Conformational transitions in semiflexible dendrimers induced by bond orientations

Abstract

We theoretically investigate the conformational properties of semiflexible dendrimers where the semiflexibility is implemented by topologically restricting the bond directions and orientations of the respective bond vectors. Molecular size (radius of gyration, R(g) and Wiener index, W), shape factor ρ, configurational free energy F, and the static structure factor, S(q) of semiflexible dendrimers are analyzed as a function of the bond orientation angle, φ. The size of the lower generation dendrimers decreases with increasing φ throughout the entire range of φ, φ ∈ (0, π). The higher generation dendrimers show a non-uniform behavior, for compressed conformations the size decreases with increasing φ, while for the expanded ones it increases with the increase in φ. A conformational transition occurs for the higher generation dendrimers from the limiting value of the hard sphere to an ideal chain with the change in φ. This conformational transition at φ = π∕2 is also reflected in the configurational free energy. The configurational free energy exhibits a discontinuous behavior with the variation of φ, and this discontinuity occurs at φ = π∕2. However, no such conformational transition is observed with the variation of the bond direction angle, θ, generation, G and functionality, f of the semiflexible dendrimers. The flexible dendrimer, i.e., at φ = π∕2 is flanked between the compressed and expanded conformations of the semiflexible dendrimers resembling a hard sphere. The Kratky plot of the structure factor of all conformations quantitatively match with the results obtained from experiments and simulations in the low q-region in respect to the position of the major Kratky peak. For higher wave numbers, the Kratky plots for all conformations of semiflexible dendrimers agree with earlier theoretical results of model dendrimers [R. La Ferla, J. Chem. Phys. 106, 688 (1997); F. Ganazzoli, R. La Ferla, and G. Raffaini, Macromolecules 34, 4222 (2001)] but are in sharp contrast to the experimental [S. Rathgeber et al., J. Chem. Phys. 117, 4047 (2002); S. Rathgeber, T. Pakula, and V. Urban, J. Chem. Phys. 121, 3840 (2004)] and simulated [M. L. Mansfield and L. I. Klushin, Macromolecules 26, 4262 (1993)] scattering curves for the higher generation dendrimers. All compressed conformations (0 < φ < π∕2) behave as compact hard spheres, while the expanded conformations (π∕2 < φ < π) are relatively more open, partially decongesting the steric crowding among the monomers with increasing φ.