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Related Concept Videos

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.
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...
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.
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Types of Fluids

Fluids can be classified into Newtonian and non-Newtonian fluids based on their response to shear stress. Newtonian fluids have a linear relationship between shear stress and the shear strain rate, following Newton's law of viscosity. Their viscosity remains constant regardless of the shear rate, making their behavior predictable and easier to analyze. Common examples include water, air, oil, and gasoline.
In contrast, non-Newtonian fluids do not follow Newton's law of viscosity, and their...

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Related Experiment Video

Updated: May 16, 2026

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

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Published on: September 26, 2016

Density functional theory for inhomogeneous ring polymeric fluids.

Jian Jiang1, Xiaofei Xu, Dapeng Cao

  • 1Division of Molecular and Materials Simulation, State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

We developed a new density functional theory (DFT) for modeling ring polymers. This approach accurately predicts ring polymer behavior, overcoming challenges in classical theories.

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Area of Science:

  • Polymer Physics
  • Statistical Mechanics
  • Computational Chemistry

Background:

  • Classical density functional theory (DFT) struggles to model ring polymers due to their unique cyclic topology without free ends.
  • Accurate theoretical models are crucial for understanding the behavior of ring polymers in various systems.

Purpose of the Study:

  • To develop a novel DFT for inhomogeneous ring polymers that accounts for their cyclic architecture.
  • To improve the prediction of thermodynamic and structural properties of ring polymers.

Main Methods:

  • Developed an algorithm to solve the integral of direct bond connectivity for ideal ring polymers.
  • Extended the excess free energy functional using an equation of state (EOS).
  • Validated the proposed DFT against configurational-bias Monte Carlo (CBMC) simulations.

Main Results:

  • The proposed EOS shows improved agreement with Monte Carlo data for compressibility factors compared to existing EOSs.
  • The DFT successfully reproduces CBMC simulation data for ring polymers.
  • Local density profiles indicate that bead density in inhomogeneous ring fluids is independent of ring size, consistent with CBMC findings.

Conclusions:

  • The new DFT provides a robust framework for modeling inhomogeneous ring polymers.
  • Ring polymer solvation forces resemble those of infinitely long linear polymers.
  • This work advances the theoretical understanding and simulation of cyclic polymer systems.