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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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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.
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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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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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Components of Stress01:23

Components of Stress

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Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and...
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Stresses under Combined Loadings01:23

Stresses under Combined Loadings

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When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
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On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation.

Yao Fu1, Jeong-Hoon Song1

  • 1Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, Colorado 80309, USA.

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Summary

This study extends the Hardy stress definition to multi-body potentials in polymers, overcoming limitations of previous methods. It establishes a reliable link between atomistic and continuum scales for complex material simulations.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Polymer Physics

Background:

  • The Hardy stress definition is currently limited to pair potentials and embedded-atom methods.
  • Basic assumptions in deriving a symmetric microscopic stress tensor obscure Hardy stress for multi-body potentials.
  • Force decomposition in Hardy stress expressions is unclear for multi-body potentials.

Purpose of the Study:

  • To demonstrate the invariance of the Hardy stress expression for polymer systems modeled with multi-body interatomic potentials.
  • To extend the applicability of Hardy stress to systems involving interactions up to four atoms.
  • To provide a reliable method for linking atomistic and continuum scales in multi-body potential systems.

Main Methods:

  • Applied central force decomposition of atomic force to analyze multi-body potentials.
  • Theoretically demonstrated and numerically tested the balance of momentum.
  • Investigated the convergence of computed Hardy stress with increasing spatial averaging volume.

Main Results:

  • Demonstrated the invariance of the Hardy stress expression for polymer systems using multi-body potentials.
  • Validated the theoretical and numerical balance of momentum for these systems.
  • Observed Hardy stress converging to virial stress with increased spatial averaging.

Conclusions:

  • The validity of momentum conservation justifies extending Hardy stress to multi-body potential systems.
  • This work establishes a feasible and reliable linkage between atomistic and continuum scales for multi-body potential systems.
  • The findings enable more accurate stress calculations in complex polymer materials.