A quantitative analysis of grain alignment in the filamentary dark clo
ud L1755 in Ophiuchus is presented. We show that the observed decrease
of the polarization-to-extinction ratio for the inner parts of this q
uiescent dark cloud can be explained as a result of the decrease of th
e efficiency of grain alignment. We make quantitative estimates of gra
in alignment efficiency for six mechanisms involving grains with eithe
r thermal or suprathermal rotation, interacting with either magnetic h
eld or gaseous how. We also make semiquantitative estimates of grain a
lignment by radiative torques. We show that in conditions typical of d
ark cloud interiors, all known major mechanisms of grain alignment fai
l. All the studied mechanisms predict polarization at least an order o
f magnitude below the currently detectable levels of similar to 1%. On
the contrary, in the dark cloud environments where A(v) <1, the grain
alignment can be much more efficient. There the alignment of suprathe
rmally rotating grains with superparamagnetic inclusions, and possibly
also radiative torques, account for observed polarization. These resu
lts apply to L1755, which we model in detail, and probably also to B21
6 and other similar dark clouds. Our study suggests an explanation for
the difference in results obtained through polarimetry of background
starlight and polarized thermal emission from the dust itself. We conj
ecture that the emission polarimetry selectively reveals aligned grain
s in the environment far from thermodynamic equilibrium, as opposed to
starlight polarization studies that probe the alignment of grains all
the way along the line of sight, including the interiors of dark quie
scent clouds, where no alignment is possible.