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Polymers: Molecular Weight Distribution01:10

Polymers: Molecular Weight Distribution

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.
Determination of Molar Masses of Polymers I01:24

Determination of Molar Masses of Polymers I

Polymerization produces macromolecules with a range of chain lengths due to the random nature of molecular growth processes. As chains form and terminate at different stages, a single polymer sample contains molecules of varying sizes rather than a uniform structure. This variability is described using average molar masses and distribution-related parameters, which together provide a comprehensive understanding of polymer characteristics.The distribution of molar masses plays a critical role in...
Polymer Classification: Crystallinity01:21

Polymer Classification: Crystallinity

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

Molecular Weight of Step-Growth Polymers

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...
Determination of Molar Masses of Polymers II01:27

Determination of Molar Masses of Polymers II

Polymer samples typically consist of macromolecular chains with a distribution of lengths, resulting in a range of molar masses rather than a single discrete value. Conventional descriptors such as the number-average molar mass and weight-average molar mass quantify this distribution but do not fully capture polymer behavior in solution..The viscosity-average molar mass provides a more realistic description of polymer behavior in solution because it accounts for the enhanced contribution of...
Polymers: Defining Molecular Weight01:01

Polymers: Defining Molecular Weight

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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Updated: Jun 4, 2026

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
09:19

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Density of states and wave function localization in disordered conjugated polymers: a large scale computational

Nenad Vukmirović1, Lin-Wang Wang

  • 1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.

The Journal of Physical Chemistry. B
|February 5, 2011
PubMed
Summary

Electronic structure calculations reveal that electrostatic potential fluctuations, not conjugation breaks, localize hole states in disordered conjugated polymers. This finding is modeled by a tight-binding approach with Gaussian on-site energy distributions.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Condensed Matter Physics

Background:

  • Disordered conjugated polymers are crucial for organic electronics.
  • Understanding their electronic structure is key to device performance.
  • Previous models often oversimplified disorder effects.

Purpose of the Study:

  • To investigate the electronic structure of strongly disordered conjugated polymers.
  • To identify the primary cause of charge carrier localization.
  • To develop a more accurate theoretical model for these materials.

Main Methods:

  • Large-scale electronic structure calculations.
  • Density functional theory (DFT) based charge patching method for Hamiltonian construction.
  • Overlapping fragments method for efficient Hamiltonian diagonalization.

Main Results:

  • Hole states are localized by electrostatic potential fluctuations, not conjugation breaks.
  • The density of hole states exhibits an exponential decay tail.
  • A 1D tight-binding model with correlated Gaussian on-site energies captures key features.

Conclusions:

  • Electrostatic disorder is the dominant factor in hole state localization.
  • The developed model provides a robust framework for predicting electronic properties.
  • This work advances the understanding of charge transport in organic semiconductors.