Title: Limits on the designability of complex colloidal crystals

Speaker: Bela Mulder (AMOLF)

Abstract:

Wouldn’t it be great if we could create colloidal particles with designed interactions that are able to self-assemble in crystals with ‘addressable complexity’, i.e., full control over the size and shape of the unit cell as well as the relative positioning of multiple particle species with that cell? Apart from the obvious practical obstacles involved (how the bleep can we make particles with designer interactions?), this idea also poses a very fundamental problem: for a given structure, what are in fact the appropriate interactions? This is the essence of the inverse problem in statistical mechanics.

In this talk I will focus on probably the simplest example of such a problem, to wit an equimolar binary mixture where I want to engineer all possible crystal structures. We attack this problem in a simplified setting by mapping it onto an Ising model with up to next-next-nearest-neighbour interactions on the square lattice. In the mean-field approximation we can (semi)analytically study the possible order-disorder transitions in the system, which yields an intriguingly structured surface in the three-dimensional phase space of the model where the transitions happen. The consequences of this structure are painfully double-faced. The only structures that can be robustly selected for by tuning the interaction parameters are the ‘boring’ ones: homogeneous state (demixing), checkerboard (antiferromagnet) and alternating stripes. All other structures can in fact also be reached directly from the disordered phase, but unfortunately only in an irreducibly fragile way, as they would require infinite precision in tuning the interaction parameters, which a priori precludes their practical realisation.

I will end with a sneak preview of how this plays out in the even more complicated case of multicomponent crystals.

The event will take place in C4.174 and a zoom link will be sent to the CSM mailing list.