We present a coarse grain representation for Gaussian chains in the presence of hard surfaces. Whereas a Gaussian chain in the bulk can be represented by a bead-spring model with a quadratic potential between adjacent beads, the presence of a surface reduces the number of allowed chain configurations and modifies the effective potential between the beads. We derive the corrected potentials for several surface geometries: a single wall, two parallel walls (slit), and a spherical or cylindrical object (nanoparticle). Those potentials can be used in any model that includes a Gaussian chain, regardless of the simulation method. As an illustration, we consider a coarse grain model of a polymeric melt and, using Monte Carlo simulations, we compute the density profiles for (i) a melt confined in a slit and (ii) a melt in the vicinity of a nanoparticle. The case of a polymeric solution confined within a slit is also addressed, and the proposed approach is shown to yield results in qualitative agreement with those obtained with field-theoretic simulations.
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