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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.
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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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Shape analysis of random polymer networks.

V Blavatska1,2, K Haydukivska1,2, Yu Holovatch1,2,3

  • 1Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine.

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|April 15, 2020
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Summary
This summary is machine-generated.

This study models random polymer networks using Erdös-Rényi graphs. Decreasing network connectedness increases the asymmetry of polymer structures, impacting their size and shape characteristics.

Keywords:
conformational propertiesnumerical simulationspath integrationpolymers

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Area of Science:

  • Polymer physics
  • Materials science
  • Network theory

Background:

  • Polymer networks are crucial in materials science.
  • Understanding their structural properties is key to controlling material behavior.
  • Random graph theory provides a framework for modeling complex networks.

Purpose of the Study:

  • To develop a model for random polymer networks based on Erdös-Rényi random graphs.
  • To investigate the relationship between network connectedness and structural asymmetry.
  • To analyze universal size and shape characteristics of polymer networks.

Main Methods:

  • Modeling polymer networks using Erdös-Rényi random graphs.
  • Representing chemical bonds as vertices and functionalities as degrees.
  • Utilizing Wei's method for numerical analysis.
  • Applying the continuous chain model for analytical solutions.

Main Results:

  • Derived universal, rotationally invariant size and shape characteristics.
  • Quantitatively showed that decreasing connectedness (c) increases structural asymmetry.
  • Observed an increase in asphericity and size ratio with decreased connectedness.

Conclusions:

  • The proposed model effectively captures polymer network behavior.
  • Network connectedness is a critical parameter influencing structural asymmetry.
  • Findings provide insights into the relationship between network topology and macroscopic properties.