Optimizing Protocols of Self-Assembly

This proposal describes a computer simulation study aimed at finding and characterizing optimal conditions for the self-assembly of nanoparticles. Self-assembly, the spontaneous organization of nanometer-sized building blocks into well-ordered and functional units, is a building mode ubiquitous in the biochemistry of life, where it produces robust and adaptable structures with a wide array of functions. When mimicked in the laboratory, as a simple and costefficient way of producing device-ready arrays of custom-designed nanoparticles, self-assembly is a much more problematic strategy: Long-range order and function are more often than not crippled by a multitude of defects that the system is unable to anneal within the time available to the experimenter. At the heart of this problem lies an intense competition between the thermodynamically stable, ordered target structure of the system and its kinetic accessibility, the outcome of which depends sensitively on a multitude of parameters associated with the interactions between particles and the applied experimental protocols. With the high number of control parameters to consider and the lack of theoretical guiding principles, reliable, high-quality self-assembly remains elusive in many experimental cases. To tackle this problem we will develop computer simulation techniques designed to overcome dynamical bottlenecks of self-assembly processes and identify regions in the space of parameters like interaction strength and specificity, solvent properties, or ion concentration, that lead to robust, defect-free assembly. The basis for these new techniques is transition path sampling, a trajectory-based simulation strategy that allows the sampling of ensembles of dynamical pathways, even if the low weight of such ensembles in the natural dynamics of the system renders them inaccessible to straightforward simulation. We propose two different transition path sampling algorithms that find, within a a set of given parameters, those values for which the corresponding assembly probability of the system is highest. We will study the properties of these algorithms on simple and transparent model systems before applying them to more sophisticated models of nanoparticle systems currently under experimental investigation. In the next step, we will extend the developed methods to the optimization of time- and space-dependent protocols like electric fields, nonuniform solvent evaporation rates, or temperature annealing protocols. In the second main thrust of the proposal, we plan to characterize "sweet spots" in parameter space with the aim of developing guiding principles for self-assembly, possibly establishing universal relationships between important system parameters and conditions for good assembly. To this end we will study the underlying structure of trajectory space with free-energy methods adapted from existing transition path sampling techniques developed for the study of the dynamical properties of glass-forming liquids. During the return phase of the fellowship, we will apply and extend the developed optimization techniques to physical problems that are not self-assembly related. Specifically, we plan to develop computer simulations for the optimization of experimental probes of water diffusivity at the air/water interface and for the synthesis of nanocrystals with controlled surface configuration and shape.

Living systems like the human body regulate their internal microscopic structure and function through self-assembly, the spontaneous transformation of an unordered collection of small building blocks into complex ordered patterns. The formation of the cell membrane from a large number of lipid molecules and the production of proteins by the ribosome are examples of such self-assembly processes. If Natures simple and effective strategy could be adapted to organize collections of synthetic nanoparticles into similarly complex arrays, many exciting new nano-technologies could be realized. However, for self-assembly to proceed as effortlessly as in living systems, the strengths of the forces between particles as well as external conditions must be just right. Characterizing and finding this sweet spot, outside of which particles form structures that are highly unordered and cannot be used for applications, has been a big challenge in the nanosciences. What guiding principals can be established for the effective self-assembly of nanoparticles? In the project Optimizing protocols of self-assembly, this question has been answered with the help of new computer simulation methods for a number of nanoparticle systems of experimental interest.?The project has significantly contributed to the understanding of the role of shape in the selfassembly of polyhedral nanocrystals. Our simulations show that, when the attractive forces between nanocrystals are only weak, dense packings form that are predicted mathematically to occur for perfect polyhedral shapes. Much more open and complex structures can be obtained, however, through the controlled introduction of attractive forces. Instead of particle shape, energetically heterogeneous interactions (such as occur between nanoparticles covered with DNA molecules) can be used to assemble complex patterns. Using a new simulation method developed within the project, we have shown that self-assembly works best when interactions allow for the correction of assembly mistakes and that, depending on the target structure, interactions of very different strengths are optimal to achieve high assembly yields. Based on these results we have devised a new experimental strategy for the hierarchical self-assembly of a variety of fascinating structures whose complexity is reminiscent of self-assembled patterns in living systems. Even more complex patterns can be achieved when self-assembly happens under the influence of external driving forces, like electric fields or mechanical agitation. Our simulations show that by controlling the frequency and amplitude of a simple periodic external force, nanoparticles can be selectively assembled into compact arrays reminiscent of dense equilibrium structures, or complex anisotropic patterns. When self-assembly is well-controlled, the properties of the resulting structure can often be tuned in striking ways. We have studied the change in structural properties of CdSe nanocrystals when a shell of a different material is self-assembled around it. Our simulations predict that for a particular shell thickness, the core can be trapped in a crystal structure that ordinarily only occurs at high pressures. For core-shell nanorods, we have shown that the electronic structure of the nanoparticle undergoes a transition when the size of the core is changed.