It should be noticed that the results obtained would greatly depend on
conditions, such asM,b/L, andb. For instance, ifM¼ 105 , we would have
rg&11 nm,D& 29? 10 ^12 m^2 ?s^1 , and the concentration needed would be about
9 %(try to check these results).
6.2.2 Viscosity
In Section 5.1.2 the effect of solute molecules and particles on viscosity is
briefly discussed. It follows that the intrinsic viscosity½Zis a measure of the
extent to which a certain solute can increase viscosity. (Remember that½Z
equals specific viscosityðZ=Zs 1 Þdivided by concentration for infinitesi-
mally small concentration.) According to the Einstein equation (5.6) the
specific viscosity of a dispersion of spheres is 2: 5 j, wherejis volume
fraction. This means that½Z¼ 2 : 5 j=cforc?0, wherecis concentration in
units of mass per unit volume. For a very dilute polymer solution the
effective volume fraction can be given as the number of molecules per unit
volumeNtimesð 4 = 3 Þpr^3 h, whererhis the hydrodynamic radius; see Eq. (6.5).
Furthermore,N¼c?M=NAV. For the amylose mentioned in the question
just discussed,rh&25 nm andM¼ 106 Da. It follows that½Zwould equal
2 : 56
4
3
pð 25? 10 ^9 Þ^36NAV
106
¼ 10 ^4 m^3 =gor 1 dl/g. The value observed is 1.15 dl/g, close to the calculated result. It can
be concluded that the hydrodynamic volume of the macromolecule (with
interstitial solvent) is far smaller than the volume calculated from the
approximate outer radius of the polymer coil, in this case about 55 nm,
leading to a difference in½Zby a factorð 55 = 25 Þ^3 &11. This implies that a
random coil molecule does not move with all its interstitial solvent, but that
it is partly permeated by solvent. (It is also said that the polymer coils are
partly draining.) On the other hand, the volume fraction, and thereby the
intrinsic viscosity, would be far smaller, here by a factor of about 70, if the
molecule did not contain interstitial solvent.
In the calculations just made, Eq. (6.4) was applied (withn¼ 0 :5). For
most polymers, this is not allowed. The theory for the relation between
viscosity and polymer conformation is rather intricate and not fully worked
out, and one mostly makes shift with the semiempiricalMark–Houwink