How to measure the flow activation energy of branched PE?

I've not heard that the activation energy can be used to measure branching. I would imagine that greater branching would lead to a higher activation energy, but since there are an infinite variation in branching, and a non-infinite set of activation energies, you will not have a unique answer.

The simplist approach is to simply assume viscosity = A * exp(-E/RT), where A is a constant, E is the activation energy, R is the gas constant and T is the absolute temperature. Measure viscosity at a range of temperatures and plot the log of them against 1/T. The slope is -E/R.

A more involved procedure is to incorporate the Williams-Landau-Ferry equation. Now E = 2.303 R * C1 * C2 * T^2 / (C2 + T - T0)^2, where R and T are as before, C1 and C2 are the WLF constants, and T0 is the reference temperature.

John Aspen Research, -

Opinions expressed herein are my own and may not represent those of my employer.

I just realized that you may not know how to determine the WLF constants C1 and C2. These are found using data from dynamic mechanical spectroscopy taken over a broad range of both temperature and frequency. Time-temperature superposition (TTS) allows you to horizontally shift both the loss and storage modulus and create a larger master curve. The amount of this shift is called aT and the WLF equation is ln aT = C1*(T-T0)/(C2 + T - T0). Obviously, this is a fair amount of work. If the first equation of my previous post gives you a straight line or near straight line, go with it.

This is a very brief description of the technique. More information is available on the internet, but I would strongly suggest finding a good book on polymer flow. The books by Ferry or Dealy are both very good. There are others too. The technique is over 50 years old, so no one can claim to be THE authority on the matter.

John Aspen Research, -www.aspenresearch.com "Turning Questions into Answers"

Opinions expressed herein are my own and may not represent those of my employer.

I remember doing this as a practical experiment in my polymer course. viscosity was measured just with a melt indexer at variable temperatures. We could clearly see the differences between HDPE and LDPE but I am not sure how discriminating it is for different HDPEs or LLDPEs. terry