Dynamic mechanical properties of agarose gels modeled by a fractional derivative model

The complex modulus (E*) and elastic modulus (E') of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that E* and E' increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient (H) and the power law exponent (beta) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.