Tube Models for Branched Polymers

In Chapter 6, various versions the tube model were presented, which can predict the linear viscoelasticity of monodisperse and polydisperse //near polymers i.e., polymers without long-chain branching (LCB). To be quantitatively accurate, these models need to include several mechanisms of polymer motion, namely  

As shown in Chapter 6, theories containing appropriate forms for all these mechanisms have often proved to be accurate in predicting the linear viscoelastic properties of linear polymers. (In Chapter 11 we will show that even the nonlinear properties of linear polymers can be predicted accurately in some cases.) In fact, theories for the linear viscoelasticity of polydisperse linear polymers are now well enough developed that one can (at least in principle) invert them to infer the molecular weight distribution from linear viscoelastic data see Chapter 8. 

perhaps one of the most important potential practical uses of rheology in the entire field of polymer science is as a method to detect and quantify the presence of long-chain branching. This potential use of rheology is more important than its use in measuring molecular weight distributions, because there are analytical methods for the latter, but for the measurement of LCB there is simply no alternative method that can detect minute levels of LCB (i.e, less than about 0.1 branch per 1,000 carbons) see Section 5.12.2. 

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