To specialized in polyesterification: Does it exist any empirical equation that describes behaviour of viscosity changes as time-dependence function? To be precise, there is a precursor solution that is heat-treated in constant temperature with viscosity measurements doing in equal periods of time and it's rising dramatically after few hours. The problem is to find a convenient model that describes it best.
The viscosity increase of such a system is dependent upon various parameters. The choice of the monomers (determining the Tg of the polymer at any instant), the desired end Mw in combination with the conversion of the reaction at any instant, the amount of hydroxyls and carboxylic groups present at any time/any conversion, the amount of branching monomer, etcetra.
With good calculation tools yo may predict any Mw at any conversion of the set of monomers you need. In such calculation, the actual Tg is generally not included. When you have a big dataset on such polymers you may include it too.
So there is no simple model.... but: In order to make it practical often the PE molecular weights are expressed in terms of intrinsic viscosity, see how both are related ot the Mark-Houwink equation in polymer books, a simple example of this, see the link. Thats the most simple way to do this.
https://books.google.nl/books?id=ZgxgZ5vfxTkC&pg=PA369&lpg=PA369&dq=relative+intrinsic+viscosity+polyester&source=bl&ots=DrGJIqkbMl&sig=J-Dl6_0hOpweQZM0LeEdw9ttSqo&hl=en&sa=X&ved=0ahUKEwiF-4ygg7nJAhUJXhQKHZI4D0c4ChDoAQghMAE#v=onepage&q=relative%20intrinsic%20viscosity%20polyester&f=false
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