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Characteristics and Nomenclature of Copolymers

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Copolymers are the products obtained from the polymerization of multiple monomer species. So, in a polymer chain itself, there can be multiple repeating units that come from different monomers. The process of synthesizing a polymer from different monomer species is called copolymerization. When two monomers are involved, the polymer is known as a bipolymer. Polymers with three and four monomers are termed terpolymers and quaterpolymers, respectively. Figure 1 depicts the copolymerization of...
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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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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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Cycloalkanes

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Cycloalkanes are saturated cyclic hydrocarbons with carbon atoms arranged in the form of rings. They have two fewer hydrogen atoms than the corresponding acyclic alkane; therefore, their general formula is CnH2n. The structural formulas of cycloalkanes are simplified using the line-angle representation. The regular polygons are used to represent the cycloalkane rings, with each side representing a carbon-carbon bond.
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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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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Enumerating Tree-Like Graphs and Polymer Topologies with a Given Cycle Rank.

Naveed Ahmed Azam1, Aleksandar Shurbevski1, Hiroshi Nagamochi1

  • 1Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-850, Japan.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm to generate all unique tree-like graphs with a specific cycle rank, including self-loops. This method aids in discovering new chemical compounds and polymer structures.

Keywords:
canonical representationchemical graphcycle rankenumerationpolymer topology

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Area of Science:

  • Graph theory
  • Computational chemistry
  • Materials science

Background:

  • Cycle rank is crucial for classifying and discovering chemical compounds.
  • Existing methods for graph enumeration can be inefficient or generate invalid structures.

Purpose of the Study:

  • To propose an efficient algorithm for enumerating non-isomorphic tree-like graphs with a given cycle rank.
  • To enable the generation of chemical compounds and polymer topologies with specific structural properties.

Main Methods:

  • Developed a canonical representation for rooted graphs.
  • Designed an algorithm to enumerate non-isomorphic graphs based on this representation.
  • Ensured the algorithm handles self-loops and avoids multiple edges.

Main Results:

  • The algorithm generates all required graphs with n vertices in O(n) time and O(n) space.
  • Demonstrated efficiency through experiments enumerating graphs by cycle rank.
  • Successfully applied the method to generate tree-like polymer topologies.

Conclusions:

  • The proposed method offers an efficient and effective way to enumerate tree-like graphs.
  • This approach facilitates the exploration and design of novel chemical compounds and polymer structures.
  • The algorithm's performance and applicability highlight its value in computational chemistry and materials science.