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Polymers: Molecular Weight Distribution

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.

Polymer Classification: Crystallinity

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 Polymers

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...

Classification and Mechanical Properties of Synthetic Polymers

Classification and Mechanical Properties of Synthetic Polymers

Synthetic polymers are classified as elastomers, fibers, or plastics based on their crystallinity. Crystallinity, the degree of long-range order in the solid state, influences the mechanical properties (stretching or contracting) of elastomers. Elastomers are flexible polymers that can expand or contract easily upon the application of an external force. They have numerous crosslinks that pull them back into their original shape when stress is removed. Silicones, for instance, are highly elastic...

Determination of Molar Masses of Polymers I

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...

Polymers: Defining Molecular Weight

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 20, 2026

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

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

Published on: September 26, 2016

Theoretically informed coarse grain simulations of polymeric systems.

Darin Q Pike¹, François A Detcheverry, Marcus Müller

¹Department of Chemical and Biological Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA.

The Journal of Chemical Physics

|September 4, 2009

Summary

This study introduces a particle-based Monte Carlo model for polymeric melts, enabling simulations across various ensembles and direct free energy calculations. The model successfully predicts phase behavior in polymer blends and diblock copolymers.

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Area of Science:

Polymer Physics
Computational Materials Science
Statistical Mechanics

Background:

Understanding polymer melt behavior is crucial for materials design.
Existing models often face challenges in accurately capturing complex phase transitions.
A unified simulation approach is needed for diverse polymer systems.

Purpose of the Study:

To develop a novel particle-based Monte Carlo formalism for simulating polymeric melts.
To enable simulations in multiple thermodynamic ensembles (nVT, nPT, semigrandcanonical, Gibbs).
To facilitate direct calculation of free energies and study phase transitions.

Main Methods:

A particle-based Monte Carlo approach is employed.
Interactions are derived from a local density functional, bridging particle and field-based models.
The formalism is applied to binary homopolymer blends and symmetric diblock copolymers.

Main Results:

The phase diagram and critical point for a binary homopolymer blend were determined.
Microphase separation in a symmetric diblock copolymer was analyzed.
Local stress distributions and the order-disorder transition temperature were calculated.

Conclusions:

The developed Monte Carlo formalism provides a versatile tool for studying polymer melt phase behavior.
The method accurately predicts key thermodynamic properties and transition points.
This approach offers a pathway for designing polymers with desired properties through simulation.