Handbook of Solvents - George Wypych - ChemTech - Ventech!

12.1 Rheological properties, aggregation, permeability 685
Viscosity, Pa s
1000
100
10
1
0.001 0.01 0.1 1 10 100
where:
[η] intrinsic viscosity
ηsp specific viscosity
ηr relative viscosity
k1 coefficient of direct interactions between pairs of molecules
k1′ coefficient of indirect (hydrodynamic) interactions between pairs of molecules
In Θ solvents, the radius of gyration of unperturbed Gaussian chain enters the following
relationship:
,
[ η] 0 = Φ 3
0Rg 0
M
[12.1.9]
where:
Φ0 coefficient of intramolecular hydrodynamic interactions = 3.16±0.5×10 24
R g,0 radius of gyration of unperturbed Gaussian chain
In good solvents, the expansion of chains causes an increase of viscosity as described
by the following equation:
αη [] η=
Φ 3
0 R
M
Shear rate, s -1
Figure 12.1.1. Viscosity vs. shear rate for 10% solution
of polyisobutylene in pristane. [Data from
C R Schultheisz, G B McKenna, Antec ‘99, SPE, New
York, 1999, p 1125.]
3
g,
0
Log viscosity, cP
0.2
-1 -0.8 -0.6 -0.4 -0.2 0 0.2
[12.1.10]
where:
13 / 13 /
α η = [ η] /[ η]
0 is and effective chain expansion factor.
Existing theories are far from being universal and precise in prediction of experimental
data. A more complex treatment of measurement data is needed to obtain characteristics
of these “rheological” liquids.
Figure 12.1.1 shows that the viscosity of a solution depends on shear rate. These data
comes from the development of a standard for instrument calibration by NIST to improve
1.2
1
0.8
0.6
0.4
Log concentration, g dl -1
Figure 12.1.2. Viscosity of polyphenylene solution in
pyrilidinone. [Data from F. Motamedi, M Isomaki,
M S Trimmer, Antec ‘98, SPE, Atlanta, 1998, p. 1772.]