The light-scattering intensity of polymer molecules in solution is proportional to the molecular weight and concentration
of the sample (4):
where, Rθ is the excess intensity of light scattered at angle θ, C is the sample concentration, Mw is the molecular weight, A2 is the second virial coefficient and K is an optical constant, which is proportional to (dn/dC)
. Because the concentration of the sample solution in SEC is highly dilute, A2 is often negligible:
where, P(θ) is the particle scattering function, which represents the angular dependency of light-scattering intensity and is related
to radius of gyration (Rg) of the polymer molecule. Depending on the size and dissymmetry of the polymer molecule, P(θ) can take on values that are equal to, or less than unity. From these equations, intensity of the static light-scattering
signal (LS) can be simplified to:
is the instrument calibration constant and dn/dC is RI increment.
In tetra detection SEC, viscosity of the polymer solution is simultaneously measured by a four-capillary viscometer at every
elution point of the chromatogram with the detector signal of (VIS):
where, [η] is intrinsic viscosity and C is the concentration of solution. The viscometer detector combined with a concentration
detector, such as UV or RI, provides local intrinsic viscosity. The molecular size of the polymer at every elution volume
can be calculated using the intrinsic viscosity.
The concentration detectors used in SEC tetra detection are UV and RI detectors. The UV absorbance detector works like a UV–Visible
spectrophotometer. The response of the detector is as follows:
is the instrument constant and the dA/dC value is equivalent to the ε1% form of the extinction coefficient. The response of the RI detector may similarly be expressed as:
is, again, the instrument constant.
To determine the molecular weight and the size of the target molecule, dn/dC values or concentrations of complexes must first be determined. dn/dC is assumed to be constant for native protein species. For heterogeneous protein conjugates, the dn/dC value will change as the chemical composition varies across the SEC separation. A true dn/dC value can only be obtained by direct determination of discrete dn/dC values at each chromatographic volume increment. The response of a RI detector is the sum of the responses of each species
(protein + PEG) as shown (1):
When the conjugate complex is detected by two different concentration detectors, UV and RI, then two equations are obtained
with two unknowns and this then can lead us to the percentage of both protein and PEG at every elution point:
dn/dC is calculated for each chromatographic volume increment with these equations and used to obtain a corrected concentration
distribution. The corrected dn/dC for each chromatographic volume increment is then used to calculate the correct Mw and size. In our calculations, we used 0.185 mL/g and 0.113 mL/g for dn/dC values of protein and PEG. dA/dC values of protein and PEG were as decribed.