Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures

Abstract

The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macro-phase separation) or micro-phase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting micro-phase separation, we observe rather striking pattern formation under confinement.

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

“…As anticipated in Ref. 24, most of its phases resemble those found in block copolymers or oil/water/surfactant mixtures. Actually, except for the lamellar, one-dimensionally modulated phase that is always superseded by others, the phase diagram reported here contains all the phases commonly predicted in block copolymer melts 25,26,38 including tubular and bicontinuous structures such as the gyroid and the double diamond.…”

“…For instance, the choice of interaction parameters corresponding to "system B" in Ref. 24, in which binary Gaussian mixtures appropriate to model dendrimer solutions were considered, does not fulfill Eq. (37) and still gives a λ-line.…”

“…At the same time, it was clearly stated that such a configuration was not meant to exhaust all the phases presented by the mixture in the inhomogeneous region and that "a rich variety of one-, two-, or three-dimensionally modulated structures (cylinders, lamellae, and crystals), similar to that encountered in block copolymer blends or in ternary oil/water/surfactant mixtures could be expected." 24 This possibility deserves to be ascertained, and in the present paper, we do so by studying in detail via DFT the phase diagram of the same model Gaussian mixture considered in Ref. 20.…”

“…Moreover, even assuming that one uses as a guide the suggestion of Ref. 24 concerning the structures found in block copolymers or in oil/water/surfactant mixtures, a new difficulty has to be faced, stemming from the fact that several of those structures display bicontinuous phases, which do not lend themselves to being represented as a superposition of functions centered at the sites of a simple Bravais lattice. In this case, it is more useful to resort to an expansion on a set of basis functions, which have the symmetries of the phase being investigated.…”

“…In Ref. 24, the interaction parameters were chosen so as to model a binary mixture of dendrimers, with one species being much more compact than the other. In general, cluster formation is favored by negative non-additivity of the interaction ranges.…”