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Polymers: Molecular Weight Distribution01:10

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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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Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
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Unlike small molecules with definite molecular weights, polymers are a mixture of individual polymer chains of varying lengths, each with a unique molecular weight.  So, the molecular weight of a polymer is expressed as an average value based on the average size of the polymer chains. The two most common forms of averages used for polymers are the number average molecular weight and weight average molecular weight.
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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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Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
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Exploring entropy measures in polymer graphs using logarithmic regression model.

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Graph entropies quantify chemical structure information. This study computes topological indices and entropy measures for polyesters and polycarbonates, revealing relationships between structure and information content.

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Area of Science:

  • Chemical Graph Theory
  • Polymer Science
  • Information Theory

Background:

  • Polymers like polyesters and polycarbonates are crucial materials.
  • Understanding their structural information is key to material science.
  • Topological indices and graph entropies offer quantitative measures.

Purpose of the Study:

  • To compute various topological indices for polyester and polycarbonate structures.
  • To calculate graph entropies for these polymers using Shannon's Entropy.
  • To analyze the correlation between topological indices and entropy measures.

Main Methods:

  • Edge partitioning based on vertex degrees for index calculation.
  • Computation of Zagreb indices, redefined Zagreb indices, atom-bond connectivity index, and geometric-arithmetic index.
  • Application of Shannon's Entropy notion for graph entropy calculation.
  • Regression modeling to establish relationships.

Main Results:

  • Numerical computation of selected topological indices and graph entropies for the studied polymers.
  • Comparison highlighting the interplay between structural descriptors and information content.
  • Identification of significant relationships through regression analysis.

Conclusions:

  • Graph entropies provide valuable insights into polymer structural complexity.
  • Topological indices and entropy measures are correlated.
  • The study establishes a quantitative link between chemical structure and information theory metrics in polymers.