Handbook of Solvents - George Wypych - ChemTech - Ventech!

12.1 Rheological properties, aggregation, permeability 689
10 S Tate, S Chiba, K Tani, Polymer, 37, No.19, 4421-4 (1996).
11 M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994).
12 M Lee, C Tzoganikis, C B Park, Antec ‘99, SPE, New York, 1999, p 2806.
12.1.2 AGGREGATION
The development of materials with an engineered morphological structure, such as
selective membranes and nanostructures, employs principles of aggregation in these
interesting technical solutions. Here, we consider some basic principles of aggregation,
methods of studies, and outcomes. The discipline is relatively new therefore for the most
part, only exploratory findings are available now. The theoretical understanding is still to be
developed and this development is essential for the control of industrial processes and
development of new materials.
Methods of study and data interpretation still require further work and refinement.
Several experimental techniques are used, including: microscopy (TEM, SEM); 1,2 dynamic
light scattering 3-6 using laser sources, goniometers, and digital correlators; spectroscopic
methods (UV, CD, fluorescence); 7,8 fractionation; solubility and viscosity measurements; 9
and acid-base interaction. 10
Dynamic light scattering is the most popular method. Results are usually expressed by
the radius of gyration, Rg, the second viral coefficient, A2, the association number, p, and the
number of arms, f, for starlike micelles.
Zimm’s plot and equation permits Rg and A2 to be estimated:
2
KC 1 ⎡ 16 R
⎤
2 g 2
= ⎢1+
π sin θ+⋅⋅⋅⎥+
2AC+⋅⋅⋅
2
2
[12.1.11]
Rθ M
λ
w ⎣⎢
3 0 ⎦⎥
where:
K optical constant
C polymer concentration
Rθ Rayleigh ratio for the solution
Mw weight average molecular weight
λ0 wavelength of light
θ scattering angle.
The following equations are used to calculate p and f:
where:
p Magg
= ; Magg = KIq→0 / C
[12.1.12]
M
R
R
g
garm
1
= f
( 1−v)/ 2
Magg mass of aggregates
M1 mass of free copolymers
I scattered intensity
Rgarm radius of gyration of linear polymer
v excluded volume exponent.
[12.1.13]