Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

The configurational properties of tail-like polymer chains with one end attached to a flat surface are studied by using dynamic Monte Carlo technique. We find that the probability distribution of the free end in z direction P(R(z)) and the density profile rho(z) can be scaled approximately by a factor beta to be a length independent function for both random walking (RW) and self-avoiding walking (SAW) tail-like chains, where the factor beta is related to the mean square end-to-end distance . The scaled P(R(z)) of the SAW chain roughly overlaps that of the RW chain, but the scaled rho(z) of the SAW chain locates at smaller betaz than that of the RW chain.