A Scaling Algorithm of Self-avoiding Chain Adsorbed on the Surface

Abstract

A single polymer chain with one end tethered to an impenetrable flat surface is simulated by using Monte Carlo simulation method. The polymer chain is generated using self-avoiding walk method in the simple cubic lattice. The monomer does Brownian motion by the bond-fluctuation method in the simulation. After a long Monte Carlo step, the conformation of the chain reaches equilibrium. There is a scaling relation between the surface contact number M and the chain length N at the critical adsorption temperature T c . The scaling algorithm is presented to determine the critical adsorption point T c by the variance between the interpolation value and the curve fitting value. The dependence of the surface contact number M on the chain length N is presented near the critical adsorption point T c by two critical exponents f and d . The results provide a new efficient method to locate the critical adsorption point and to find out the critical exponents.