The basic method for determination of mechanical properties of polymers is rheology using oscillating excitation. This method is the foundation of many research areas of the group of Prof. Wilhelm. In analogy to the non-linear optics, the amplitude and the frequency of the exitation can be raised steadily, finally resulting in an non-linear answer of the material. The FT-Rheology is a special, high sensitive extension of normal oscillating Rheology to the non-linear regime that has been developed in our group.  

Actual working fields in the research strand FT-Rheology are on the one side further development of the method itself, e.g. improvements in resolution via intelligent data recording (oversampling). On the other hand, we also work on different evaluation techniques of the non-linear response functions. Recently, we presented a new non-linearity parameter Q that is extremely sensitive for the topology of polymers, especially for long-chain branching. Another aspect of this strand is the comparison of non-linear information with numerical simulation, e.g. constitutive equations for polymer meltsA. FT-Rheology offers an experimental approach for the non-linearity effects predicted by theory and can be used for comparisons or for the adjustment of nonlinearity parameters, e.g. in the Giesekus-model. A further point belonging in this research strand is the work about flow anomalies in polymer processing.

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

FT-Rheology travels the world

A basic idea of our work is the knowledge transfer with other research groups interested in non-linear rheology. Up to now, approximately 30 copies of the FT-Rheology (Distribution of FT-Rheology worldwide) were installed all over the world. The latest cooperations on the topic of FT-Rheology were with the MIT (Prof. G. McKinley), Caltech ( Prof. J. Kornfield) and Harvard (Prof. Weitz).

Please have a look at the current map that shows locations where FT-Rheology is currently used. Many people visited our group or group members traveld the world. Most exciting travels have brought group members to New Zealand and Saudi Arabia.