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

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 bondfluctuation 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 Tc. The scaling algorithm is presented to determine the critical adsorption point Tc 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 Tc by two critical exponents φ and δ. The results provide a new efficient method to locate the critical adsorption point and to find out the critical exponents.