Chemistry Reference
In-Depth Information
Fig. 2.21
A typical
Zimm plot
θ
=0
KC/R
C=0
sin
2
θ
/2 + KC
Because scattering varies with different angles from the main beam of light, the results must be
extrapolated to zero concentration and zero angle of scattering. This is done simultaneously by a
method developed by Zimm. A typical Zimm plot is illustrated in Fig.
2.21
.
A very popular technique for determining molecular weights and molecular weight distributions is
ge
permeation chromatography
. It is also called size exclusion chromatography [
69
,
70
]. The proce-
dure allows one to determine
l
M
n
, and the molecular weight distribution in one operation. The
procedure resembles HPLC. It separates molecules according to their hydrodynamic volumes or their
effective sizes in solutions. The separation takes place on one or more columns packedwith small porous
particles. As the solution travels down the columns, there is retention of the polymer molecules by the
pores of the packing. It was postulated in the past that the separation that takes place bymolecular sizes is
due to smaller molecules diffusing into all the pores while the larger ones only into some of the pores.
The largest molecules were thought to diffuse into none of the pores and pass only through the interstitial
volumes. As a result, polymer molecules of different sizes travel different distances down the column.
This means that the molecules of the largest size (highest molecular weight) are eluted first because they
fit into the least number of pores. The smallest molecules, on the other hand, are eluted last because
they enter the greatest number of pores and travel the longest path. The rest fall in between. The process,
however, is more complex than the above postulated picture. It has not yet been fully explained. It was
found, for instance, that different gels display an almost identical course in the relation of dependence of
V
R
(retention volume) to the molecular weight. Yet study of the pores of different gels show varying
cumulative distributions of the inner volumes. This means that there is no simple function correlating
the volume and/or the size of the separated molecules with the size and distribution of the pores [
69
].
Also, the shape of the pores that can be inferred from the ratio of the area and volume of the inner pores is
very important [
70
]. Different models were proposed to explain the separation phenomenon. These were
reviewed thoroughly in the literature. They are beyond the scope of this topic.
As indicated above, the volume of the liquid that corresponds to a solute eluting from the columns
is called the retention volume or elution volume (
M
w
and
V
R
). It is related to the physical parameters of the
column as follows:
V
R
¼ V
o
þ KV
1
where,
V
o
¼
the interstitial volume of the column(s)
K ¼
the distribution coefficient
V
1
¼
the internal solvent volume inside the pores
The total volume of the columns is
V
T
that is equal to the sum of
V
O
and
V
1
. The retention volume
can then be expressed as follows:
V
R
¼ V
O
ð
1
þ KÞþKV
T
