LAUSR

The eigen-polynomials of the Rouse matrix for the G-generation dendritic chains with arbitrary spacer length (n), and functionalities of the central segment (f0) and outer segments (f) are derived with the aid of graph theoretical method. The exact expression for the radius of gyration with arbitrary f and f0 has also been obtained by using the relationships between the coefficients and the roots of eigen-polynomial. For the special case of the standard dendrimers with no spacer, i.e., f0 = f and n = 0, the approximate eigenvalues are obtained and agree with the numerical results very well. Based on the eigenvalues obtained, the dynamic properties of this class of dendrimers, the intrinsic storage moduli G′(ω) and loss moduli G″(ω), are calculated and compared to those of linear and starlike chains. The graph theoretical method we developed is useful for dealing with the polymer chains with complex topological structures, especially suitable when the chain graph possesses certain symmetric elements.