Chemical morphogenesis: recent experimental advances in reaction-diffusion system design and control

Chemistry-mechanics-geometry coupling in positive electrode materials: a scale-bridging perspective for mitigating degradation in lithium-ion batteries through materials design

Despite their rapid emergence as the dominant paradigm for electrochemical energy storage, the full promise of lithium-ion batteries is yet to be fully realized, partly because of challenges in adequately resolving common degradation mechanisms. Positive electrodes of Li-ion batteries store ions in interstitial sites based on redox reactions throughout their interior volume. However, variations in the local concentration of inserted Li-ions and inhomogeneous intercalation-induced structural transformations beget substantial stress. Such stress can accumulate and ultimately engender substantial delamination and transgranular/intergranular fracture in typically brittle oxide materials upon continuous electrochemical cycling. This perspective highlights the coupling between electrochemistry, mechanics, and geometry spanning key electrochemical processes: surface reaction, solid-state diffusion, and phase nucleation/transformation in intercalating positive electrodes. In particular, we highlight recent findings on tunable material design parameters that can be used to modulate the kinetics and thermodynamics of intercalation phenomena, spanning the range from atomistic and crystallographic materials design principles (based on alloying, polymorphism, and pre-intercalation) to emergent mesoscale structuring of electrode architectures (through control of crystallite dimensions and geometry, curvature, and external strain). This framework enables intercalation chemistry design principles to be mapped to degradation phenomena based on consideration of mechanics coupling across decades of length scales. Scale-bridging characterization and modeling, along with materials design, holds promise for deciphering mechanistic understanding, modulating multiphysics couplings, and devising actionable strategies to substantially modify intercalation phase diagrams in a manner that unlocks greater useable capacity and enables alleviation of chemo-mechanical degradation mechanisms.

Iodine clocks: applications and untapped opportunities in materials science

Iodine clocks are fascinating nonlinear chemical systems with a glorious past and a promising future. The dynamic removal of iodine from these systems by different means can have important consequences for their reaction dynamics, and could be exploited for time-controlled autonomous dissipative self-assembly. Here, the untapped opportunities offered by iodine clocks for materials science, especially for the time-programming of supramolecular assembly and sol–gel transition, are reviewed and discussed with the hope of arousing the interest on the subject and stimulating new research directions.

Reaction-diffusion phenomena in antagonistic bipolar diffusion fields

Operating natural or artificial chemical systems requires nonequilibrium conditions under which temporal and spatial control of the process is realizable. Open reaction-diffusion systems provide a general way to create such conditions. A key issue is the proper design of reactors in which the nonequilibrium conditions can be maintained. A hydrogel with flow-through channels is a simple, flexible, and easy-to-make device in which chemical reactions are performed in the diffusion field of localized separated sources of reactants. Two reactants separated in two channels create a bipolar antagonistic diffusion field, where the reaction intermediates firmly separate in space. Numerical simulations and corresponding experiments are performed to present this inhomogeneous diffusion field-induced chemical separation in sequential reactions. A remarkable result of this bipolar spatial control is localized wave phenomena in a nonlinear activatory-inhibitory reaction. These findings may help design functioning artificial nonequilibrium systems with the desired spatial separation of chemicals.

Reaction-Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors

Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction-diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.

Out-of-Equilibrium Colloidal Assembly Driven by Chemical Reaction Networks

Transient assembled structures play an indispensable role in a wide variety of processes fundamental to living organisms including cellular transport, cell motility, and proliferation. Typically, the formation of these transient structures is driven by the consumption of molecular fuels via dissipative reaction networks. In these networks, building blocks are converted from inactive precursor states to active (assembling) states by (a set of) irreversible chemical reactions. Since the activated state is intrinsically unstable and can be maintained only in the presence of sufficient fuel, fuel depletion results in the spontaneous disintegration of the formed superstructures. Consequently, the properties and behavior of these assembled structures are governed by the kinetics of fuel consumption rather than by their thermodynamic stability. This fuel dependency endows biological systems with unprecedented spatiotemporal adaptability and inherent self-healing capabilities. Fascinated by these unique material characteristics, coupling the assembly behavior to molecular fuel or light-driven reaction networks was recently implemented in synthetic (supra)molecular systems. In this invited feature article, we discuss recent studies demonstrating that dissipative assembly is not limited to the molecular world but can also be translated to building blocks of colloidal dimensions. We highlight crucial guiding principles for the successful design of dissipative colloidal systems and illustrate these with the current state of the art. Finally, we present our vision on the future of the field and how marrying nonequilibrium self-assembly with the functional properties associated with colloidal building blocks presents a promising route for the development of next-generation materials.

Stripes on finite domains: Why the zigzag instability is only a partial story

Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical, and biological media and to macro-scale vegetation and cloud patterns. Their formation is usually due to a primary symmetry breaking of a uniform state to stripes, often followed by secondary instabilities to form zigzag and labyrinthine patterns. These secondary instabilities are well studied under idealized conditions of an infinite domain; however, on finite domains, the situation is more subtle since the unstable modes depend also on boundary conditions. Using two prototypical models, the Swift-Hohenberg equation and the forced complex Ginzburg-Landau equation, we consider finite size domains with no flux boundary conditions transversal to the stripes and reveal a distinct mixed-mode instability that lies in between the classical zigzag and the Eckhaus lines. This explains the stability of stripes in the mildly zigzag unstable regime and, after crossing the mixed-mode line, the evolution of zigzag stripes in the bulk of the domain and the formation of defects near the boundaries. The results are of particular importance for problems with large timescale separation, such as bulk-heterojunction deformations in organic photovoltaic and vegetation in semi-arid regions, where early temporal transients may play an important role.

Designing Stationary Reaction-Diffusion Patterns in pH Self-Activated Systems

Since Alan Turing's 1952 pioneering work, reaction-diffusion (RD) processes are regarded as prototype mechanisms for pattern formation in living systems. Though suspected in many aspects of morphogenetic development, pure RD patterns have not yet been demonstrated in living organisms. The first observations of an autonomous development of stationary chemical patterns were made in the early 1990s. In this Account, we discuss the recent developments for producing stationary pH RD patterns in open spatial reactors. The theoretical analysis of the early experiments anticipated the possibility of finding Turing patterns in a wide range of oscillatory reactions if one could control the kinetic and diffusional rate of some key species. However, no experimentally effective method to produce stationary Turing patterns was attained before 2009, and the number of systems stagnated at two until then. The two precursor reaction systems benefited from unplanned favorable chemical properties of the RD media. Theoretical studies point out that appropriate diffusion rate differences are necessary to produce stationary patterns since a competition between an effective short distance self-activation and a long distance inhibitory process is required. This differential diffusion would naturally lead to differential exchange rates between the RD system and its feed environment, an aspect somewhat overlooked in theoretical and in primal experimental approaches. Our pattern design method takes this aspect into account. A slower diffusion of a self-activated species (here, protons), produced in the RD part of the spatial reactor, generates the accumulation of this species compared to the other species. This accumulation has to be at least partly compensated by an independent scavenging reaction. The above requirement naturally brought us to focus on two-substrate pH oscillatory reactions. Stationary RD patterns are now well documented in six pH driven reaction systems. Furthermore, the coupling with a pH dependent metal ion complexing agent led to stationary patterns in calcium ion concentration. Our effective semiempirical design method does not require a detailed knowledge of the reaction kinetics; thus it is applicable to a broad spectrum of reactions and even to synthetic biological systems. It is based on simple dynamic arguments and on general topological characteristics of a nonequilibrium phase diagram. We first illustrate our method with numerical simulations, based on a realistic but idealized general model of the two-substrate pH-oscillator reaction family, and provide a refined view of the topology of the resulting phase diagrams. Then, we exemplify its effectiveness by observations made in distinct pH self-activated systems. Analogies and differences between experiments and the model calculations are pointed out. Besides standard hexagonal arrays of spots and parallel stripes, hitherto undocumented dynamic phenomena, such as randomly blinking areas and complex dynamic and stationary filamentous structures, were observed. The main challenge, to find low-mobility complexing agents that would selectively and reversibly bind a species controlling the self-activatory kinetic path of the reaction, was readily overcome in multiple ways by anions of weak acids: not only by polymeric substances but in some cases by a pH color indicator or even smaller molecules, depending on their proton binding affinity.

Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes

We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Comb-like Turing patterns embedded in Hopf oscillations: Spatially localized states outside the 2:1 frequency locked region

A generic mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using a 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either π phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension. Derivation and analysis of three Hopf-Turing amplitude equations in two space dimensions reveal a local dynamics pinning mechanism for Hopf fronts, which in turn allows the emergence of perpendicular (to the Hopf front) Turing states. The results are shown to agree well with the comb-like core size that forms inside spiral waves. In the context of 2:1 resonance, these localized states form outside the 2:1 resonance region and thus extend the frequency locking domain for spatially extended media, such as periodically driven Belousov-Zhabotinsky chemical reactions. Implications to chlorite-iodide-malonic-acid and shaken granular media are also addressed.

Contribution to an effective design method for stationary reaction-diffusion patterns

The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.

Analysis of anchor-size effects on pinned scroll waves and measurement of filament rigidity

Inert, spherical heterogeneities can pin three-dimensional scroll waves in the excitable Belousov-Zhabotinsky reaction. Three pinning sites cause initially circular rotation backbones to approach equilateral triangles. The resulting stationary shapes show convex deviations that increase with decreasing anchor radii. This dependence is interpreted as a transition between filament termination at large surfaces and true, local pinning of a continuous curve. The shapes of the filament segments are described by a hyperbolic cosine function which is predicted by kinematic theory that considers filament tension and rigidity. The latter value is measured as (1.0±0.7)×10-6 cm4/s.