## Wednesday, April 28, 2010

### The Cox-Merz Rule Rules

I've always viewed the Cox-Merz Rule as my savior, despite it being difficult to roll off the lips smoothly. A workhorse test in rheology is dynamic mechanical analysis in which an oscillitory stress/strains is applied to the sample. This is great to do in the lab, but it is totally different from most practical situations that polymers are used in, where the applied shears are, if not constant, are at least in only one direction. I get asked about the difference quite a bit and thankfully there is the Cox-Merz rule.

Simply put, the steady state shear viscosity at a given shear rate is equal to the dynamic viscosity at the same frequency:

h($\dot \gamma$) = h*(w) when $\dot \gamma$= w

The rule is more-or-less empirical - it works for many common polymers but there is no (strong) theoretical background that it should work for all polymers and it certainly doesn't.

I'm always happy with anyone asking me the question as it is a terrific one and shows that the person is seriously thinking about what is being tested. There are way too many tests that do not match up with reality in the least, and too many people do not question the differences.

Anonymous said...

Hi;
It is useful article , thank you

I knew that the Polymer nanocomposites do not obey the cox-merz relation.

My Q is

Thanks

John said...

It certainly does work. Here's a link to pages in a book I found showing data. (Look at Figure 12.2 on page 316.)

Anonymous said...

Thank you John; I got it and it was in agreement with my results.
I am studying the rhological behaviour of PET nanocomposites

Anonymous said...

Sorry Mr. John;

I forget to ask you Q!
Why PET does not obey Cox-Merz while PP and most of the homo-polymer obey it?

Cheers

And, I comment under this post.

I see many people do dynamic test, often using TTS, to evaluate the zero-shear viscosity (exactly, the zero-frequency complex viscosity). This process bases on the validity of the Cox-Merz rule but in most of these cases people don't confirm this validity first

Typically a liquid like terminal zone of G'~w^2 and G''~w always gives a plateau of complex viscosity. Whether or not this viscosity value always equals to the zero shear value under steady state flow test is problematic.

Anonymous said...

Hi but this is only valid on molecular based systems? what about food suspensions?

John said...

@Anonymous 12:14

Try it and see. I wouldn't expect it to be the case as the items you are talking about are of a more complex structure and those are the types of materials that struggle with the rule. But again, try it and see.

KG Alton said...

I would think not. This rule does not apply to dilute solutions of polysaccharides or anything with strong hydrogen bonding. It works for homoploymers because the underlying model includes only the weak associative forces of each macromolecule when they slide against each other.

I have run across one article that was able to describe this relationship for fluids with a yield stress which more common in food stuffs.

Best regards,

Kris

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