Spherical Nanoindentation of Polyacrylamide Hydrogels Using the Bioindenter from Anton Paar

Table of Content

Experimental Setup and Nanoindentation Conditions
     Elastic Modulus (EIT)
     Effect of Loading Times on Elastic Modulus
     Comparison of Elastic Modulus Values Between ISO 14577 and Hertz Model


Hydrogels, shown in Figure 1, are materials that are extremely soft and have a high liquid content. These materials have been recently used in numerous areas of clinical and biological research, for example from tissue regeneration and osteoporosis through to hemorrhage control. There are many hydrogels that are believed to be promising candidates for regeneration or replacement of many different types of tissues or even as growth substrates for other types of soft tissues present in the human body. An in-depth knowledge of the mechanical properties of hydrogels is therefore required for appropriate and effective application of these materials for specific growth, cellular regeneration and tissue replacement [1,2]. For instance, the mechanical and structural properties of the growth substrate can serve as a biomechanical modulator of cellular behavior and thus, determine the quality and function of the growing cell. Further, it has been found that homeostasis of tissues can be largely influenced by the elasticity of the hydrogel substrate [3]. This process is critical for efficient regeneration of tissues. Measurement of elastic – and in general term mechanical – properties of hydrogels used in biomedicine are therefore extremely important.

Figure 1. Typical hydrogel samples in a Petri dish.

This article presents the results of measurements of creep and mechanical properties of different types of soft polyacrylamide hydrogels using a new nanoindentation device for bioindentation known as Bioindenter (BHT). The Bioindenter has been specifically developed for use in the biomechanical domain which typically needs different sample handling and testing conditions when compared to ‘traditional’ hard materials.

Based on the successful Ultra Nanoindentation Tester (UNHT), the nanoindentation device leverages its exceptional high resolution and thermal stability in both displacement and force measurements. There is a need for normal loads in micronewtons and displacements in tens of micrometers because the biological materials are very soft, and at the same time good thermal stability is critical to determine the materials’ creep properties. The indentation process has been adapted and established for automated testing in liquids as well as testing of samples with uneven surfaces. These indentation procedures enable the measurement of both elastic and time-dependent properties of biomedical and biological samples.

Polyacrylamide (PAAm) hydrogels have been considered for the purpose of this analysis, as they are a common growth substrate employed in many biological laboratories for tissue replacement or cell cultivation. The mechanical properties of PAAm hydrogels can be easily customized to achieve elastic moduli ranging between ~10 kPa and up to ~200 kPa, and thus they are considered to be suitable candidates for demonstrating the bioindentation procedures over a wide range of elastic properties.

Experimental Setup and Nanoindentation Conditions

After a preliminary study [3], four concentrations of polyacrylamide (PAAm) hydrogels were chosen for the nanoindentation experiments - 0.05%, 0.1%, 0.2% and 0.8%. This range of polyacrylamide hydrogels is believed to have appropriate mechanical properties to promote stem cell cultures so as to differentiate and form specific cell types. Further, the selected concentrations of PAAm span a relatively wide range of elastic modulus from ~20 kPa to ~200 kPa (i.e. tenfold increase) and these concentrations are known to show critical time-dependent or creep behavior. Nanoindentation tests were then carried out with the Bioindenter device using a spherical indenter with 500 µm radius made of ruby.

Shown in Figure 2 is the Bioindenter device used during a measurement, with the indenter approaching the surface of the PAAm hydrogel submerged in water. The unique long shaft indenter has a shaft measuring just 1 mm diameter to reduce the buoyancy and capillary effects. PAAm sheets with about ~2 mm thickness and 20x20 mm dimensions were positioned in a 35 mm diameter Petri dish. Both water and hydrogel possess a similar density and the latter would usually float in water. As a result, a stainless steel washer was employed to keep the hydrogel on the bottom of the Petri dish.

Figure 2. The Bioindenter setup with the polyacrylamide (PAAm) sample fully immersed in water. Note the long shaft indenter specially designed for indentation in liquids. The hydrogel was pressed down via a stainless steel washer.

All tests were carried out at room temperature, keeping the sample fully immersed in water so as to prevent drying. The nanoindentation procedure was established so that evaluation can be made of time-dependent response of the PAAm hydrogels: the loading and unloading times were set to 1, 10, 30 and 60 seconds. In all the experiments, a hold period of 100 seconds at the maximum load (Fmax) of 50 µN was maintianed. During this long hold period, the increased penetration depth was tracked and the time-dependent properties of the individual concentrations could thus be compared. These nanoindentation conditions caused a mean contact pressure of ~2 kPa to ~4 kPa, which is also satisfactory for different types of biological materials.

The load-displacement data was examined by means of the Hertz solution for a spherical contact on the loading part (1), where E* represents reduced modulus (which can be set equal to elastic modulus of the sample as the indenter can be considered as a non-compressible body), P is the indentation load, h is the indentation depth and R is the radius of the indenter. The unloading part of the indentation curve was examined in accordance with the ISO 14577 [4] standard. The indentation creep (CIT) was also measured in accordance with Equation (2) where hi and he respectively represent the depth at the beginning and the end of the hold period.




Elastic Modulus (EIT)

The nanoindentation experiments demonstrated large variations in mechanical properties of the four concentrations of PAAm hydrogels. Figure 3 shows typical load-displacement curves achieved on all four types of PAAm hydrogels with a loading time of 10 seconds. It was observed that the buoyancy and capillary forces on the indenter were negligible and the adhesion effects were also minimal, without causing any negative influence on the measurement. The contact point was easily determined: the contact point is defined as the point where the normal force began to increase monotonically. This simple and easy detection of contact point was made possible by the independent true force sensor in the Bioindenter device. The elastic modulus, as measured in accordance with the Hertz equation for spherical contact (1) on the loading portion of the load-displacement curve, differed between 37 kPa for the lowest 0.05% PAAm concentration and 122 kPa for the highest 0.8% PAAm concentration.

Figure 3. Typical load-displacement curves obtained on the tested polyacrylamide gels (500 µm radius spherical indenter, 10 s loading time, 100 s hold period).

Figure 4. Typical penetration depth versus time indentation curves (10 seconds loading). This data was used for evaluation of creep. Corresponding force profile (dashed line) is also shown.

Effect of Loading Times on Elastic Modulus

The elastic modulus from the loading curves of separate concentrations of the PAAm hydrogel differed with the length of the loading time: If the loading time is shorter, the elastic modulus is higher. The elastic modulus was 122 kPa for the 0.8% PAAm and 1 second loading, while the elastic modulus of the same material reduced to 75 kPa for 60 second loading.

Figure 5. Creep (CIT) of the four tested gels as a function of loading time.


Significant creep (penetration depth increase during hold period at constant force Fmax) was seen during the nanoindentation experiments. The level of creep can be estimated through the CIT value (2), acquired from the hold period. The creep values differed between ~8% for the 0.8% PAAm concentration and ~20% for the 0.05% PAAm concentration. In all the samples, shorter loading times result in greater creep during the hold period. Figure 5 shows creep as a function of loading time for all tested concentrations of the PAAm hydrogels. The CIT value stabilized at about 10% for longer loading times (≥30 seconds), regardless of the concentration of PAAm hydrogels. While a relatively long hold period was defined (100 seconds), the penetration depth continued to increase towards the end of the hold period for lower concentration hydrogels (0.05% and 0.1%) and faster loading (1 seconds and 10 seconds). The penetration depth, on the other hand, was almost stable towards the end of the hold period on samples containing higher PAAm concentration (0.2% and 0.8%) and above 30 second loading times. Such wide variations in creep behavior highlight the significance of the characterization of time-dependent properties of materials, including hydrogels, containing large fractions of liquid.

Comparison of Elastic Modulus Values Between ISO 14577 and Hertz Model

Based on the analysis of the unloading portion of the load-displacement curve, the values of elastic modulus were measured in accordance with ISO 14577 (Oliver&Pharr) standard. Most commercial nanoindentation software packages include this type of analysis, but its validity for such extremely soft materials has to be confirmed. Hence, comparison was made between Hertz fit on loading and ISO 14577 fit on unloading. Table 1 shows the comparison of the elastic modulus values acquired by these two methods.

Table 1. Elastic modulus values calculated by Hertz and ISO 14577.

Young's modulus [kPa]
Hertz fit to loading
Loading time 0.05% 0.1% 0.2% 0.8%
1 s 36.9±1.1 49.7±0.7 62.8±1.2 121.8±2.8
10 s 37.1±0.9 43.9±0.7 55.5±2.4 111.0±3.1
30 s 32.3±0.4 40.1±0.8 49.1±3.6 77.4±4.6
60 s 31.0±0.1 38.5±1.7 45.3±1.4 74.6±2.2
ISO 14577 (Oliver&Pharr) fit to unloading
Loading time 0.05% 0.1% 0.2% 0.8%
1 s 24.2±0.5 31.1±0.8 36.7±1.9 74.4±1.9
10 s 22.6±0.3 27.1±0.4 34.5±0.9 77.8±0.9
30 s 22.0±0.4 25.4±0.7 33.3±1.0 65.7±1.0
60 s 21.3±0.6 27.1±0.9 34.1±1.8 65.9±1.8


General Measurement Remarks

The outcomes of the indentation experiments demonstrated that local characterization of mechanical properties of extremely soft materials immersed in liquids can be performed, but an instrument and a reliable measurement protocol should be available. The indentation procedure involves the use of a spherical indenter with large radius, extremely low loads (few tens of µN), complete immersion of the sample in liquid and a long hold period. Simultaneously, the nanoindentation device should be able to measure large displacement due to the very low compliance of biological materials and hydrogels. The adhesion and capillary forces were found to be negligible. These were initially believed to negatively influence the normal force measurements.

Elastic Modulus

Commercially available indentation software usually calculates the elastic modulus of the tested material from the unloading portion of the load-displacement curve, but then the validity of this approach has to be confirmed. Moreover, the analysis of the indentation results by Hertzian fit on the loading part revealed significant variations from the elastic modulus measured from the unloading part: values acquired by Hertz fit on loading were found to be ~50% higher over those measured by the ISO 14577.  But this difference virtually disappeared in the case of stiffer PAAm hydrogels.


The tested hydrogels as well as similar materials show marked creep behavior. With regard to PAAm hydrogels, the CIT values differed from ~8% up to ~20% and during the hold period the depth increase was up to 4 µm in 100 seconds. Thus, it is imperative to include a hold period in the loading protocol and apply different loading times to characterize the material’s time-dependent properties. Therefore, the entire analysis of such nanoindentation experiments should include the standard ISO 14577 analysis as well as an analysis of the creep data as recommended in literature [5, 6].

Figure 6. Ratio of elastic modulus calculated by the ISO 14577 standard (O&P) and Hertz fit.

Hertz and ISO 14577 Analysis

The comparison of the results of Hertzian fit on the loading portion and ISO 14577 analysis on the unloading portion of the indentation curve demonstrate that both methods produce similar results for higher concentrations of PAAm hydrogels. This also corresponds with the creep data, demonstrating that higher concentrations of PAAm (stiffer material) have less distinct creep properties and that standard indentation analysis (ISO 14577 or Hertz) can be applied. Close correlation of results of both methods also demonstrates that the ISO 14577 method can even be applied on materials deforming elastically. On the other hand, the calculation of hardness is not relevant for such types of materials because most of these materials completely recover after unloading, without leaving any residual impression.


This article has demonstrated the results of bioindentation experiments performed on highly soft polyacrylamide hydrogels. For such types of materials, the measurement procedure was effectively applied using the Bioindenter with a spherical indenter of 500 µm radius, hold period of 100 seconds and maximum load of 50 µN. During the experiments, a wide range of loading conditions was applied and creep properties can be determined in addition to elastic modulus. In all the examples, shorter loading time results in larger creep and higher elastic modulus. For constant loading time, increasing concentration of the PAAm hydrogel leads to increased elastic modulus. The time dependent properties of hydrogels are shown to be critical when characterizing the mechanical properties of these materials, and such measurements should be allowed by the bioindentation protocol (including an appropriate instrument). Further, the Hertzian fit and ISO 14577 standard fit provided elastic modulus values that showed significant variations in both methods, particularly for low PAAm concentrations. For higher concentrations of PAAm hydrogels, the agreement between the ISO 14577 standard and Hertz model was surprisingly good, indicating that in the first approximation the ISO 14577 results can be used.


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This information has been sourced, reviewed and adapted from materials provided by Anton Paar TriTec SA.

For more information on this source, please visit Anton Paar TriTec SA.

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