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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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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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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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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...
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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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Classical Wigner model based on a Feynman path integral open polymer.

S Karl-Mikael Svensson1, Jens Aage Poulsen1, Gunnar Nyman1

  • 1Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden.

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|January 22, 2021
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Summary
This summary is machine-generated.

A new method improves sampling for the classical Wigner model, aiding quantum nuclear dynamics approximations. This approach shows promise for various potentials and systems, converging towards the Wigner limit.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Nuclear dynamics

Background:

  • The classical Wigner model approximates quantum dynamics of atomic nuclei.
  • Accurate sampling of the initial quantum mechanical distribution is crucial for the Wigner model.

Purpose of the Study:

  • To introduce and test a novel method for sampling the initial quantum mechanical distribution for the classical Wigner model.
  • To evaluate the performance of the new method for various potentials and system dimensions.

Main Methods:

  • Developed and tested two versions of a new sampling method.
  • Applied the method to one-dimensional quartic oscillators, double well potentials, and multi-dimensional systems coupled to harmonic baths.
  • Compared results with the Feynman-Kleinert linearized path integral method.

Main Results:

  • Both versions of the new method consistently converge towards the classical Wigner limit.
  • Effective convergence was achieved for one-dimensional systems.
  • Approximating harmonic bath sampling with classical mechanics significantly enhanced numerical performance for multi-dimensional systems.
  • The new method outperformed the Feynman-Kleinert method in reproducing exact classical Wigner results for the double well potential.

Conclusions:

  • The new sampling method is a potentially useful tool for approximating quantum nuclear dynamics using the classical Wigner model.
  • The method demonstrates good performance, especially for one-dimensional systems, and shows advantages over existing techniques for specific cases.
  • Further investigation on other correlation functions and systems is warranted.