Discussion
From the dynamic mechanical analysis of a polymer sample with a phase angle of 30°, the relationship between storage modulus (E') and loss modulus (E'') can be expressed as
Answer: A
The relation is E' = \(\sqrt{3}\) E''.
In dynamic mechanical analysis the loss tangent is the ratio of loss to storage modulus, \(\tan\delta = E''/E'\). With \(\delta = 30^{\circ}\):
\[ \begin{aligned} \frac{E''}{E'} &= \tan 30^{\circ} = \frac{1}{\sqrt{3}} \\ E' &= \sqrt{3}E'' \end{aligned} \]
\(E'' = \sqrt{3}E'\) is the case \(\delta = 60^{\circ}\). The two options with a factor 2 use \(\sin\) or \(\cos\) of 30° (0.5 and \(\sqrt{3}/2\)) instead of the tangent.
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