Influence of excluded volume on the conformational property of tail-like chain on the simple cubic lattice

The influence of excluded volume on the conformational property of linear tail-like chain with one end attached to a flat surface is investigated by means of dynamic Monte Carlo method. Conformational properties such as mean-square end-to-end distance 〈R²〉, mean-square radius of gyration 〈S²〉 and mean asphericity parameter 〈A〉 are calculated for random walking (RW) and self-avoiding walking (SAW) tail-like chains on the simple cubic lattice. We find that the EV has nearly the same effect on 〈R²〉 as on 〈S²〉: (1) 〈R²〉_SAW/〈R²〉_RW≈〈S²〉_SAW/〈S²〉_RW∝n^0.204±0.05, where n is the chain length, and (2) the limiting value of 〈R²〉/〈S²〉≈7.7 for both chains. The distribution P(R) of the SAW tail-like chain can be expressed as a R⁴ correction of that of the RW one. We find that the value 〈A〉 of the SAW tail-like chain is bigger than that of the RW tail-like chain for all chain lengths, and the limiting values are 0.446±0.006 and 0.403±0.005 respectively.