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Related Concept Videos

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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While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
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Updated: Dec 22, 2025

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Structural universality in disordered packings with size and shape polydispersity.

Ye Yuan1, Wei Deng1, Shuixiang Li1

  • 1Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China. yuanyepeking@pku.edu.cn.

Soft Matter
|May 2, 2020
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Summary

Disordered jammed packings with coupled size and shape variations show universal packing density relationships. Larger particles pack denser, a trend preserved when particle shapes are similar, revealing a universal packing behavior.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Disordered jammed packings are complex systems with applications in various fields.
  • Understanding the structural properties of these packings, especially with polydispersity, is crucial.
  • Previous studies focused on size polydispersity, but coupled size and shape effects are less understood.

Purpose of the Study:

  • To numerically investigate disordered jammed packings with both size and shape polydispersity.
  • To generalize the observation of denser packing by larger particles to systems with coupled shape dispersity.
  • To establish a universal relationship between local compactness and particle size in polydisperse packings.

Main Methods:

  • Numerical investigation of frictionless superellipsoidal particles.
  • Implementation of set Voronoi tessellation to evaluate local specific volume.
  • Definition of normalized free volume (vf) and normalized particle size (A) for compactness analysis.
  • Consideration of three systems: mixed-shape, size-polydisperse, and coupled size-shape polydisperse packings.

Main Results:

  • A universal relationship, vf(A), was found for size-polydisperse packings, independent of specific particle shapes or dispersity.
  • This universality was validated using a mean-field approximation.
  • For coupled size and shape polydispersity, the master curve vf(A) is preserved if particles have similar shape factors (αc); deviations occur when αc dispersity is high.

Conclusions:

  • The study reveals a universal packing behavior (vf(A)) in disordered jammed packings with coupled size and shape polydispersity.
  • The dispersity of particle shapes, quantified by αc, influences the deviation from this universal curve.
  • Polydisperse packings can be understood as combinations of building blocks with a universal packing relation.