Related Experiment Video
Updated: Jul 6, 2026
09:43
Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
Published on: August 13, 2019
Constitutive equation for polymer networks with phonon fluctuations
Rasmus Hansen1, Anne Ladegaard Skov, Ole Hassager
1Center for Fluid Dynamics at DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
Summary
This study extends phonon fluctuation theory for polymer networks, developing nonlinear constitutive equations. The sliplink and phonon models align with experimental data, unlike the tube model.
Area of Science:
- Polymer Physics
- Materials Science
- Statistical Mechanics
Background:
- Phonon fluctuations influence polymer network mechanics.
- Xing's research provided a Helmholtz free energy expression for these fluctuations.
Purpose of the Study:
- To extend Xing's results by deriving nonlinear constitutive equations for polymer networks.
- To compare the sliplink, tube, and phonon fluctuation models with experimental data.
Main Methods:
- Constructed nonlinear constitutive equations for general, volume-conserving deformations.
- Derived constitutive equations for the sliplink and tube models.
- Compared model predictions with experimental data from Xu and Mark, and Wang and Mark.
Main Results:
- The sliplink and phonon fluctuation models show consistency with each other and with experimental data.
- Elastic moduli derived from the models were compared with those from chemical stoichiometry.
- The tube model demonstrated inconsistency with both other models and experimental data.
Conclusions:
- The phonon fluctuation model and sliplink model provide a consistent framework for polymer network elasticity.
- The tube model requires further refinement to align with experimental observations and theoretical predictions.
Related Concept Videos
01:08Molecular 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...
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...
01:16IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
According to Hooke's law, the vibrational frequency is directly proportional to the...
01:04Anionic Chain-Growth Polymerization: Mechanism
The mechanism for anionic chain-growth polymerization involves initiation, propagation, and termination steps. In the initiation step, a nucleophilic anion, such as butyl lithium, initiates the polymerization process by attacking the π bond of the vinylic monomer. As a result, a carbanion, stabilized by the electron‐withdrawing group, is generated. The resulting carbanion acts as a Michael donor in the propagation step and attacks the second vinylic monomer, which acts as a Michael acceptor.
01:10Polymers: 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.
01:21Polymer 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...
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...
01:01Polymers: 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...
The number average molecular weight (Mn) is the summation of the number...