Spontaneous Pattern Formation Research Articles

Linear, self-assembled patterns appearing spontaneously as a result of DNA-CTMA lipoplex Langmuir-Blodgett deposition on a solid surface

Recently, solid forms of deoxyrybonucleic acid (DNA) and its lipoplex with hexadecyltrimethylammonium chloride (CTMA) have been studied with great interest, because of potential applications outside life sciences. In the present work we report on spontaneous formation of characteristic self-assembled linear patterns formed with DNA-CTMA on solid support. For this purpose a single-step technique based on Langmuir-Blodgett scheme has been successfully implemented. DNA-CTMA lipoplex is found to be capable of forming insoluble films at the air/water interface. The lipoplex subjected to compression on the free water surface and then transferred onto mica substrate, usually disintegrates into isolated islands. However, if a certain combination of experimental parameters is applied, the DNA-CTMA monolayer splits into elongated parallel structures.

Spatial Memory and Taxis-Driven Pattern Formation in Model Ecosystems

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births and deaths are negligible. This phenomenon is particularly prevalent in populations of larger, vertebrate animals who often reproduce only once per year or less. To understand spatial arrangements of animal communities on such timescales, we use a class of diffusion–taxis equations for modelling inter-population movement responses between N ge 2 populations. These systems of equations incorporate the effect on animal movement of both the current presence of other populations and the memory of past presence encoded either in the environment or in the minds of animals. We give general criteria for the spontaneous formation of both stationary and oscillatory patterns, via linear pattern formation analysis. For N=2, we classify completely the pattern formation properties using a combination of linear analysis and nonlinear energy functionals. In this case, the only patterns that can occur asymptotically in time are stationary. However, for N ge 3, oscillatory patterns can occur asymptotically, giving rise to a sequence of period-doubling bifurcations leading to patterns with no obvious regularity, a hallmark of chaos. Our study highlights the importance of understanding between-population animal movement for understanding spatial species distributions, something that is typically ignored in species distribution modelling, and so develops a new paradigm for spatial population dynamics.

Millisecond fluid pattern formation in the nip of a gravure printing machine

Rapid fluid splitting in a gravure printing press is studied using high-speed video imaging. The fluid flow and dynamics of the liquid-air meniscus in the wedge between a rigid printing cylinder and a planar substrate plate is singular at the contact point, and the capillary pressure behind the meniscus appears to diverge here. In case of lamella splitting conditions (in contrast to point splitting) a continuous meniscus is forming over the complete width of the contact zone. Spontaneous pattern formation, i.e. viscous fingering, is observed. We study the effect of a periodic gravure pattern on the movement of the liquid meniscus close to the nip. Differently from earlier observations on smooth surfaces we find that finger frequency does not algebraically scale with printing velocity, but exhibts a lock-in phenomenon. Pattern size scales with integer multiples of the raster width of the gravure pattern. We elaborate a tentative explanation for the rapid emptying of gravure cells in the moment of lift-off of the printing form and substrate, indicating that finger instability and cell emptying flows are mutually coupled by the local pressure gradients on the 10-μm scale.

Interplay between Spinodal Decomposition and Gelation and Their Role in Two- and Three-Dimensional Pattern Formation at the Gelatin Gel Surface

Understanding the mechanisms underlying the spontaneous formation of Liesegang patterns based on the prenucleation and postnucleation models is of critical importance for understanding pattern formation in nature. In contrast to the rapid experimental and theoretical advances in understanding within the framework of the prenucleation model, discussion of the postnucleation model is mostly limited to numerical analysis. To construct a standard model for a chemical experiment discussed in terms of the postnucleation model, we have investigated the pattern formation mechanism in a mixed system containing gelatin, starch, and sugar. Fluorescence and differential interference contrast microscopy revealed a process of two-dimensional spinodal decomposition into gelatin-rich and gelatin-poor phases. Since the gelation temperature of the gelatin-rich phase was higher, spatially periodic gelation proceeded selectively in the gelatin-rich phase. As both two-dimensional spinodal decomposition and three-dimensional g...

Electronic Structure Mosaicity of Monolayer Transition Metal Dichalcogenides by Spontaneous Pattern Formation of Donor Molecules.

Modulating the electronic structure of semiconducting materials is critical to developing high-performance electronic and optical devices. Transition metal dichalcogenides (TMDCs) are atomically thin semiconducting materials. However, before they can be used successfully in electronic and optical devices, modulation of their carrier concentration at the nanometer scale must be achieved. Molecular doping has been successful in modulating the carrier concentration; however, the scientific approach for selective and local carrier doping at the nanometer scale is still missing. Here, we demonstrate a proof-of-concept of modulating the carrier concentration of TMDCs laterally on a scale of around 100 nm using spontaneous pattern formation of an ultrathin film consisting of molecular electron dopants. When the water made contact with the molecular film (∼10 nm), a spontaneous pattern formation was observed on both the monolayer and bulk TMDCs. We revealed that the pattern-formation dynamics and nanoscopic flow rate of the molecules were highly dependent on the thickness of the TMDCs, since the band gap varies based on the number of layers. Analyses of topographic images of the molecular patterns and photoluminescence spectra of the TMDCs indicated that the spontaneously patterned molecular films induced a local carrier doping. Our results demonstrate a spontaneous formation of a mosaic electronic structure. This work is useful for making tiny-scale electronic junctions on TMDCs and semiconducting materials to make numerous p/n junctions simultaneously for optoelectronic devices.

Ion bombardment induced atom redistribution in amorphous targets: MD versus BCA

Atom redistribution is an important mechanism of ion bombardment induced spontaneous pattern formation in amorphous or amorphized targets. It may be characterized by either molecular dynamics (MD) simulations or by Monte Carlo (MC) simulations based on the binary collision approximation (BCA). In this work we analyze problems of the BCA approach in predicting atom redistribution by comparing MC and MD simulations of recoil events in amorphized Si. We find that the MC results critically depend on the displacement energy used, on the choice of the free flight paths and maximum impact parameters, and on the construction of the trajectories. Moreover, the net atom redistribution as determined by MD is significantly larger for recoils starting near the surface than for bulk recoils. The effect is not reproduced by the MC simulations.

Inwardly Rotating Spirals in a Nonoscillatory Medium.

We report the spontaneous formation of spiral patterns observed at a downward-facing free surface of a horizontal liquid film. The surface is unstable to the Rayleigh-Taylor instability and the resulting liquid discharge from the film can occur in the form of propagating liquid curtains. They are born at the film circular periphery and exhibit patterns of inwardly rotating spiral arms. With the help of a phenomenologically constructed cellular automaton, we show that the patterns arise from the phase locking leading to periodic liquid discharge at constant flow rate over the whole film surface.

Spontaneous precipitation pattern formation by crystallites of Mn-Fe-based Prussian blue analogues in agarose gel.

Precipitation patterns spontaneously formed by Mn–Fe-based Prussian blue analogues (Mn–Fe PBAs) in agarose gel were investigated over wide concentration ranges for the outer (0.10 ≤ [Mn2+] ≤ 0.70 M) and inner electrolytes (0.01 ≤ [[Fe(CN)6]3−] ≤ 0.35 M). The precipitation patterns were classified into five types: continuous in the inner electrolyte gel, continuous in the outer electrolyte gel, a very short band close to the gel boundary, periodic bands in the inner electrolyte gel, and filament-like patterns in the inner electrolyte gel. The concentrations found to be suitable for applications as pulsatile 137Cs adsorbent delivery materials, for which the periodic patterns were most distinct and frequently occurring, were [Mn2+] ≈ 0.55 M and [[Fe(CN)6]3−] ≈ 0.10 M. The filament-like pattern, reported here for the first time, was generated near the cylindrical gel surface in a local, stochastic, and two-dimensional manner. Scanning electron microscopy (SEM) images of the periodic band patterns indicate that the Mn–Fe PBA precipitates in periodic patterns consist of cubic crystallites (3–10 μm, each side), suggesting significant contributions from Ostwald ripening to the precipitation process. In contrast, precipitates in the filament-like pattern consist of relatively smaller cubic crystallites (≲1 μm, each side), implying an important role of rapid nucleation in the formation of this structure. SEM observations also suggest that, overall, agarose gels support crystallite ripening more effectively, and hence also better suppress the formation of definite periodic bands, than water-glass gels. These findings provide useful information for future applications of self-assembled Mn–Fe PBA patterns in gels.

Guiding self-organized pattern formation in cell polarity establishment.

Spontaneous pattern formation in Turing systems relies on feedback. Patterns in cells and tissues however often do not form spontaneously, but are under control of upstream pathways that provide molecular guiding cues. The relationship between guiding cues and feedback in controlled biological pattern formation remains unclear. We explored this relationship during cell polarity establishment in the one-cell-stage C. elegans embryo. We quantified the strength of two feedback systems that operate during polarity establishment, feedback between polarity proteins and the actomyosin cortex, and mutual antagonism amongst polarity proteins. We characterized how these feedback systems are modulated by guiding cues from the centrosome. By coupling a mass-conserved Turing-like reaction-diffusion system for polarity proteins to an active gel description of the actomyosin cortex, we reveal a transition point beyond which feedback ensures self-organized polarization even when cues are removed. Notably, the baton is passed from a guide-dominated to a feedback-dominated regime significantly beyond this transition point, which ensures robustness. Together, this reveals a general criterion for controlling biological pattern forming systems: feedback remains subcritical to avoid unstable behaviour, and molecular guiding cues drive the system beyond a transition point for pattern formation.

Self-organized wrinkling of liquid crystalline polymer with plasma treatment

Abstract

Tuning Transition-Metal Dichalcogenide Field-Effect Transistors by Spontaneous Pattern Formation of an Ultrathin Molecular Dopant Film.

Spontaneous pattern formation is an energetically favorable process and is shown in nature in molecular-scale assembly, biological association, and soft material organizations. The opposite regime, the artificial process, which is widely applied to the fabrication of semiconducting devices, such as lithographic techniques, requires enormous amounts of energy. Here, we propose a concept of tuning the properties of semiconducting MoS2 and WSe2 devices using the spontaneous pattern formation of adjacent molecular films. The film used was a 10 nm thick ultrathin film of a molecular electron dopant, which exhibited spontaneous pattern formation and dynamically transformed the morphology of tiny holes, a network, a maze, and dots on substrates, including SiO2, MoS2, and WSe2. These patterns were exhibited only when the film came in contact with water and was tuned with temperature and time. The specific lengths of the patterns were less than 200 nm, which is sufficiently smaller than the exfoliated ∼10 μm semiconducting MoS2 and WSe2 flakes. The properties of the field-effect devices of MoS2 and WSe2 were found to be modified according to the pattern formation process of the ultrathin molecular film on the device. This concept applies the spontaneous patterning phenomena shown in nature to the fabrication and optimization of electronic devices by using molecular films and their responses to the external environment.

Role of Electrolyte in Liesegang Pattern Formation.

Pattern formation based on the Liesegang phenomenon is considered one of the useful models for gaining a mechanistic understanding of spontaneous spatiotemporal pattern formations in nature. However, for more than a century, the Liesegang phenomenon in chemical systems has been investigated by using electrolytes as both the reaction substrate and aggregation promoter, which has obfuscated the role of the electrolyte. Here, we distinguish the electrolyte (Na2SO4) from the reaction substrates (Ag+ ion and citrate), where Na2SO4 does not participate in the reaction step and acts as an aggregation promoter. The addition of Na2SO4 in Ag+-citrate-type Liesegang rings gave well-resolvable clear bands with a larger spacing coefficient. The observed changes were discussed by using the classical DLVO (Derjaguin-Landau-Verwey-Overbeek) theory, where the role of the electrolyte is to shield the electrostatic repulsive interaction among the reaction products. Furthermore, the numerical simulation of the reaction-diffusion equation with different aggregation thresholds reproduced the salt-dependent change in the spacing coefficient. We expect that an understanding of the exact role of the electrolyte as the aggregation promoter reported here will offer novel insight into how nature spontaneously forms beautiful spatiotemporal patterns.

Grand Challenges in Soft Matter Physics

As its name implies, soft matter science deals with materials that are easily deformed. These materials, which include polymers, gels, colloids, emulsions, foams, surfactant assemblies, liquid crystals, granular materials, and many biological materials, have in common that they are organized on mesoscopic length scales, with structural features that are much larger than an atom, but much smaller than the overall size of the material. The large size of the basic structural units and the relatively weak interactions that hold them together are responsible for the characteristic softness of these materials1, but they also lead to many other distinct features of soft materials [1], such as sensitivity toward thermal fluctuations and external stimuli and a slow response with long relaxation times, often resulting in non-trivial flow behavior and arrest in non-equilibrium states. These features make soft matter problems challenging. In hard condensed matter physics, it is often possible to accurately predict material properties based on the interactions between the individual atoms, which are typically organized on a regular crystalline lattice. For soft matter systems, with their intrinsically heterogeneous structure, complex interactions across different length scales, and slow dynamics, this is much more difficult. The subtle interplay between interactions and thermal fluctuations can lead to complex emergent behavior, such as spontaneous pattern formation, self-assembly, and a large response to small external stimuli. Because of the wide range of materials and systems that can be classified as soft matter, soft matter science is an inherently interdisciplinary field, in which physics, chemistry, materials science, biology, nanotechnology, and engineering come together. For a field that is so broad in scope, it is impossible to do justice to the entire range of outstanding problems or even to identify two or three key challenges. For this reason, I will only highlight a small (and highly personal) selection of current challenges in the field. The interdisciplinary nature of the field will be evident from these examples.

Resonance in modulation instability from non-instantaneous nonlinearities

To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability from non-instantaneous nonlinearities in photorefractive crystals. With a temporally periodic modulation in the external bias voltage, corresponding to a modulation in the nonlinear strength, an enhancement in the visibility of MI at resonant frequency is reported through spontaneous optical pattern formations. Theoretical curves obtained from a nonlinear non-instantaneous Schrödinger equation give good agreement to experimental data.

Spontaneous patterns in coherently driven polariton microcavities

We consider a polariton microcavity resonantly driven by two external lasers which simultaneously pump both lower and upper polariton branches at normal incidence. In this setup, we study the occurrence of instabilities of the pump-only solutions towards the spontaneous formation of patterns. Their appearance is a consequence of the spontaneous symmetry breaking of translational and rotational invariance due to interaction induced parametric scattering. We observe the evolution between diverse patterns which can be classified as single-pump, where parametric scattering occurs at the same energy as one of the pumps, and as two-pump, where scattering occurs at a different energy. For two-pump instabilities, stripe and chequerboard patterns become the dominant steady-state solutions because cubic parametric scattering processes are forbidden. This contrasts with the single-pump case, where hexagonal patterns are the most common arrangements. We study the possibility of controlling the evolution between different patterns. Our results are obtained within a linear stability analysis and are confirmed by finite size full numerical calculations.

Experimental observation of the emergence of Peregrine-like events in focusing dam break flows.

Simple photonic fiber-based workbenches have been able to emulate well-known nonlinear wave dynamics occurring in deep or shallow water conditions. Here, by investigating the nonlinear reshaping of a flat-top pulse upon propagation in an anomalous dispersive optical fiber, we observe that typical signatures of focusing dam break flows and Peregrine-like breather events can locally coexist in spontaneous pattern formations. The experimental measurements are in good agreement with our numerical predictions.

Self-organization: the fundament of cell biology.

Self-organization refers to the emergence of an overall order in time and space of a given system that results from the collective interactions of its individual components. This concept has been widely recognized as a core principle in pattern formation for multi-component systems of the physical, chemical and biological world. It can be distinguished from self-assembly by the constant input of energy required to maintain order-and self-organization therefore typically occurs in non-equilibrium or dissipative systems. Cells, with their constant energy consumption and myriads of local interactions between distinct proteins, lipids, carbohydrates and nucleic acids, represent the perfect playground for self-organization. It therefore comes as no surprise that many properties and features of self-organized systems, such as spontaneous formation of patterns, nonlinear coupling of reactions, bi-stable switches, waves and oscillations, are found in all aspects of modern cell biology. Ultimately, self-organization lies at the heart of the robustness and adaptability found in cellular and organismal organization, and hence constitutes a fundamental basis for natural selection and evolution.This article is part of the theme issue 'Self-organization in cell biology'.

Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces.

Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System.

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Generic Mechanism for Pattern Formation in the Solvation Shells of Buckminsterfullerene.

Accurate description of solvation structure of a hydrophobic nanomaterial is of immense importance to understand protein folding, molecular recognition, drug binding, and many related phenomena. Moreover, spontaneous pattern formation through self-organization of solvent molecules around a nanoscopic solute is fascinating and useful in making template-directed nanostructures of desired morphologies. Recently, it has been shown using polarizable atomistic models that the hydration shell of a buckminsterfullerene can have atomically resolved ordered structure, in which C60 atomic arrangement is imprinted. In analyzing any peculiar behavior of water, traditionally, emphasis has been placed on the long-ranged and orientation-dependent interactions in it. Here, we show through molecular dynamics simulation that the patterned solvation layer with the imprints of the hydrophobic surface atoms of the buckminsterfullerene can be obtained from a completely different mechanism arising from a spherically symmetric, short-ranged interaction having two characteristic lengthscales. The nature of the pattern can be modified by adjusting solvent density or pressure. Although solute–solvent dispersion interaction is the key to such pattern formation adjacent to the solute surface, the ordering at longer lengthscale is a consequence of mutual influence of short-range correlations among successive layers. The present study thus demonstrates that the formation of such patterned solvation shells around the buckminsterfullerene is not restricted to water, but encompasses a large class of anomalous fluids represented by two-lengthscale potential.