A general equation relating the lattice and continuum model adsorption interaction parameters of an ideal polymer chain anchored to a planar surface is derived by substituting the exact continuum solution for the free chain end distribution function into the lattice model boundary condition. The similarity between the lattice and continuum model was demonstrated for chains of both infinite and finite length and for all three regimes corresponding to attractive, repulsive and adsorption-threshold energy of polymer-surface interaction.
Gorbunov, A. A., Skvortsov, A. M., van Male, J., & Fleer, G. J. (2001). Mapping of continuum and lattice models for describing the adsorption of an ideal chain anchored to a planar surface. Journal of Chemical Physics, 114, 5366-5375. https://doi.org/10.1063/1.1346686