Mapping of continuum and lattice models for describing the adsorption of an ideal chain anchored to a planar surface

An ideal polymer chain anchored to a planar surface is considered by using both lattice and continuum model approaches. A general equation relating th e lattice and continuum model adsorption interaction parameters is derived in a consistent way by substituting the exact continuum solution for the fr ee chain end distribution function into the lattice model boundary conditio n. This equation is not mathematically exact but provides excellent results . With the use of this relation the quantitative equivalence between lattic e and continuum results was demonstrated for chains of both infinite and fi nite length and for all three regimes corresponding to attractive, repulsiv e and adsorption-threshold energy of polymer-surface interaction. The obtai ned equations are used to discuss the distribution functions describing the tail of an anchored macromolecule and its adsorbed parts. For the tail-rel ated properties the results are independent of the microscopic details of t he polymer chain and the adsorbing surface. One interesting result obtained in the vicinity of adsorption threshold point is a bimodal tail length dis tribution function, which manifests chain populations with either tail or l oop dominance. The properties related to the number of surface contacts con tain, apart from universal scaling terms, also a nonuniversal factor depend ing on microscopic details of polymer-surface interaction. We derived an eq uation for calculating this nonuniversal factor for different lattice model s and demonstrated excellent agreement between the lattice results and the continuum model. (C) 2001 American Institute of Physics.