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相关概念视频

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

Polymers: Molecular Weight Distribution

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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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Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

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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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Characteristics and Nomenclature of Copolymers01:24

Characteristics and Nomenclature of Copolymers

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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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Cationic Chain-Growth Polymerization: Mechanism00:57

Cationic Chain-Growth Polymerization: Mechanism

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The cationic polymerization mechanism consists of three steps: initiation, propagation, and termination. In the initiation step of the polymerization process, the π bond of a monomer gets protonated by the Lewis acid catalyst, which is formed from boron trifluoride and water. The protonation of the π bond generates a carbocation stabilized by the electron‐donating group. In the propagation step, the π bond of the second monomer acts as a nucleophile and attacks the...
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Polymers02:34

Polymers

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The word polymer is derived from the Greek words “poly” which means “many” and “mer” which means “parts”. Polymers are long chains of molecules composed of repeating units of smaller molecules, known as monomers. They either occur naturally, such as DNA and proteins, or can be constructed synthetically, like plastics. They have varied structural characteristics, such as linear chains, branched chains, or complex networks, that contribute to the...
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On end-point distribution for directed polymers and related problems for randomly forced Burgers equation.

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

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关于定向聚合物的分区函数的因子化公式

Tobias Hurth1, Konstantin Khanin2, Beatriz Navarro Lameda3

  • 1Institute for Mathematics, Freie Universität Berlin, Arnimallee 9, 14195 Berlin, Germany.

Journal of statistical physics
|October 23, 2023
PubMed
概括

本研究引入了一个因子化公式,用于弱失序状态下指向的聚合物分区函数. 这项研究扩展了先前的发现,表明在聚合物亚弹道系统中,误差项很小.

关键词:
定向的聚合物是指向的分区函数 分区函数在随机环境中随机步行.软弱性障碍是一种虚弱性障碍.

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Particles without a Box: Brush-first Synthesis of Photodegradable PEG Star Polymers under Ambient Conditions
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Using Polystyrene-block-polyacrylic acid-coated Metal Nanoparticles as Monomers for Their Homo- and Co-polymerization
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Using Polystyrene-block-polyacrylic acid-coated Metal Nanoparticles as Monomers for Their Homo- and Co-polymerization

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科学领域:

  • 可能性理论概率理论.
  • 统计力学 统计力学
  • 数学物理 数学物理

背景情况:

  • 随机潜力的定向聚合物是统计力学中的一个关键模型.
  • 了解无序系统中的聚合物行为对于各种科学领域至关重要.

研究的目的:

  • 为定向聚合物的点对点分区函数建立一个因子化公式.
  • 分析虚弱无序状态中的错误项的行为,并扩展先前的结果.

主要方法:

  • 用分区函数的分解式来计算分区函数.
  • 分析分区函数和过渡概率的分数.
  • 调查错误项在较长时间间隔中的行为.

主要成果:

  • 证明了点对点分区函数的分解式.
  • 证明误差值在子弹道系统的起点和终点上均小.
  • 导出限制分区函数的空间和时间相关性的异向.

结论:

  • 这项研究将西奈关于误差项小性的结果扩展到更广泛的聚合物动态范围.
  • 这些发现为在无序介质中定向聚合物的统计性质提供了新的见解.