radius of gyration than linear polymers and this result in a g-value of less than one
in the SEC-MALLS. The g-value is the ratio of the radius of gyration of branched
polymer to that of a linear polymer and, by definition, g ¼ 1 for non-branched
polymers. A decrease in the g-value towards higher molecular weight indicates an
increased fraction of branched chains at the high M W end. These components of
long relaxation times have a large effect on low shear rheological responses.
Melt flow behavior in comparison with the molecular weight and MWD from
SEC is a sensitive, yet relatively simple and reliable, way of detecting the LCB.
This approach is however always indirect; one needs to compare the rheological
responses to those of linear polymers of similar molecular weight and similar
MWD. Even though the effects of the metallocene-generated LCB go beyond the
effect of broadening the MWD [92, 93, 98–100], it may be a challenge to distinguish between these two. Characterization of the temperature dependence of rheological behavior [97, 100, 101] often offers a convenient way to distinguish
between LCB and MWD effects.
The zero-shear viscosity η 0 of linear polymers scales exponentially with molecular weight [102] above the critical chain length M c , but LCB polymers repeatedly
deviate from this dependency. In comparison to linear polymers of similar M w ,
polymers with low levels of LCB exhibit enhanced zero-shear viscosity values and,
in a qualitative sense,
13 C-NMR-based LCB content often [85, 92, 93], but not
always [100], correlates well with the viscosity increase. For long-chain branched
LDPE, the η 0 in comparison to linear polyethylene of similar M w is lower [103,
104]. A zero-shear viscosity η 0 value higher than that of the corresponding linear
polymers of similar M w is reported to occur at an LCB content of 0.2 LCB/10,000 C
but the increase becomes more pronounced as the LCB content grows [85, 91, 92,
105, 106]. This feature of low amounts of LCB has also been utilized to explore the
extent of metallocene LCB [13, 85, 106, 107].
Figure 3 illustrates utilization of the SEC-based M w and the low shear rate
viscosity to show LCB in narrow MWD metallocene-catalyzed polyethylene
samples [94]. For this comparison, η 0 (from creep measurements) or complex
viscosity η*(ω ¼ 0.01 rad s
À1 from oscillatory shear) values were plotted against
the SEC-measured M w . The solid line in Fig. 3 depicts literature-reported correlation of η 0 and M w for linear polyethylenes [98]. Experimental η 0 results for a linear
reference polyethylene sample (IUPAC5A) follow the literature relationship. In
contrast, values of η 0 or η*(ω ¼ 0.01 rad s
À1 ) for six experimental samples are up
to 50-fold higher than the η 0 expected values for linear polymers of similar
molecular weight. This deviation indicates a long-chain branched structure in the
polymers. Figure 3 also shows the
13 C-NMR-determined values of branching
(branches longer than six carbons) in these ethylene homopolymers. It is seen
that even the samples with barely detectable amounts of LCB have clearly elevated
low shear rate viscosity values.
Naturally, measures other than just a qualitative difference are of high interest
and a variety of indices and procedures have been proposed as a measure for
LCB from rheological behavior contra either the SEC-measured narrow MWD
[93, 100, 106] or branching content from NMR [85, 106, 107]. Numerous approaches
196
J. Seppa ¨la ¨ et al.
in the SEC-MALLS. The g-value is the ratio of the radius of gyration of branched
polymer to that of a linear polymer and, by definition, g ¼ 1 for non-branched
polymers. A decrease in the g-value towards higher molecular weight indicates an
increased fraction of branched chains at the high M W end. These components of
long relaxation times have a large effect on low shear rheological responses.
Melt flow behavior in comparison with the molecular weight and MWD from
SEC is a sensitive, yet relatively simple and reliable, way of detecting the LCB.
This approach is however always indirect; one needs to compare the rheological
responses to those of linear polymers of similar molecular weight and similar
MWD. Even though the effects of the metallocene-generated LCB go beyond the
effect of broadening the MWD [92, 93, 98–100], it may be a challenge to distinguish between these two. Characterization of the temperature dependence of rheological behavior [97, 100, 101] often offers a convenient way to distinguish
between LCB and MWD effects.
The zero-shear viscosity η 0 of linear polymers scales exponentially with molecular weight [102] above the critical chain length M c , but LCB polymers repeatedly
deviate from this dependency. In comparison to linear polymers of similar M w ,
polymers with low levels of LCB exhibit enhanced zero-shear viscosity values and,
in a qualitative sense,
13 C-NMR-based LCB content often [85, 92, 93], but not
always [100], correlates well with the viscosity increase. For long-chain branched
LDPE, the η 0 in comparison to linear polyethylene of similar M w is lower [103,
104]. A zero-shear viscosity η 0 value higher than that of the corresponding linear
polymers of similar M w is reported to occur at an LCB content of 0.2 LCB/10,000 C
but the increase becomes more pronounced as the LCB content grows [85, 91, 92,
105, 106]. This feature of low amounts of LCB has also been utilized to explore the
extent of metallocene LCB [13, 85, 106, 107].
Figure 3 illustrates utilization of the SEC-based M w and the low shear rate
viscosity to show LCB in narrow MWD metallocene-catalyzed polyethylene
samples [94]. For this comparison, η 0 (from creep measurements) or complex
viscosity η*(ω ¼ 0.01 rad s
À1 from oscillatory shear) values were plotted against
the SEC-measured M w . The solid line in Fig. 3 depicts literature-reported correlation of η 0 and M w for linear polyethylenes [98]. Experimental η 0 results for a linear
reference polyethylene sample (IUPAC5A) follow the literature relationship. In
contrast, values of η 0 or η*(ω ¼ 0.01 rad s
À1 ) for six experimental samples are up
to 50-fold higher than the η 0 expected values for linear polymers of similar
molecular weight. This deviation indicates a long-chain branched structure in the
polymers. Figure 3 also shows the
13 C-NMR-determined values of branching
(branches longer than six carbons) in these ethylene homopolymers. It is seen
that even the samples with barely detectable amounts of LCB have clearly elevated
low shear rate viscosity values.
Naturally, measures other than just a qualitative difference are of high interest
and a variety of indices and procedures have been proposed as a measure for
LCB from rheological behavior contra either the SEC-measured narrow MWD
[93, 100, 106] or branching content from NMR [85, 106, 107]. Numerous approaches
196
J. Seppa ¨la ¨ et al.