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A profoundly fundamental question at the interface between physics and biology remains open: what are the minimum requirements for emergence of complex behaviour from nonliving systems? Here, we address this question and report complex behaviour of tens to thousands of colloidal nanoparticles in a system designed to be as plain as possible: the system is driven far from equilibrium by ultrafast laser pulses that create spatiotemporal temperature gradients, inducing Marangoni flow that drags particles towards aggregation; strong Brownian motion, used as source of fluctuations, opposes aggregation. Nonlinear feedback mechanisms naturally arise between flow, aggregate and Brownian motion, allowing fast external control with minimal intervention. Consequently, complex behaviour, analogous to those seen in living organisms, emerges, whereby aggregates can self-sustain, self-regulate, self-replicate, self-heal and can be transferred from one location to another, all within seconds. Aggregates can comprise only one pattern or bifurcated patterns can coexist, compete, endure or perish.
Order, diversity and functionality spontaneously emerge in nature, resulting in hierarchical organization in far-from-equilibrium conditions through stochastic processes, typically regulated by nonlinear feedback mechanisms1,2. However, current understanding of the fundamental mechanisms and availability of experimental tools to test emerging theories on the subject are lacking. Most current understanding is from model systems3,4,5 that are either too simple to generate rich, complex dynamics collectively2 or so artificial that they have little relevance to actual physical systems. On the other hand, real-life systems, living organisms being the ultimate examples, are so complicated that it is difficult to isolate the essential factors for emergence of complex dynamics1,2. Specific instances of characteristically life-like properties, such as self-replication or self-healing, have been demonstrated in various microscopic systems6,7,8,9,10,11, but they were never observed collectively in a single system that is simple enough to allow identification of mechanisms of emergence.
Dissipative self-assembly is a practical experimental platform to study the fundamental mechanisms of emergent complex behaviour by providing settings akin to those found in nature: far-from-equilibrium conditions12,13,14,15,16, a time-varying external energy input12,13,14,15,16,17, nonlinear feedback mechanisms16,18,19,20,21,22, fast kinetics15,16,22,23, spatiotemporal control15,16,22,23 and a medium to efficiently dissipate the absorbed energy12,13,14,15,16,17. However, previous experimental demonstrations either relied on specific interactions between the building blocks and the external energy source24,25,26 or were limited to certain materials and/or sizes21,26,27,28. Furthermore, most of them were strongly limited by their slow kinetics14,29 and there was little room for fluctuations (Brownian motion was usually weak), where the nonlinear feedback mechanisms were often neglected, unemployed or unidentified.
Here, we report far-from-equilibrium self-assembly of tens to thousands of colloidal nanoparticles with fast kinetics that exhibits complex behaviour, analogous to those commonly associated with living organisms, namely, autocatalysis and self-regulation, competition and self-replication, adaptation and self-healing and motility. We do not use functionalized particles or commonly employed interaction mechanisms, such as optical trapping, tweezing, chemical or magnetic interactions. Instead, we designed a simple system that brings together the essential features: nonlinearity to give rise to multiple fixed points in phase space (hence, possibility of multiple steady states), each corresponding to a different pattern and their bifurcations2; positive and negative feedback to cause exponential growth of perturbations and their suppression, respectively18,19,22; fluctuations to spontaneously induce transitions through bifurcations1; and finally, spatiotemporal gradients to drive the system far from equilibrium, whereby the spatial part allows regions with different fixed points to coexist and the temporal part leads to dynamic growth or shrinkage of these regions.
Emergence of complex behaviour from this plain system can be understood intuitively under the guidance of our toy model, numerical simulations and experimental observations. The laser-sustained thermal gradient not only keeps the system away from thermal equilibrium but, together with the boundary conditions imposed by the bubbles, also creates different local conditions corresponding to different fixed points: a given location can support, say, a square lattice of self-assembled particles, while a hexagonal lattice exists nearby. Each fixed point has a finite basin of attraction both in the phase space and real space, delineated by the spatially varying conditions. In response to perturbations, such as a shift of a bubble boundary or the omnipresent Brownian motion, the original pattern is recovered (self-healing) if the disturbed state remains within the basin of attraction. If the perturbation is large enough that the disturbed state falls outside of the basin of attraction, it switches to a different pattern (self-adaptation) or can be disassembled. A spatiotemporal gradient can also enlarge or shrink the region where a given pattern is the fixed point. In the former case, the pattern can grow (self-replication) or sustain itself (self-regulation). When two nearby regions supporting different patterns come into contact, competition ensues at their boundary: Brownian motion acting on each particle can displace it just enough that the particle leaves a pattern and joins the adjacent one if this stochastic perturbation is large enough and in the right direction. Consequently, the pattern boundaries are dynamic and if the conditions are favourable, one pattern can grow at the expense of another, demonstrating an analogue of interspecies competition. Similarly, motility can be understood as arising in response to temporal gradients that are small enough that the self-healing property can hold the aggregate together as it moves.
How to cite this article: Ilday, S. et al. Rich complex behaviour of self-assembled nanoparticles far from equilibrium. Nat. Commun. 8, 14942 doi: 10.1038/ncomms14942 (2017).
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And instead of Ea we had what? What tells us about how equilibrium constants changes with temperature? If you have a reaction and you heat up the reaction, how do you know which direction it shifts? What is our predictive tool? Delta H, right.
And I will show you a little movie of two molecules coming together. They are going to circle each other and figure out if they have the critical energy to react, and when they have that critical energy you will know it, and go onto product.
And let's consider why this is true. Let's look at the same reaction we looked at with mechanisms last time and figure out what all the K observed terms are. Are there small rate constants? Are there equilibrium constants? What does K-obs really mean? And then we can think about how temperature would affect those values.
And, if we approximate that, then we can solve for this intermediate in terms of an equilibrium expression. Again, the first step fast and reversible, the second step slow. This is pretty much in equilibrium.
Not much of this intermediate is being siphoned off to products. We can solve by setting up an equilibrium expression. Here is the equilibrium expression. Equilibrium constant for Step 1 equals rate constant for the forward reaction over rate constant for the reverse reaction equals products over reactants.
We know how this affected. And here is our expression that we looked at before. Now, what about the equilibrium constant? How do you know what is going to happen with an equilibrium constant, if it will get bigger or smaller with temperature? What is the equation that relates equilibrium constants and temperature? Van Hoff, right.
It depends on delta H. It depends on whether the reaction is endothermic or exothermic. And here is that expression. You can see these are really very similar expressions. Here we have the equilibrium constants.
Let's consider this particular one here. Again, little K is always going to increase with temperature. The equilibrium constant, in this case, will decrease because it is an exothermic reaction. This particular reaction is exothermic.
The rate constant is only going to increase a little bit because this is a small number. On the other hand, if delta H is a big number, and you are told delta H is a big number, then the equilibrium constant should be very sensitive to changes in temperature.
You should see a big difference in the equilibrium constants because this is a really big number. This particular reaction is an example where increasing the temperature can actually decrease the observed rate.
And the effect is because of the delta H. Again, a large activation energy means that the rate constant is very sensitive to changes in temperature, a large delta H means that the equilibrium constant is very sensitive to changes in temperature. 1e1e36bf2d
