Chemistry Reference
In-Depth Information
3.1.7
Ebulliometry
In this method, the boiling points of solutions of known concentration are com-
pared to those of the solvent, at the same temperature. The apparatus tends to be
complicated, and errors are possible from ambient pressure changes and the ten-
dency of polymer solutions to foam. Present-day commercial ebulliometers are
not designed for molecular weight measurements in the range of major interest
with synthetic polymers. The method is therefore only used in laboratories that
have designed and built their own equipment.
3.1.8
Cryoscopy (Freezing Point Depression)
This is a classical method for measurement of molecular weights of micromolecu-
lar species. The equipment is relatively simple. Problems include the elimination
of supercooling and selection of solvents that do not form solid solutions with
solutes and do not have solid phase transitions near their freezing temperatures.
Cryoscopy is widely used in clinical chemistry (where it
is often called
“osmometry”) but is seldom used for synthetic polymers.
3.1.9
End-Group Determinations
End-group analysis is not a colligative pr
ope
rty measurement in the strict sense of
the concept. It can be used to determine
M
n
of polymer samples if the substance
contains detectable end groups, and the number of such end groups per molecule
is known beforehand. (Recall that a branched molecule can have many ends.)
Since the concentration of end groups varies inversely with molecular weight,
end group methods tend to become unreliable at h
igh
er molecular weights. They
can be used, where they are applicable at all, up to
M
n
near 50,000.
End group analysis has been applied mainly to condensation polymers, since
these materials must have relatively reactive end groups if they are to polymerize.
If such polymers are prepared from two different bifunctional monomers the pro-
ducts can contain either or both end group types, and the concentrations of both
are preferably measured for the most reliable molecular weight determinations.
The most important measurement techniques of this type rely on chemical
analysis, with so
me
use of radioisotope and spectroscopic analyses as well.
The value of
M
n
is derived from the experimental data according to
M
n
5
realp
(3-36)
where
r
is the number of reactive groups per macromolecule,
e
is the equivalent
weight of reagent,
a
is the weight of polymer, and
p
is the amount of reagent
used. Thus, if 2.7 g of a polyester that is known to be linear and to contain acid
groups at both ends requires titration with 15 mL 0.1
N
alcoholic KOH to reach a
phenolphthalein endpoint
M
n
5
2
3
56
3
2
:
7
½
1000
=ð
15
3
0
:
1
3
56
Þ 5
3600
Here
r
5
2
,e
5
56 (mol wt of KOH),
a
5
2.7, and the term in brackets is
p
.
