Reports: ND755662-ND7: Quantifying the Interactions Between Nanoparticles and Block Copolymer Defects
Robert A. Riggleman, PhD, University of Pennsylvania
Many of the properties of polymer nanocomposites, such as their electrical and optical properties, require precise control of interparticle spacing. Since block copolymers naturally have an equilibrium structure with nanoscale features, block copolymer phases are a promising candidate for assembling nanoparticles. However, a challenge is that nanoparticles are often attracted to and stabilize defects in block copolymers, preventing ordered self-assembly over large length scales. The goal of this New Directions project was to understand the interactions of nanoparticles with defects in block copolymers, and it served as my groups first financial support in the area of block copolymers.
Figure 1: (top) Segregation of nanoparticles (dark isosurfaces) to tilt grain boundaries in block copolymers . (bottom) Influence of nanorod geometry on the tendency of nanorods to adopt a vertical alignment in block copolymer cylinders .
The primary goal of this work was to understand the segregation of nanoparticles to grain boundaries in block copolymers, and we made significant strides in this direction across three publications . First, we systematically studied the strength of segregation of spherical nanoparticles to tilt grain boundaries in lamellarforming block copolymers. We found that the free energy of segregation to the grain boundary scaled with the volume of the nanoparticles, and similarly other additives such as homopolymers followed the same behavior . Surprisingly, our data was not describable with the grain boundary segregation models commonly used in crystalline solids such as the Langmuir-Mclean model. In two other studies, we examined the distribution of rod-like nanoparticles in block copolymer thin films. Experiments had found that nanorods tended to segregate to the underlying substrate, and our simulations found that this was a result of the wetting conditions at the substrate . Later computational studies from our group identified systems that promote vertical nanorod orientation  and have been borne out in recent experiments (in preparation).
Figure 2: Influence of solvent evaporation rate on the distribution of polymer-grafted nanoparticles in a block copolymer thin film .
In addition to our work examining the distribution of nanoparticles around block copolymer defects, we have additionally used the support from this award to apply novel simulation methods to common block copolymer processing techniques. Most significantly, we have developed a method for extending our field-theoretic simulations techniques to non-equilibrium conditions so that we can study dynamic processes . We found that the method is more computationally efficient than comparable dynamic methods such as dissipative particle dynamics (DPD) and it exactly captures the equilibrium thermodynamics of the underlying model. As a result, we believe this method will be instrumental in future field-theoretic simulations studies and enable the study of processes that were not possible before. In our first published work using the method, we studied how solvent vapor annealing can be used to control the distribution of polymer-grafted nanoparticles in block copolymer thin films (see Figure 2). We found that when the solvent evaporation rate is much higher than the particle diffusion rate (high Peclet number), the nanoparticles are trapped in the distribution they adopt in the swollen film. In contrast, at low Peclet numbers the nanoparticles have time to diffuse to their equilibrium dry film state.
The support of this project has had a substantial impact on the career of both the PI and the student primarily supported by the award. This support and the publications resulting from this work  played an instrumental role in the promotion of the PI to Associate Professor with tenure, and work supported by this effort has been presented at numerous conferences, department seminars, and industrial companies in the past two years. The student primarily this project, Huikuan Chao, successfully defended his PhD thesis and currently has a postdoctoral position at CalTech. The final months of this project have supported a second student, Benjamin Lindsay, who is in the fourth year of his PhD and has provided a detailed account of the interactions between nanoparticles within block copolymer domains.
 Chao, H., Lindsay, B. J., and Riggleman, R. A. The Journal of Physical Chemistry B 121, 1119811209
 Rasin, B., Chao, H., Jiang, G., Wang, D., Riggleman, R. A., and Composto, R. J. Soft matter 12(7), 21772185 (2016).
 Koski, J., Hagberg, B., and Riggleman, R. A. Macromolecular Chemistry and Physics 217(3), 509518 (2016).
 Chao, H., Koski, J., and Riggleman, R. A. Soft Matter 13(1), 239249 (2017).
 Koski, J. P. and Riggleman, R. A. The Journal of Chemical Physics 146(16), 164903 (2017).
 Kumar, S. K., Ganesan, V., and Riggleman, R. A. The Journal of Chemical Physics 147(2), 020901 (2017).
 Sharick, S., Koski, J., Riggleman, R. A., and Winey, K. I. Macromolecules 49(6), 22452256 (2016).