Handbook of Size Exclusion Chromatography and Related ...

shifts to applied laser light, which may be monitored via the autocorrelation
function G 2(t) [Eq. (26)].
G2(t) ¼ 1
T
ð t
0
I(t)I(t þt)dt (26)
where T¼temperature [K], t¼time, I¼intensity of scattered laser light, and
t¼correlation period.
Indirect Laplace transformation of G2(t) yields G2(t), which contains the
translational diffusion coefficient (DT) (72) [Eq. (27)].
G2(t) ¼A 1þCi
" #
ð tmax
tmin
DT(t)
t2 e ( t=t) 2
dt
with t¼ 1
DTh 2
(27)
where D T¼translational diffusion coefficient, h¼scattering vector, and A,
C¼coefficients.
According to Stokes/Einstein [Eq. (28)] DT of observed glucans and
glucan aggregates may be correlated with radius RH or diameter (d)of amoving
equivalent sphere.Inthecase ofglucan aggregates,diameterdrather isthelength
of coherent segments and, thus, dfor glucans is used as coherence length lcoh of
molecular and/or supermolecular glucan segments.
DT ¼ kBT
!lcoh
6phRH
(28)
where kB ¼Boltzman constant, T¼temperature [K], and h¼viscosity of
solution.
Results from mobility investigations within glucan solutions by means of
photon correlation spectroscopy reflect asituation having two main populations:
. Amajor mass fraction (Fig. 30a) with dimensions (lcoh) in the range
10–30 nm, which represents the molecular dissolved starch glucans;
. A minor, but not negligible, fraction (Fig. 30b) with dimensions (lcoh)in
the range 100–800 nm representing glucan aggregates.
Additionally, translational diffusion coefficient analysis of starch glucan
solutions shows the source of many problems in the analysis of these materials.
Depending on the applied principle of observation, (mass-sensitive refractive
index variations or volume-square of coherent objects by scattering intensities)
either individual glucan molecules (Fig. 30a) or glucan aggregates (Fig. 30b)
dominate the experimental data. If this fact is not considered, SEC-DRI/LS
experiments of starch glucans in particular provide information about supermolecular
aggregates and not about constituent glucan molecular weights.
© 2004 by Marcel Dekker, Inc.