statistical ensemble inequivalence is a known issue for single polymers.
- Previous work showed ensemble inequivalence for Gaussian chains confined to a half-space.
- This study extends the analysis to more complex confining geometries.
Purpose of the Study:
- To investigate ensemble inequivalence in polymers under various surface confinements.
- To analyze the pressure-volume equation of state in different confined geometries.
- To understand the role of fluctuations in ensemble inequivalence.
Main Methods:
- Analysis of polymer chains in Helmholtz and Gibbs ensembles.
- Examination of chains in rectangular, spherical, and cylindrical confinement.
- Study of directed polymers and tethered chains in confined spaces.
Main Results:
- Confinement generally leads to significant statistical ensemble inequivalence.
- Ensemble equivalence is recovered in the limit of squashing confinement.
- Strong persistent fluctuations are identified as the cause of inequivalence.
Conclusions:
- Confinement effects on polymer ensembles are geometry-dependent.
- Understanding ensemble inequivalence is vital for interpreting single-molecule experiments.
- The findings offer insights into phenomena like polymer caging.
Related Concept Videos
01:10Polymers: Molecular Weight Distribution
4.5K
For any given polymer, the weight average molecular weight (Mw) is higher than, if not equal to, the number average molecular weight (Mn). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.
4.5K
01:26Polymer Classification: Stereospecificity
3.1K
Polymerization generates chiral centers along the entire backbone of a polymer chain. Accordingly, the stereochemistry of the substituent group has a significant effect on polymer properties. Polymers formed from monosubstituted alkene monomers feature chiral carbons at every alternate position in the polymer backbone. Relative to the predominant orientation of substituents at the adjacent chiral carbons, the polymer can exist in three different configurations: isotactic, syndiotactic, and...
3.1K
01:08Molecular Weight of Step-Growth Polymers
2.7K
Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
2.7K
02:11Conformations of Cyclohexane
15.0K
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...
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...
15.0K
01:01Polymers: Defining Molecular Weight
3.6K
Unlike small molecules with definite molecular weights, polymers are a mixture of individual polymer chains of varying lengths, each with a unique molecular weight. So, the molecular weight of a polymer is expressed as an average value based on the average size of the polymer chains. The two most common forms of averages used for polymers are the number average molecular weight and weight average molecular weight.
The number average molecular weight (Mn) is the summation of the number...
The number average molecular weight (Mn) is the summation of the number...
3.6K
01:14Polymer Classification: Architecture
3.6K
Polymers are classified as linear or branched on the basis of their chain architecture. The polymer chains in linear polymers have a long chain-like structure with minimal to no branching at all. Even if a polymer features large substituent groups on the monomer, which appear as branches to the skeleton, it is not considered a branched polymer. A branched polymer contains secondary polymer chains that arise from the main polymer chain. The branching occurs when the polymer growth shifts from...
3.6K