  The surface energy constraint puts a limit on the smallest fragment
$s_{surf}$ that can be produced after a collision. Based on analytical
considerations, this mechanism has been recently identified as been potentially
able to prevent the production of small dust grains in debris discs and cut off
their size distribution at sizes larger than the blow-out size. We numerically
investigate the importance of this effect to find under which conditions it can
leave a signature in the small-size end of a disc's particle size distribution
(PSD). An important part of this work is to map out, in a disc at steady-state,
what is the most likely collisional origin for micron-sized grains, in terms of
the sizes of their collisional progenitors. We implement, for the first time,
the surface energy constraint into a collisional evolution code. We consider a
debris disc extending from 50 to 100AU and 2 different stellar types. We also
consider two levels of stirring in the disc: dynamically "hot" (e=0.075) and
"cold" (e=0.01). For all cases, we derive $s_{surf}$ maps as a function of
target and projectile sizes, $s_t$ and $s_p$, and compare them to equivalent
maps for the dust-production rate. We then compute disc-integrated PSDs and
estimate the imprint of the surface energy constraint. We find that the
($s_p$,$s_t$) regions of high $s_{surf}$ values do not coincide with those of
high dust production rate. As a consequence, the surface energy constraint has
generally a weak effect on the system's PSD. The maximum $s_{surf}$-induced
depletion of $\mu$m-sized grains is $\sim 30$% and is obtained for a sun-like
star and a dynamically hot case. For the e=0.01 cases, the surface energy
effect is negligible compared to the massive small grain depletion induced by
another mechanism: the natural imbalance between dust production and
destruction rates in low-stirring discs identified by Thebault&Wu(2008).
