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Related Concept Videos

Radical Chain-Growth Polymerization: Chain Branching01:17

Radical Chain-Growth Polymerization: Chain Branching

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...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
Radical Chain-Growth Polymerization: Mechanism01:09

Radical Chain-Growth Polymerization: Mechanism

The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this species into the...
Gradually Varying Flow01:29

Gradually Varying Flow

Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

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 catalyst, high molecular...
Radical Chain-Growth Polymerization: Overview01:10

Radical Chain-Growth Polymerization: Overview

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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Crossover transition in flowing granular chains.

Xialing Ulrich1, Eliot Fried, Amy Q Shen

  • 1Department of Mechanical, Aerospace & Structural Engineering, Washington University in St Louis, Missouri 63130, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary

Granular chains in a rotating tumbler exhibit complex dynamics, forming mixed packing structures. Chain length influences their movement, transitioning from self-avoiding to random walks as they grow.

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Area of Science:

  • Physics of granular materials
  • Soft matter physics
  • Complex systems dynamics

Background:

  • Understanding the behavior of granular materials is crucial in various scientific and industrial applications.
  • Flowing granular chains exhibit unique dynamical and statistical properties influenced by confinement and chain length.

Purpose of the Study:

  • To investigate the dynamical and statistical behavior of two-dimensional granular chains in a rotating tumbler.
  • To characterize the influence of chain length on system conformation and flow dynamics.

Main Methods:

  • Experimental study using a rotating tumbler to confine granular chains in two dimensions.
  • Analysis of chain dynamics, including cascades and packing arrangements.
  • Measurement of system porosity and mean-square end-to-end distance.

Main Results:

  • Observed cascades of chains along the free surface, leading to mixed porous/laminar packing.
  • Identified crossover transitions in chain conformation from 2D self-avoiding walk to 2D random walk.
  • These transitions are dependent on chain length, specifically when self-contact becomes possible.

Conclusions:

  • The length of granular chains significantly impacts their dynamical and statistical behavior in confined flow.
  • Chain conformation transitions are a key indicator of how chain length affects packing and flow in granular systems.