Mechanism for Rapid Self-Assembly of Block Copolymer Nanoparticles

Amphiphilic block copolymers in solution spontaneously self-assemble when the solvent quality for one block is selectively decreased. We demonstrate that, for supersaturation ratio changes [$d(S)/dt$] over ${10}^5$ per second from equilibrium, nanoparticles are obtained with a formation mechanism and size dependent on the jumping rate and magnitude. The threshold rate for homogeneous precipitation is determined by the induction time of a particle, equivalent to the diffusion limited fusion of copolymer chains to form a corona of overlapping soluble brushes. Via determination of the induction time with a novel confined impinging jets mixer and use of a scaling relation, the interfacial free energy of a block copolymer nanoparticle was measured for the first time.

Figure 1

Rapid self-assembly of diblock copolymer nanoparticles via a diffusion limited fusion dominated process from starting conditions of high supersaturation and homogeneous solution. (I) Particle nucleation occurs rapidly and simultaneously with intramolecular and intermolecular insoluble blocks. (II) The nascent particles proceed to fuse with each other depending on the magnitude of the steric and electrostatic insertion barriers until a critical size, that corresponding to an overlapping brush corona. (III) Remaining copolymer must fuse to create nascent particles or find particles with a low insertion barrier. The resulting particles are kinetically frozen, not reaching the equilibrium size due to a slow solvent mediated unimer exchange rate.

Figure 2

Rapid self-assembly of diblock copolymer nanoparticles in a CIJ mixer induced by selective nonsolvent addition to a stream of soluble copolymer. Jet velocities of 8.5 to $0.1\mathrm{m}/\mathrm{s}$ are shown. The resulting particle hydrodynamic diameter via dynamic light scattering (3) is shown to be a strong function of the characteristic time for mixing [Eq. (2)] of the two solvent streams (1,2) until homogeneous kinetics are obtained, $D{a}_p<1$. The mixing time and aggregation time are equivalent at the break point, $D{a}_p=1$.

Figure 3

Determination of the interfacial free energy of a diblock copolymer nanoparticle via use of a scaling relation [Eq. (5)] for induction time versus supersaturation. The induction time is nucleation followed by diffusion limited growth to critical size nanoparticle equivalent to an overlapping brush which is determined via the characteristic mixing time at a Damköhler number of 1 (Fig. 2). The $C_{\mathrm{c}\mathrm{m}\mathrm{c}}$ estimate $={10}^{-6}\mathrm{w}\mathrm{t}\%$ and $\alpha =369$.