Lignin: Functional Biomaterial with Potential in Surface Chemistry and Nanoscience - The Nanoscience and Technology of Renewable Biomaterials - page 184

0.20 M (p)
0.50 M (s)
0.75 M (s)
1.0 M (s)

0

10 − 11 10 − 10 10 − 9 10 − 8

D (m 2 s − 1 )

Figure 7.4 Log-normal distributions of self-diffusion coefficients on some sample super-
natants (s) and one precipitates (p) obtained at different NaCl concentrations. The curve
showing the lowest mass-weightedmedian self-diffusion coefficient is obtained frommea-
surementsonare-dissolvedKLprecipitate.TheKLmacromoleculesinthesupernatantsshow
increasinglyfaster self-diffusion, indicatingadecrease inmolecularweightdue toprecipita-
tionastheionicstrengthofthesamplesolutionsincreases.Reproducedwithpermissionfrom
Norgrenetal.(2001a).

Self-aggregation of colloidal particles into larger clusters has been subjected to serious
scientific studies for more than a century. For aggregation due to Brownian motion, two
well-defined limiting regimes of kinetics have been identified; DLCA and RLCA (Leath
and Reich 1978, Weitz et al . 1987, Weitz et al . 1991, Julien and Botet 1987, Lin et al .
1989, Lin et al . 1990ab, Hildago-Alvarez et al . 1996). The rapid diffusion-limited
cluster(colloid)-cluster(colloid) aggregation is the result of negligible repulsive forces
between the colloidal particles, following the von Smoluchowski equations, and thus
causing particles to stick upon contact and to form loosely jointed and highly dis-
ordered structures. In case of reaction-limited cluster(colloid)-cluster(colloid) aggre-
gation, several collisions are possible before the particles finally aggregates since the
sticking probability is much lower as a result of a substantial repulsive force (electro-
static, electrosteric) between the particles. The creation of somewhat denser aggregates
is characteristic in the RLCA regime. It has further been shown that the described
processes are universal in the sense that they are independent of the detailed nature
of the colloid, if the essential physical interactions are the same (Lin et al . 1989).
The mentioned two classes of aggregation processes and their crossover behaviour are
suggested to be sufficient to describe the complete range of kinetic aggregation (Lin
et al . 1990b).
Aggregation kinetics are often quantified in terms of stability ratios, W , defined as
the ratio of the rate constant for DLCA to the experimentally determined rate constant
for formation of doublets (Reerink and Overbeek 1954, Evans and Wennerstr om 1994).
As the ionic strength in the system increases, the stability ratio approaches unity, which
is where the CCC of an electrolyte is most strictly defined. A theoretical W can be
calculated by integration of an assumed total interaction potential, which might be derived
from the DLVO-theory (Reerink and Overbeek 1954, Evans and Wennerstr om 1994).
Figure 7.5 shows the kinetics of KL aggregate formation and growth, as followed
by quasi-elastic light scattering (QELS). The measurements were performed at 70 ◦ C,