Introduction
A gel can be considered as a solid three-dimensional network that spans the volume of a liquid medium. This network structure can result from physical or chemical interactions, resulting in the formation of physical and chemical gels, respectively with varying degrees of stiffness. Chemical gels include materials such as vulcanized rubbers and cured epoxy resins where the cross-links are covalent in nature. Physical gels are formed through intermolecular associations as a result of hydrogen bonding, Van der Waals forces or electrostatic interactions. Such gels include particulate gels, clay dispersions and associative polymers to name a few.
For a fully cured elastic solid, the gel modulus, G, can be estimated from the following expression:
where v is the number of ‘elastically effective’ network strands per unit volume, k is the Boltzmann constant and T is the temperature. While physical gels do not necessarily conform to this relationship, the value of G is never the less related to the elastic network characteristics and interactions, which may be dependent on polymer/particle concentration, electrical charge or composition.
Consequently G (or the Elastic modulusThe complex modulus (elastic component), storage modulus, or G’, is the “real” part of the samples the overall complex modulus. This elastic component indicates the solid like, or in phase, response of the sample being measurement. Elastic Modulus, G’, in dynamic oscillatory tests) is an important parameter for characterizing gels. For an ideal gel, G’ should be independent of frequency since structural RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation cannot occur; however, many gels show some frequency dependence indicative of structural RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation over different timescales. This RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation process is also important when characterizing gels.
One way to capture both characteristics is from a frequency sweep test which captures the change in G’ as a function of angular frequency, w. At the gel point, G’ generally shows a power law dependence with frequency, which can be characterized using the following model.
where k is known as the RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation strength and n the RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation exponent.
For an ideal gel n has a value of 0 which indicates that no structural RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation occurs (in the measured frequency range anyway). A value greater than 0 suggests some degree of structural RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation, quantified by the magnitude of n. Numerically k is just the value of G’ at an angular frequency (ω) of 1 rad/s.
An additional parameter of interest is the phase angle δ, which can reflect imperfections in the gel structure, or parts of the structure, which are not ‘elastically effective’. A perfect gel will have a phase angle of zero while any value between 0 and 45º suggests some degree of viscous damping which can facilitate RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation.
Another characteristic of gels is the yield StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress, which is the StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress required to break down the three-dimensional network structure and induce flow. There are various methods for determining the yield StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress, however, one of the most sensitive methods is an oscillatory amplitude sweep, which involves measuring the elastic StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress component, σ’ (associated with the elastic structure through G’) as a function of StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain amplitude. The yield StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress is then taken as the peak StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress and the StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain at which this occurs, the yield StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain, which is related to the brittleness of the structure (see Figure 1).
It should be noted that the Power Law ModelThe power law model is a common rheological model to quantify (typically) the shear thinning nature of a sample, with the value closer to zero indicating a more shear thinning material.power law model should only be used to fit data over the measured frequency range since deviations from such behavior may occur at lower or higher frequencies.
Experimental
- Three gel systems including a hair gel, a Xanthan-Mannan gum complex and an associative polymer-surfactant system were evaluated.
- Rotational rheometer measurements were made using a Kinexus rheometer with a Peltier plate cartridge and using cone-plate measuring system1, and using standard pre-configured sequences in the rSpace software.
- A standard loading sequence was used to ensure that both samples were subject to a consistent and controllable loading protocol.
- All rheology measurements were performed at 25°C.
- The tests involved performing a StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain-controlled frequency sweep within the linear viscoelastic range and fitting a Power Law ModelThe power law model is a common rheological model to quantify (typically) the shear thinning nature of a sample, with the value closer to zero indicating a more shear thinning material.power law model to the data to determine k and n as defined in equation 2.
- The yield StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress and StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain were determined in the same sequence by performing a subsequent amplitude sweep test beyond the critical StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain.
Results and Discussion
Figure 2 shows G’ plotted against ω for the different gels performed at 25°C and the model fit parameters. These results show that the hair gel is the stiffest of the three gels with a k value of 301 Pa compared with values of 194 Pa and 63 Pa for the gum complex and associative thickener, respectively.
It can also be seen for both the hair gel and gum complex that G’ varies very little with frequency suggesting little structural RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation is occurring with time. This is reflected in the RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation exponent n which is close to zero in both cases. In contrast, the associative polymer shows a much steeper gradient corresponding with a higher n value of 0.2.
Figure 3 shows the results from the StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain amplitude sweep performed at 1 Hz, including the corresponding values of yield StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress and StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain, as determined from a peak analysis.
The hair gel appears to have the highest Yield StressYield stress is defined as the stress below which no flow occurs; literally behaves like a weak solid at rest and a liquid when yielded.yield stress, followed by the gum complex and the associative thickener. The hair gel will therefore require more StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress input to initiate flow.
In terms of yield StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain, the highest value was measured for the gum complex thus indicating a more ductile structure. The associative polymer has the lowest value, suggesting a comparatively more brittle structure.
Conclusion
Three gels were evaluated using oscillatory testing. Time-dependent gel properties were evaluated from a frequency sweep and the RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation strength k and RelaxationWhen a constant strain is applied to a rubber compound, the force necessary to maintain that strain is not constant but decreases with time; this behavior is known as stress relaxation. The process responsible for stress relaxation can be physical or chemical, and under normal conditions, both will occur at the same time. relaxation exponent n estimated from a Power Law ModelThe power law model is a common rheological model to quantify (typically) the shear thinning nature of a sample, with the value closer to zero indicating a more shear thinning material.power law model fit of G’. In addition, Yield StressYield stress is defined as the stress below which no flow occurs; literally behaves like a weak solid at rest and a liquid when yielded.yield stress and StrainStrain describes a deformation of a material, which is loaded mechanically by an external force or stress. Rubber compounds show creep properties, if a static load is applied.strain were evaluated from a subsequent amplitude sweep. The results demon-strate how such an approach can be used to quantify and compare the properties of different gel systems.
Please note that testing is recommended to be undertaken with cone and plate or parallel plate geometry – with the latter being preferred for dispersions and emulsions with large particle sizes. Such material types may also require the use of serrated or roughened geometries to avoid artefacts relating to slippage at the geometry surface.