Storage modulus (G’) and loss modulus (G”) for beginners

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Video Transcript

Hey guys, I’m here in Sanya at the moment in China. It’s a bit like “China’s Hawaii”! It’s a beautiful Resort and I’m helping Brookfield.

Brookfield is bringing out a new instrument, which could be bringing some of the higher-end rheological capabilities to a wider audience.  It really works with my ethos and that of my team back in the UK.

We’ve been discussing storage modulus and loss modulus a lot in the last few days. These were two properties that I found really difficult to get to grips with when I was first learning rheology, so what I’d like to do is to try and give you a sense of what they mean. Not so much mathematically but what they really mean in terms of how products handle. I’m going to take a rather unscientific approach and let me know what you think.

Imagine you have a sponge, like a bathroom sponge or something you would wash your car with. Imagine you completely drenched that sponge in water. The overall wet soap mass of that sponge has a certain resistance to deformation and we can think of this as the complex modulus we would denote this by G* if we’re working in shear. Now the sponge itself has a certain rigidity that contributes to the complex modulus and because the sponge is an elastic solid we can think about this contribution as ‘G Prime’/’the storage modulus’ or the ‘elastic modulus’.

The water also contributes to the overall resistance to deformation, and because water is inelastic, or what we call viscous, we can think about this contribution to the complex modulus as the ‘loss modulus’ or the ‘viscous modulus’. Now imagine if we soak the sponge in syrup or honey, or we used a stiffer sponge. In both cases the complex modulus would be higher, as a result of the greater elastic or viscous contributions.

The contributions are not just straight addition, but vector contributions, the angle between the complex modulus and the storage modulus is known as the ‘phase angle’. If it’s close to zero it means that most of the overall complex modulus is due to an elastic contribution. This is just a clever way of saying that the product is more of a solid than a liquid, and then if you deform it, as long as you don’t push it beyond what we call the ‘yield point’ it’s going to bounce back again to its original shape. If it’s closer to 90 degrees then the complex modulus is nearly all due to viscous contributions. In other words this time the product is more of a liquid than a solid and if you deform it it’s not going to bounce back, there’ll be a permanent deformation.

Tan Delta the tangent of the phase angle is therefore just the ratio of the viscous to elastic effects. So complex modulus and phase angle are great ways to describe a material because they’re just measures of the rigidity and the bounce-back ability of that material.

I hope my rather simplified explanation of G Prime and G double prime here makes it a little bit less daunting for you. If you have any further questions, please don’t hesitate to contact me or the team Go to the website at rheologylab.com and hopefully see you at the next video!