Short Communication: Property ModellingCalculation of relaxation spectra from mechanical spectra in MATLAB

A MATLAB function that discretizes the kernels that describe the dependence of storage and loss modulus on angular frequency is advanced. The discretization function along with Tikhonov regularization algorithms were used to calculate the relaxation spectrum from oscillatory measurements in shear. The L-curve criterion for selection of the optimum regularization parameter was also employed and the numerical calculations were performed in MATLAB. The discretization function was validated using artificial data and subsequently applied to treat mechanical spectra of PDMS specimens. Numerical treatment of storage and loss moduli data produced relaxation spectra with well resolved peaks. The novel approach presented is a comprehensive numerical solution producing well-resolved relaxation spectra from dynamic measurements.