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Related Concept Videos

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.
The number average molecular weight (Mn) is the summation of the number...
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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

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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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Polymer Classification: Crystallinity01:21

Polymer Classification: Crystallinity

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Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Step-Growth Polymerization: Overview01:03

Step-Growth Polymerization: Overview

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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.
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Polymer Physics by Quantum Computing.

Cristian Micheletti1, Philipp Hauke2, Pietro Faccioli3

  • 1Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy.

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|September 3, 2021
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Summary
This summary is machine-generated.

Researchers developed a new quantum annealing method to simulate dense polymer mixtures, overcoming a major challenge in computational physics. This quantum approach efficiently samples polymer configurations, advancing soft-matter system modeling.

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Area of Science:

  • Computational Physics
  • Soft-Matter Physics
  • Quantum Computing

Background:

  • Sampling equilibrium ensembles of dense polymer mixtures is computationally challenging.
  • Lattice-based polymer models are widely used but difficult to simulate at high densities.

Purpose of the Study:

  • To develop a novel computational framework for simulating dense polymer mixtures.
  • To leverage quantum annealing for solving complex polymer modeling problems.

Main Methods:

  • Developed a formalism using interacting binary tensors.
  • Formulated polymer properties (self-avoidance, branching, looping) as quadratic tensor interactions.
  • Utilized quantum annealing machines (D-Wave) to solve discrete energy-minimization problems for microstate generation.

Main Results:

  • Successfully demonstrated the sampling of polymer mixtures across a range of densities.
  • Showcased the capability of the tensor formalism on a quantum annealer.
  • Generated microstates of different lattice polymer ensembles efficiently.

Conclusions:

  • The developed tensor-based formalism provides a viable method for simulating dense polymer mixtures using quantum annealing.
  • This approach harnesses quantum computing for advancements in modeling filamentous soft-matter systems.
  • Offers a promising direction for applying quantum machines to complex discrete models.