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Related Concept Videos

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.
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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.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Polymer Classification: Architecture01:14

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Polymers are classified as linear or branched on the basis of their chain architecture. The polymer chains in linear polymers have a long chain-like structure with minimal to no branching at all. Even if a polymer features large substituent groups on the monomer, which appear as branches to the skeleton, it is not considered a branched polymer. A branched polymer contains secondary polymer chains that arise from the main polymer chain. The branching occurs when the polymer growth shifts from...
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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.
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Effective structure of a system with continuous polydispersity.

Palak Patel1, Manoj Kumar Nandi1, Ujjwal Kumar Nandi1

  • 1Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India.

The Journal of Chemical Physics
|January 27, 2021
PubMed
Summary
This summary is machine-generated.

Treating polydisperse systems as a single component causes artificial softening. This study introduces a pseudospecies approach to accurately model polydispersity, crucial for understanding complex particle systems.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Computational Chemistry

Background:

  • Polydisperse particle systems are complex due to numerous partial structure factors.
  • Treating them as a single component introduces artificial softening, complicating analysis.
  • Accurate modeling is essential for understanding material properties and behavior.

Purpose of the Study:

  • To develop a method to describe polydisperse systems using fewer pseudospecies (M << N).
  • To avoid artificial softening observed in effective one-component models.
  • To determine the optimal number of pseudospecies (M0) and maximum treatable polydispersity (Δσ0).

Main Methods:

  • Utilizing potential energy and pair excess entropy to estimate M0.
  • Defining Δσ0 based on system parameters and interaction potentials.
  • Analyzing the dependence of M0 and Δσ0 on polydispersity and interaction types.

Main Results:

  • M0 depends on polydispersity and interaction potential; Δσ0 depends more strongly on potential.
  • Softer potentials allow for higher tolerance to polydispersity.
  • Even 1% polydispersity significantly deviates from a monodisperse system.

Conclusions:

  • The pseudospecies approach offers an accurate alternative to effective one-component models for polydisperse systems.
  • Care must be taken to distinguish polydispersity effects from artificial softening in analyses.
  • The findings are particularly relevant for large-scale systems due to M0's independence from system size.