Aggregation Rate Measurements by Zero-Angle
Time-Resolved Multiangle Laser Light Scattering
Ke Wang, Anup K. Singh, and John H. van Zanten*
Chemical Engineering Department, North Carolina State University,
Raleigh, North Carolina 27695-7905, and Chemical & Radiation Detection Laboratory,
Sandia National Laboratories, Livermore, California 94550
Received July 31, 2001. In Final Form: December 18, 2001
A new method for determining second-order aggregation rate constants via time-resolved multiangle
laser light scattering is introduced. A major advantage of this approach is that second-order aggregation
rate constants are determined without any assumptions regarding the dimer intraparticle interference
or form factor. The second-order aggregation rate constants are calculated from the temporal variation
of the zero-angle excess Rayleigh ratio within the context of von Smoluchowski’s well-established model
of colloidal aggregation. The new method is illustrated with two systems: (1) GM1-bearing liposomes
aggregated in the presence of the cholera toxin B subunit and (2) sulfonated polystyrene latex aggregated
in the presence of CaCl2. Whereas the method is demonstrated to be particularly well-suited for investigating
slow aggregation processes, rapid aggregation processes are also accessible if proper precautions are taken.
Introduction
The stability and aggregation kinetics of liquid-
dispersed colloidal particles lies at the heart of many
technological processes including ceramic, magnetic, opti-
cal, and electrical material manufacturing; wastewater
treatment; pharmaceutical formulation; and paint, coating
and ink development. The kinetic stability of colloidal
dispersions is of great significance to all colloid science.
For instance, stability studies are often utilized in
investigations of fundamental interparticle forces and
hydrodynamic interactions. These stability studies are
typically focused on investigations of aggregation or
coagulation processes, particularly during their earliest
stages, which facilitates the interpretation of the experi-
mental measurements.
Colloidal aggregation phenomena have been studied
by a wide variety of techniques. The most unambiguous
methods involve direct counting via ultramicroscopy or
particle counting.
1-4
Unfortunately, these approaches are
tedious and, as such, are not suitable for routine inves-
tigations of colloidal stability. Whereas turbidimetry
provides a rapid means of qualitatively assessing ag-
gregation phenomena,
5,6
difficulties remain with quan-
titatively interpreting these measurements, although it
should be noted that work is proceeding in this area.
7,8
Additionally, static
9,10
and dynamic
11,12
light scattering
methods are frequently used to monitor colloidal stability.
However, when considered individually, these previous
light scattering methods require a priori knowledge of
the dimer intraparticle interference or form factor, which
is typically approximated by the Rayleigh-Gans-Debye
method. This approximation was recently shown to be
erroneous for sufficiently large scattering angles.
13
Swiss
researchers recently described a combined dynamic and
static light scattering method that obviates the need for
assuming an analytical form for the dimer form factor.
14
One potential downfall of their proposed method is its
economic viability, as it requires simultaneous dynamic
and static light scattering measurements to be made at
several angles, which is a potentially expensive under-
taking if one considers the cost of purchasing multiple
autocorrelators. Therefore, an alternative dimer-form-
factor-independent method for determining second-order
aggregation rate constants would be attractive.
In this paper, a new method for determining second-
order aggregation rate constants from time-resolved
multiangle laser light scattering is reported. The second-
order aggregation rate constants are determined from the
temporal variation of the excess Rayleigh ratio at zero
scattering angle analyzed within the framework of von
Smoluchowski’s aggregation model. The primary advan-
tage of this method is that it does not require a priori
knowledge of the dimer intraparticle interference or form
factor, unlike other individual light scattering methods.
The method’s utility is demonstrated with two completely
different types of colloidal aggregation processes: (1)
cholera toxin B subunit-induced aggregation of GM1-
bearing liposomes and (2) CaCl
2
-induced aggregation of
sulfonated polystyrene latex particles. The method is
shown to be particularly useful for monitoring relatively
slow aggregation processes.
Materials and Methods
Materials. Ganglioside GM1, L-R-distearoylphosphatidyl-
choline (DSPC), cholesterol, and cholera toxin B subunit were
obtained from Sigma Chemical Co. (St. Louis, MO). Unilamellar
liposomes with a composition of DSPC/cholesterol/GM1 in a 47.5:
* Corresponding author. E-mail: john_vz@ncsu.edu.
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2421 Langmuir 2002, 18, 2421-2425
10.1021/la011207o CCC: $22.00 © 2002 American Chemical Society
Published on Web 02/21/2002