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関連する概念動画

Molecular Weight of Step-Growth Polymers01:08

Molecular Weight of Step-Growth Polymers

2.7K
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...
2.7K
Characteristics and Nomenclature of Copolymers01:24

Characteristics and Nomenclature of Copolymers

3.2K
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...
3.2K
Step-Growth Polymerization: Overview01:03

Step-Growth Polymerization: Overview

4.3K
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...
4.3K
Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

3.9K
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...
3.9K
Polymers: Molecular Weight Distribution01:10

Polymers: Molecular Weight Distribution

4.6K
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.
4.6K
Radical Chain-Growth Polymerization: Overview01:10

Radical Chain-Growth Polymerization: Overview

3.1K
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...
3.1K

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関連する実験動画

Updated: Jan 14, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

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確率的共重合プロセスの一クラスに対する数学的解析

David F Anderson1, Jingyi Ma2, Praful Gagrani3

  • 1Department of Mathematics, University of Wisconsin-Madison, Madison, USA.

Bulletin of mathematical biology
|January 13, 2026
PubMed
まとめ

本研究は、確率的共重合モデルを厳密に解析し、ポリマー成長とモノマー分数の基準を確立する。過渡状態の数理的手法が開発され、複数のモノマータイプに一般化される。

キーワード:
連続時間マルコフ連鎖境界過程共重合生命の起源ポリマー成長再帰と遷移確率的モデリング木状状態空間

さらに関連する動画

Ethylene Polymerizations Using Parallel Pressure Reactors and a Kinetic Analysis of Chain Transfer Polymerization
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Ethylene Polymerizations Using Parallel Pressure Reactors and a Kinetic Analysis of Chain Transfer Polymerization

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Synthesis of Monodisperse Cylindrical Nanoparticles via Crystallization-driven Self-assembly of Biodegradable Block Copolymers
11:42

Synthesis of Monodisperse Cylindrical Nanoparticles via Crystallization-driven Self-assembly of Biodegradable Block Copolymers

Published on: June 20, 2019

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関連する実験動画

Last Updated: Jan 14, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

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Ethylene Polymerizations Using Parallel Pressure Reactors and a Kinetic Analysis of Chain Transfer Polymerization
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Ethylene Polymerizations Using Parallel Pressure Reactors and a Kinetic Analysis of Chain Transfer Polymerization

Published on: November 27, 2015

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Synthesis of Monodisperse Cylindrical Nanoparticles via Crystallization-driven Self-assembly of Biodegradable Block Copolymers
11:42

Synthesis of Monodisperse Cylindrical Nanoparticles via Crystallization-driven Self-assembly of Biodegradable Block Copolymers

Published on: June 20, 2019

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科学分野:

  • 高分子科学
  • 統計物理学
  • 確率過程

背景:

  • 共重合プロセスは高分子科学において基本的である。
  • 物理学文献における以前の分析は、発見的手法に依存していた。
  • 正確な予測のためには、厳密な数学的枠組みが必要である。

研究 の 目的:

  • 共重合における遷移、ヌル再帰、および正再帰の基準を確立すること。
  • 遷移状態における限定的なモノマー分数を決定すること。
  • 確率的共重合におけるポリマー成長速度を分析すること。

主な方法:

  • 厳密な数学的議論の開発。
  • 確率的共重合モデルの分析。
  • 有限個のモノマータイプへの技術の一般化。

主要な成果:

  • システムパラメータに基づいて再帰特性の基準を導出した。
  • 遷移状態におけるモノマータイプの限定された画分を定量化した。
  • 遷移状態におけるポリマー成長速度を確立した。

結論:

  • 数学的厳密性は、共重合における発見的手法による結果を検証および拡張する。
  • 開発された方法は、一般化された共重合モデルに適用可能である。
  • 本研究は、より複雑な確率的プロセスの分析の基礎を提供する。