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Polymer Classification: Architecture

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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...

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The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...

Anionic Chain-Growth Polymerization: Mechanism

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The mechanism for anionic chain-growth polymerization involves initiation, propagation, and termination steps. In the initiation step, a nucleophilic anion, such as butyl lithium, initiates the polymerization process by attacking the π bond of the vinylic monomer. As a result, a carbanion, stabilized by the electron‐withdrawing group, is generated. The resulting carbanion acts as a Michael donor in the propagation step and attacks the second vinylic monomer, which acts as a Michael acceptor.

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Ziegler–Natta polymerization is another form of addition or chain‐growth polymerization used for synthesizing linear polymers over branched polymers. The catalyst used for polymerization is the Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, who developed it in 1953. This catalyst is an organometallic complex of titanium tetrachloride and triethyl aluminum, with the active form of the catalyst being an alkyl titanium compound. Using the Ziegler–Natta catalyst, high molecular...

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The polymerization process that involves carbanion as an intermediate is called anionic polymerization. It is also a type of addition or chain-growth polymerization. Anionic polymerization gets initiated by a strong nucleophile such as an organolithium or a Grignard reagent. The most commonly used initiator for anionic polymerization is butyl lithium. Monomers involved in anionic polymerization must possess a vinyl group bonded to one or two electron-withdrawing groups. For instance,...

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Updated: Jul 7, 2026

Covalent Attachment of Single Molecules for AFM-based Force Spectroscopy

Covalent Attachment of Single Molecules for AFM-based Force Spectroscopy

Published on: March 16, 2020

Knot localization in adsorbing polymer rings.

B Marcone¹, E Orlandini, A L Stella

¹Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 1, 2008

Summary

Knotted polymer rings adsorbing onto a surface show localized knots, similar to unknotted rings. This knot localization occurs with adsorption but has a gradual transition.

Area of Science:

Polymer physics
Statistical mechanics
Computational chemistry

Background:

Polymer adsorption is crucial in surface science and nanotechnology.
Understanding the behavior of knotted polymers is essential for various applications.
The influence of topology on polymer adsorption remains an active research area.

Purpose of the Study:

To investigate the adsorption behavior of knotted polymer rings on an attractive surface.
To determine if knot topology affects adsorption critical properties.
To analyze the localization of knots in the adsorbed phase.

Main Methods:

Monte Carlo simulations on a cubic lattice.
Modeling polymers as self-avoiding polygons.
Analysis of adsorption transition temperature, crossover exponent (phi), and metric exponent (nu).

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Measurement of the average length of the knotted portion.

Main Results:

Adsorption transition temperature, crossover exponent (phi), and metric exponent (nu) are unaffected by knot topology.
Adsorbed knots exhibit localization.
Knot localization transition is linked to adsorption but shows a less sharp temperature dependence.
In the adsorbed phase, knot localization is strong and consistent with the flat knot model.

Conclusions:

Polymer knot topology does not alter critical adsorption properties.
Knot localization is a distinct phenomenon triggered by adsorption.
The degree of knot localization shows complex temperature dependence in the adsorbed phase.