260
Carbohydrate Analysis
A
2
is the second virial coefFcient, a mea-
sure of the solute–solvent interaction that
may be important for charged molecules
at low ionic strength or where the solution
is moderately concentrated.
N
A
is Avogadro’s number
h
r
2
g
i
is the
z
-average mean square of the
radius of gyration (
R
G
, which reflects the
average displacement of each residue from
the molecular centre. Eq. 6)
R
2
G
=
<
r
2
g
>
=
X
i
n
i
M
2
i
h
r
2
g
i
i
X
i
n
i
M
2
i
(
6
)
Use of Eq. (2) normally involves extrapo-
lation of theta to zero angle. The molecular
weight and radius of gyration are deter-
mined by plotting
Kc
R
θ
against sin
2
(
θ/
2)
(Zimm plot) to yield an often almost linear
curve whose intercept gives
M
w
and whose
slope at low angles gives the radius of gyra-
tion and hence the hydrodynamic volume.
When combined with the separating
power of high-performance size-exclusion
chromatography (HPSEC), light scattering
forms an important tool for the polysaccha-
ride analyst. A typical SEC-MALLS system
includes an RI detector, placed after the
MALLS detector, for determining the con-
centration of the eluting polysaccharides.
2.3.2
Size-exclusion Chromatography
Size-exclusion chromatography (SEC) has
proved
to
be
a
useful
technique
for
separating carbohydrates on the basis of
their molecular size. Molecules are eluted
in order of decreasing molecular size
from a stationary phase containing a wide
range of different size pores, allowing
greater access and hence slower elution
for smaller molecules. SEC has difFculty
in determining the absolute molecular size
of polysaccharides in which there is a
requirement for similar carbohydrates, of
known molecular weight, for calibration.
In combination with MALLS detection,
however, exact values for polysaccharide
molecular weight polydispersity can be
routinely determined.
The drawback of this technique is that
separation of very large molecules is rela-
tively poor due to the difFculty in manu-
facturing the required high-performance,
high-porosity resins. Also, there can some-
times be losses or poor chromatography
due to nonspeciFc absorption. ±or these
reasons, SEC is to some extent being re-
placed by Feld flow fractionation.
2.3.3
Field Flow Fractionation
±ield flow fractionation (±±±) is a tech-
nique for separating polymers on the
basis of their size. In combination with
MALLS,
it
is
capable
of
determining
molecular weight distributions of com-
plex polysaccharides and delivering far
superior resolution to that obtained by
SEC-MALLS for high molecular weight
materials (
>
100 000 Da). The separatory
principle of the method is the reduction in
the diffusion coefFcient with increase in
molecular size (more exactly, their hydro-
dynamic size). Molecules to be separated
are carried through a thin rectangular
channel with at least one of the broader
surfaces permeable to small molecules and
aqueous solvent (±ig. 4). An introduced
cross flow forces the molecules against
this permeable surface. Larger molecules
with low diffusion constants are left in
the slow-moving carrier stream at this
surface, whereas molecules with greater
diffusion coefFcients are able to leave the
surface and be carried along more quickly
by the fast stream of aqueous solvent
further out. Thus, molecules will leave
the system in order of their diffusion
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