Handbook of Size Exclusion Chromatography and Related ...

to sDR(V) when either nPS ¼nPB ¼constant, or when (more generally)
pS(V)¼constant. Solving for the unknowns in Eqs (1) and (2), one obtains:
w(V)¼
pS(V)¼
1
kDRnPB
nPB nPS
nPB
sDR(V)þ nPB nPS
kUVnPB
þ
1
kUV
kDRnPB
sDR(V)
sUV(V)
sUV(V) (3)
Thesignal-to-noiseratioofachromatogramishigh atitsmaximumbutlow
near to the baseline. Also, large systematic errors can occur at the chromatogram
tails. In Eqs (3) and (4), the values in parentheses are constants. Thus, the
following can be noted: (a) w(V) results from a linear combination of
the chromatograms, and therefore it is relatively “well behaved” from the point
of view of the propagation of errors, and (b) pS(V)is obtained from asignals
ratio, and therefore acceptable estimations are only feasible in the midchromatogram
region.
From the PS and PB standards, the individual calibrations logMPS(V)and
logMPB(V)areobtained.Then,thecopolymermolarmassM(V)canbecalculated
by interpolation with the copolymer composition, as follows (43):
logM(V)¼pS(V)logMPS(V)þ[1 pS(V)]logMPB(V) (5)
Alternatively, the following expression has been derived on the basis of the
universalcalibration,andforcaseswhere thehomopolymercalibrationsarelinear
and parallel to each other (47):
M(V)¼
MPS(V)
1þ(r 1)[1 pS(V)]
where r¼MPS(V)=MPB(V)¼constant. Equation (6) has been later extended for
cases where the homopolymer calibrations exhibit different slopes (48).
Equations (1–6) are strictly applicable to linear block SB copolymers as in
Example 2. However, the same equations are here applied to the SBR copolymer
of Example 1. In Examples 1and 2, acommon set of calibrations were used. The
detectors were calibrated as follows (45): (a) different masses of PS and PB
homopolymers were injected, (b) the total chromatogram areas were represented
vs. the injected masses, (c) three straight lines were adjusted, and (d) the slopes
yielded kUV ¼25800; kDR nPS ¼272,300 and kDR nPB ¼223,500. The
homopolymer calibrations are represented in Figs 1c and 2c. Their analytical
expressions are: log MPS ¼ 0:1821 V þ 12:8219, and log MPB ¼ 0:1821 Vþ
12:5202.
© 2004 by Marcel Dekker, Inc.
(4)
(6)