(276h) Displacive Transformations in Floppy Colloidal Crystals: Unearthing the Role of Hydrodynamic Interactions

The existence of displacive, or Martensitic, transformations in binary colloidal crystals comprised of DNA-functionalized micron-scale particles is now established. Casey et al. [1] observed such a transformation from a CsCl (bcc) ‘parent’ crystal into a CuAu (fcc) ‘child’ crystal phase in multiple instances. Subsequently, we have observed similar transformations in a multitude of settings, generating a panoply of binary child phases using different combinations of particle sizes and interaction strengths. The unexpected ubiquity of displacive transformations in these assemblies is interesting because it offers the possibility of increasing the diversity of accessible structures with spherically-symmetric, short-ranged interactions.

A particularly puzzling feature of these transformations is observation that the child configurations are generally not consistent with thermodynamic expectations: out of many energetically degenerate child configurations resulting from many equivalent transformation pathways, the experimental observation is that a single configuration (and therefore pathway) is selected. Indeed, molecular dynamics or Brownian dynamics simulations lead to this expected outcome, generating child configurations that exhibit stacking disorder, at odds with the experiments. Jenkins et al. [2] put forth the suggestion that hydrodynamic drag is responsible for this effect. Different transformation pathways are subject to different drag exerted by the entrained water solvent, leading to a biasing of the transformation outcome.

Here, we study further this hypothesis by performing detailed simulations of the CsClàCuAu transformation with a variety of hydrodynamic approximations. First, we employ Multi-particle Collision Dynamics (MPCD) coupled with molecular dynamics (MD) to explore the role of long-range hydrodynamic interactions as a function of the solvent viscosity [3,4]. We also explore the role of short-ranged interactions by including a lubrication correction to the MPCD dynamics. Finally, we compare the results to other approximate methods, namely Brownian dynamics simulation (BD) with the Rotne-Prager-Yamakawa (RPY) mobility tensor [5]. For each case, we analyze the transformation kinetics and outcome and link these observations to the fluctuations exhibited by the crystals within each representation.

[1] M. T. Casey, R. T. Scarlett, W. B. Rogers, I. Jenkins, T. Sinno, and J. C. Crocker, Nature Communications 3, 1209 (2012).

[2] I. C. Jenkins, M. T. Casey, J. T. McGinley, J. C. Crocker, and T. Sinno, Proceedings of the National Academy of Sciences 111 (13), 4803-4808 (2014).

[3] A. Malevanets and R. Kapral, J. Chem. Phys. 110, 8605-8613 (1999).

[4] M. Ripoll, K. Mussawisade, R. Winkler, and G. Gompper, Physical Review E 72, 016701 (2005).

[5] D. L. Ermak, J. Chem. Phys. 62, 4189 (1975).