  The thinning of liquid bridges under capillary stress occurs in widespread
processes like jetting, dripping, and spraying, and creates a strong
extensional flow capable of stretching dissolved polymers. If the elastic
stress exceeds the viscous stress, an exponential `elastocapillary' (EC)
thinning regime arises, yielding a timescale $\tau_{EC}$ commonly considered to
be the longest relaxation time of the polymer $\lambda$. A longstanding
question is why $\tau_{EC}$ depends on the polymer concentration, even at high
dilutions where $\lambda$ should be constant in theory. To date this is
understood in terms of intermolecular interactions that arise as polymers
stretch. However, we show how the concentration dependence of $\tau_{EC}$ can
be explained by considering the molecular weight distribution (MWD) inherent in
real polymer samples. We demonstrate this by blending low-$M$ and high-$M$
polymer samples with narrow MWDs at dilute concentrations and in different
proportions, and by measuring $\tau_{EC}$ for each blend in capillary thinning
experiments. A simple model qualitatively reproduces the experimental results,
showing how elastic stresses generated by the polymer build up prior to the EC
regime due to sequential stretching of decreasing molecular weight species in
the MWD. Since the elastic stress generated by each species depends on its
concentration, the fraction of the MWD that is required to stretch in order to
induce the EC regime depends on the total polymer concentration $c$. For higher
$c$ the EC regime is induced by stretching of a higher-$M$ (longer $\lambda$)
fraction of the MWD, and results in a longer measurement of $\tau_{EC}$. Our
results have significant implications for the application of capillary thinning
measurements to extensional rheometry, for the interpretation of such
measurements, and for the understanding of elastocapillary thinning dynamics in
general.
