Chemistry Reference
In-Depth Information
Ð
M
i
¼1
M
M
r
d
M
f
ð
M
Þ
¼
0
M
r
¼
M
ðr
1
Þ
d
M
;
(2)
Ð
M¼1
M
f
ð
M
Þ
¼
0
with
M
1
¼
M
w
, or by using one of those average molecular masses
and the polydispersity
P
, which is the ratio of
M
w
to
M
n
:
M
n
and
M
2
¼
M
w
M
n
:
P
¼
(3)
There might be a variety of different counterions in a polyelectrolyte, therefore,
the quota of different counterions can be used to further characterize a polyelectro-
lyte. That quota can undergo some changes, e.g., when a polyelectrolyte is dis-
solved in an aqueous solution of electrolytes or of other polyelectrolytes. The
degree of dissociation of a polyelectrolyte is also often used for characterization.
However, from the view of thermodynamics, that property depends on the sur-
roundings and therefore it is more suited for characterizing the state of a polyelec-
trolyte instead of characterizing the polyelectrolyte itself.
Various experimental methods such as potentiometric titration, conductometry,
polarography, electrophoresis, spectroscopy (NMR, UV/VIS), osmometry, light
scattering (static and dynamic laser light scattering, X-ray scattering, and neutron
scattering), viscometry, sedimentation, and chromatography (e.g., size exclusion
chromatography and gel electrophoresis) have been used to characterize polyelec-
trolytes in aqueous solutions (for a recent review cf. Dautzenberg et al. [
12
]).
Experimental information on the average molecular mass of a polyelectrolyte is
mostly derived from laser light scattering, osmometry or viscometry, i.e., from
methods that are also used to determine the thermodynamic properties of polyelec-
trolyte solutions, e.g., the activity of water. The polydispersity of polyelectrolytes is
usually determined by size-exclusion chromatography. Potentiometric titration is
often used to determine the degree of functionalization and the chemical reaction
equilibrium constants for the dissociation/protonation reactions, i.e., properties
characterizing the number of anionic groups saturated by hydrogen ions (in an
anionic polyelectrolyte) or the number of protonated groups (in a cationic polyelec-
trolyte). The number of ionic groups in an anionic polyelectrolyte is sometimes
determined by atomic absorption spectroscopy. X-ray structural analysis and neu-
tron scattering are typical methods for investigating the structure of polyelectro-
lytes. From the viewpoint of thermodynamics, a polyelectrolyte should be
characterized by all single polymers comprising the polyelectrolyte sample, the
number of functional groups (ionic as well as neutral groups), the state of the ionic
groups (e.g., number and nature of dissociable counterions of anionic groups as well
as the number of protonated cationic groups), the secondary structure, and the
concentration of any single polyelectrolyte in the sample. However, that informa-
tion is almost never available. In most cases, the chemical nature of such polyelec-
trolyte samples is only characterized by the backbone monomers and the kind of
