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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.
3.4K
Molecular Weight of Step-Growth Polymers01:08

Molecular Weight of Step-Growth Polymers

2.2K
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...
2.2K
Polymers: Defining Molecular Weight01:01

Polymers: Defining Molecular Weight

2.9K
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...
2.9K
Polymer Classification: Crystallinity01:21

Polymer Classification: Crystallinity

2.8K
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.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
2.8K
Radical Chain-Growth Polymerization: Chain Branching01:17

Radical Chain-Growth Polymerization: Chain Branching

1.9K
The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...
1.9K
Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

3.3K
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...
3.3K

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Related Experiment Video

Updated: Jun 26, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

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

Published on: September 26, 2016

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Statistics of Gaussian polymer chains in harmonic applied fields.

John P Mikhail1,2, Gregory C Rutledge1,2

  • 1Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 10, 2024
PubMed
Summary

We developed an analytical model for polymer chains in harmonic fields, providing key statistical mechanics insights. This model aids understanding polymer behavior under confinement and stress in various applications.

Keywords:
Gaussian chainMonte Carlo simulationharmonic fieldpolymerpolymer confinement

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DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
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Last Updated: Jun 26, 2025

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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
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Area of Science:

  • Polymer Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • The behavior of polymers under external forces is crucial for understanding material properties.
  • Existing models often simplify polymer chain interactions and external fields.

Purpose of the Study:

  • To develop a general analytical model for a continuous Gaussian polymer chain in a harmonic potential.
  • To derive statistical mechanics properties, including partition functions and moment generating functions (MGFs).

Main Methods:

  • Formulation of a general analytical model for a continuous Gaussian chain.
  • Evaluation of statistical mechanics using derived potential.
  • Derivation of closed-form expressions for key chain properties.
  • Comparison with Monte Carlo simulations and literature data.

Main Results:

  • Obtained closed-form expressions for squared radius of gyration, potential energy, partition function, and MGF for the center of mass.
  • Validated the analytical model against discrete Gaussian chain simulations.
  • Demonstrated the model's applicability to polymer confinement and deformation studies.

Conclusions:

  • The developed analytical model accurately describes polymer chain behavior in harmonic fields.
  • Provides a theoretical framework for analyzing polymer confinement and deformation.
  • Offers insights applicable to experimental, theoretical, and simulation-based polymer research.