The most common approach for measuring time-dependent viscoelastic properties of a material on a rotational rheometer is to perform small amplitude oscillatory shear (SAOS) over a range of oscillation frequencies – commonly referred to as a frequency sweep – where the sample is oscillated back and forth with a given stress or strain. Here the oscillation frequency, measured in rad/s, is equivalent to 1/t, with t the deformation time of the material.

Let’s consider a sample of Play Putty which is a viscoelastic material. At short deformation times (high frequencies) Play Putty will bounce or tear because the material behaves elastically – deformation energy is largely stored in the material structure. Conversely, if we deform the material at long times (low frequencies) it flows. This is because the structure can rearrange on these longer timescales, dissipating the stored elastic energy.

PLAY PUTTY VIDEO – CLICK TO PLAY

A frequency sweep measures this behavior in terms of the elastic modulus (G’) and viscous modulus (G”), which quantify how solid or liquid like a material is under different deformation conditions – see a ‘Basic Introduction to Rheology’. This information can be used to fingerprint a materials viscoelastic behavior and microstructure, with some common responses shown below for a viscoelastic solid, gel, and viscoelastic liquid. Note, Play Putty is classed as a viscoelastic liquid although this material, and polymeric materials in general, can show all types of behavior over a wide enough time-scale.

While most people use oscillatory testing to get this information, it is possible to get the same information from a creep test – a creep test involves applying a constant uni-directional stress to the sample and seeing how it deforms or strains with time. This data is often reported in terms of the creep compliance (J) and plotted against time as shown below.

While creep and oscillatory tests, and the results generated, are often considered independently they are in fact intrinsically linked. As with spectroscopic techniques such as NMR, the time domain data can be transformed to the frequency domain using mathematical procedures such as the Fourier transform or equivalent algebraic procedures** ^{1}**. One such algebraic procedure is based on an approach widely used in the field of microrheology for converting the mean square displacement to complex modulus

**which has since been adapted for converting creep data also**

^{2}**. This method can be found in the Kinexus rSpace software by searching for Analyse_0050 in rFinder. This is also outlined in a new technical note, that can be downloaded here.**

^{3}So, what are the benefits of performing a creep experiment in the time domain and transforming the data to the frequency domain? Well, since each time point corresponds with an angular frequency then theoretically all frequencies up to 1/t_{max} can be sampled continuously, significantly reducing the time needed to access low-frequency data. For example, to measure down to 0.001 rad/s with a creep test would take 1000 seconds, or 16 minutes and 40 seconds. In comparison, a single full oscillation cycle at 0.001 rad/s would take 6,283 seconds, equivalent to 105 minutes, and that corresponds to a single data point at that frequency!

Below is some data for a polymer melt measured using a frequency sweep test (circles) and a creep test (squares). The frequency measurement consists of 18 measurement points taken over 12 minutes. The converted creep data consists of 120 points measured in just 100 seconds and extending a decade lower in frequency to 0.01 rad/s. For comparison, to reach that same frequency with oscillation testing (based on oscillation settings employed here) would take approximately 45 minutes, so significantly longer.

This approach has also been used as an alternative to Multiwave Oscillation for determining the true gel point of network polymers** ^{4}** and for performing Time-Temperature Superposition more efficiently

**.**

^{5}While there are clearly benefits of using creep testing for accessing low-frequency data quickly, the two approaches are very much complementary with oscillation testing giving access to higher frequency data, which can be acquired relatively quickly in this test mode, while creep testing gives access to the lower frequency data which would be difficult to access in a reasonable experimental time-frame using oscillatory testing.

**References **

- Ferry JD: Viscoelastic Properties of Polymers, Wiley, New York (1980)
- Mason TG: Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation, Rheologica Acta 39 (2000) 371-378
- Duffy J.J, Rega C.A, Jack R, Amin S: An algebraic approach for determining viscoelastic moduli from creep compliance through application of the Generalised Stokes-Einstein relation and Burgers model, Appl. Rheol. 26:1 (2016) 15130
- Larsson M, Duffy J, Murphy, S and Hill A: Using Creep testing as an alternative to Multiwave Oscillation for determining the true gel point of network polymers, Annual Transactions of the Nordic Rheology Society, Vol. 25 (2017)
- Larsson M: Time-Temperature Superposition using Creep Recovery to moduli conversion for Master curve generation, Annual Transactions of the Nordic Rheology Society, Vol. 26 (2018)