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The WLF equation is a consequence of time–temperature superposition (TTSP), which mathematically is an application of Boltzmann's superposition principle. It is TTSP, not WLF, that allows the assembly of a compliance master curve that spans more time, or frequency, than afforded by the time available for experimentation or the frequency range ...
An alternative model suggested by Arrhenius is also used. The WLF model is related to macroscopic motion of the bulk material, while the Arrhenius model considers local motion of polymer chains. Some materials, polymers in particular, show a strong dependence of viscoelastic properties on the temperature at which they are measured.
The National Academy of Sciences called Ferry "a towering figure in polymer science". [2] The University of Wisconsin said that he was "undoubtedly the most widely recognized research pioneer in the study of motional dynamics in macromolecular systems by viscoelastic techniques".
FENE-P is one of few polymer models that can be used in computational fluid dynamics simulations since it removes the need of statistical averaging at each grid point at any instant in time. It is demonstrated to be able to capture some of the most important polymeric flow behaviors such as polymer turbulence drag reduction and shear thinning.
where is the polymer's characteristic persistence length, is the Boltzmann constant, and is the absolute temperature. At finite temperatures, the end-to end distance of the polymer will be significantly shorter than the maximum length . This is caused by thermal fluctuations, which result in a coiled, random configuration of the undisturbed ...
In this equation is the attraction from the osmotic effect. ∂ f ∂ a {\displaystyle {\frac {\partial f}{\partial a}}} is the repulsion due to chain molecules confined between plates. p {\displaystyle p} is on order of r {\displaystyle \langle r\rangle } , the mean end-to-end distance of chain molecules in free space.
A man who falsely advertised his flat for rent to scam numerous people out of thousands of pounds has pleaded guilty to nine counts of fraud. Kyle Jackson, of Hart Close, Wilton, Wiltshire ...
Excluded volume causes the ends of a polymer chain in a solution to be further apart (on average) than they would be were there no excluded volume (e.g. in case of ideal chain model). The recognition that excluded volume was an important factor in analyzing long-chain molecules in solutions provided an important conceptual breakthrough, and led ...