Effect of solvent quality and electrostatic interactions on size and structure of dendrimers. Brownian dynamics simulation and mean-field theory

Conformational properties of neutral and charged dendrimers in dilute solutions of different quality have been investigated by a mean-field analytical approach and by Brownian dynamics (BD) computer simulation for systems up to generation six. Radial monomer distribution and mass distribution functions, radii of gyration, and structure factors have been studied as functions of solvent quality, effective charge of the terminal groups, and Debye screening radius. For high-generation dendrimers BD simulations show that the dendrimers hardly fluctuate. Swelling of both neutral and charged dendrimers is reasonably described by a generalized Flory mean-field theory in which the two-body virial term is replaced by the sum of the excluded-volume and two-body attraction terms. A non-Gaussian term taking into account the finite extensibility of spacers and a Coulomb term in the form of the Debye-Hiickel approximation have been included as well. The theta-point for a single dendrimer molecule is defined as the characteristic energy of the excluded-volume interactions when the linear expansion factor a is equal to unity. In contrast to linear polymers, the theta-point defined in such way is different from that calculated as the characteristic energy when scaling relation for a good-solvent conditions stops to be valid. Dendritic terminal groups are distributed through the whole volume of the molecule, but the maximum of this distribution is shifted toward the periphery with increase of Debye screening radius and effective charge of a terminal group. It is shown that fractal dimension of a neutral dendrimer depends on both its generation number and spacer length.