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Fig. 6. Force–length isotherms are plotted to demonstrate the force
correction for a typical thermoelastic test of Araneus MA silk at an
extension of 27%. (A) The force on a fibre at a relative length of 1.27 is
plotted for temperatures of 283 K (reference temperature) and at 298 K. The
dashed line shows the regression between the force measured at 298 K and a
relative length of 0.99, which was calculated based on the thermal swelling
coefficient of 1x10–4°C–1 for
Araneus MA silk. Owing to the small value of the correction, the
uncorrected and corrected isotherms are difficult to distinguish. (B) The
force at a relative length of 1.27 is measured at 283 K (reference
temperature) and at 298 K. At the reference temperature of 283 K, the relative
length at zero force is 1.0 and a relative length of 1.27 is equivalent to an
extension of 27%. However, with a thermal swelling coefficient of
–1x10–2°C–1, the zero force
length at 298 K is reduced to 0.85. This occurs because, at 298 K, the initial
length has decreased because of a thermal de-swelling, and thus the extension
of the fibre has increased. At 298 K, an extension of 27% occurs at a relative
length of 1.08. The linear regression between the measured force and the zero
force length (dashed line) is solved at 1.08 to determine the force at a
constant extension of 27%, and is represented by the black triangle. An
exaggerated thermal swelling coefficient of
–1x10–2°C–1 was chosen to
better demonstrate the correction process.
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