Periodic Reporting for period 3 - Ph.D. (Phase map of dynamic, adaptive colloidal crystals far from equilibrium)
Berichtszeitraum: 2022-11-01 bis 2022-12-31
The ERC Ph.D. project scrutinizes a fundamental question at the heart of the condensed matter, statistical and nonlinear physics: When far from equilibrium, in the presence of fluctuations, and faced with multiple steady states with small energy differences, how does a system evolve? This question underlies innumerable phenomena happening in complex systems every day, which we cannot predict, mimic, or control.
Dynamic adaptive systems are ubiquitous in nature, but they are too complex for a first-principles approach. Experimental systems created in the lab suffer from the same problem. Our uniquely simple colloidal system operates far from equilibrium under highly nonlinear and strongly stochastic conditions, where potential energy surfaces change over time and due to varying external parameters. Therefore, self-assembled aggregates of mesoscale particles can form various patterns ranging from the five basic Bravais lattices (in 2D) to more complex lattices resulting from their superpositions, such as quasicrystals, clathrates, Moiré patterns, honeycomb, and kagome lattices, and more. These crystals exhibit dynamic adaptive behaviour similar to those commonly associated with living organisms.
In the ERC Ph.D. project, we use these dissipative colloidal crystals as a model system to address this fundamental question. Our goal is to create a phase map, similar to a phase diagram of thermodynamics, but where each phase (here, crystal pattern) is dynamic and of finite occupation probability. We will use a convenient tool, fitness landscapes, which originates from evolutionary biology, to describe the stability of each phase in various conditions. We will further ask if this control can be extendable down to the few-nm scale, where fluctuations are much more substantial, and if and how these findings change when using nonidentical, in size or shape, active or passive particles?
Dynamic adaptive systems are ubiquitous in nature, but they are too complex for a first-principles approach. Experimental systems created in the lab suffer from the same problem. Our uniquely simple colloidal system operates far from equilibrium under highly nonlinear and strongly stochastic conditions, where potential energy surfaces change over time and due to varying external parameters. Therefore, self-assembled aggregates of mesoscale particles can form various patterns ranging from the five basic Bravais lattices (in 2D) to more complex lattices resulting from their superpositions, such as quasicrystals, clathrates, Moiré patterns, honeycomb, and kagome lattices, and more. These crystals exhibit dynamic adaptive behaviour similar to those commonly associated with living organisms.
In the ERC Ph.D. project, we use these dissipative colloidal crystals as a model system to address this fundamental question. Our goal is to create a phase map, similar to a phase diagram of thermodynamics, but where each phase (here, crystal pattern) is dynamic and of finite occupation probability. We will use a convenient tool, fitness landscapes, which originates from evolutionary biology, to describe the stability of each phase in various conditions. We will further ask if this control can be extendable down to the few-nm scale, where fluctuations are much more substantial, and if and how these findings change when using nonidentical, in size or shape, active or passive particles?
The main idea of the ERC Ph.D. project stemmed from our earlier study published in Nature Communications in 2017 and reported the first dynamic adaptive colloidal crystals of a multiplicity of patterns that emerged and were sustained far from equilibrium. We showed simple, passive, identical colloidal particles with non-specific interactions exhibit complex pattern formation adaptive behaviour. The revelation that simple physical mechanisms are sufficient for the observed complexity suggested that the self-assembly mechanism should be independent of the chemical, morphological, and other specific details of the particles being assembled. To verify this hypothesis, we used ~3-nm CdTe quantum dots (in water and organic solvents), 500-nm pure polystyrene spheres (in water), ~0.7-μm soft spheres of Micrococcus luteus and ~1-μm × 2-μm rod-like, Escherichia coli bacterial cells, ~5-μm elliptical, Saccharomyces cerevisiae yeast cells, and ~15-μm MCF10A normal human mammary gland cells (all in their respective growth media). In a study published in Nature Physics in 2020, we showed that the emergence and growth of dissipative aggregates of a large variety of constituents exhibited the same scale-free autocatalytic aggregation dynamics. Further, the interface fluctuations of the growing aggregates obey Tracy-Widom statistics. Universal scaling of macroscopic observables was known for systems at or near thermodynamic equilibrium. However, it was unclear if far-from-equilibrium systems could exhibit such universal scaling until our work.
Comprehensive analyses of fluctuations in a dissipative system exhibiting high complexity is a sine qua non. Therefore, we first showed that colloidal particles were uncorrelated before turning the laser on for the first time. However, these particles became correlated once the laser was turned on, exhibiting giant number fluctuations (Nature Communications, 2017). Clearly, the statistics of these fluctuations deviated from the Gaussian probability distribution and disobeyed the Central Limit Theorem. We subsequently showed that the new probability distribution is that of Tracy-Widom statistics that holds for a large class of driven systems with correlated units (Nature Physics, 2020). These findings further motivated us to study fluctuations of disassembling aggregates. Therefore, in a study published in the Journal of Physics: Condensed Matter in 2021, we measured the density fluctuations of the disassembling aggregates and show that they were anomalously suppressed at long wavelengths. This finding uncovered hyperuniformity, colloquially referred to as the hidden order, in seemingly disordered particle configurations. We were the first to show the dynamic evolution of hyperuniform configurations in a dissipative system, and we uncovered persistent hyperuniformity even when the particles were distancing from each other.
Comprehensive analyses of fluctuations in a dissipative system exhibiting high complexity is a sine qua non. Therefore, we first showed that colloidal particles were uncorrelated before turning the laser on for the first time. However, these particles became correlated once the laser was turned on, exhibiting giant number fluctuations (Nature Communications, 2017). Clearly, the statistics of these fluctuations deviated from the Gaussian probability distribution and disobeyed the Central Limit Theorem. We subsequently showed that the new probability distribution is that of Tracy-Widom statistics that holds for a large class of driven systems with correlated units (Nature Physics, 2020). These findings further motivated us to study fluctuations of disassembling aggregates. Therefore, in a study published in the Journal of Physics: Condensed Matter in 2021, we measured the density fluctuations of the disassembling aggregates and show that they were anomalously suppressed at long wavelengths. This finding uncovered hyperuniformity, colloquially referred to as the hidden order, in seemingly disordered particle configurations. We were the first to show the dynamic evolution of hyperuniform configurations in a dissipative system, and we uncovered persistent hyperuniformity even when the particles were distancing from each other.
At the end of the ERC Ph.D. project, we expect to address the original question we posed at the beginning “When far from equilibrium, in the presence of fluctuations, and faced with multiple steady states with small energy differences, how does a system evolve?” Predicting or controlling every major choice of a complex system we see in nature may be too difficult or impossible. However, identifying similar emergent dynamics for a large variety of materials from few-nm quantum materials, mesoscale passive or active particles, and micron-scale living organisms, quantifying the relevant parameters, formulating the underlying mechanisms, and transforming this into a generalised theoretical framework has excellent prospects to further advance multiple research fields from physical to social sciences.