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Related Concept Videos

Molecular Weight of Step-Growth Polymers01:08

Molecular Weight of Step-Growth Polymers

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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.
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
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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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Polymers: Defining Molecular Weight01:01

Polymers: Defining Molecular Weight

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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.
The number average molecular weight (Mn) is the summation of the number...
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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.
Many natural and synthetic polymers are produced by...
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Ziegler–Natta Chain-Growth Polymerization: Overview01:17

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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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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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Updated: Sep 26, 2025

Characterization of Synthetic Polymers via Matrix Assisted Laser Desorption Ionization Time of Flight MALDI-TOF Mass Spectrometry
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Molecular Weight Distribution Control for Polymerization Processes Based on the Moment-Generating Function.

Jianhua Zhang1, Jinzhu Pu2, Mifeng Ren3

  • 1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China.

Entropy (Basel, Switzerland)
|April 23, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel control algorithm to precisely regulate polymer molecular weight distribution using moment-generating functions and B-spline models. The method effectively controls styrene polymerization, optimizing polymer properties.

Keywords:
B-splinemolecular weight distributionmoment-generating function

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Area of Science:

  • Polymer Chemistry
  • Chemical Engineering
  • Control Systems

Background:

  • Polymer properties are significantly influenced by molecular weight distribution.
  • Precise control over molecular weight distribution is crucial for tailoring polymer characteristics.
  • Existing methods may lack the precision required for complex polymerization processes.

Purpose of the Study:

  • To develop and validate a control algorithm for regulating polymer molecular weight distribution.
  • To utilize moment-generating functions and B-spline models for enhanced control.
  • To demonstrate the algorithm's effectiveness in a styrene polymerization process.

Main Methods:

  • A control algorithm based on the moment-generating function was proposed.
  • The B-spline model was employed to approximate the molecular weight distribution.
  • Subspace state space system identification was used to identify system dynamics.
  • A new performance criterion incorporating the moment-generating function was constructed for optimal control input.

Main Results:

  • The B-spline model effectively approximates the molecular weight distribution of styrene polymers.
  • The proposed control method successfully regulates the molecular weight distribution towards a desired profile.
  • The control algorithm demonstrated effectiveness in a practical styrene polymerization setting.

Conclusions:

  • The developed control algorithm offers a robust method for precise molecular weight distribution regulation.
  • The integration of moment-generating functions and B-spline modeling provides an effective control strategy.
  • This approach enables better control over polymer properties by managing molecular weight distribution.