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Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Types of Damping

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...

Step-Growth Polymerization: Overview

Step-Growth Polymerization: Overview

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...

Anionic Chain-Growth Polymerization: Mechanism

Anionic Chain-Growth Polymerization: Mechanism

The mechanism for anionic chain-growth polymerization involves initiation, propagation, and termination steps. In the initiation step, a nucleophilic anion, such as butyl lithium, initiates the polymerization process by attacking the π bond of the vinylic monomer. As a result, a carbanion, stabilized by the electron‐withdrawing group, is generated. The resulting carbanion acts as a Michael donor in the propagation step and attacks the second vinylic monomer, which acts as a Michael acceptor.

Radical Chain-Growth Polymerization: Mechanism

Radical Chain-Growth Polymerization: Mechanism

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 the...

Ziegler–Natta Chain-Growth Polymerization: Overview

Ziegler–Natta Chain-Growth Polymerization: Overview

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 catalyst, high molecular...

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The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton

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Dynamical hysteresis in a self-oscillating polymer gel.

Debojyoti Das¹, Moupriya Das, Deb Shankar Ray

¹Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.

The Journal of Chemical Physics

|August 18, 2012

Summary

Ionic polymer gels exhibit dynamical hysteresis during chemical oscillations, showing a unique response loop. This behavior is influenced by temperature and thermal noise, similar to stochastic resonance.

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Area of Science:

Polymer Science
Chemical Kinetics
Nonlinear Dynamics

Background:

Ionic polymer gels can exhibit complex behaviors when subjected to chemical oscillations.
Understanding the dynamics of swelling-deswelling is crucial for applications involving responsive materials.

Purpose of the Study:

To investigate the dynamical hysteresis in ionic polymer gels undergoing rhythmical swelling-deswelling kinetics.
To analyze the factors influencing the hysteresis loop area, including temperature and thermal noise.

Main Methods:

Theoretical analysis of gel kinetics under chemical oscillation.
Numerical simulations to model the hysteresis loop and its dependence on parameters.
Investigation of the integrated probability of polymer residence in different states.

Main Results:

Demonstrated dynamical hysteresis in ionic polymer gels, characterized by a non-vanishing response function--concentration hysteresis loop area.
Observed dependence of the loop area on temperature.
Identified a turnover in loop area as a function of thermal noise strength, indicating stochastic resonance.

Conclusions:

Ionic polymer gels display complex dynamical hysteresis driven by chemical oscillations.
The observed phenomena, including stochastic resonance-like behavior, provide insights into the fundamental physics of soft matter systems.
The findings are supported by both analytical models and numerical simulations.