Dendrimers are a class of novel polymer materials, which have received a lot of attention in past decades. The property of a dendrimer material strongly depends on the conformational details of the molecules, including the monomer density distribution, the functional end-group distribution, and the molecular size. In this paper, we consider a dendrimer composed of flexible and long spacers, immersed in the athermal or good solvent. We employ a self-consistent field theory (SCFT) with a pre-averaged excluded volume potential., We calculate the density profiles of the segments and the radius of gyration R of the dendrimers, analyze the stretched conformation of the spacers, and discuss the scaling laws between the dendrimer size and its topologic parameters. Our main results are:(1) The segment density of the dendrimers obeys the "dense-core" model, and decreases smoothly along the radial direction. (2) Due to the folding-back conformation, the local density of the end-segments is proportional to the local segment density. The density profile of the end-segments does not have a lifted peak at the outer layer of the spherical molecule. (3) The conformation of the spacers with lower generation numbers is strongly stretched in the central region where the segments are crowded. The first-generation spacers are mostly stretched. However, the spacers with higher generation numbers are much weakly stretched in the outer region. (4) Our self-consistent field theory calculations give the scaling law of the dendrimer size R~(GP)1/5N2/5, where G is the generation number of the dendrimer, P is the spacer segment number, and N is the total segment number. This agrees with the Flory mean field calculation for dendrimer based on full segment number. But it disagrees with the pioneer theories based on a linear side chains and the results from Monte Carlo simulations, which gave R~(GP)2/5N1/5. We attribute this disagreement to the limited bond length in simulations and the unlimited stretchable spacers in SCFT. (5) If G is fixed, the scaling law is simplified to R~P3/5 in good solvent, which agrees with the pioneer theories.
石梦, 杨颖梓, 邱枫. 柔性树枝形大分子溶液的自洽场理论计算[J]. 化学学报, 2014, 0(0): 0-0.
Shi Meng, Yang Yingzi, Qiu Feng. Self-Consistent Field Theory Studies of Flexible Dendrimer in Good Solvent. Acta Chim. Sinica, 2014, 0(0): 0-0.