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.
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.
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!
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
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.
|Please see also the full list of publications|
|The Intrinsic Mechanical Nonlinearity 3Q0(ω) of Linear Homopolymer Melts||M.A. Cziep, M. Abbasi, M. Wilhelm; Novel Trends in Rheology VII, AIP Conference Proceedings 1843 0400002 (2017) ISBN 978-0-7354-1513-3; DOI: 10.1063/1.4982991|
|A Review on Nonlinear Oscillatory Shear tests: Analysis and Application of Large Amplitude Oscillatory shear (LAOS)||K. Hyun, C.O. Klein, M. Wilhelm, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, G.H. McKinley; Prog. Polym. Sci. 36 1697-1753 (2011); DOI 10.1016/j.progpolymsci.2011.02.002|
|Establishing a New Nonlinear Coefficient Q from FT-Rheology, first investigations on entangled linear and branched Polymer melts||K. Hyun, M. Wilhelm;
Macromolecules 42 411-422 (2009); DOI 10.1021/ma8017266
|Fourier-Transform Rheology||M. Wilhelm; Feature Artikel; Macromol. Mater. Eng. 287 83-105 (2002)|