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Related Concept Videos

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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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Chain-growth or addition polymerization is successive addition reactions of monomers with a polymer chain. In radical chain-growth polymerization, the reaction proceeds via a free-radical intermediate. The free radical is formed from radical initiators, which spontaneously generate free radicals by homolytic fission. Organic peroxides (such as dibenzoyl peroxide, as shown in Figure 1) or azo compounds are popular radical initiators. A low concentration ratio of radical initiator to monomer is...
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The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this...
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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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Olefin Metathesis Polymerization: Ring-Opening Metathesis Polymerization (ROMP)01:16

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Ring-opening metathesis polymerization or ROMP involves strained cycloalkenes as starting materials. The mechanism of ROMP proceeds by reacting cycloalkene with Grubbs catalyst to give metallacyclobutane intermediate which undergoes a ring-opening reaction to form new carbene. The new carbene reacts with another molecule of cycloalkene. Repetition of these steps leads to the formation of an unsaturated open-chain polymer product. All these steps are reversible, however, relieving the ring...
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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...
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Random Knotting in Fractal Ring Polymers.

Phillip M Rauscher1, Juan J de Pablo1,2

  • 1Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.

Macromolecules
|October 3, 2022
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Summary
This summary is machine-generated.

We established a connection between ring polymer topology and self-similarity. The probability of a trivial knot decays exponentially with chain size, but knotting length dependence on fractal dimension is complex.

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Area of Science:

  • Polymer Physics
  • Statistical Mechanics
  • Theoretical Chemistry

Background:

  • Ring polymer systems exhibit topological effects and self-similarity.
  • The relationship between these phenomena is not well understood.

Purpose of the Study:

  • To establish a connection between topological effects and self-similarity in ring polymers.
  • To study the random knotting probability for ring polymers with varying fractal dimensions.

Main Methods:

  • Theoretical modeling
  • Computer simulations
  • Scaling arguments
  • Analytical calculations

Main Results:

  • The probability of a trivial knot decays exponentially with chain size (N): P₀(N) ∝ exp(-N/N₀).
  • The knotting length (N₀) shows a complex double-exponential dependence on fractal dimension (d), not explained by simple scaling.
  • Findings are consistent in 2D and 3D systems.

Conclusions:

  • A clear link between fractal dimension and knotting probability in ring polymers has been formulated.
  • Simple scaling theories are insufficient to describe the observed dependencies.
  • The study provides a foundation for understanding complex polymer topologies.