Fourier transform rheology is the most frequently used method to interpret the nonlinear rheological behavior of complex fluids under large amplitude oscillatory shear (LAOS). However, the unclear relationship between the higher harmonics and the fundamental harmonic obscures the physical meaning of the nonlinear functions. Here, we hypothesize that all the nonlinear oscillatory shear functions and normal stress functions can be expressed as linear combinations of linear viscoelastic functions or their derivatives at different frequencies under both strain-controlled LAOS (LAOStrain) and stress-controlled LAOS (LAOStress). We check this hypothesis using the time-strain separable Wagner model, Giesekus model, and modified Leonov model. We find such correlations between the nonlinear material functions and the linear material functions are intrinsic for viscoelastic liquids under LAOStrain, and for viscoelastic solids under LAOStress. Finally, these correlations are justified by a viscoelastic standard polydimethylsiloxane, an ethylene–octene multiblock copolymer melt, and a typical simple yield stress material (0.25 wt. % Carbopol).
Under microwave irradiation, agglomerates of nanospherical amorphous calcium magnesium phosphate (ACMP) particles were precipitated from a source solution with Ca 2+ , Mg 2+ , and PO 4 3À . These precipitates were achieved when Mg 2+ was added no less than three times concentrated of Ca 2+ . Otherwise, the as-precipitated powder would only be a mixture of brushite (DCPD) and calcium sodium phosphate (CNP) with poor Mg 2+ substitution. As compared to the mixture of DCPD and CNP, the as-formed ACMP presented great densification during sintering. Moreover, the as-sintered products were bioactive with final composition of magnesium pyrophosphate (MPP), b-tricalcium phosphate (b-TCP), and calcium pyrophosphate (CPP).
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