Another “caveat” was raised by theory, which revealed the main chain stiffness
to decrease from the middle of the chain towards the ends. This relates to the fact
that the steric repulsion between the side chains becomes less at both ends due to
the hemispherical volume accessible. In addition, the motion of segments near the
chain ends is less restricted [66, 70, 75–77]. Accordingly, application of the
wormlike chain model with uniform chain stiffness is somewhat questionable, but
for long main chains this effect is most probably not pronounced.
3.3.1 Polymethacrylate-Polystyrene Brushes in Toluene
and Cyclohexane
A series of cylindrical brush polymers was synthesized with a polymethacrylate
(PMA) main chain and polystyrene (PS) side chains of various side chain molar
masses, M
sc , or side chain degrees of polymerization, 6 < P
sc < 33. The aim was
to experimentally investigate the length per repeat unit, l m , the Kuhn statistical
segment length, l k , and the side chain extension in terms of the cross-sectional
radius of gyration, R gc , as well as the segment distribution within the cylindrical
cross-section The full scattering envelope was measured by a combination of
SLS and SANS. The cross-sectional radius of gyration was determined from the
cross-sectional Guinier plot, i.e., ln(qI(q)) versus q
2 , with I(q) being the absolute
scattering intensity and q the scattering vector. The resulting R gc values are shown
in Fig. 14 for measurements in the very good solvent toluene and in the poor
solvent cyclohexane. Fits to the scaling law R gc ¼ k(M n
sc )
a [78, 79] yields values
in toluene, a ¼ 0.61 À 0.67, and in cyclohexane, a ¼ 0.56. Here, k is a fitting
constant and M n
sc is the number average molar mass of the side chains. However,
these results should be taken with caution due to the small side chain molar masses
investigated, but they are qualitatively in good agreement with the simulation
results of the previous section.
From the Holtzer plot of qI(q) versus q [63], the mass per length, M L , was
determined, which translates into the length per monomer unit:
l m ¼ M 0 =M L
(3)
with M 0 as the molar mass of one repeat unit (Fig. 15a, b). In cyclohexane,
l m ¼ 0.207 nm (solid black line in Fig. 15) is obtained, which is significantly
lower than l m ¼ 0.25 nm, the usual value for vinylic chains. The situation in
toluene is less clear: The average over all values yields l m ¼ 0.241 (solid red line
in Fig. 15). A least square fit indicates a decrease of l m with increasing side chain
molar mass (dotted red line in Fig. 15). For small side chains l m ¼ 0.26 is obtained.
The experimental uncertainty is, however, too large to allow for an unambiguous
interpretation. In addition, the factorization of the scattering envelope into main and
side chain form factors might not be justified if the cross-terms between side and
main chain scattering are not negligible [64].
136
K. Binder et al.
to decrease from the middle of the chain towards the ends. This relates to the fact
that the steric repulsion between the side chains becomes less at both ends due to
the hemispherical volume accessible. In addition, the motion of segments near the
chain ends is less restricted [66, 70, 75–77]. Accordingly, application of the
wormlike chain model with uniform chain stiffness is somewhat questionable, but
for long main chains this effect is most probably not pronounced.
3.3.1 Polymethacrylate-Polystyrene Brushes in Toluene
and Cyclohexane
A series of cylindrical brush polymers was synthesized with a polymethacrylate
(PMA) main chain and polystyrene (PS) side chains of various side chain molar
masses, M
sc , or side chain degrees of polymerization, 6 < P
sc < 33. The aim was
to experimentally investigate the length per repeat unit, l m , the Kuhn statistical
segment length, l k , and the side chain extension in terms of the cross-sectional
radius of gyration, R gc , as well as the segment distribution within the cylindrical
cross-section The full scattering envelope was measured by a combination of
SLS and SANS. The cross-sectional radius of gyration was determined from the
cross-sectional Guinier plot, i.e., ln(qI(q)) versus q
2 , with I(q) being the absolute
scattering intensity and q the scattering vector. The resulting R gc values are shown
in Fig. 14 for measurements in the very good solvent toluene and in the poor
solvent cyclohexane. Fits to the scaling law R gc ¼ k(M n
sc )
a [78, 79] yields values
in toluene, a ¼ 0.61 À 0.67, and in cyclohexane, a ¼ 0.56. Here, k is a fitting
constant and M n
sc is the number average molar mass of the side chains. However,
these results should be taken with caution due to the small side chain molar masses
investigated, but they are qualitatively in good agreement with the simulation
results of the previous section.
From the Holtzer plot of qI(q) versus q [63], the mass per length, M L , was
determined, which translates into the length per monomer unit:
l m ¼ M 0 =M L
(3)
with M 0 as the molar mass of one repeat unit (Fig. 15a, b). In cyclohexane,
l m ¼ 0.207 nm (solid black line in Fig. 15) is obtained, which is significantly
lower than l m ¼ 0.25 nm, the usual value for vinylic chains. The situation in
toluene is less clear: The average over all values yields l m ¼ 0.241 (solid red line
in Fig. 15). A least square fit indicates a decrease of l m with increasing side chain
molar mass (dotted red line in Fig. 15). For small side chains l m ¼ 0.26 is obtained.
The experimental uncertainty is, however, too large to allow for an unambiguous
interpretation. In addition, the factorization of the scattering envelope into main and
side chain form factors might not be justified if the cross-terms between side and
main chain scattering are not negligible [64].
136
K. Binder et al.