POLYFLOW - Time-temperature equivalence in rheology - Building the mastercurve
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How and where can one apply the time-temperature equivalence? Time-temperature equivalence (or superposition) can e.g. be applied in the measurements of linear properties G' and G". Usually, devices allow a measurement within a given interval of frequencies. However, when performing measurements at different temperatures, it is possible to expand the interval of frequencies. Indeed, if one does not necessarily know the dependence of linear properties with respect to temperature, it is reasonable to assume that the dependence is the same for G' and G". Hence the ratio tan(delta) = G"/G' does not depend on the temperature. These curves will anyway differ, according to the temperature. Therefore one can shift them in the horizontal direction, towards lower or higher frequencies) in order to connect them. Usually, an experiment performed at a lower temperature would correspond to an experiment at a higher temperature within a higher interval of frequencies, it will therefore require a displacement of the curve towards the right (higher frequencies). The identification of the corresponding shift factor will characterise the dependence with respect to temperature for subsequent analysis; this concerns e.g. the complex viscosity. The attached figure originating from the Ph.D. thesis of I. Vittorias [1] is quite instructive. [1]: I. Vittorias, Fourier-Transform rheology applied on homopolymer melts of different architectures. Experiments and finite element simulations, Ph.D. Thesis, Technische Universitaet Darmstadt (2006). |
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