Techniques in oscillatory shear rheology - Indian Institute of ...

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4 Abhijit P. Deshpande1.2 Typical responseExample variations of G ′ and G ′′ are shown in Fig. 2 for a polymer melt, emulsionand a crosslinking polymer. For the polymer melt (Fig. 2(a)), at very low frequency,viscous behaviour is observed. At higher frequencies, the behaviour is largely governedby the entanglements between polymer molecules. This region is also referredto as the plateau region, due to relatively constant moduli. At very high frequencies,the response is almost elastic. This response is also referred to as the glassy behaviour.It should be noted that the change from viscous to elastic behaviour is observedover a couple of decades in frequency (a change of 100) in case of Maxwellmodel. However, for most materials this change, if at all observed, occurs over severaldecades. For polymer melts, the moduli change by 4 orders of magnitude for a7-8 orders of magnitude change in frequency.The rheology of the emulsions is strongly influenced by the state of flocculation[9]. Unflocculated or weakly flocculated emulsions show a crossover point betweenG ′ and G ′′ . This crossover frequency is associated with a characteristic relaxationtime for the onset of the terminal or flow region for the emulsion. Highlyconcentrated stabilized emulsions show a gel-like response, implying G ′ to be largerthan G ′′ and both being almost constant with respect to frequency. Fig. 2(b) showsthe normalized response of emulsions (with different stabilizer concentrations). Asmentioned, G ′ is larger than G ′′ . Both change by an order of magnitude in the rangeof frequencies investigated [9]. Therefore, a plateau-like region can be observed asthe overall response. Similar to the entanglement plateau region in case of polymer,this region in emulsions may be due to interactions between emulsifiers fromneighbouring droplets [9].Fig. 2(c) shows evolution of linear viscoelastic response for a sample undergoinggelation. In this case, sodium acrylate is being crosslinked in the presence of freeradicalcrosslinker. Initially, G ′ is observed to be lower than G ′′ . With crosslinkingreaction and network formation, both G ′ and G ′′ increase. Near the gel point, thereViscoelasticViscousStressElasticFig. 1 Stress strain during acycle for different materialsStrain
Techniques in oscillatory shear rheology 5is a crossover in G ′ and G ′′ and subsequently G ′ is larger than G ′′ [10]. Once thereaction is complete and gel is formed, both G ′ and G ′′ become constant. G ′ and G ′′for the gel are almost independent of frequency.The overall response to SAOS, as exemplified in Fig. 2 is very complex comparedto simplistic response exhibited by Maxwell model, which is characterized by asingle relaxation time. We understand the overall response by analyzing it to be dueto combinations of several relaxation times.1.3 Relaxation time spectrumThe overall material response is visualized in terms of combinations of severalmechanisms and modes. Each of the modes is described in terms of a Maxwellmodel. Therefore, overall response of material can be captured through a combi-ModuliG"G’(a)Frequency10 5 Time (s)Modulus (Pa)10 010 −5G′G′′(b)(c)10 −100 300 600 900 1200 1500Fig. 2 Representative oscillatory shear response: (a) polymer (b) oil in water emulsions [9] (c)evolution during gelation [10]
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