Chemistry Reference
In-Depth Information
regime, respectively, and
c
*
[
4 (Morris
et al.
, 1981). Exceptions
from this behaviour have been reported for hydrocolloid solutions in
which chain-chain interactions have been modified to attain 'extreme'
solvent conditions (high/low pH, high ionic strength). Also, acquisition
of a large number of
η
]
∼
η
sp
data around
c
*
has, for some hydrocolloids, led
to the identification of two critical concentrations,
c
*
and
c
**
(Castelain
et al
., 1987; Launay
et al
., 1997), with a slope of
∼
2.3 in the transition
region (
c
*
<
c
**
).
The discussion so far has considered concentrated solutions as tem-
porary networks in which the physical junctions, the entanglements,
are continuously formed, disrupted and reformed among the chains. A
further class of molecular theory for hydrocolloids with flexible back-
bones is based on reptation models (de Gennes, 1971) in which each
macromolecule is confined in a tube-like region with contours varying
over time and the molecule can only move by diffusion along the tube.
Hydrocolloids with rigid backbones can be treated as long rods with
the relative orientation of each rod being random as long as the sys-
tem is not sheared; the whole system appears to be isotropic. Above a
critical polymer concentration formation of a liquid, crystalline phase
is observed for rigid rod molecules in which a preferred direction of
molecular orientation takes place as, for example, for xanthan gum (Lee
and Brant, 2002a, 2002b). As a consequence, the viscosity increases
drastically.
The shear viscosity of sufficiently dilute hydrocolloid solutions is
Newtonian. With increasing concentration, shear-thinning behaviour
is often observed, which can be fitted with the model functions. A
multitude of these can be found in rheology textbooks (see, for exam-
ple, Barnes
et al
., 1989; Macosko, 1994; Larson, 1998; Lapasin and
Pricl, 1999; Mezger, 2006), and nowadays the software packages of
rheometers tend to have these models programmed in as data-fitting
options. The simplest type of shear-thinning behaviour is the power law
or Ostwald-de Waele behaviour:
c
<
n
−
1
η
=
k
˙
γ
(4.4)
where
k
is the flow coefficient (or consistency constant) and
n
is the
power law index. For
n
1, the flow behaviour is Newtonian, and
k
equals the viscosity of the solution. For
n
=
<
1, the hydrocolloid solution
is shear thinning, and
n
1 denotes shear-thickening behaviour (i.e.
an increase in shear viscosity with the increasing shear rate, which is
observed for structured liquids of suspension characters rather than for
single-phase hydrocolloid solutions).
The Cross model (4.5) considers power law behaviour at intermediate
shear rates. At sufficiently low or high shear rates, the shear viscosity is
>
