Numerical computation of relaxation spectra from mechanical measurements in biopolymers

Calculation of Relaxation Spectra from Stress Relaxation Measurements

“…Conclusion of the resting time is usually identified when storage modulus (G') reaches a pseudo-equilibrium plateau at semi-logarithmic scale, which indicates that most of the measurable stresses introduced during loading of the material have been decayed. Figure 1 demonstrates the effect of resting time on the reproducibility of the stress relaxation experiment with data taken from the literature for highly hydrated gluten networks (Kontogiorgos et al, 2009). The curves superimpose closely in semilogarithmic plots for all different relaxation periods (20 sec to 10 h) as a result of adequate resting time at the geometry of the instrument prior to measurement.…”

“…However, several trials should be performed so as to find the relaxation time that provides a well-resolved spectrum in a reasonable experimental timeframe. In the case of hydrated gluten 30 min relaxation time was found to result in spectra with practically same resolution with the samples that were left to relax for 10 h (Kontogiorgos et al, 2009). A final note on data collection concerns the scale that storage modulus should be recorded.…”

“…In addition, biopolymer ageing during experimentation, possible slippage, and other time dependent effects (gelation, aggregation of the chains) contribute to experimental artifacts that may not correspond to true molecular motion of the biopolymer under investigation. www.intechopen.com Therefore, experimentation with various relaxation times should be preferably conducted until a practically well resolved and stable spectrum is achieved (Kontogiorgos et al, 2009). This is illustrated in Figure 1 where hydrated gluten samples left to relax for different periods of time.…”

“…After collection of raw data, calculation of the relaxation spectrum is possible with a regularization method. In a previous work (Kontogiorgos et al, 2009) we have used and compared three different regularization algorithms (Hansen, 2002;Marino, 2007;Wendlandt, 2005) that employ different approaches in their structure. Hansen's algorithms were the fastest requiring only a few seconds to analyze large datasets.…”

“…This operation is necessary to transform the problem into the corresponding matrix form for numerical analysis with the aid of computers. To discretize kernel K(s, t) = exp(-t/s) MATLAB routine discr can be used that is published elsewhere and the reader can easily reproduce the MATLAB code in a personal computer (Kontogiorgos et al, 2009). In this algorithm the user sets the high and low boundaries of the relaxation spectrum and the algorithm creates a discrete space where the solution x λ ranges using the real experimental time as one of its parameters.…”