Macromolecules
Article
measurements of the glass transition temperature were performed on
the first and second heating to 350 °C. Trials of different heating rates
(reported in detail elsewhere)38 confirmed that the heating rates used
were sufficiently rapid to avoid significant in situ cure and to capture
the “as-cured” glass transition temperature on the first heating. The
glass transition temperature measured on the second heating (after
exposure to 350 °C) was then taken as the “fully cured” glass transition
temperature. The fully cured glass transition temperature obtained via
oscillatory TMA was then compared to the fully cured glass transition
temperature obtained via DSC after heating to 350 °C. The oscillatory
TMA values were found to be 4 9 °C higher than the DSC values on
average.
(absolute value of t > 0.5), and deviations in smooth data comprising a
cluster of neighboring points. The deviations were then tabulated
based on their numbers and subtotaled based on the corresponding
network compositions (with tables provided in the Supporting
Information). It was found that all of the clusters of significant devia-
tion in the smoothed data contained at least 50% of the components
SiMCy or LECy, with the majority of these clusters containing
conetworks composed primarily of SiMCy and LECy. Similar, but less
dramatic, trends were seen for the other categories of deviations, with
deviations being most common in SiMCy-rich conetworks and in
conetworks with at least 50% SiMCy or LECy.
Since the difference was not statistically significant (it was similar
to the value of the random error in the TMA glass transition tempera-
ture measurements), the two measurements were considered similar
enough that the glass transition temperatures of the uncured resin
(obtainable only by DSC) were used without modification in the
diBenedetto equation, along with the as-cured and fully cured glass
transition temperature values obtained by TMA. Based on measure-
ments of partly cured samples, a value of 0.37 was estimated and
subsequently used for the parameter λ in the diBenedetto equation.
The uncertainty in λ was relatively large, at about 0.1; however,
changes in the value of λ did not affect the significance of conversion
as a regression variable, only the value of the regression coefficient.
Moreover, the standard errors of these regression coefficients were
25−50% of their respective values; hence, a relative error of 25% in
λ produced only a marginal increase in the uncertainty associated with
the regression coefficient.
Using the appropriate measure of composition and, where appro-
priate, the degree of conversion, as independent variables, the key
experimental parameters (31 in total) were analyzed via robust regres-
sion, using a bisquare weighting function and an iterative weighting
algorithm available in MATLAB and described in detail in the refer-
ences listed in the program.39−42 For iteration, the default weighting
parameter of 4.655 was utilized. Given the large numbers of data
points analyzed, the likelihood of encountering apparent outliers due
to random variation was quite high. The use of the robust regression,
which assigned lower weight to the outliers, but did not ignore them,
was considered the most appropriate method for dealing with these
outliers. In cases where the degree of cure was not significant at the
90% confidence level, it was excluded as an independent variable for
further analysis.
ASSOCIATED CONTENT
* Supporting Information
Sections S1.1−S1.31 (results and discussion on a variable-by-
variable basis), Tables S1−S3, Figures S1.1−S1.31, S2.1−S2.31,
and S3.1−S3.31 (normal probability, residual, and smoothed
residual plots for all variables, respectively), and Section S2
(derivation of CTE model). This material is available free of
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AUTHOR INFORMATION
Corresponding Author
■
ACKNOWLEDGMENTS
■
Support from the Air Force Office of Scientific Research, the
Air Force Research Laboratory, and the National Research
Council Research Associateship Program (JR) is gratefully
acknowledged.
REFERENCES
■
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dx.doi.org/10.1021/ma202513h | Macromolecules 2012, 45, 211−220