Correlation between shape and size of linear polymer chains

The correlation between shape (measured by the asphericity parameter A) and size (measured by the square end-to-end distance R2 or the square radius of gyration S2) is investigated using a Monte Carlo technique for linear chains random grown on the three-choice tetrahedral lattice. A positive correlation is found, indicating that a chain conformation of small size is usually more spherical than that of large size. Moreover, the correlation coefficients CA,R2 and CA,S2 are chain length dependent; they decrease with increasing chain length n. The asphericity parameter 〈A〉 is dependent on the bond energy ε and can be expressed as 〈A〉=α+β exp (ε) for not very short chain (n⩾400). The value α is nearly independent of n while β decreases with n. The result can be explained by the correlation between shape and size.