Handbook of Solvents - George Wypych - ChemTech - Ventech!

684 George Wypych
cosity of such mixtures but none is sufficiently universal to replace measurement. Further
details on solvent mixtures are included in Chapter 9.
The addition of solute(s) further complicates rheology because in such mixtures solvents
may not only interact among themselves but also with the solute(s). There are also interactions
between solutes and the effect of ionized species with and without solvent
participation. Only very dilute solutions of low molecular weight substances exhibit Newtonian
viscosity. In these solutions, viscosity is a constant, proportionality factor of shear
rate and shear stress. The viscosity of these solutions is usually well described by the classical,
Einstein’s equation:
η= η ( 1+ 25 . φ)
[12.1.2]
s
where:
ηs solvent viscosity
φ volume fraction of spheres (e.g. suspended filler) or polymer fraction
If φis expressed in solute mass concentration, the following relationship is used:
φ= NVc
M
where:
N Avogadro’s number
V molecular volume of solute ((4/3)πR 3 ) with R - radius
c solute mass concentration
M molecular weight
Combination of equations [12.1.2] and [12.1.3] gives:
η−η ηsc
s
=
25 . NV
M
[12.1.3]
[12.1.4]
The results of studies of polymer solutions are most frequently expressed in terms of
intrinsic, specific, and relative viscosities and radius of gyration; the mathematical meaning
of these and the relationships between them are given below:
⎛η−η
[ η]
= lim⎜
c→0⎜
⎝ ηsc
η
sp
c
lnη
c
s
⎞
⎟
⎠
2
= [] η + k [] η c +⋅⋅⋅
r
1
[] η [ η] 2
= − k′ c +⋅⋅⋅
1
[12.1.5]
[12.1.6]
[12.1.7]
η
ηr = ηsp
+ 1 =
[12.1.8]
η
s