Frequency sweep generates a rheological "fingerprint” or spectrum as the sample responds (i.e. deforms) to changing oscillatory (back-forth) movement, typically 0.1-20Hz (6.3-126radians/sec) that can be easily adjusted.  This frequently requested assay measures viscoelastic changes vs frequency that include stiffness (complex modulus, G*), solid nature (elastic or storage modulus, G'), liquid nature (viscous or loss modulus, G"), solid or liquid tendency (phase angle), complex viscosity and tan delta (G"/G'). 

 

This assay is useful to study polymer and biomolecule viscoelastic behavior and arrangement such as entanglement and relaxation in various matrices and conditions.  In this context, a routine application for frequency sweep is demonstrating rheological equivalence, or lack thereof, for batch-to-batch consistency and stability to support process and formulation development.  In addition, this along with other rheology assays are used to quantify differences among suspected adulterated and counterfeit materials to support clients involved with legal and IP (Intellectual Property) challenges.

 

It is important to ensure that this assay is performed well within the sample's particular temperature dependent LVER (Linear Viscoelastic Region) that is determined with an amplitude sweep.  This ensures the sample's rheological integrity is maintained during the various frequency modulated assays to obtain valid results.

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A frequency modulated test is a particularly helpful alternative to assay some samples that tend to displace from assay plates during a rotational assay such as shear rate ramp at relatively low shear rates (<25sec-1), especially when a smaller gap is not possible due to solids that could bind plate movement.  In addition, cohesive samples like dough tend to easily displace from plates during rotational assays.  Whereas the rotational shear rate ramp output is viscosity (n), the corresponding output for an oscillatory modulated assay such as amplitude and frequency sweep is "complex viscosity" (n*) noted in Figure 2 below.  Depending on sample properties, it is important to note that "viscosity" obtained with rotational assays and "complex viscosity" determined with oscillatory assays are not necessarily the same value (see references about "Cox-Merz Rule-Netzsch" and "Cox-Merz Rule-TA"). ​​​

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Figure 1 shows the classic viscoelastic response vs frequency for Silly Putty placed between an oscillating upper plate and stationary lower plate. At low frequency it is a slowly flowing viscoelastic liquid (G" dominant); whereas, at higher frequencies it is a bouncing viscoelastic solid (G' dominant).  The inserted pictures show Silly Putty at rest (slow event=very low frequency) slowly flows as a viscoelastic liquid, yet when rolled into a ball and dropped on a surface (fast event=high frequency) it bounces as a viscoelastic solid.  The G'G" crossover at approx. 3.5Hz (G'=G"; tan delta (G"/G' =1; phase angle = 45deg) defines the liquid-solid transition associated with molecular relaxation time and disentanglement.