Multimolecular Structure Formation with Linear Dendritic Copolymers

The formation of complex macromolecular structures can be achieved by harnessing self-assembly of well-defined macromolecular building blocks in solution. In this work, we investigate linear-dendritic copolymers, which are dendrimers with chemically different linear chains grafted to their terminal groups. We consider the case of a selective solvent, which is a good solvent for the grafted linear chains and a poor solvent for the dendritic core, so that single molecules also form micelles with a brushlike shell of linear chains. An example could be PEGylated PAMAM dendrimers in aqueous solution. We develop a mean-field model to predict the size of multimolecular micelles formed under equilibrium conditions and at finite concentration of the linear-dendritic copolymers. Out of the combination of the many molecular parameters, which characterizes the linear-dendritic copolymers with flexible spacers, we identify two scaling parameters, which control the free energy of the multimolecular micellar state, and we provide an analytical solution for the most probable number of molecules per micelle in the limit of large micelles. The theoretical model is compared with simulation results using the bond fluctuation model with explicit solvent. The simulations also provide the time evolution of the micelle populations, and we derive the free energy of fusion for a two-molecular state both based on the reaction equation and from the calculation of the potential of mean force between two molecules. Our work provides a systematic concept how to control size and shape of the multimolecular dendritic structures by tuning their molecular parameters. The particular property of linear-dendritic copolymers is well defined in terms of small number of molecules per micelle, which can be switched in a discrete way by changing the solvent properties.