Grain alignment theory has reached the stage where quantitative predictions of the degree of alignment and its variations with optical depth are possible .
With the goal of studying the effect of clumpiness on the sub-millimeter and far infrared polarization we computed the polarization due to alignment via radiative torques within clumpy models of cores and molecular clouds .
Our models were based upon a highly inhomogeneous simulation of compressible magnetohydrodynamic turbulence .
A Reverse Monte-Carlo radiative transfer method was used to calculate the the intensity and anisotropy of the internal radiation field , and the subsequent grain alignment was computed for a power-law distribution sizes using the DDSCAT package for radiative torques .
The intensity and anisotropy of the intracloud radiation field show large variations throughout the models , but are generally sufficient to drive widespread grain alignment .
The P - I relations for our models reproduce those seen in observations .
We show that the degree of polarization observed is extremely sensitive to the upper grain size cut-off , and is less sensitive to changes in the radiative anisotropy .
Furthermore , despite a variety of dust temperatures along a single line of sight through our core and amongst dust grains of different sizes , the assumption of isothermality amongst the aligned grains does not introduce a significant error .
Our calculations indicate that sub-mm polarization vectors can be reasonably good tracers for the underlying magnetic field structure , even for relatively dense clouds ( A _ { V } \sim 10 to the cloud center ) .

The current predictive power of the grain alignment theory should motivate future polarization observations using the next generation of multi-wavelength sub-mm polarimeters such as those proposed for SOFIA .