Using the theory of elasticity of polymer gels we show that large-scale
cross-link density patterns written into the structure of the network in the
melt state, can be revealed upon swelling by monitoring the monomer density
patterns. We find that while isotropic deformations in good solvent yield
magnified images of the original pattern, anisotropic deformations distort the
image (both types of deformation yield affinely stretched images in θ
solvents). We show that in ordinary solids with spatially inhomogeneous profile
of the shear modulus, isotropic stretching leads to distorted density image of
this profile under isotropic deformation. Using simple physical arguments we
demonstrate that the different response to isotropic stretching stems from
fundamental differences between the theory of elasticity of solids and that of
gels. Possible tests of our predictions and some potential applications are
discussed.Comment: 16 pages, 3 figure
