Search results
Results from the WOW.Com Content Network
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 ...
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.
This is the average length a polymer molecule must diffuse to escape from its particular tube, and so the characteristic time for this to happen can be calculated using diffusive equations. A classical derivation gives the reptation time t {\displaystyle t} :
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 ...
Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equation for the Gibbs free energy change for mixing a polymer with a solvent. Although it makes simplifying ...
Persistence length measurement of single stranded DNA is viable by various tools. Most of them have been done by incorporation of the worm-like chain model. For example, two ends of single stranded DNA were tagged by donor and acceptor dyes to measure average end to end distance which is represented as FRET efficiency.
The Flory–Fox equation relates the number-average molecular weight, M n, to the glass transition temperature, T g, as shown below: =, where T g,∞ is the maximum glass transition temperature that can be achieved at a theoretical infinite molecular weight and K is an empirical parameter that is related to the free volume present in the polymer sample.
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.