Abstract
The rheological characterisation of viscoelastic materials undergoing a sol-gel transition at the Gel Point (GP) has important applications in a wide range of industrial, biological, and clinical environments and can provide information regarding both kinetic and microstructural aspects of gelation. The most rigorous basis for identifying the GP involves exploiting the frequency dependence of the real and imaginary parts of the complex shear modulus of the critical gel (the system at the GP) measured under small amplitude oscillatory shear conditions. This approach to GP identification requires that rheological data be obtained over a range of oscillatory shear frequencies. Such measurements are limited by sample mutation considerations (at low frequencies) and, when experiments are conducted using combined motor-transducer (CMT) rheometers, by instrument inertia considerations (at high frequencies). Together, sample mutation and inertia induced artefacts can lead to significant errors in the determination of the GP. Overcoming such artefacts is important, however, as the extension of the range of frequencies available to the experimentalist promises both more accurate GP determination and the ability to study rapidly gelling samples. Herein, we exploit the frequency independent viscoelastic properties of the critical gel to develop and evaluate an enhanced rheometer inertia correction procedure. The procedure allows acquisition of valid GP data at previously inaccessible frequencies (using CMT rheometers) and is applied in a study of the concentration dependence of bovine gelatin gelation GP parameters. A previously unreported concentration dependence of the stress relaxation exponent (α) for critical gelatin gels has been identified, which approaches a limiting value (α = 0.7) at low gelatin concentrations, this being in agreement with previous studies and theoretical predictions for percolating systems at the GP.
Highlights
Inertial effects can dominate rheological measurements performed by combined motor-transducer (CMT) rheometers on low viscosity systems or samples with weak gel network structures (Krieger, 1990), such effects being most severe at high frequencies (Klemuk and Titze, 2009; Krieger, 1990; Lauger and Stettin, 2016; and Walters, 1975)
The deviation in the root positions (±6.9◦) should alert the experimentalist to inadequacies in the Gel Point (GP) acquisition procedure, which may be caused by several experimental issues, for example; sample mutation (Hawkins et al, 2010 and Mours and Winter, 1994); sample inertia (Schrag, 1977); evaporation of the sample (Hellstrom et al, 2015); under/over/asymmetric loading (Ewoldt et al, 2015) or instrument inertia
The corrected instrument inertia constant (It) was determined using Enhanced Rheometer Inertia Correction (ERIC); Fig. 1(b) shows the deviation in the root positions for a range of instrument-geometry assembly (It) with the “optimum” value being determined as 21.5422 μNm2
Summary
Inertial effects can dominate rheological measurements performed by combined motor-transducer (CMT) rheometers ( known as controlled stress rheometers) on low viscosity systems or samples with weak gel network structures (Krieger, 1990), such effects being most severe at high frequencies (Klemuk and Titze, 2009; Krieger, 1990; Lauger and Stettin, 2016; and Walters, 1975). Separate motor-transducer (SMT) rheometers ( known as controlled strain) are not susceptible to instrument inertia artefacts since the torque sensing element remains static during data acquisition (Franck, 2003). An inertia correction is routinely applied to raw storage modulus data (G raw) by the software controlling CMT rheometers such that. A momentum balance can be used to show that the inertial term has no imaginary component (Klemuk and Titze, 2009), and the loss modulus, G , is unaffected by the presence of instrument inertia (Franck, 2005). Instrument manufacturers recommend caution where δraw exceeds a stated value that is dependent on the rheometer model, e.g., the TA Instruments
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