Simulation of a flexible polymer tethered to a flat adsorbing surface

A lattice self‐avoiding polymer chain with one end attached to an adsorbing flat surface is simulated using Monte Carlo method. The chain model has z = 26 bond vectors with bond length being 1, $\sqrt 2$ , and $\sqrt 3$ on the simple cubic lattice. The dependence of the number of surface contacts M on temperature T in the unit E / k B with E the interacting energy and k B the Boltzmann constant and chain length N is investigated by a finite‐size scaling law M = N ϕ ( a 0 + a 1 ( T − T c ) N 1 /δ + O (( T − T c ) 2 N 2 /δ )) near the critical adsorption point T c . It was estimated that T c = 1.625 and the exponents ϕ = 0.52 and δ = 1.63. It was observed that both mean square end‐to‐end distance 〈 R 2 〉 and mean square radius of gyration 〈 R   g 2 〉 reach minimum at T c . And we discover that the asphericity parameter 〈 A 〉 is independent of chain length at T c . A simple relationship is discovered between T c and bond vector number n b for lattice chain models, and which can be extended to nonlattice chain models by introducing an attraction range fraction f . © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012