FT-Rheology - basic idea and realization
The basic idea of FT-Rheology is the application of sinusoidal strain to materials that respond in a non-linear way. This leads to the appearance of higher harmonic contributions during a rheological measurement.
The reason why the higher harmonics show up is as follows:
Let's assume that we have a viscosity (or the spring constant) that depends on the applied shear rate:
You might ask why the expansion includes only even terms? That's simply due to the fact that we would like to have the same response if we shear in either direction. Next, we apply oscillatory shear and for simplicity we write this in the complex notation:
Now, we put the two equations together in Newton's viscosity law:
A Fourier-transformation of the time dependant torque is able to unravel in a very sensitive way the components of the higher harmonics at odd multiples of the applied excitation frequency.
To detect experimentally the higher harmonics we developed the following set-up:
The set-up is basically an extension of a commercial rheometer. Typical S/N reaches 100.000 : 1, the detection of up to 71 harmonics was, in this setup, immediately feasible.If you ask about possible applications of FT-Rheology, you can think about anything that implies non-linear mechanical response in materials in general because FT-Rheology as a method is of course not limited to polymers!
Here is a small list of projects that are currently under way:
Sensitivity improvement of the experimental set-up
Comparison between experimental results and finite-element predictions
Shear induced aging and quality control, e.g. for industrial processes
Shear induced crystallizat
Evolution of the higher harmonics during the phase alignment of block-copolymer
Zusammenhang zwischen Vernetzung und höheren Harmonischen in Kautschuken
Relation between topology and non-linear response
Effect of charges, pH and solid content in dispersions towards the non-linear response