Handbook of Size Exclusion Chromatography and Related ...

where for species i, Kri ¼ refractometer constant, dn/dc ¼ specific refractive
index increment, and c i ¼ concentration. The viscometer provides a signal
proportional to the specific viscosity of the sample:
4DP
hsp ¼
(Ip 2DP)
where h sp is the specific viscosity, DP is the differential pressure across the middle
of the capillary bridge of the viscometer, and Ip is the inlet pressure. Thus, at every
elution increment,
DPi ¼ 1
" #
hspi 2 (2 þ hspi) At the very dilute concentrations used in SEC, the intrinsic viscosity at each
increment, [h] i ¼ h spi=ci. Thus, the set of data points ci and [h]i are collected
across the entire SEC chromatogram. These dilute concentrations also enable
simplification of the basic Rayleigh light scattering equation to:
kci
R(Q) i
¼
1
MiP(Q)
where k is a constant dependent upon wavelength, refractive index, dn/dc, and
R(Q) is the excess Rayleigh scattering factor (2). The P(Q) term approaches unity
for molecules having sizes less than 1/20 of the wavelength of the incident light.
In TDS, the hydrodynamic radius of the molecule, Rh is given by:
Rh ¼ 3 [h]M
p
4 0:025
The radius of gyration, Rg, can be determined from the Flory–Fox and Ptitsyn–
Eizner equations (8,9):
where,
© 2004 by Marcel Dekker, Inc.
Rg ¼ 1
6
1=2
[h]M
F
F ¼ 2:55 10 21 (1 2:631 þ 2:861 2 ) and 1 ¼ (2a 1)=3
Ip
1=3
1=3