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1.
J Am Chem Soc ; 2024 Jul 03.
Artigo em Inglês | MEDLINE | ID: mdl-38959136

RESUMO

Self-organization of inorganic matter enables bottom-up construction of materials with target shapes suited to their function. Positioning the building blocks in the growth process involves a well-balanced interplay of the reaction and diffusion. Whereas (supra)molecular structures have been used to template such growth processes, we reasoned that molecular assemblies can be employed to actively create concentration gradients that guide the deposition of solid, wire-like structures. The core of our approach comprises the interaction between myelin assemblies that deliver copper(II) ions to the tips of copper dendrites, which in turn grow along the Cu2+ gradient upon electrodeposition. First, we successfully include Cu2+ ions among amphiphile bilayers in myelin filaments, which grow from tri(ethylene glycol) monododecyl ether (C12E3) source droplets over air-water interfaces. Second, we characterize the growth of dendritic copper structures upon electrodeposition from a negative electrode at the sub-mM Cu2+ concentrations that are anticipated upon release from copper(II)-loaded myelins. Third, we assess the intricate growth of copper dendrites upon electrodeposition, when combined with copper(II)-loaded myelins. The myelins deliver Cu2+ at a negative electrode, feeding copper dendrite growth upon electrodeposition. Intriguingly, the copper dendrites follow the Cu2+ gradient toward the myelins and grow along them toward the source droplet. We demonstrate the growth of dynamic connections among electrodes and surfactant droplets in reconfigurable setups─featuring a unique interplay between molecular assemblies and inorganic, solid structures.

2.
J Am Chem Soc ; 146(9): 6006-6015, 2024 Mar 06.
Artigo em Inglês | MEDLINE | ID: mdl-38391388

RESUMO

Droplets are attractive building blocks for dynamic matter that organizes into adaptive structures. Communication among collectively operating droplets opens untapped potential in settings that vary from sensing, optics, protocells, computing, or adaptive matter. Inspired by the transmission of signals among decentralized units in slime mold Physarum polycephalum, we introduce a combination of surfactants, self-assembly, and photochemistry to establish chemical signal transfer among droplets. To connect droplets that float at an air-water interface, surfactant triethylene glycol monododecylether (C12E3) is used for its ability to self-assemble into wires called myelins. We show how the trajectory of these myelins can be directed toward selected photoactive droplets upon UV exposure. To this end, we developed a strategy for photocontrolled Marangoni flow, which comprises (1) the liquid crystalline coating formed at the surface of an oleic acid/sodium oleate (OA/NaO) droplet when in contact with water, (2) a photoacid generator that protonates sodium oleate upon UV exposure and therefore disintegrates the coating, and (3) the surface tension gradient that is generated upon depletion of the surfactant from the air-water interface by the uncoated droplet. Therefore, localized UV exposure of selected OA/NaO droplets results in attraction of the myelins such that they establish reconfigurable connections that self-organize among the C12E3 and OA/NaO droplets. As an example of communication, we demonstrate how the myelins transfer fluorescent dyes, which are selectively delivered in the droplet interior upon photochemical regulation of the liquid crystalline coating.

3.
Phys Rev Lett ; 132(20): 208201, 2024 May 17.
Artigo em Inglês | MEDLINE | ID: mdl-38829102

RESUMO

Acid-induced release of stored ions from polyacrylic acid hydrogels (with a free surface fully permeable to the ion and acid) was observed to increase the gel osmotic pressure that leads to rapid swelling faster than the characteristic solvent absorption rate of the gel. The subsequent equilibration of the diffusing ion concentration across the gel surface diminishes the osmotic pressure. Then, the swollen gel contracts, thereby completing one actuation cycle. We develop a continuum poroelastic theory that explains the experiments by introducing a "gel diffusiophoresis" mechanism: Steric repulsion between the gel polymers and released ions can induce a diffusio-osmotic solvent intake counteracted by the diffusiophoretic expansion of the gel network that ceases when the ion gradient vanishes. For applications ranging from drug delivery to soft robotics, engineering the gel diffusiophoresis may enable stimuli-responsive hydrogels with amplified strain rates and power output.

4.
J Am Chem Soc ; 145(16): 8882-8895, 2023 Apr 26.
Artigo em Inglês | MEDLINE | ID: mdl-37053499

RESUMO

Solute-solvent interactions play a critical role in multiple fields, including biology, materials science, and (physical) organic, polymer, and supramolecular chemistry. Within the growing field of supramolecular polymer science, these interactions have been recognized as an important driving force for (entropically driven) intermolecular association, particularly in aqueous media. However, to date, solute-solvent effects remain poorly understood in the context of complex self-assembly energy landscapes and pathway complexity. Herein, we unravel the role of solute-solvent interactions in controlling chain conformation effects, allowing energy landscape modulation and pathway selection in aqueous supramolecular polymerization. To this end, we have designed a series of oligo(phenylene ethynylene) (OPE)-based bolaamphiphilic Pt(II) complexes OPE2-4 bearing solubilizing triethylene glycol (TEG) chains of equal length on both molecule ends, but a different size of the hydrophobic aromatic scaffold. Strikingly, detailed self-assembly studies in aqueous media disclose a different tendency of the TEG chains to fold back and enwrap the hydrophobic molecular component depending on both the size of the core and the volume fraction of the co-solvent (THF). The relatively small hydrophobic component of OPE2 can be readily shielded by the TEG chains, leading to only one aggregation pathway. In contrast, the decreased capability of the TEG chains to effectively shield larger hydrophobic cores (OPE3 and OPE4) enables different types of solvent quality-dependent conformations (extended, partly back-folded and back-folded), which in turn induce various controllable aggregation pathways with distinct morphologies and mechanisms. Our results shed light on previously underappreciated solvent-dependent chain conformation effects and their role in governing pathway complexity in aqueous media.

5.
Small ; 19(20): e2206800, 2023 May.
Artigo em Inglês | MEDLINE | ID: mdl-36799188

RESUMO

Dissipative chemical systems hold the potential to enable life-like behavior in synthetic matter, such as self-organization, motility, and dynamic switching between different states. Here, out-of-equilibrium self-organization is demonstrated by interconnected source and drain droplets at an air-water interface, which display dynamic behavior due to a hydrolysis reaction that generates a concentration gradient around the drain droplets. This concentration gradient interferes with the adhesion of self-assembled amphiphile filaments that grow from a source droplet. The chemical gradient sustains a unique orbiting of the drain droplet, which is proposed to be driven by the selective adhesion of the filaments to the front of the moving droplet, while filaments approaching from behind are destabilized upon contact with the hydrolysis product in the trail of the droplet. Potential applications are foreseen in the transfer of chemical signals amongst communicating droplets in rearranging networks, and the implementation of chemical reactions to drive complex positioning routines in life-like systems.

6.
Langmuir ; 38(35): 10799-10809, 2022 09 06.
Artigo em Inglês | MEDLINE | ID: mdl-36005886

RESUMO

Self-organization of meso- and macroscale structures is a highly active research field that exploits a wide variety of physicochemical phenomena, including surface tension, Marangoni flow, and (elasto)capillary effects. The release of surface-active compounds generates Marangoni flows that cause repulsion, whereas capillary forces attract floating particles via the Cheerios effect. Typically, the interactions resulting from these effects are nonselective because the gradients involved are uniform. In this work, we unravel the mechanisms involved in the self-organization of amphiphile filaments that connect and attract droplets floating at the air-water interface, and we demonstrate their potential for directional gradient formation and thereby selective interaction. We simulate Marangoni flow patterns resulting from the release and depletion of amphiphile molecules by source and drain droplets, respectively, and we predict that these flow patterns direct the growth of filaments from the source droplets toward specific drain droplets, based on their amphiphile depletion rate. The interaction between such droplets is then investigated experimentally by charting the flow patterns in their surroundings, while the role of filaments in source-drain attraction is studied using microscopy. Based on these observations, we attribute attraction of drain droplets and even solid objects toward the source to elastocapillary effects. Finally, the insights from our simulations and experiments are combined to construct a droplet-based system in which the composition of drain droplets regulates their ability to attract filaments and as a consequence be attracted toward the source. Thereby, we provide a novel method through which directional attraction can be established in synthetic self-organizing systems and advance our understanding of how complexity arises from simple building blocks.


Assuntos
Citoesqueleto , Água , Microscopia , Tensão Superficial , Água/química
7.
Phys Chem Chem Phys ; 24(39): 23980-24001, 2022 Oct 12.
Artigo em Inglês | MEDLINE | ID: mdl-36172850

RESUMO

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.


Assuntos
Hidrodinâmica , Difusão , Termodinâmica
8.
Angew Chem Int Ed Engl ; 58(33): 11344-11349, 2019 08 12.
Artigo em Inglês | MEDLINE | ID: mdl-31119831

RESUMO

Controlling the nanoscale morphology in assemblies of π-conjugated molecules is key to developing supramolecular functional materials. Here, we report an unsymmetrically substituted amphiphilic PtII complex 1 that shows unique self-assembly behavior in nonpolar media, providing two competing anti-cooperative and cooperative pathways with distinct molecular arrangement (long- vs. medium-slipped, respectively) and nanoscale morphology (discs vs. fibers, respectively). With a thermodynamic model, we unravel the competition between the anti-cooperative and cooperative pathways: buffering of monomers into small-sized, anti-cooperative species affects the formation of elongated assemblies, which might open up new strategies for pathway control in self-assembly. Our findings reveal that side-chain immiscibility is an efficient method to control anti-cooperative assemblies and pathway complexity in general.

9.
Angew Chem Int Ed Engl ; 58(43): 15273-15277, 2019 Oct 21.
Artigo em Inglês | MEDLINE | ID: mdl-31436902

RESUMO

The formation of well-defined finite-sized aggregates represents an attractive goal in supramolecular chemistry. In particular, construction of discrete π-stacked dye assemblies remains a challenge. Reported here is the design and synthesis of a novel type of discrete π-stacked aggregate from two comparable perylenediimide (PDI) dyads (PEP and PBP). The criss-cross PEP-PBP dimers in solution and (PBP-PEP)-(PEP-PBP) tetramers in the solid state are well elucidated using single-crystal X-ray diffraction, dynamic light scattering, and diffusion-ordered NMR spectroscopy. Extensive π-π stacking between the PDI units of PEP and PBP as well as repulsive interactions of swallow-tailed alkyl substituents are responsible for the selective formation of discrete dimer and tetramer stacks. Our results reveal a new approach to preparing discrete π stacks that are appealing for making assemblies with well-defined optoelectronic properties.

10.
Nature ; 481(7382): 492-6, 2012 Jan 18.
Artigo em Inglês | MEDLINE | ID: mdl-22258506

RESUMO

Self-assembly provides an attractive route to functional organic materials, with properties and hence performance depending sensitively on the organization of the molecular building blocks. Molecular organization is a direct consequence of the pathways involved in the supramolecular assembly process, which is more amenable to detailed study when using one-dimensional systems. In the case of protein fibrils, formation and growth have been attributed to complex aggregation pathways that go beyond traditional concepts of homogeneous and secondary nucleation events. The self-assembly of synthetic supramolecular polymers has also been studied and even modulated, but our quantitative understanding of the processes involved remains limited. Here we report time-resolved observations of the formation of supramolecular polymers from π-conjugated oligomers. Our kinetic experiments show the presence of a kinetically favoured metastable assembly that forms quickly but then transforms into the thermodynamically favoured form. Quantitative insight into the kinetic experiments was obtained from kinetic model calculations, which revealed two parallel and competing pathways leading to assemblies with opposite helicity. These insights prompt us to use a chiral tartaric acid as an auxiliary to change the thermodynamic preference of the assembly process. We find that we can force aggregation completely down the kinetically favoured pathway so that, on removal of the auxiliary, we obtain only metastable assemblies.


Assuntos
Polimerização , Polímeros/química , Ligação Competitiva , Dicroísmo Circular , Cinética , Modelos Moleculares , Proteínas/química , Tartaratos/química , Termodinâmica
11.
J Am Chem Soc ; 139(39): 13867-13875, 2017 10 04.
Artigo em Inglês | MEDLINE | ID: mdl-28891291

RESUMO

Control over the helical organization of synthetic supramolecular systems is intensively pursued to manifest chirality in a wide range of applications ranging from electron spin filters to artificial enzymes. Typically, switching the helicity of supramolecular assemblies involves external stimuli or kinetic traps. However, efforts to achieve helix reversal under thermodynamic control and to understand the phenomena at a molecular level are scarce. Here we present a unique example of helix reversal (stereomutation) under thermodynamic control in the self-assembly of a coronene bisimide that has a 3,5-dialkoxy substitution on the imide phenyl groups (CBI-35CH), leading to "molecular pockets" in the assembly. The stereomutation was observed only if the CBI monomer possesses molecular pockets. Detailed chiroptical studies performed in alkane solvents with different molecular structures reveal that solvent molecules intercalate or form clathrates within the molecular pockets of CBI-35CH at low temperature (263 K), thereby triggering the stereomutation. The interplay among the helical assembly, molecular pockets, and solvent molecules is further unraveled by explicit solvent molecular dynamics simulations. Our results demonstrate how the molecular design of self-assembling building blocks can orchestrate the organization of surrounding solvent molecules, which in turn dictates the helical organization of the resulting supramolecular assembly.

12.
Proc Natl Acad Sci U S A ; 110(43): 17205-10, 2013 Oct 22.
Artigo em Inglês | MEDLINE | ID: mdl-24101463

RESUMO

Here, we report an engineering approach toward multicomponent self-assembly processes by developing a methodology to circumvent spurious, metastable assemblies. The formation of metastable aggregates often hampers self-assembly of molecular building blocks into the desired nanostructures. Strategies are explored to master the pathway complexity and avoid off-pathway aggregates by optimizing the rate of assembly along the correct pathway. We study as a model system the coassembly of two monomers, the R- and S-chiral enantiomers of a π-conjugated oligo(p-phenylene vinylene) derivative. Coassembly kinetics are analyzed by developing a kinetic model, which reveals the initial assembly of metastable structures buffering free monomers and thereby slows the formation of thermodynamically stable assemblies. These metastable assemblies exert greater influence on the thermodynamically favored self-assembly pathway if the ratio between both monomers approaches 1:1, in agreement with experimental results. Moreover, competition by metastable assemblies is highly temperature dependent and hampers the assembly of equilibrium nanostructures most effectively at intermediate temperatures. We demonstrate that the rate of the assembly process may be optimized by tuning the cooling rate. Finally, it is shown by simulation that increasing the driving force for assembly stepwise by changing the solvent composition may circumvent metastable pathways and thereby force the assembly process directly into the correct pathway.


Assuntos
Algoritmos , Modelos Químicos , Nanoestruturas/química , Polímeros/química , Simulação por Computador , Cinética , Estrutura Molecular , Polimerização , Polivinil/química , Temperatura , Termodinâmica
13.
J Am Chem Soc ; 137(39): 12677-88, 2015 Oct 07.
Artigo em Inglês | MEDLINE | ID: mdl-26354151

RESUMO

While the sensitive dependence of the functional characteristics of self-assembled nanofibers on the molecular structure of their building blocks is well-known, the crucial influence of the dynamics of the assembly process is often overlooked. For natural protein-based fibrils, various aggregation mechanisms have been demonstrated, from simple primary nucleation to secondary nucleation and off-pathway aggregation. Similar pathway complexity has recently been described in synthetic supramolecular polymers and has been shown to be intimately linked to their morphology. We outline a general method to investigate the consequences of the presence of multiple assembly pathways, and show how kinetic analysis can be used to distinguish different assembly mechanisms. We illustrate our combined experimental and theoretical approach by studying the aggregation of chiral bipyridine-extended 1,3,5-benzenetricarboxamides (BiPy-1) in n-butanol as a model system. Our workflow consists of nonlinear least-squares analysis of steady-state spectroscopic measurements, which cannot provide conclusive mechanistic information but yields the equilibrium constants of the self-assembly process as constraints for subsequent kinetic analysis. Furthermore, kinetic nucleation-elongation models based on one and two competing pathways are used to interpret time-dependent spectroscopic measurements acquired using stop-flow and temperature-jump methods. Thus, we reveal that the sharp transition observed in the aggregation process of BiPy-1 cannot be explained by a single cooperative pathway, but can be described by a competitive two-pathway mechanism. This work provides a general tool for analyzing supramolecular polymerizations and establishing energetic landscapes, leading to mechanistic insights that at first sight may seem unexpected and counterintuitive.


Assuntos
1-Butanol/química , Piridinas/química , Dicroísmo Circular , Interações Hidrofóbicas e Hidrofílicas , Cinética , Modelos Moleculares , Estrutura Molecular , Temperatura
14.
Chemistry ; 21(52): 19257-64, 2015 Dec 21.
Artigo em Inglês | MEDLINE | ID: mdl-26555139

RESUMO

A unique example of supramolecular polymerisation in water based on monomers with nanomolar affinities, which yield rod-like materials with extraordinarily high thermodynamic stability, yet of finite length, is reported. A small library of charge-neutral dendritic peptide amphiphiles was prepared, with a branched nonaphenylalanine-based core that was conjugated to hydrophilic dendrons of variable steric demand. Below a critical size of the dendron, the monomers assemble into nanorod-like polymers, whereas for larger dendritic side chains frustrated growth into near isotropic particles is observed. The supramolecular morphologies observed by electron microscopy, X-ray scattering and diffusion NMR spectroscopy studies are in agreement with the mechanistic insights obtained from fitting polymerisation profiles: non-cooperative isodesmic growth leads to degrees of polymerisation that match the experimentally determined nanorod contour lengths of close to 70 nm. The reported designs for aqueous self-assembly into well-defined anisotropic particles has promising potential for biomedical applications and the development of functional supramolecular biomaterials, with emerging evidence that anisotropic shapes in carrier design outperform conventional isotropic materials for targeted imaging and therapy.

15.
J Am Chem Soc ; 136(24): 8540-3, 2014 Jun 18.
Artigo em Inglês | MEDLINE | ID: mdl-24911245

RESUMO

The nature of supramolecular structures could be strongly affected by the pathways followed during their formation just as mechanisms and final outcomes in chemical reactions vary with the conditions selected. So far this is a largely unexplored area of supramolecular chemistry. We demonstrate here how different preparation protocols to self-assemble peptide amphiphiles in water can result in the formation of different supramolecular morphologies, either long filaments containing ß-sheets or smaller aggregrates containing peptide segments in random coil conformation. We found that the assembly rate into ß-sheets decreases in the presence of a destabilizing "good" solvent like hexafluoroisopropanol (HFIP) and is affected by transient conditions in solution. Also the peptide amphiphile investigated spontaneously nucleates the ß-sheet-containing filaments at a critical fraction of HFIP in water below 21%. Furthermore, ß-sheet assemblies have a high kinetic stability and, once formed, do not disassemble rapidly. We foresee that insights into the characteristic dynamics of a supramolecular system provide an efficient approach to select the optimum assembly pathway necessary for function.


Assuntos
Peptídeos/síntese química , Tensoativos/síntese química , Cinética , Conformação Molecular , Peptídeos/química , Tensoativos/química
16.
Adv Sci (Weinh) ; : e2307919, 2024 Jun 17.
Artigo em Inglês | MEDLINE | ID: mdl-38887869

RESUMO

Quorum sensing enables unicellular organisms to probe their population density and perform behavior that exclusively occurs above a critical density. Quorum sensing is established in emulsion droplet swarms that float at a water surface and cluster above a critical density. The design involves competition between 1) a surface tension gradient that is generated upon release of a surfactant from the oil droplets, and thereby drives their mutual repulsion, and 2) the release of a surfactant precursor from the droplets, that forms a strong imine surfactant which suppresses the surface tension gradient and thereby causes droplet clustering upon capillary (Cheerios) attraction. The production of the imine-surfactant depends on the population density of the droplets releasing the precursor so that the clustering only occurs above a critical population density. The pH-dependence of the imine-surfactant formation is exploited to trigger quorum sensing upon a base stimulus: dynamic droplet swarms are generated that cluster and spread upon spatiotemporally varying acid and base conditions. Next, the clustering of two droplet subpopulations is coupled to a chemical reaction that generates a fluorescent signal. It is foreseen that quorum sensing enables control mechanisms in droplet-based systems that display collective responses in contexts of, e.g., sensing, optics, or dynamically controlled droplet-reactors.

17.
J Am Chem Soc ; 134(32): 13482-91, 2012 Aug 15.
Artigo em Inglês | MEDLINE | ID: mdl-22808949

RESUMO

The influence of the ratio between poor and good solvent on the stability and dynamics of supramolecular polymers is studied via a combination of experiments and simulations. Step-wise addition of good solvent to supramolecular polymers assembled via a cooperative (nucleated) growth mechanism results in complete disassembly at a critical good/poor solvent ratio. In contrast, gradual disassembly profiles upon addition of good solvent are observed for isodesmic (non-nucleated) systems. Due to the weak association of good solvent molecules to monomers, the solvent-dependent aggregate stability can be described by a linear free-energy relationship. With respect to dynamics, the depolymerization of π-conjugated oligo(p-phenylene vinylene) (OPV) assemblies in methylcyclohexane (MCH) upon addition of chloroform as a good solvent is shown to proceed with a minimum rate around a critical chloroform/MCH solvent ratio. This minimum disassembly rate bears an intriguing resemblance to phenomena observed in protein unfolding, where minimum rates are observed at the thermodynamic midpoint of a protein denaturation experiment. A kinetic nucleation-elongation model in which the rate constants explicitly depend on the good solvent fraction is developed to rationalize the kinetic traces and further extend the insights by simulation. It is shown that cooperativity, i.e., the nucleation of new aggregates, plays a key role in the minimum polymerization and depolymerization rate at the critical solvent composition. Importantly, this shows that the mixing protocol by which one-dimensional aggregates are prepared via solution-based processing using good/poor solvent mixtures is of major influence on self-assembly dynamics.

18.
Angew Chem Int Ed Engl ; 51(45): 11297-301, 2012 Nov 05.
Artigo em Inglês | MEDLINE | ID: mdl-22936630

RESUMO

The interplay of two subsequent aggregation processes results in a symmetry-breaking phenomenon in an achiral self-assembling system. Partially fluorinated benzene-1,3,5-tricarboxamide molecules self-assemble into a racemic mixture of one-dimensional P- and M-helical aggregates, followed by bundling into optically active higher-order aggregates or fibers.

19.
Angew Chem Int Ed Engl ; 51(26): 6426-31, 2012 Jun 25.
Artigo em Inglês | MEDLINE | ID: mdl-22593079

RESUMO

Saluting the sergeant: Phg-BTA (see scheme) cooperatively self-assembles into helical aggregates and shows unprecedented racemization behavior in the presence of base. In thermodynamically controlled conditions, the addition of a small amount of chiral auxiliary to this mixture results in a deracemization reaction and a final enantiomeric excess of 32 %. A theoretical model is presented to understand in detail the results obtained.


Assuntos
Polímeros/química , Isomerismo , Estrutura Molecular
20.
Nat Commun ; 11(1): 386, 2020 01 20.
Artigo em Inglês | MEDLINE | ID: mdl-31959819

RESUMO

Materials that perform complex chemical signal processing are ubiquitous in living systems. Their synthetic analogs would transform developments in biomedicine, catalysis, and many other areas. By drawing inspiration from biological signaling dynamics, we show how simple hydrogels have a previously untapped capacity for non-equilibrium chemical signal processing and integration. Using a common polyacrylic acid hydrogel, with divalent cations and acid as representative stimuli, we demonstrate the emergence of non-monotonic osmosis-driven spikes and waves of expansion/contraction, as well as traveling color waves. These distinct responses emerge from different combinations of rates and sequences of arriving stimuli. A non-equilibrium continuum theory we developed quantitatively captures the non-monotonic osmosis-driven deformation waves and determines the onset of their emergence in terms of the input parameters. These results suggest that simple hydrogels, already built into numerous systems, have a much larger sensing space than currently employed.

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