46 | www.CosmeticsandToiletries.com Vol. 130, No. 7 | September 2015
TESTING | C&T
where the elastic modulus becomes dominant over
the viscous modulus. On these timescales, the polymer chains have insufficient time to free themselves
from entanglements, causing tension in the chain
segments between coupling points and hence elastic
dominant behavior. The length of this plateau relates
to the MW of the polymer and also its concentration.
Further, at extremely high frequencies, polymer solutions undergo a phase transition to give a glass-like
response equivalent to what is usually seen below the
glass-transition temperature, where polymer motion
is highly restricted except for localized vibrational
and rotational modes of deformation.
Quantifying viscoelasticity is an essential precursor to incorporating a polymer in a formulation
in such a way as to confer consumer appeal. To do
so, rotational rheometry is a standard technique
used for oscillatory testing; see the Introduction to
Viscoelasticity sidebar. However, this technique is
limited in cases of exceedingly high frequency testing
or weakly structured, dilute solutions due to inertial
effects associated with both the sample and instrument. As an alternative, microrheology is emerging as
an approach to address these issues and a technique
based on this principle is described in more detail in
the next case study.
Case Study 2: Microrheology
Microrheology is based on the principle of the
movement of probe particles dispersed within a
suspension or solution is related to the viscosity and
INTRODUCTION TO VISCOELASTICITY
Many polymer solutions exhibit viscoelastic properties. Under certain circumstances they flow in a liquid-like
way and in other conditions they do not, becoming more solid or gel-like.
Rheological characterization determines whether a sample has greater viscous tendencies—i.e., is more likely
to flow—or is predominantly elastic, with more structural stability, under specific and relevant conditions.
Viscoelasticity can be quantified via oscillatory testing using a rotational rheometer. This involves the
application of shear stress (or shear strain) as a sinusoidal wave. Since the stress is applied in wave form, it
is possible to observe whether the resultant strain is in phase with the applied force or whether there is a lag,
quantified by the phase angle.
Phase angle is zero (in phase) for an ideal solid and π/2 radians (one quarter of a cycle) out of phase for an
ideal liquid, with viscoelastic materials having a value somewhere between the two. The parameter’s storage
modulus (Gʹ) and loss modulus (Gʹʹ) are derived from these phase angles and can be used to assess whether
viscous or elastic behavior is dominant:
If Gʹ > Gʹʹ the sample exhibits solid-like behavior; i.e., elastic properties dominate.
If Gʹ < Gʹʹ the sample exhibits liquid-like behavior; i.e., viscous properties dominate.
The relative size of Gʹ and Gʹʹ can vary depending on the time scale over which shear is applied to the sample.
Oscillatory testing at high frequency assesses behavior in a relevant way to relatively short timescale processes,
such as those encountered during rapid deformation. In contrast, low frequency testing is more indicative of slow
deformation processes, such as those encountered during storage.
viscoelasticity of the system. In relation, dynamic
light scattering (DLS) is one technique used to track
such movement of probe particles. Taken together,
DLS microrheology can be successfully implemented
with much smaller sample volumes than are typically
needed for a mechanical rotational rheometer; it is
also well-suited for polymer solution characterization. 5
To compare the rheological performance of a
cross-linked polymer with linear polymers of higher
and lower MW, the LHA and XHA samples produced
for Case Study 1, 5 mg/mL of each of these samples
were analyzed, along with a high molecular weight
linear sample, HHA, using DLS microrheologyb.
Figure 4 shows the resulting flow profiles; here, a table
is included showing MW, IV and Rg data measured
during the GPC/SEC experiments, along with the
corresponding calculated values of c*.
At 5 mg/mL, the concentrations of the tested
solutions were below the c* for XHA, which had the
highest c* of the three samples. The flow profile for
XHA showed that correspondingly, it exhibited the
most dilute solution behavior. As the Introduction
to Viscoelasticity sidebar explains, the Gʹʹ was in fact
dominant at all frequencies, meaning the solutions
would flow and have limited elasticity.
The LHA had a lower c*, much closer to the test
concentration. For this solution, the Gʹ was much
higher than for XHA, and at higher frequencies, Gʹ
and Gʹʹ became close and parallel with a gradient of
b Zetasizer Nano ZSP, Malvern Instruments