This paper presents a detailed study of the scattering polarization profiles
formed under partial frequency redistribution (PRD) in two thermal models of
the solar atmosphere. Particular attention is given to understanding the
influence of several atmospheric parameters on the emergent fractional linear
polarization profiles. The shapes of these $Q/I$ profiles are interpreted
in terms of the anisotropy
of the radiation field, which in turn depends on the source function
gradient that sets the angular variation of the specific intensity. We define
a suitable frequency integrated anisotropy factor for PRD that can be
directly related to the emergent linear polarization. We show that complete
frequency redistribution is a good approximation to model weak
resonance lines. We also
show that the emergent linear polarization profiles can be very sensitive to the thermal
structure of the solar atmosphere and, in particular, to spatial variations of the
damping parameter.