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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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Molecular Weight of Step-Growth Polymers01:08

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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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Step-Growth Polymerization: Overview01:03

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Step-growth or condensation polymerization is a stepwise reaction of bi or multifunctional monomers to form long-chain polymers. As all the monomers are reactive, most of the monomers are consumed at the early stages of the reaction to form small chains of reactive oligomers, which then combine to form long polymer chains in the late stages. Hence, the reaction has to proceed for a long time to achieve high molecular weight polymers.
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Polymers: Defining Molecular Weight01:01

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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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Radical Chain-Growth Polymerization: Overview01:10

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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 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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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Loop statistics in polymers in crowded environment.

K Haydukivska1, V Blavatska1

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

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|March 3, 2016
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Summary
This summary is machine-generated.

This study investigates polymer loop formation in disordered environments. Structural defects in the polymer chain

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Area of Science:

  • Polymer Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Understanding polymer chain behavior in disordered environments is crucial for materials science.
  • The formation of loops within polymer chains influences their macroscopic properties.
  • Previous studies often simplified environmental disorder or focused on short chains.

Purpose of the Study:

  • To analyze the probability of forming a single loop in a flexible polymer chain within a disordered environment.
  • To investigate the impact of correlated structural defects on loop formation probability.
  • To determine how loop position and length scale with chain properties in d dimensions.

Main Methods:

  • Utilized a continuous chain model for polymer representation.
  • Applied the direct polymer renormalization group scheme for analysis.
  • Calculated critical exponents governing loop formation probabilities.

Main Results:

  • Quantified the scaling of loop formation probability with loop length.
  • Determined the influence of correlated structural defects on loop statistics.
  • Established a power-law relationship for defect correlation (∼r⁻ᵃ).

Conclusions:

  • The presence of structural defects significantly decreases the probability of loop formation in polymer macromolecules.
  • Results provide quantitative insights into polymer self-assembly in complex media.
  • Findings are relevant for designing polymers with specific conformational properties.