Handbook of Size Exclusion Chromatography and Related ...

Consider an alternative procedure to Eqs (7). In Eq. (3), replace first
w(V), sUV(V), and sDR(V)with wc (V), sc DR (V), and sc UV (V), respectively.If the
resulting equation is combined with Eq. (7), then the following can be derived:
w(V)¼
ð
h(V,~V)w c (~V)d~V (8)
Equation(8)suggestsanalternativeprocedureforcalculatingw c (V):(a)use
Eq. (3) to obtain the (broadened) mass “chromatogram” w(V), and (b) correct
w(V)for instrumental broadening through Eq. (8). Compared with the normal
procedure of inverting Eq. (7), this methodrequires of asingle inversion,and it is
therefore preferable from the point of view of the propagation of errors.
Equation (8) cannot be extended to pS(V), however. This is because
[unlikeEq.(3)],Eq.(4)isnonlinear.Wehereproposetocalculatep c S (V)asfollows
[see Eq. (1)]:
p c S (V)¼ sc UV (V)
kUVw c (V)
where sc UV (V) is the corrected UV chromatogram [obtained by inversion of
Eq.(7b)];andwc (V)isthecorrectedmass“chromatogram”[obtainedbyinversion
of Eq. (8)].
Figure 2b presents the corrected mass “chromatogram” wc (V), when
calculated by inverting w(V) through Eq. (8) with a singular value decomposition
algorithm (53). The corrected UV chromatogram sc UV (V ) of Fig. 2a was calculated
from sUV(V) using the same inversion algorithm (53). In the midchromatogram
region, the slope of pc S (V) increases steadily with the molar mass. Also, large
errors in pc S (V) are apparent at the chromatogram tails, where compositions larger
than 1 and lower than 0 were obtained. The corrected molecular weights
log M c (V) of Fig. 2c were calculated by interpolation with pc S (V). From wc (V) and
log M c (V), the corrected MWD of Fig. 2d was found. As expected, this
distribution is narrower than the uncorrected MWD. The change in breadth is
quantified by the (rather large) variation in the polydispersity (from 1.27 without
correction to 1.10 with correction, Fig. 2d).
The CCDs (with and without correction for instrumental broadening) are
presented in Fig. 2e. The corrected CCD [wc ( pc S )] was obtained from wc (V) and
pc S (V). Unlike the MWD, the corrected CCD is broader than the uncorrected CCD.
By assuming accurate measurements of the instantaneous mass and composition,
the global average composition is unaffected by the instrumental broadening.
For this reason, it seems preferable to calculate the global composition directly
from w(V ) and pS(V), rather than from wc (V) and pc S (V). The corrected and
uncorrected global compositions ( pc S and pS, respectively) are compared in Fig. 2e.
© 2004 by Marcel Dekker, Inc.
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