Hello,
I would like ask a question about I have mentioned above point, How could we calculate Polymer Critical Entanglement concentration? and Is this possible of measuring viscosity by Rheometer?
Dear Sagar Kumbhar, it is important to know that the onset of entanglements occurs beyond a certain critical molecular weight Mc. Entanglements are physical crosslinks, they influence both melt and solution properties. The relaxation time and viscoelasticity are strongly dependent on their existence. They have a detrimental effect on all processes dealing with viscosity such as electrospinning. Please find the following interesting documents. My Regards
https://link.springer.com/article/10.1007%2FBF00712317
https://polymerdatabase.com/polymer%20physics/Crossover%20Length.html
https://doi.org/10.1021/acs.chemmater.8b05114
https://doi.org/10.1021/ma00059a012
https://doi.org/10.1002/polb.20150
https://www.researchgate.net/post/How-does-one-calculate-the-molecular-weight-of-entanglements-of-an-ultra-high-molecular-weight-glassy-polymer
https://doi.org/10.1080/00222349908248106
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6610359/
https://doi.org/10.1021/cr60239a001
https://doi.org/10.1103/PhysRevE.76.026101
https://doi.org/10.1002/pol.1959.1203713101
Hi ;
Entanglement is a physical phenomenon that cannot be observed directly. The entanglements appear as physical nodes forming a temporary network. There is a molar mass, called critical mass Mc, beyond which the viscosity varies with the mass according to a power law of exponent 3.4.
Similarly, in the glassy state, the polymer is fragile below a critical mass. According to these topological models, we consider that the critical mass Mc is twice the mass between entanglements Me. The simplest method to implement is to measure the storage modulus as a function of frequency. Indeed, studies of the creep limit complacency, as well as the viscosity as a function of the molar mass, are perfectly verified only for linear polymers. For branched polymers, deviations from this viscosity law are systematically observed and we must use exponential laws
My regards
The above explanation is good as far as it goes, but I believe the terms used are imprecise. The symbol Mc is not a "critical molar mass" but a critical molecular weight, beyond which, as stated, viscosity varies with molecular weight to the 3.4 power. "Molar mass" to me would mean the weight corresponding to 1 mole of a material, not interchangeable with the term molecular weight. The term "fragile" is not precise. It means "easily broken". Please define more precisely what is meant in this context. Have no idea what "creep limit complacency" means.
Dear Prof. Richard R. Eley, even the notion 'molecular weight (MW)' is not correct, just we get used with this terminology, because 'weight' is a force, which means it has a Newton (N) unit, so logicaly the MW should have (N/mol) unit, which is not the true case. This is a remark that we usually put as a footnote in academic courses. I prefer to use the 'molecular mass (g/mol)' instead. My Regards
Dear Abdelkader: You are correct-- strictly speaking, "molecular weight" is imprecise as well. Of course, those who use this conventional term understand that the units are atomic mass units (amu), or more usefully, g/mol. I like "molecular mass" better, but I doubt that the terminology is likely to be corrected any time soon. Still wondering about "creep limit complacency". Regards, Richard
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