Chemistry Reference
In-Depth Information
Oscillatory shear measurements typically employ a concentric cylinder
geometry, where an oscillatory shear stress (denoted variously as
, with
units of pascals) is induced across an annular volume of sample, whose
deformation (shear strain,
σ
or
τ
γ
) is measured. The loss (viscous) modulus (
G
″
) and
storage (elastic) modulus (
G
′
) of the material can be derived from the ampli-
tudes and phase offset (
δ
) of the applied stress and measured strain oscilla-
tions. The loss factor, tan
δ
, is given by the ratio of viscous to elastic response
(
G
) and is particularly useful in characterizing liquid-to-gel transitions.
Finally, varying the shear rate in a
frequency sweep
allows the identifi cation of
characteristic deviations between viscous and elastic behaviors, such as yield-
ing and shear thinning behavior. Mezzenga et al. (2005) have suggested that
signature rheological properties exist for different LLC phases. Their work
involved identifying characteristic relaxation times based on a crossover
between
G
″
/
G
′
-dominated behaviors derived from frequency sweep mea-
surements, as shown in Figure 4.4.
A recent development in rheological studies of LLC systems has been the
advent of particle tracking microrheology (PTM). Here, hard colloidal spheres
in the submicrometer size range are introduced into the LLC formulation, and
the dynamics of their motion (in the form of a mean-square displacement,
MSD) are calculated from intensity autocorrelation functions measured using
diffusing wave spectroscopy (DWS) (Alam and Mezzenga, 2011; Mason et al.,
1997). These dynamics are related to the viscoelastic properties of the LLC
mesophase within which the particles are embedded.
′
and
G
″
10
2
la3d
Cubic
Pn3m
Cubic
Hex.
10
1
35
40
45
50 55
Temp. (°C)
60
65
70
Figure 4.4
τ
max
) versus temperature for LLCs composed of 80 wt %
Dimodan U/J and 20 wt % water. Time
Relaxation time (
τ
max
is obtained by the crossover of
G
′
and
G
″
.
τ
max
with temperature is associated with the Ia3d phase region,
while positive slope characterizes the Pn3m region. The drop of
A negative slope of
τ
max
beyond 62°C is
consistent with the appearance of the hexagonal phase, as measured at 65°C by SAXS
(Mezzenga et al., 2005 ).
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