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Polarization carries information about the magnetic fields in interstellarclouds. The observations of polarized dust emission are used to study the roleof magnetic fields in the evolution of molecular clouds and the initial phasesof star-formation. We study the grain alignment with realistic simulations,assuming the radiative torques to be the main mechanism that spins the grainsup. The aim is to study the efficiency of the grain alignment as a function ofcloud position and to study the observable consequences of these spatialvariations. Our results are based on the analysis of model clouds derived fromMHD simulations. The continuum radiative transfer problem is solved with MonteCarlo methods to estimate the 3D distribution of dust emission and theradiation field strength affecting the grain alignment. We also examine theeffect of grain growth in cores. We are able to reproduce the results of Cho &Lazarian using their assumptions. However, the anisotropy factor even in the 1Dcase is lower than their assumption of $\gamma = 0.7$, and thus we get lessefficient radiative torques. Compared with our previous paper, the polarizationdegree vs. intensity relation is steeper because of less efficient grainalignment within dense cores. Without grain growth, the magnetic field of thecores is poorly recovered above a few $A_{\rm V}$. If grain size is doubled inthe cores, the polarization of dust emission can trace the magnetic field linespossibly up to $A_{\rm V} \sim 10$ magnitudes. However, many of the prestellarcores may be too young for grain coagulation to play a major role. Theinclusion of direction dependent radiative torque efficiency weakens thealignment. Even with doubled grain size, we would not expect to probe themagnetic field past a few magnitudes in $A_{\rm V}$.

Predictions of polarized dust emission from interstellar clouds: spatial variations in the efficiency of radiative torque alignment