Handbook of Size Exclusion Chromatography and Related ...

3. Calculate the g 0 branching parameter from the ratio (at any givenmolar
mass) between the intrinsic viscosity of the branched polymer and the
intrinsic viscosity of the linear homolog, yielding:
g 0 (M)¼ [h](M)
KM a 1 (11)
where K and a are the Mark–Houwink parameters of the linear
homolog.
4. Calculate the gbranching parameter (which is based on the radii of
gyration), which is related to g 0 through the following empirical
expression:
[g(M)] 1 ¼g 0 (M) (12)
where 1depends on the polymer, the solvent, and the temperature, and
is generally unknown for copolymers.
5. Calculate bn(M)by inverting the following nonlinear equation, which
was theoretically derived for trifunctional branching points (9,12):
" # 1=2
g(M)¼ 1þ bn(M)
7
1=2
þ 4bn(M)
9p
1 (13)
An SEC analysis may be improved when measurements are compared with
predictions produced by representative polymerization models. For the
investigated graft copolymer, the 1exponent of Eq. (12) was adjusted from
comparing SEC measurements of g 0 (M)with theoretical predictions of g(M)
provided by apolymerization model (11,12,54). For THF at 258C, the exponent
resultedin1ffi2(12).For thesamesolventandtemperature,theMark–Houwink
parameters of alinear SB diblock copolymer with asimilar global composition
and equivalent molecular weight range were taken from the literature, yielding
K¼3:2 10 4 dL/g and a¼0:693 (23).
The IV and DR chromatograms are presented in Fig. 3a. From the ratio
sDR(V)=sUV(V) and Eq. (4), an almost constant pS(V) was observed. For this
reason, the DR signal was made proportional to the instantaneous mass. The
intrinsic viscosity [h](V) was calculated from Eq. (10), but is not presented here.
The universal calibration resulted in log M(V) [h](V) ¼ 18:09 0:3041 V
(12). The experimental MWD of Fig. 3c was determined from [h](V ) and the
universal calibration. The experimental BD was estimated from Eqs (10)–(13)
(Fig. 3d). This function is represented by a continuous curve in Fig. 3d, but with
the data points concentrated at integer values of the number of branches.
Finally, compare the SEC results with theoretical predictions by a
polymerization model (Figs. 3b, c, and d). For the total copolymer, the following
© 2004 by Marcel Dekker, Inc.