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Related Concept Videos

Polymer Classification: Architecture01:14

Polymer Classification: Architecture

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...
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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...
Anionic Chain-Growth Polymerization: Mechanism01:04

Anionic Chain-Growth Polymerization: Mechanism

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.
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm magnitude.
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Anionic Chain-Growth Polymerization: Overview01:20

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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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Related Experiment Video

Updated: May 29, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Ideal linear-chain polymers with fixed angular momentum.

Matthew Brunner1, J M Deutsch

  • 1Department of Physics, University of California Santa Cruz, Santa Cruz, California 95064, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

We derived the exact radius of gyration for a linear polymer using statistical mechanics and functional integration. Simulations confirmed these findings, revealing universal scaling in spinning polymers.

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Area of Science:

  • Statistical mechanics
  • Polymer physics
  • Computational physics

Background:

  • Understanding polymer behavior is crucial in various scientific fields.
  • Investigating polymers under angular momentum provides insights into their dynamic properties.

Purpose of the Study:

  • To derive the exact radius of gyration for a linear polymer chain with fixed angular momentum.
  • To compare theoretical results with computational simulations.
  • To explore the anisotropic nature of spinning polymers.

Main Methods:

  • Statistical mechanics analysis of a linear polymer chain.
  • Exact derivation of the radius of gyration using functional integration.
  • Large-scale simulations of noninteracting rigid links at fixed angular momentum.

Main Results:

  • The theoretical derivation of the radius of gyration matches simulation results, accounting for finite-size corrections.
  • Simulations reveal the anisotropic nature of a spinning polymer.
  • Universal scaling of polymer size along the angular momentum direction was observed.

Conclusions:

  • The study provides an exact theoretical framework for polymer size under angular momentum.
  • Simulations validate the theoretical model and highlight anisotropic behavior.
  • Observed universal scaling offers fundamental insights into spinning polymer dynamics.