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Cationic Chain-Growth Polymerization: Mechanism

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The cationic polymerization mechanism consists of three steps: initiation, propagation, and termination. In the initiation step of the polymerization process, the π bond of a monomer gets protonated by the Lewis acid catalyst, which is formed from boron trifluoride and water. The protonation of the π bond generates a carbocation stabilized by the electron‐donating group. In the propagation step, the π bond of the second monomer acts as a nucleophile and attacks the generated carbocation,...

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Updated: Jun 25, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Contest based on a directed polymer in a random medium.

Clément Sire¹

¹Laboratoire de Physique Théorique-IRSAMC, UPS and CNRS, Université de Toulouse, 31062 Toulouse, France. clement.sire@irsamc.ups-tlse.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2009

Summary

This summary is machine-generated.

This study introduces a game model of directed polymers in random media. The game

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Area of Science:

Statistical Physics
Probability Theory
Game Theory

Background:

Directed polymers in random media are modeled using a novel one-parameter game.
The game involves two players aiming to maximize their score and minimize their opponent's return.

Purpose of the Study:

To analyze the score distribution and identify transitions in a game derived from polymer physics.
To investigate the mechanism behind the traveling wave front velocity in this model.

Main Methods:

A one-parameter game is defined, simulating a directed polymer in a random medium.
The probability distribution of the final score (S_n) is analyzed for a game of length n.
The behavior of the traveling wave profile is examined for varying game parameters.

Main Results:

The final score distribution exhibits a traveling wave form, Prob(S_n=m)=f(m-vn).
The wave profile shows an unusual double exponential decay for large positive and negative values.
A transition occurs where one player achieves its maximum theoretical score.

Conclusions:

The front velocity (v) is proposed to be selected by nonlinear marginal stability mechanisms.
This mechanism is relevant for traveling wave problems with exponentially decaying profiles.
The findings offer insights into the dynamics of directed polymers and related wave phenomena.