Introduction

Active colloidal particles that respond to external fields, chemical reactions, and light exhibit emergent dynamics observed in biological systems, such as propulsion1,2,3,4,5, self-organization6, synchronized motion6,7, dynamic assembly8,9,10,11, leader-follower behavior12, swarming13,14, and standing waves15. Active colloidal matter has been shown to rapidly transport through porous media and confinement16,17, pickup and deliver cargo18,19, sense biomolecules20, and complete tasks using swarm dynamics14. Electric fields have proven highly versatile in directing colloidal assembly by stimulating directional interparticle interactions between colloids, such as dipole-dipole interactions, that can form colloidal molecules11,21, crystals22, and spinners23,24. On the other hand, electric fields can stimulate electrokinetic fluid flows that induce mutual hydrodynamic interactions between colloids to generate colloidal swimmers or assemblies with tunable structure3,25,26. However, stimuli driven active colloids are generally limited to exhibiting a single steady state behavior, such as assembly of a unique structure or a single propulsion mode, in response to a constant external stimulus. Similar to robotic systems, the external stimulus must be actively modulated to reconfigure the active colloids into different states (e.g., Fig. 1a, b)1,18,21,27,28.

Fig. 1: Transient colloidal crystals mediated by electrochemical reaction products.
figure 1

a Three assembly states of colloids: randomly packed (R), hexagonal close packed (H), and separated (S). b Conventional stimuli directed assembly requires actively changing the stimulus (e.g., voltage) to modify the assembly state. c This work demonstrates the use of a time invariant multimode electric stimulus to effect transient assembly and disassembly of colloidal crystals. After applying the initial stimulus, this approach requires no active intervention to effect state changes.

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Inspired by biological systems, researchers have discovered synthetic reaction networks that exhibit transient assembly states, broadly referred to as chemically fueled dissipative assembly29,30,31. Here chemical fuel is added to an ensemble of building blocks, such as colloids32,33,34,35, polymers36,37,38,39, proteins40, or small molecules29,41,42, that activates them to assemble43. The assembled structures persist while fuel is available and autonomously disassemble via a separate reaction pathway when fuel is exhausted. Dissipative assembly therefore enables forming transient soft materials that autonomously degrade following a single initial injection of chemical fuel. In particular, a few methods have been discovered for transiently assembling colloids, including enzymatic DNA reaction networks44,45,46,47,48,49, pH clock reactions35,50, and chemical reaction induced changes to colloid surface chemistry32,33,34.

However, limitations exist for applying these chemical reaction networks to colloidal assembly. The slow diffusion of colloids leads to sluggish dynamics (~hrs to days) compared to directed colloid assembly with external fields (seconds)33. Likewise, chemical reaction cycles generate chemical waste that builds up over several reaction cycles and can interfere with the reaction network32,40. Finally, reaction cycles that directly impact colloidal interactions, for instance by rendering colloids solvophobic, can form undesirable kinetically trapped irreversible aggregates32,33,51. Recent work by the Guan lab has utilized electrochemical reactions to overcome some of these limitations52,53. Here, an electrochemical redox couple stimulates assembly of redox active molecular building blocks. This approach enables rapid assembly and autonomous disassembly of molecular hydrogels. Aside from chemical fuels that directly react with colloid surface ligands, reaction networks that generate pH transients have also been utilized to program autonomous colloidal systems50. Seminal work by Heuser et al. created pH spikes by mixing a basic buffer with a proton releasing organic species, which were used to form transient colloidal assemblies35. More complex transient pH cycles have since been developed that utilize enzymatic reactions and pH oscillators50,54.

Benzoquinone (BQ), an electroactive molecule, has been utilized to electrochemically modulate pH in microfluidic devices55,56,57 and synthesize hydrogels58. Rath et al. demonstrated that BQ redox can cause colloid separation in an oscillatory electric field by repulsive colloidal scale electroosmotic fluid flows but did not demonstrate transient responses59. Here we present a hybrid approach to assemble transient colloidal crystals that combines aspects of electric field-directed and chemically fueled dissipative assembly. Colloids form transient colloidal crystals that autonomously disassemble and reassemble in response to electrochemically generated pH transients. We utilize a time-invariant multimode electric stimulus to drive competing electrokinetic flows between colloids and an electrochemical reaction cycle that generates pH transients that temporally modulate flow magnitudes. As a result, colloidal crystals autonomously alternate between transient assembled and separated states with lifetimes ranging from a few seconds to nearly 500 s (Fig. 1c). The rapid reconfiguration times and wide tunability contrast prior chemically fueled systems that have lifetimes typically ranging from hours to days. The electrochemical reaction network modifies the local solution pH and does not alter colloid surface chemistry, which mitigates irreversible aggregation seen in conventional fuel driven approaches. In contrast to prior work showing pH spikes of > 50% required to induce transient assembly, this system only requires pH spikes of ~10%. We expect this mechanism can be broadly applied to tune transient behavior of other types of active colloids, such as colloidal motors or functional colloidal gels. Likewise, we expect this approach can be extended to other soft materials and molecules that respond to pH changes, such as polymer hydrogels and small molecule hydrogelators.

Results and discussion

BQ redox produces pH transients at the cathode

BQ undergoes a series of proton-coupled single electron reduction reactions to form hydroquinone (QH2), which increases the pH near the cathode in unbuffered solutions due to proton consumption56,57,60. At near neutral pH the proton concentration is low (\(\sim 0.1\,\mu M\)) and BQ reduction occurs via the following pathway:

$${BQ}+{e}^{-}\to {Q}^{-\cdot }$$
(1)
$${Q}^{-\cdot }+{e}^{-}\to {Q}^{2-}$$
(2)
$${Q}^{2-}+2{H}^{+}\leftrightarrow {{QH}}_{2}$$
(3)

Here \({Q}^{-\cdot }\) is the semiquinone radical and \({Q}^{2-}\) is the quinone dianion. On the other hand, BQ is electrooxidized at the anode by electrocatalytically generated hydroxyl radicals. Previous works have reported BQ electrooxidation by metal oxide electrocatalysts, such as tin or lead oxide, at potentials below that of water electrolysis61,62. Intermediate products of BQ electrooxidation include organic acids (e.g., maleic acid) and humic substances (small aromatic polymers), while complete BQ oxidation forms carbon dioxide and water63.

We performed cyclic voltammetry (CV) on a freshly prepared aqueous BQ solution in a pH = 6.6, 100 mM KCl electrolyte (Fig. 2a; See Methods for details). We observed a reduction peak at approximately –430 mV vs. Ag/AgCl (-233 mV vs standard hydrogen electrode (SHE)) and a single oxidation peak near 230 mV vs. Ag/AgCl (427 mV vs SHE). The reduction peak possibly represents BQ electroreduction to quinone dianions (reactions (1) and (2)), which occurs at a potential of –286 mV vs. SHE64. The oxidation peak is likely a combination of QH2 oxidation and BQ oxidation. The latter corresponds to conversion of BQ to organic acids and humic substances, which prior works have demonstrated occurs near a potential +300 mV vs. SHE61,63. We note that factors including electrode material and electrolyte lead to differences between the potentials measured here and literature values62. The formation of organic acids and humic substances was confirmed by mass spectrometry measurements of oxidized BQ solutions (Fig. S1).

Fig. 2: Electrochemical BQ redox generates reproducible pH transients.
figure 2

a Cyclic voltammogram of a freshly prepared 10 mM BQ solution in 100 mM KCl. b, c Schematic illustrations of (b) the sample cell (cross-section view, not to scale) and (c) the multimode electric potential used for colloidal assembly (not to scale). d Fluorometrically measured pH within ~10 \(\mu m\) of the cathode as a function of time for repeated application of a multimodal electric potential consisting of a \(\varDelta {\varPhi }_{{AC}}=2{V}\), 400 Hz oscillatory potential superimposed with a \(\varDelta {\varPhi }_{{DC}}=\) –200 mV steady potential. Yellow regions indicate when the potential was on and red regions when the potential was off. Source data are provided as a Source Data file.

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Several prior works have shown that electrochemical BQ reduction causes pH increases near the cathode55,56,57. We subjected a 10 mM BQ solution in 1 mM KCl between two tin doped indium oxide (ITO) electrodes to repeated applications of a multimode electric potential consisting of a 2 V amplitude, 400 Hz oscillatory potential offset by a -200 mV steady potential (Fig. 2b, c) and measured the resulting pH change near the cathode using a pH-sensitive fluorophore, fluorescein (Fig. 2d; see Fig. S2 and Methods for details). Control experiments showed that the fluorescein acted solely as a pH indicator for the solution and exhibited no preferential binding to the colloids (Fig. S3). Prior to application of the multimode electric potential the solution pH was constant at about 6.6. Upon first application of the multimode electric potential, the pH increased within seconds to about 7.1 and then decayed to 6.75 over 30 s. The pH dropped back to about 6.6 when the potential was removed. The pH near the cathode consistently reached a maximum of 7.1–7.2 five seconds after applying the potential and subsequently declined to 6.7–6.8 after 30 s for each potential application.

The steady potentials used to generate pH transients were smaller (–50 to –250 mV) than the redox potentials observed in the CV. Chronoamperometry measurements showed nearly no Faradaic current flowed and no significant pH change occurred when applying only steady potentials in the range of –50 to –250 mV to BQ solutions. Interestingly, the Faradaic current increased with increasing oscillatory potential amplitude for constant steady potential and increasing steady potential for constant oscillatory potential amplitude and frequency (Figs. S4, S5). This indicates steady and oscillatory components of the potential were necessary to create pH transients. Prior work on electrochemical oxidation of organic molecules has shown that organic molecules are first oxidized to an intermediate adsorbed state that is susceptible to further oxidation61. This suggests the multimode potential supplies a sufficient electrochemical driving force to generate the activated intermediate states of BQ necessary to drive the redox reactions.

Collective dynamics of colloids under multimode electric potentials

Monodisperse 4 µm diameter silica particles were suspended in freshly prepared 10 mM BQ and 1 mM KCl and allowed to settle to the bottom electrode (cathode) by gravity where they remained colloidally stable. The separation between cathode and anode was 320 μm. Applying a 2 V, 400 Hz oscillatory potential caused the particles to assemble into two-dimensional hexagonally close packed (HCP) colloidal crystals due to contractile electrohydrodynamic (EHD) flow surrounding each colloid25,26,65,66,67,68. Superimposing negative steady potentials on this oscillatory potential formed transient colloidal crystals displaying various transient states with lifetimes of seconds to tens of seconds (Fig. 3a–d) (See Supplementary Movies 1, 2, 3, and 4 for full optical microscopy videos at each steady potential). Prior to each experiment, particles were aggregated with only an oscillatory potential and were then allowed to reach an initial state (I) with the colloids separated by a few particle radii by removing the applied potential for 10 s. The multimodal electric potential was applied at t = 5 seconds and remained constant throughout the experiment. Figure 3e shows the corresponding average interparticle separation of the colloids as a function of time while Fig. 3f, g show the maximum average interparticle separation and particle separation time as a function of superimposed DC potential. Application of a 2 V, 400 Hz oscillatory potential with a -25 mV steady potential formed colloidal crystals with no intermediate states (\(I\to H\)) (Fig. 3a), similar to applying a low frequency oscillatory electric potential. However, superimposing a steady potential of –75 mV on the oscillatory potential caused particles to assemble into colloidal crystals for about a second, separate by several particle diameters for ~10 s, and then reconstitute into colloidal crystals (\(I\to H\to S\to H\)) (Fig. 3b). Further increasing the steady potential to –200 mV effected nearly immediate separation of the colloids followed by assembly of colloidal crystals after about 35 s (\(I\to S\to H\)) (Fig. 3c). Finally, increasing the steady potential to –225 mV or above caused the particles to immediately and permanently separate, reaching a steady state separation after about 45 s (\(I\to S\)) (Fig. 3d). Interestingly, for steady potentials between –50 and –200 mV the steady potential determined the sequence of intermediate transient states visited by the colloids. The maximum separation and time separated increased monotonically with increasing steady potential in this range (Fig. 3f, g). Potentials between –50 mV and –100 mV yielded the sequence \(I\to H\to S\to H\), while potentials between –125 mV and –200 mV yielded \(I\to H\). We note that if colloids were initially assembled into a hexagonal state by applying the oscillatory potential first, then the sequence of transient states did not depend on applied steady potential (viz. Fig. 4). The transient assembly and disassembly of colloidal crystals did not occur for the same multimode potentials without BQ in solution.

Fig. 3: Transient colloidal crystals formed by multimode electric potentials.
figure 3

a–d Time lapsed images showing the collective response of colloids to multimode electric potentials consisting of a 2 V, 400 Hz oscillatory potential with various steady potentials (\(\varDelta {\varPhi }_{{DC}}\)). The potential was applied at t = 5 s and held constant throughout the experiment. Letters in each image indicate the assembly state at that time, I = initial state, S = separated state, H = hexagonal state. e Average interparticle separation of an ensemble of colloids normalized to the initial particle separation (<S > / < S > 0) as a function of time for the multimode potentials used in (a–d). f Total time separated (tsep) and (g) maximum average interparticle separation (<S>max/<S > 0) of colloids (defined in (e) for \(\varDelta {\varPhi }_{{DC}}=-75{mV}\)) as a function of steady potential. The data points in (f) and (g) represent the mean of three experiments while the error bars are ±1 standard deviation of the mean. Source data are provided as a Source Data file.

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Fig. 4: Transient colloidal crystals exhibit widely tunable transient states by changing the electrode spacing.
figure 4

a Images of colloids undergoing an \(I\to S\to H\) transformation for a multimode potential consisting of a 2.5 V, 400 Hz oscillatory potential and a superimposed –500 mV steady potential. b Time dependent average interparticle separations of colloidal crystals during the \(I\to S\to H\) transition for various electrode separations and steady potentials superimposed on a 2.5 V, 400 Hz oscillatory potential. Open and closed symbols correspond to 650 µm and 1 mm electrode separations, respectively. c Images of colloids undergoing an \(H\to S\to H\) transformation with an initially applied 2.5 V, 400 Hz oscillatory potential. A –500 mV steady potential was superimposed at t = 8 s. d Time dependent average interparticle separation of colloidal crystals during the \(H\to S\to H\) transition for various electrode separations and steady potentials superimposed on a 2.5 V, 400 Hz oscillatory potential. e, f Separation time for a \(H\to S\to H\) transition as a function of steady potential superimposed on a 2.5 V, 400 Hz oscillatory potential. The electrode separation was (e) 160 µm and (f) 650 µm. Scale bars: 20 µm. The data points in (e) and (f) represent the mean of three experiments while the error bars are ±1 standard deviation of the mean. Source data are provided as a Source Data file.

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Electrode spacing mediates transient state lifetimes

Adjusting the steady potential permitted modulating the intermediate separation state duration (tsep) over one order of magnitude. Interestingly, we found that varying the electrode separation distance between 160 μm and 1 mm enabled tuning the separation time of the colloids over several orders of magnitude. Figure 4a shows snapshots taken during an I → H → S transition occurring with an electrode separation of 650 μm and a multimode potential comprised of a 2.5 V, 400 Hz oscillatory potential and –500 mV steady potential. Here the particles remained separated for nearly 200 s (Fig. 4b). Interestingly, large steady potentials > −400 mV, which caused only separation for smaller electrode separations, effected long time scale transient separation for 650 μm (Fig. 4b, open markers) and 1 mm (Fig. 4b, filled markers) electrode separations (See Supplementary Movies 5, 6, 7, and 8 for optical microscopy videos). Remarkably, the longest separation time we observed for the I → H → S transition was nearly 500 s for a 1 mm electrode separation (green filled triangles, Fig. 4b).

Application of a pure oscillatory potential to generate an initial hexagonal state enabled varying the lifetime of the transient separation state while maintaining the same sequence of intermediate states (Fig. 4c, d). Figure 4c shows snapshots of the colloids during this transition, where a 2.5 V, 400 Hz oscillatory potential was initially applied followed by adding a –500 mV steady potential at t = 0 s. Figure 4d presents interparticle separation as a function of time for the 650 μm electrode separation at various steady potentials during the H → S → H transition (See Supplementary Movies 9, 10, and 11 for optical microscopy videos). Upon superimposing a steady component on the oscillatory potential, particles initially separated and later reconstituted into a hexagonal steady state with separation times ranging from about 10 to 200 s. Figure 4e, f shows the dependence of the separation time (tsep) at different steady potentials for 160 μm and 650 μm electrode separations for the case of the H → S → H transition. tsep increased with increasing steady potential magnitude and ranged from about 2 to 30 s for 160 μm electrode separation and 20 to 200 s for 650 μm electrode separation. Remarkably, tsep could be widely tuned by both steady potential and electrode separation, ranging over two orders of magnitude from approximately 2–500 s.

Colloid assembly state correlates with pH

We simultaneously measured the time dependent average interparticle separation and normalized fluorescein emission near the cathode when applying multimode electric potentials with varying steady potential (Fig. 5). Due to the presence of colloidal particles and lack of emission filter needed to observe the non-fluorescent particles, we could not measure absolute pH in this case. Here the maximum particle separation distance and separation time increased with increasing superimposed steady potential (Fig. 5a). The fluorescein emission intensity displayed transient responses similar to the interparticle separation (Fig. 5b). The transient peaks in fluorescence emission increased as a function of steady potential and led the maximum interparticle separation time by ~5 s and ~10 s for –200 mV and –250 mV, respectively. The observed increase in peak fluorescence emission with increasing superimposed steady potential provided initial evidence suggesting the important role of pH in the transient colloidal crystals. The variable resistivity of different ITO electrodes produced qualitatively different colloidal behavior between different sample cells, which explains why colloids aggregated at –100 mV in Fig. 5a and exhibited transient separation in Fig. 3.

Fig. 5: Transient assembly and disassembly of colloidal crystals correlated in time with solution pH.
figure 5

a Average interparticle separation of a colloidal crystal and (b) fluorescence emission intensity of fluorescein near the cathode as a function of time after application of a 400 Hz, 2 V oscillatory potential with different superimposed steady potentials. Source data are provided as a Source Data file.

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Transient colloidal crystals form over repeated consecutive potential applications

Dissipative assembly systems display cyclic autonomous assembly and disassembly with similar dynamics for repeated, consecutive injections of chemical fuel43. Here we applied consecutive multimode potentials of 2.5 V, 400 Hz superimposed with a –400 mV steady potential and measured the average interparticle separation and fluorescein emission intensity near the cathode (See Supplementary Movie 12 for optical microscopy video). Figure 6a displays particles in separated (S) and hexagonal crystal states (H) during the first and second cycle of applying the multimodal potential. The higher background intensity of the images of state S indicates an elevated solution pH. Conversely, images of the H state had a lower fluorescence intensity due to decay of the pH transient over time. Figure 6b shows the average interparticle separation and fluorescein emission intensity near the cathode for 4 consecutive cycles of applying the multimodal potential. Each consecutive potential application yielded transient colloidal crystals with a similar separation time of \(\approx \) 3 s and maximum interparticle separation of\(\,\approx 2\). The fluorescein emission for each potential application showed a similar transient response.

Fig. 6: Transient colloidal crystal separation and assembly correlates in time with pH transients and can be repeated over nearly 50 cycles before irreversibly separating.
figure 6

a Images of colloids in separated (S) and crystal (H) states over several cycles of applying a 2.5 V, 400 Hz oscillatory potential and a superimposed –400 mV steady potential. b The corresponding average interparticle separation of a colloidal crystal (blue circles, left y-axis) and the fluorescein emission intensity near the cathode (solid red line, right y-axis). Yellow and red shading indicate when the multimode potential was off and on. c Images of colloids in S and H states at various cycles of applying a 2 V, 400 Hz oscillatory potential and a superimposed –400 mV steady potential. d The corresponding average interparticle separation of a colloidal crystal over 53 cycles. e The separation time (blue circles, left y-axis) and maximum separation (red circles, right y-axis) as a function of cycle number. Scale bars: 40 µm. Source data are provided as a Source Data file.

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Build-up of chemical waste byproducts generally limits dissipative assembly to only a few reaction cycles before chemical waste modifies the transient response. To test the repetition ability of the transient colloidal crystals, we repeatedly applied the same stimulus to the colloids. We subjected the colloids to repeated application and removal of a 2 V, 400 Hz oscillatory potential with a superimposed –400 mV steady potential over approximately 1.5 h. The potential was applied for 50 s during each cycle and then removed for 10 s. After the 40th cycle the potential was applied until most of the separated particles reconstituted HCP crystals. Figure 6c shows the S and H states during the 36th and 53rd cycles. Up to the 52nd cycle, colloids displayed \(I\to S\to {H}\) transitions with varying separation time and maximum separation distance. After 53 cycles the colloids failed to reassemble into hexagonal crystals. Supplementary Movies S13 and S14 provide a comprehensive overview of the experiment. Figure 6d shows the interparticle separation as a function of time, where each spike represents a cycle. Figure 6e shows the normalized maximum separation (red curve) and separation time (blue curve) as a function of cycle number (Ncycle). The maximum interparticle separation increased monotonically with cycle number throughout the entire experiment, while the separation time increased for about 10 cycles and then remained constant at about 30 s for nearly 30 cycles. The average maximum separation was 1.6 ± 0.3 over the first 40 cycles. The separation time increased between the 6th and 40th cycles with a mean tsep of 43 ± 6 s. tsep increased rapidly following the 40th cycle and reached 277 s by the 52nd cycle. This continuously increasing tsep at larger cycle numbers suggests that long-term cycling induces irreversible changes in the reaction network. The gradual accumulation of reaction by-products may lead to a slower decay of the transient pH spike or irreversible increase in pH over time.

Numerical model for BQ redox reaction network

Experiments showing both time and magnitude correlation of pH transients and interparticle separation of colloids strongly suggested pH mediated the transient colloidal crystal behavior. Likewise, experiments showing strong effects of electrode separation and potential on transient lifetimes suggest solute transport and reaction kinetics play an important role in determining the pH transient. We developed a mathematical model and numerically simulated the BQ reaction network under steady potential bias to uncover the origin of the pH transients (see Supplementary Note 1 in the Supplementary Information for additional details). Briefly, the simulated sample cell consisted of two parallel plate electrodes separated by electrolyte with a constant electric potential applied to the cathode and the anode held at ground (Fig. 7a). BQ and intermediate species reduction occurred at the cathode (x = 320 \(\mu m\) or 650 \(\mu m\)) while BQ oxidation occurred at the anode (x = 0 \(\mu m\)). Reversible protonation-deprotonation reactions and water autodissociation occurred in the bulk electrolyte. Species underwent transport via diffusion and electromigration in the electrolyte.

Fig. 7: 1D, transient, electrochemical model of the BQ redox reaction network.
figure 7

a Schematic illustration of the electrochemical and chemical reactions included in the model. The anode is located at the origin. The initial species concentrations were 1 mM KCl, 10 mM BQ, 0.5 mM BQ*−, and 0.25 μM H+ (pH = 6.6). b Time dependent concentration profiles of various species averaged within 50 μm of the anode (upper panel) and cathode (lower panel) for an applied potential of –200 mV and electrode spacing of 320 μm. c, d pH averaged within 50 μm of the cathode as a function of time for various steady potentials for electrode spacings of (c) 320 μm and (d) 650 μm. Source data are provided as a Source Data file.

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The electrochemical reduction pathway of BQ is well-known in literature; however, the BQ oxidation reaction mechanism is not well established. One potential mechanism for the transient pH increase near the cathode is concurrent consumption of protons at the cathode and generation of protons at the anode. Here we propose that generation of an organic acid (AH), such as maleic acid, by anodic BQ oxidation provided the requisite proton source. Proton diffusion to the cathode could generate the time delay to effect a pH spike. Prior works on electrochemical BQ oxidation have proposed that BQ first adsorbs to the anode and is oxidized to generate an activated intermediate (BQ*−) that is susceptible to hydroxyl radical attack61. The precise nature of this species is not currently known, but it must be negatively charged to satisfy charge balance. Subsequent oxidation of BQ*− forms organic acids (AH). This oxidative reaction pathway is supported by mass spectrometry data (Fig. S1) that shows maleic acid and BQ oligomers in oxidized BQ solutions. These results agree with prior work showing formation of organic acids and non-conductive polymer films on electrodes during quinone electrooxidation61,63. As discussed above and shown in Figs. S4, S5, redox reactions did not occur for steady potentials of –50 mV to –250 mV alone but required a superimposed oscillatory potential to provide sufficient driving force. One potential explanation for this observation is that the oscillatory potential is required to generate BQ*−. The oscillatory potential was 2–4 V in experiments, which exceeds the expected potential stability window of BQ. The pH changes observed during colloidal assembly and disassembly require proton concentration changes of ~1 \(\mu M\). BQ*− concentrations at the \(\mu M\) scale are therefore sufficient to generate the observed responses. In other words, while we have not yet identified the specific identity of BQ*−, provided it subsequently releases protons the required concentration can be much lower than the initial value of BQ. We included BQ*− at an initial concentration 5% of that of BQ to account for the absence of the oscillatory potential and modeled oxidative organic acid generation as a single electron anodic oxidation of BQ*−. The precise molecular structure of BQ*− is unknown, but it is possible that it contains a carbanion on the phenyl ring as this would render the intermediate species a good nucleophile, facilitating further anodic oxidation to form organic acids. While this approach leaves open questions about the precise oxidation mechanism, the numerical model results below show this reaction network reproduces the salient features of the experiments.

We used finite element analysis (FEA) implemented in COMSOL to solve the time dependent 1-D reaction-diffusion equations with the flux of charged species also driven by electromigration. The exchange current densities, redox potentials, diffusion coefficients, and pKa for each reaction were acquired from literature when possible and estimated if not available (See Tables S1, S2 and Supplementary Note 1 in the Supplementary Information for details). To simplify the model, we utilized a monoprotic organic acid (AH) with pKa = 2, equivalent to that of the first deprotonation reaction for maleic acid. One final component of the model that was necessary to match simulated pH to experiments for each electrode spacing was a sheet resistor in the electrochemical cell. The sheet resistance could be due to formation of a thin nonconductive polymer film on the anode surface that causes ohmic drop. The wider electrode spacing (640 μm) required a larger sheet resistance to match simulations to the experimental pH values, which could be due to the larger applied steady potentials.

The model was solved for the concentration of all species as a function of time and spatial position (Figs. S6–S9 show time dependent concentration profiles for all species at two applied potentials and an electrode spacing of 320 μm). Figure 7b shows the average concentration of several species within 50 μm of the anode (top plot) and cathode (bottom plot) as a function of time for \(\Delta \Phi_{DC}=-200\;{mV}\). The AH, A−, and H+ concentrations near the anode increased rapidly over a few seconds due to BQ*− oxidation. The concentration of AH was about 50% that of A− and H+ due to the pKa value of AH. The concentration of each species increased monotonically and the proton concentration reached a steady state value after a few seconds. Interestingly, the average proton concentration near the cathode showed a minimum at about 5 s while the OH−, QH−, and Q2− showed a maximum. The quinone dianion, Q2−, and its singly protonated counterpart, QH−, have a pKa near 11, indicating they will be fully protonated at equilibrium at the typical cell pH. The consumption of protons by QH− and Q2− therefore caused the pH increase near the cathode. The simulations revealed that the transient pH increase at the cathode was due to continuous proton generation at the anode, which generated a low pH front that diffused to the cathode. Figure 7c shows the time dependent pH averaged within 50 μm of the cathode for several applied potentials and an electrode spacing of 320 μm. Similar to experimental observations, the pH increased for about 5 s and then decreased over 10–20 s. The maximum pH increased with increasing applied potential, also consistent with experiments (cf., Fig. 4). For applied potential magnitudes < –150 mV the pH decayed over ten seconds, while potentials more negative than –300 mV led to a permanent pH increase over a time of ~10 s. These features, including the maximum pH, time scale of the transient increase, and impact of applied potential, are qualitatively similar to the experimental measurements shown previously. Figure 7d shows the pH transients for several steady potentials for an electrode separation of 650 μm. Here we see that increasing the electrode separation increased the time required for pH to reach a maximum (~20 s) compared to the smaller electrode spacing. Likewise, the pH decayed over hundreds of seconds. These features are consistent with experiments demonstrating a nearly order of magnitude increase in the colloid separation time when increasing electrode spacing. The more sluggish pH transients are due to a combination of the increased proton diffusion time and slower electrode reaction kinetics. This model together with experimental results indicates pH transients stemmed from interacting acidic and basic pH fronts generated at the anode and cathode, respectively.

Electrokinetic flow scaling analysis for transient colloidal crystals

Attraction and repulsion between colloids occurred over several particle diameters, indicating that pH dependent changes to colloid surface charge were not responsible for the transient colloidal crystals. The Debye length was ~10 nm in these experiments, which is two orders of magnitude smaller than the colloid interaction length scale observed during experiments. Instead, prior work has shown that colloids near charged electrodes generate toroidal electrokinetic fluid flows at their surface that can be either extensile or contractile, entraining or repelling neighboring particles3,25,26,65,66,68,69,70. Micron sized colloids in dilute electrolytes tend to form 2D colloidal crystals under low frequency oscillatory electric fields (<1 kHz) due to contractile EHD fluid flow around each particle25,26,65,66,67,68,71. The EHD fluid flow magnitude near a colloid in a 1 mM electrolyte is predicted to be effectively invariant with solution pH over the range of 6–859. Conversely, prior work has shown that colloids in alkaline electrolytes (KOH, NaOH) separate due to the mismatch between anion and cation diffusivity, which generates a rectified steady electric field that induces an extensile electroosmotic (EO) flow around each particle59,65,72. Here, increasing hydroxyl ion concentration near the cathode increases the magnitude of the EO flow, causing repulsive hydrodynamic forces between neighboring particles59. We propose that a competition between EHD and EO flows mediates dynamics of the transient colloidal crystals. To test this mechanism, we developed a hydrodynamic scaling model for a pair of colloids interacting via mutual drag forces generated by contractile EHD flow (\({U}_{{EHD}}\), attractive drag force) and a pH dependent extensile EO flow (\({U}_{{EO}}\left({pH}\right)\), repulsive drag force). The relative pair velocity of the particles (\({U}_{{relative}}\left({pH}\right)\)) is

$${U}_{{relative}}({pH})=-2\left[{{K}_{0}U}_{{EHD}}+{U}_{{EO}}\left({pH}\right)\right]$$
(4)

Here \({K}_{0}\) is a fitting parameter and the factor of two accounts for the fluid flow around each particle. By convention, a negative relative velocity corresponds to particle separation. The force balance utilizes previously derived scaling arguments for \({U}_{{EHD}}\) and \({U}_{{EO}}\left({pH}\right)\) with minor modifications (See Supplementary Note 2 in the Supplementary Information for details). The EHD flow scaling model includes the single fitting parameter, \({K}_{0}\). Prior work has shown a value of \(K_0 \approx 0.01\) reconciles the scaling result to experimental measurements3,59.

We experimentally measured the pH transients for a multimode potential consisting of a 2 V, 400 Hz oscillatory potential with various superimposed steady potentials (Fig. 8a, see Fig. S10 for pH calibration curve). The pH at –50 mV steady potential was nearly constant with a transient increase of ~0.1 points, consistent with experiments that displayed only colloidal crystal assembly with no transient states near this condition. The pH transiently increased to 6.8 and 7.2 for potentials of –100 mV and –200 mV and then decayed to near the initial pH after about 30 s, consistent with pH profiles accompanying transient colloidal crystals. The pH showed a permanent increase to near 8 for a steady potential of –300 mV, consistent with the pH profile accompanying permanent separation of colloids. The pH transients observed in experiments showed similar qualitative shape, pH values, and decay times compared to the numerical kinetic model (cf., Fig. 7c). Figure 8b shows the pH transients for several steady potentials applied to a sample cell with a 650 μm electrode separation. Here the pH values peaked after about 20 s for each applied potential and decayed to near the initial value after hundreds of seconds, consistent with experiments and simulations.

Fig. 8: Pairwise particle force balance for transient colloidal crystals.
figure 8

Experimentally measured time dependent pH for electrode separations of (a) 320 μm and (b) 650 μm and various steady potentials. The oscillatory potential was 2 V, 400 Hz. c EHD (UEHD), EO (UEO), and relative particle velocity (URelative) magnitudes as a function of pH. A positive (negative) velocity magnitude represents a net contractile (extensile) flow that entrains (repels) neighboring particles. d Relative particle velocity as a function of time using the experimental pH transients in (a) as inputs to calculate UEO. The fitting parameter for the EHD flow was set to \({K}_{0}=0.0145\) for (b, c). e Optical microscopy images of 500 nm polystyrene tracer particles around a fixed 4 μm silica particle. Insets show the electric potentials applied at each time point. The oscillatory potential was 400 Hz, 2.5 V amplitude and the steady potential was −125 mV. Source data are provided as a Source Data file.

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The time dependent relative pair velocity was computed as a function of time with Eq. (4) by using the experimental pH measurements (Fig. 8a) to calculate the hydroxyl ion concentration near the cathode and EO flow magnitude. The EHD flow magnitude was nearly constant with pH and the EO flow magnitude became increasingly negative (repulsive) with increasing pH due to the increasing rectified electric field magnitude (Fig. 8c). Figure 8d shows the time dependent particle pair velocities for each steady potential. The scaling model showed that particles will monotonically approach each other over time at a steady potential of –50 mV, consistent with the formation of colloidal crystals with no transient states at small steady potentials. The pair velocity at –100 mV was initially attractive for several seconds, repulsive for about 5 s, and then returned to attractive after about 7 s, qualitatively consistent with experimental observations of colloids displaying an \(I\to H\to S\to H\) sequence at this potential. At -200 mV the pair velocity became repulsive nearly immediately after applying the multimode potential due to a rapid increase in solution pH near the cathode. The pair velocity became increasingly repulsive for about 5 s then decayed and became attractive at around 25 s, consistent with experiments that showed an \(I\to S\to H\) sequence at -200 mV. The increased time range of repulsive flow with increasing steady potential is consistent with the experimental observations of increased separation time with increasing steady potential. At –300 mV, the repulsive pair velocity rapidly decreased to a minimum after 5 s and then increased to a steady state repulsive pair velocity after ~30 s, consistent with the \(I\to S\) sequence observed in experiments at this condition. This hydrodynamic scaling model displayed dynamics qualitatively consistent with experimental observations of transient colloidal crystal dynamics. The scaling model predicted pair velocities on the order of \(\mu m/s\), consistent with experiments where colloids traversed distances of several particle diameters over tens of seconds (cf., Fig. 3). We note that the pH spikes leading to transient colloid separation are relatively small (~10% increase) compared to prior works that utilized pH spikes for reconfiguring soft materials, which were on the order of ~50% or more. This is because the magnitude of the AREF field and repulsive EO flow are sensitive to pH and small pH changes can cause a flow direction inversion.

Control experiments were performed to support the scaling model, including tracer particle experiments and pH-dependent assembly experiments. Here 500 nm carboxyl-functionalized polystyrene spheres served as flow tracers around a 4 μm silica particle fixed to the electrode to test whether a flow inversion occurred at the particle surface upon applying a multimode electric potential (Fig. 8e, Supplementary Movie 15). Application of a 2.5 V, 400 Hz oscillatory potential caused attraction between the colloid and tracers due to contractile EHD flow around the central particle. Subsequently, the application of a superimposed steady potential repelled the tracers, consistent with an extensile EO flow. The tracer particles were subsequently attracted to the central silica particle about 50 s after application of the multimode potential. These experiments provided strong experimental evidence that a flow direction inversion caused transient colloidal crystals.

Prior work showed that colloids in low frequency oscillatory electric fields separated when dispersed in dilute alkaline electrolytes like NaOH and KOH65. As a test of the proposed model above, we exposed colloids in different pH solutions prepared from mixtures of KCl and KOH to pure oscillatory electric fields with no BQ present. We found that colloids separated in a 400 Hz frequency, 2 V amplitude oscillatory potential when the pH of the electrolyte was > ~10 (Fig. S11). This is larger than the pH of ~7.2 found to cause transient colloid separation in our experiments. Recent theoretical work by Jarvey et al. sheds light on this disparity73. Their work demonstrated that electrochemical flux of ions due to electrode reactions can also generate rectified electric fields from applied oscillatory potentials. It is possible that electrochemical redox reactions generated a rectified electric field in addition to the transient pH. Further modeling work is required to understand how ion flux impacts the electrokinetic flows.

Mechanism for transient colloidal crystals

Experiments and modeling are consistent with transient colloidal crystals forming due to coupling between transient pH changes near the cathode surface and repulsive EO flows between colloids. Figure 9a shows a schematic illustration summarizing the proposed mechanism. At small steady potentials (<–100 mV), time invariant contractile EHD flows initially formed colloidal crystals for a few seconds by overwhelming weak repulsive EO flow generated by relatively small initial pH increases. Application of larger steady potentials (>–100 mV) rapidly increased the repulsive EO flow magnitude and the initial transient crystallization step was bypassed. Within 1–2 s, the colloidal crystals separated as the pH at the cathode increased. At a critical pH and time the resulting extensile EO flow overcame the EHD flow and separated the colloids. The time the particles remained separated increased with increasing steady potential due to the direct proportionality between the steady potential and magnitude of transient pH increase. Simultaneously, BQ oxidized at the anode to form organic acids, which released protons that diffused to the cathode. The characteristic diffusion time scale of the protons, \({\tau }_{D} \sim \frac{{l}^{2}}{{D}_{{H}^{+}}}=\frac{{\left(320 \, \mu m\right)}^{2}}{9.3\times {10}^{-9}{m}^{2}/s} \sim 10s\), agrees well with experimental decay times of the pH transients. Protons neutralized the hydroxyl ions, which diminished the pH transient and the EO flow at the cathode, allowing contractile EHD flow to dominate once again and reconstitute the colloidal crystals. Increasing the electrode spacing increases the diffusion time scale of protons in a quadratic fashion, which in part explains the increased time scale for the pH spike to decay in the thicker electrode cells. Additionally, increasing the electrode separation will decrease the amount of potential drop contributing to the electrochemical reactions, which will in turn decrease the rate at which pH increases and decreases.

Fig. 9: Schematics illustrating the mechanism for transient colloidal crystals.
figure 9

a Transport phenomena underlying pH spikes and transient colloidal crystals. b Reaction network mediating transient separation of colloids.

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Redox reaction network and comparison to chemical fuel driven dissipative assembly

Figure 9b shows the proposed BQ redox reaction cycle that mediates transient colloidal crystal dynamics. In the context of fuel driven dissipative assembly we are interested in identifying the ‘chemical fuel,’ the forward and backward reactions that drive transient behavior, and demonstrating the key differences between the present system and prior works. The BQ was reduced to quinone dianions at the cathode, which have a high pKa of ~11 and rapidly consume protons, increasing the solution pH. The release of hydroxyl ions from water ionization triggered the repulsive EO flow that separates the colloids. In this context, BQ can be considered a pre-fuel molecule and hydroxyl ions the chemical fuel that activate the colloidal crystal dynamics. Generation of organic acids at the anode and their subsequent diffusion to the cathode and recombination with protons depletes the hydroxyl ion fuel concentration. Here protons act as a deactivator species in the reaction network.

Typical chemical fuel concentrations utilized in fuel driven dissipative assembly are on the order of millimolar or larger. However, as pH controls the colloidal dynamics here the reaction network must only generate hydroxyl ions and protons in μM concentrations. Numerical simulations showed that <1% of the BQ converted to products to generate this concentration of hydroxyl ions (Figs. S6–S9). The minimal decrease in BQ concentration during the reaction enables cycling the transient colloidal crystals over dozens of consecutive electric potential applications (cf., Fig. 5). The kinetic model predicts that relatively low concentrations of chemical byproducts are generated in this reaction cycle. QH2 and organic acids are generated in the highest concentrations (μM). However, we found that repeated cycling over dozens of electric stimulus applications caused quantitative and qualitative changes to the transient behavior of the colloids. We observed an increase in separation time and separation distance with cycle number. This suggests the magnitude of the repulsive EO flow and thus the pH spike increased with increasing cycle number. It is possible that polymerized humic substance precipitation on the anode modifies the electrochemical reaction kinetics over time. Humic substance deposition could potentially block surface reaction sites, suggesting this is a possible mechanism for the loss of transient colloid behavior after many cycles.

Recent work on electrically stimulated dissipative assembly of small molecules utilized direct or indirect redox reactions to assemble and transiently disassemble nanofibrillar structures on electrodes52,53. This previous work draws some parallels to the present work in that the dynamics are generally faster (minutes to tens of minutes) compared to chemical fuel driven assembly, electrochemical reactions drove assembly and disassembly, and lower concentrations of chemical waste were generated. However, the electrochemical redox reaction cycles in prior works required multiple prefuel and fuel molecules with concentrations carefully optimized based on kinetic models. In this work, we added a single molecule, BQ, which generated all the chemical species required to effect transient assembly of colloids.

Some chemical fuels for dissipative colloid assembly directly react with colloid surface ligands, converting them from a solvophilic to solvophobic state, effectively destabilizing the colloids to cause transient aggregation. The resulting aggregates are disordered and can readily become kinetically trapped32,33,51. To date, no fuel driven dissipative systems have generated ordered colloidal assemblies. In the present work, the transient colloidal assemblies assume an HCP structure and the colloid surface chemistry changes minimally during the reaction cycle. Instead, electrokinetic flows acting over several particle diameters caused mutual attraction or repulsion between colloids. Long-ranged attraction was balanced by short-ranged repulsion due to electric double layer overlap, which prevented the colloids from permanently aggregating. The sustained colloidal stability enabled cycling the colloidal crystals over nearly 50 cycles with no irreversible aggregate formation.

Chemical fuel driven dissipative assembly of micron scale colloids generally creates transient aggregates that persist for up to one day33,34, while transient nanoparticle aggregates persist for several hours32,35. The slow dynamics of conventional dissipative colloid assembly are rooted in the diffusion-based processes that form and break up transient aggregates. Likewise, solvophobic patches on colloids become buried in aggregate cores during dissipative assembly, limiting solvent access needed to break apart the aggregates33,51. The rapid dynamics of the present system derive from convection-driven assembly and disassembly of colloidal crystals. Here electrokinetic fluid flows with velocities on the order of \(\mu m/s\) mutually entrain neighboring colloids. Prior work showed that active repulsion by EO flow between particles separated colloidal crystals by up to five times faster than pure diffusion59. As such, the present system displays dynamics similar to field driven assembly of colloids, where particles rearrange on rapid time scales approaching single seconds. Intriguingly, by tuning the electrode spacing, the reconfiguration time of the colloids can approach nearly 10 min. The electrode separation parameter lends unique tunability in the timescale for the transient colloid behavior.

In conclusion, we demonstrated transient colloidal crystals that autonomously alternated between assembled and separated states with dynamics mediated by an electrochemical redox reaction network. The transient separation of the colloidal crystals correlated in time with transient pH spikes near the cathode and displayed reproducible dynamics over nearly 30 sequential electric stimulus applications. A mathematical reaction-diffusion model for the electrochemical BQ redox reaction network reproduced the transient pH spikes and their dependence on steady potential magnitude and electrode separation. This model uncovered the chemical mechanism for the transient pH to be opposing and interacting alkaline and acid pH wave fronts at the cathode and anode. The transient increase in hydroxyl ion concentration at the cathode triggered a repulsive extensile EO flow around each colloid, causing transient separation of the colloids. The experimental observations were broadly consistent with a hydrodynamic scaling model for two particles experiencing competing contractile EHD flow and extensile EO flow. This study is the first to combine aspects of external field directed assembly of colloids and fuel driven dissipative assembly to form transient colloidal crystals with tunable, rapid, and autonomous dynamics. This work opens the door for using electrochemical reaction networks to drive diverse electrostatic and electrokinetic colloidal phenomena, such as induced charge electrokinetic flows and dipolar interactions. Here the electrochemical reactions generate species that modulate the strength of electric field induced interparticle interactions in time. We envision that autonomously reconfiguring transient colloidal crystals could find applications as life-like soft materials in areas such as active camouflage, dynamic optical elements, and microrobots.

Methods

Cyclic voltammetry

CV measurements were performed using a Gamry Reference 600+ potentiostat. The liquid sample contained 10 mM benzoquinone in 100 mM KCl electrolyte. We utilized a Ag/AgCl reference electrode in 3 M KCl, an ITO working electrode, and a platinum reference electrode. The CV was performed with a scan rate of 150 mV/s and 2 mV step size.

Electrochemical cell assembly and chemical reagents

The experimental setup and materials are similar to those described in prior works59. Briefly, static electrochemical cells were created by placing two glass slides coated with ITO together with thin insulating spacers with thicknesses of 160 μm, 320 μm, 640 μm, or 1 mm. An arbitrary wave generator (AWG) was used to apply multimode electric potentials. The AWG applied potentials to the working electrode (WE), which was the bottom electrode, in reference to a floating ground (top electrode).

Monodisperse silica particles were purchased from Polysciences, Inc. and had a nominal diameter of 4 μm. The particles were not functionalized and had a zeta potential of about –50 mV59. Particles were dispersed in an electrolyte solution at a concentration of 0.1 w/w% and rinsed three times by centrifugation to remove surfactants and preservatives. Stock solutions of para-benzoquinone (Sigma Aldrich, 99.5%) were prepared fresh for each experiment and used immediately. All samples were prepared in an electrolyte solution containing 1 mM KCl in 18.2 MΩ DI water. BQ was added to the electrolyte to achieve a final concentration of 10 mM. Video microscopy was conducted using an inverted optical microscope set to bright field mode and the movies were recorded using a charge-coupled device (CCD) camera.

Fluorescence based pH measurements

A 10 mM aqueous fluorescein solution was diluted into a 10 mM BQ and 1 mM KCl solution to a 10 μM final concentration for fluorometric pH measurements. Fluorescence video microscopy on an inverted fluorescence microscope (Zeiss Axio Observer 7) was used to detect the pH changes near the WE in real time. Fluorescein was excited with a 475 nm LED and the emission was captured with a 20x objective lens focused on the cathode and then passed through a 515 nm long pass filter before recording on a Peltier cooled black and white or RGB CCD camera. The objective had a numerical aperture of 0.4, giving a depth of field of ~10 μm. Videos and images of fluorescence emission were processed in ImageJ by measuring the average intensity of the image area as a function of time. The emission data were corrected for photobleaching by fitting an exponential curve to the first five seconds of the data when the voltage was off and then subtracting the curve from the data74. Aqueous solutions of 10 µM fluorescein in phosphate buffered saline with the pH adjusted using 1 M NaOH were used for pH calibration curves. Each data point in the calibration curve was the average intensity of at least 3 fluorescence microscope images. The error bars were smaller than the size of the data points. Calibration curves were generated by plotting fluorescence emission normalized to the emission of the pH 6.6 buffer as a function of pH (Figs. S2, S10). These curves were utilized to convert time dependent fluorescence emission during the electrochemical reaction to absolute pH units in Fig. 2 (Fig. S2) and 8 (Fig. S10).

Mass spectrometry

Electrospray ionization mass spectrometry (ESI-MS) experiments were performed using direct analysis in real time (DART) ESI-MS operating in negative mode (AccuTOF, JEOL, USA, Inc.). Mass spectra were acquired at a rate of one spectrum per second over an m/z range of 50–800. Each mass spectrum was averaged over about one minute.

Image analysis

Video microscopy data were processed in ImageJ to extract images for figures. Average interparticle separation of colloids as a function of time was measured with an in-house MATLAB code that tracks the centers of each colloid in each frame using conventional image binarization and object tracking. Nearest neighbors for each particle were determined by Voronoi tessellation. The average interparticle separation, \( < S > ,\) was determined by taking the average nearest neighbor distance of all colloids in a cluster. Colloids at the edge of the cluster were excluded because the Voronoi tessellation fails at the cluster edge.