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 ...
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.
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.
The kinetic theory of gases allows accurate calculation of the temperature-variation of gaseous viscosity. The theoretical basis of the kinetic theory is given by the Boltzmann equation and Chapman–Enskog theory, which allow accurate statistical modeling of molecular trajectories.
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 ...
The newly formed nucleophile will then attack the atom X in another monomer molecule, and the sequence would repeat until the polymer is formed. [21] Anionic ring-opening polymerizations (AROP) involve nucleophilic reagents as initiators. Monomers with a three-member ring structure - such as epoxides, aziridines, and episulfides - undergo ...
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 ...
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} :