| We analyze branching polymers, called dendrimers, grafted to a flat surface, called a brush, which perfectly fill space above the surface, called a melt, with continuously defined branching profiles. The profiles we consider are representative of traditionally branching and statistically branching dendrimers. Using the ansatz of a parabolic monomer interaction pressure, derived from the polymer brush system and appropriated through an analogy to a time dependent mass in a gravitational potential, analytical solutions for the hight of a monomer from the grafting surface as a function of its position on the polymer chain were found. We were then able to numerically solve for the density of free ends as a function of height. Within our ansatz, there exists a degeneracy of the free energy with respect to an individual dendrimers maximal height. We find that the dendrimer melt brush consists of dendrimers shaped like buoys located at all heights attached to the grafting surface by a highly stretched web of monomers. |
