Spatio-temporal control of the phase separation of chemically active immotile colloids

: Understanding and controlling phase separation in nonequilibrium colloidal systems are of both fundamental and applied importance. In this article, we investigate the spatiotemporal control of phase separation in chemically active immotile colloids. We show that a population of silver colloids can spontaneously phase separate into dense clusters in hydrogen peroxide (H 2 O 2 ) due to phoretic attraction. The characteristic length of the formed pattern was quantified and monitored over time, revealing a growth and coarsening phase with different growth kinetics. By tuning the trigger frequency of light, the lengths and growth kinetics of the clusters formed by silver colloids in H 2 O 2 can be controlled. In addition, structured light was used to precisely control the shape, size, and contour of the phase-separated patterns. This study provides insight into the microscopic details of the phase separation of chemically active colloids induced by phoretic attraction, and presents a generic strategy for controlling the spatiotemporal evolution of the resulting mesoscopic patterns.


INTRODUCTION
Mixtures can phase separate in systems driven away from thermal equilibrium by external energy input.Such non-equilibrium phase separation is widely found from colloids [1][2][3] and polymers [4,5], to biological processes [6,7] and astrophysical events [8].Understanding non-equilibrium phase separation enables the development of materials with tailored electrical, magnetic and optical properties, while advancing research fields such as soft matter physics, materials science, chemistry and biology.A grand challenge of nonequilibrium phase separation lies in its spatiotemporal control, which involves manipulating the formation, growth, and organization of structures in non-equilibrium systems in real-time.
Colloids are an excellent model system for addressing this problem, as they are highly tunable in particle sizes, shapes, and interactions.Examples of non-equilibrium phase separation in colloids include selfpropelled Janus particles exhibiting motility-induced phase separation [9][10][11][12], charged colloids that develop into tunable colloid crystal and colloidal swarms under external electric fields [13], and three dimensional structures of DNA-functionalized colloids responding to environmental changes [14].Among them, phase separation mediated by chemically induced interaction is particularly attractive because of the long range nature of interparticle interactions, the ease of experimental setup, and the large library of chemical reactions to choose from.Notable examples include dynamic, motile clusters formed by Fe 2 O 3 [15] or AuPt colloids [16,17] that phoretically attract each other, and bio-mimicking, shape-morphing clusters formed by chemically interacting colloids [2,18].
Despite these demonstrations of non-equilibrium phase separation in chemically active colloids, there has been limited control over the resulting patterns, including their shapes, sizes, and evolution kinetics.In this study, we address this gap by the phase separation of chemically active but immotile silver (Ag)-coated microspheres as a model system.We have previously reported that such microspheres form clusters of growing sizes in H 2 O 2 [19], similar to those formed by Au microspheres in N 2 H 4 aqueous solutions [20], and clusters formed by TiO 2 [21] or AgCl microparticles under UV light [22].Here, we clarify the microscopic details of the phase separation of Ag colloids, quantify the characteristic length of the mesoscopic patterns and monitor their evolution kinetics, and develop a technique based on structured light to control such phase separation in both space and time.These findings deepen our understanding of the fundamental principles governing non-equilibrium phase separation, and could inspire new avenues for the controlled assembly of colloidal matter in applications of colloidal lasers [23], swarm control of microrobots [24], and encryption [25].

Phase separation of Ag colloids: Phenomenon and kinetics
Our following discussion is based on the key observation that silicon dioxide (SiO 2 ) microspheres halfcoated with silver (Ag) (Figure 1A) attracted each other in H 2 O 2 (Figure 1B) and formed clusters.These clusters were loose, long and interconnected at the beginning, but over time grew larger, more round in shape and more separte from each other.Two phases were formed; one is the cluster that is liquid-like, and the other is the gas-like voids between clusters where colloids sparsely populated.An example is given in Figure 1C and Video S1, where 5 μm SiO 2 -Ag microspheres of a population density of 17% suspended in 0.001 wt% H 2 O 2 formed clusters of ~100 μm in size in 100-200 s.
Janus SiO 2 -Ag microspheres (referred to hereafter as "Ag colloids") were used throughout this study because they were more uniform in size, less likely to stick to each other or to the substrate, and formed clusters of more regular shapes than pure Ag microspheres, which showed qualitatively the same phase separation (Figure S5 and Video S2).Also note that although Janus SiO 2 -Ag microspheres are known to selfpropel in H 2 O 2 [26,27], they become essentially immotile when the population density is larger than 4% (17% for the current study) due to the elevated ionic strength from the dissolution of Ag in H 2 O 2 that suppresses the motility of Ag colloid, as explained in details in a previous study [19].
Natl Sci Open, 2024, Vol.3,20230050 We describe the phase separation kinetics of Ag colloids by measuring the 2D packing fraction (Figure 1D) and characteristic length (Figure 1E) of the formed clusters as a function of time.The characteristic length is obtained by calculating the spatial correlation function (see Figure S3 for details).Phase separation proceeded in a two-stage growth and coarsening that can be distinguished by calculating the first derivative of the packing fraction over time (Figure S6).In the growth stage (0-46 s in the example in Figure 1), Ag particles quickly formed small clusters, which continued to attract surrounding particles until all particles entered the clusters.During this stage, the packing fraction of the clusters rapidly increased to its maximum, and the characteristic length grew with ~t0.22 , where t is the elapsed time.Next, the population of Ag colloids transitioned to the coarsening stage (46-200 s), in which the clusters fused with each other.The packing fraction of the clusters during this stage decreased slightly over time, possibly because clusters grew denser and into 3D.The characteristic length during the coarsening stage first increased with ~t1.2 (46-96 s), then slowed down to ~t0.11 (96-200 s) due to the formation of large clusters that were too far apart to merge.
The power coefficient over time of only the growth stage is used below to describe the temporal evolution of the clusters of Ag colloids, not only because the coefficients in the coarsening stage are more complex, but also because the backbone structures of the phase separated patterns have already formed during the growth stage.

Phase separation of Ag colloids: Microscopic details
We propose that Ag colloids attract each other by ionic diffusiophoresis (Figure 2A).To elaborate, we propose that Ag colloids are oxidized in H 2 O 2 by Ag + 1/2 H 2 O 2 = Ag + + OH − .
(1) An Ag colloid thus releases Ag + and OH − , the latter diffusing much faster than the former (5.27×10 −9 m 2 s −1 vs. 1.65×10 −9 m 2 s −1 ) [27,28].To maintain charge neutrality in the bulk solution, an electric field is generated that points from an Ag colloid outward.Nearby negatively charged colloidal particles thus migrate toward the ion-releasing colloid by electrophoresis (F EP ), a process known as ionic diffusiophoresis.At the same time, the same electric field pushes the positively charged layer of the fluid above the negatively charged bottom substrate.The resulting ionic diffusio-osmotic flow pushes the colloidal particles away from the ionreleasing Ag colloid (F EO ).Thus, F EP and the F EO have the same physical origin but point in opposite directions.According to the Smoluchowski equation [29], the drift velocity of the particle u is given as where is the permittivity of the solution, p and s are the surface zeta potentials of particle and substrate, respectively, and E is the electric field.In our experiments, the zeta potential is −51.2 mV for pure Ag colloids, −56.9 mV for SiO 2 microspheres, and −44.6 mV for the glass substrate (see Supplementary information for measurement).Accordingly, we speculate that the net transport of a Janus SiO 2 -Ag micro- sphere is dominated by electrophoresis (F EP > F EO ), so that an Ag colloid attracts its neighbors and they collectively form a cluster.This mechanism based on ionic diffusiophoresis is qualitatively supported by two pieces of evidence.First, using a pH-sensitive fluorescence probe molecule [24,30], we detected a significant increase in pH near an Ag colloid in H 2 O 2 (Figure 2B).This rise in pH is consistent with the production of OH − in Eq. ( 1).Second, the electrokinetic nature of the interparticle attraction was supported by a decrease in its magnitude upon adding salt (Figure S7), which is known to decrease the magnitude of ionic diffusiophoresis [31][32][33].

Controlling the phase separation of Ag colloids by adjusting fuel concentrations
It is intuitive to imagine that tuning the concentration of fuel molecules (H 2 O 2 in this case) would conveniently control the patterns formed by phase separation, because H 2 O 2 concentration is directly related to the reaction rate of eq. ( 1).Therefore, increasing H 2 O 2 concentration would increase the ionic flux, the magnitude of the resulting electric field, and therefore the strength of the interparticle attraction.However, experiments in Figure 3B showed the counter-intuitive results that larger clusters were formed at lower H 2 O 2 concentrations, while experiments under different H 2 O 2 concentrations yielded similar growth kinetics.In addition, clusters formed at higher H 2 O 2 concentrations were more branched and less smooth than those found at lower H 2 O 2 concentrations.
One possible reason for such discrepancy between experiments and our intuition is that Ag colloids tend to stick to each other at higher ionic strength, which resulted from higher reaction rates at higher H 2 O 2 concentrations.In addition, higher H 2 O 2 concentrations also lead to stronger inter-particle attraction.As a result, stronger attraction and sticking could prevent particles from freely migrating and prevent clusters from merging, so that more branched, tighter clusters were formed at higher H 2 O 2 concentrations.More subtly, the reaction kinetics of Ag could be affected by the H 2 O 2 concentration, so that more ions (or ions other than OH − ) could be produced at higher H 2 O 2 concentrations [26,34].We do not fully understand, nor do we have direct evidence for, either possibility.However, it is reasonable to argue that adjusting the concentration of H 2 O 2 is not an ideal method to control the phase separation of Ag colloids.

Controlling the phase separation of Ag colloids with light: Temporal modulation
To more precisely control their phase separation, we introduce an additional repulsive interaction between Ag colloids via photochemistry.This is inspired by earlier studies from the Sen lab [22,35] and our early studies [36] showing that in the presence of H 2 O 2 , Cl − and under UV, Ag colloids spontaneously oscillate between an episode of fast, directional motion and a period of slow, diffusive motion.
In addition to an oscillatory motion, these Ag colloids attract and repel each other when light is turned off and on (Figure 4A), respectively.As a result, Ag colloids phase separates in the same phenomenological manner as described earlier: individual Ag colloids nucleate into small, interconnected islands that gradually coarsen (Figure 4C).However, the oscillating population under intermittent illumination phase separated with slower kinetics than non-oscillating Ag colloids without illumination (Figure 4B).This is likely due to the interparticle repulsion during the half-cycles of UV illumination that impedes the formation of dense clusters.Despite this impedance, clusters still formed because attraction dominated over repulsion over one cycle of light on and off.The oscillation of Ag colloids in H 2 O 2 is speculated to result from oscillatory chemical reactions occurring on the Ag coating, but details remain elusive and are beyond the scope of this study.Although the chemical details of the oscillation remain unknown, it is reasonable to speculate that the attraction between Ag colloids in the dark is caused by the same oxidation of Ag by H 2 O 2 as described in Eq. ( 1) and Figure 2. The repulsion under illumination, on the other hand, is likely to be a reverse reaction, such as the photodecomposition of AgCl, releasing Ag + and H + .To support such speculation, Figure S8 shows an increase and a decrease in the fluorescence intensity of pH-sensitive fluorescent dyes around such an oscillating Ag colloid when light is switched off and on, respectively, consistent with the production of OH − and H + during these two operations.
One of the key features of such photoactive oscillating Ag colloids is that the magnitude of their attraction or repulsion is related to the duration of the light and dark episodes, and thus to the frequency at which light is switched on and off (hereafter referred to as the "trigger frequency").More specifically, Figure S9 shows that both attraction and repulsion weaken at higher trigger frequencies, possibly because a high trigger frequency will cause a weak oscillation reaction and thus a weak effective attraction.It is therefore possible to tune the strength of the interparticle interactions by tuning the trigger frequencies.For example, Figure 5A shows that the effective pair-wise attractive force between two Ag colloids, defined as the time-averaged interparticle forces ( ), decreased by a factor of three from 0.02 to 0.0073 pN when the trigger frequency was increased from 0.25 to 1 Hz.As a result, both experiments and Brownian dynamics simulations (see Supplementary information for details) in Figure 5B-D and Video S3 show that the phase separation slows down and the characteristic length of the clusters decreases upon increasing the trigger frequency of light.Tuning the trigger frequency of light thus becomes an effective method for tuning both the structure and the growth kinetics of the phase separation patterns of Ag colloids.

Controlling the phase separation of Ag colloids with light: Spatial control
In addition to modulating the structure and the kinetics of the phase separation patterns, light can also precisely control where the phase separation occurs, as well as dictate the contour of the phase-seperated patterns.Such spatial control takes advantage of structured light technology, which projects arbitrary light patterns of programmable brightness and trigger frequency.
Figure 6 showcases a number of ways in which the phase separation of Ag colloids was manipulated in space (Video S4).For example, Figure 6A shows two adjacent regions where Ag colloids formed clusters of different sizes under two light patches of trigger frequencies of 1 and 0.25 Hz, respectively.Figure 6B and C, on the other hand, show that the phase separation of Ag colloids can be limited to regions of different sizes (Figure 6B) or aspect ratios (Figure 6C) under corresponding light patterns.In particular, the results in Figure 6C show that light patches thinner than the characteristic length of a phase-separated Ag cluster forced Ag Natl Sci Open, 2024, Vol.3, 20230050 colloids into bands instead of islands, and the shapes and sizes of these bands followed exactly those of the projected light patterns.This feature was further leveraged to write fine letters with phase-separated Ag colloids (Figure 6D).
Moreover, the contours of the patterns formed by the phase separation of Ag colloids tended to follow the shapes of the projected light patterns, resulting in patterns with square, circular, hexagonal, or triangular contours (Figure 6E).This effect is likely due to the fact that only those Ag colloids that are inside a light pattern can be activated.As a result, those that are just inside the light pattern constantly attract particles from outside, increasing the particle concentration at the pattern's edge in the process.These regions then serve as nucleation centers, leading to phase separation patterns that follow the contours of the light patterns.

DISCUSSION AND CONCLUSION
We have shown that a population of Ag colloids, either Janus SiO 2 -Ag microspheres or pure Ag particles, can spontaneously phase separate into dense clusters in H 2 O 2 .Such phase separation is driven by the attraction of Ag colloids to each other, possibly because Ag oxidizes in H 2 O 2 and generates an electric field that electrophoretically attracts nearby particles.The characteristic length of the formed pattern was quantified and monitored over time, revealing a growth and a coarsening stage with different growth kinetics.Taking advantage of the fact that Ag colloids attract each other in the dark but repel each other under illumination, both the characteristic lengths and the growth kinetics of Ag colloid clusters can be controlled by tuning the trigger frequency of the light, so that higher frequencies lead to smaller clusters that grow more slowly.In addition, light patterns of programmable shapes control where the phase separation occurs, as well as the shape and size of the formed patterns.The patterns and their growth kinetics were qualitatively reproduced by computer simulations.However, the characteristic length of the clusters formed in the experiment is larger than the corresponding simulation result.Such a difference may be caused by the fact that the interparticle interaction potential in our models is approximated as a constant potential decaying with the interparticle distance, instead of being solved by the reaction-diffusion of chemical species as in the experiments.More specifically, we speculate that the overlap of the concentration fields of many particles within a cluster reduces the attraction of a nearby particle to the cluster, allowing particles outside a cluster to diffuse more freely and clusters to coarsen faster than a simulated cluster without chemical diffusion.The effect of many-body interactions on the phase separation of chemically active colloids is being investigated in a separate study.On a fundamental level, this study provides insights into the microscopic details of phase separation of chemically active colloids caused by phoretic attraction.Although some qualitative description of the evolutionary kinetics of such a phase separation process has been given in this article, detailed analysis and theory are being sought and will be published separately.On an applied level, this study has used structured light technology to achieve unprecedented spatiotemporal control over the phase separation of chemically active colloids based on the oscillation of Ag colloids under light.Notably, this control has been achieved at the population level, while allowing each individual colloid to move and assemble freely, so that the fine details of the pattern formed are still governed by the intrinsic interplay within the system, rather than dictated by external intervention.Although the colloidal system and its interactions in the current study are entirely chemical in nature, the principle of tuning the effective attraction between individual colloids by alternating between attraction and repulsion can be generally applied to other colloidal systems driven by, for example, electromagnetic fields.

Figure 1
Figure 1 Phase separation of Ag colloids.(A) Scanning electron micrograph of a SiO 2 -Ag microsphere.(B) SiO 2 -Ag particles attract each other in dilute H 2 O 2 .(C) Optical micrographs of the phase separation of SiO 2 -Ag (dark) with population density φ = 17% in 0.001 wt% H 2 O 2 aqueous solution.(D) The 2D packing fraction of clusters and (E) the characteristic length of the clusters in (C) as a function of time.The particle density is obtained by identifying the area fraction of the particles by imageJ, see Figure S2 for details.The characteristic length (L) refers to the length corresponding to the first root of the spatial correlation function of the micrographs, see Figure S3 for details.Both the x and y axis in (E) are in log10 scale.Solid red lines in (E) are linear fits.

Figure 2
Figure 2 Ag colloids attract each other by ionic diffusiophoresis.(A) Schematic diagram of a SiO 2 -Ag microsphere attracting an inert microsphere by ionic diffusiophoresis in H 2 O 2 .The Ag cap reacts with H 2 O 2 and releases Ag + and OH − , which leads to a self-generated electric field that points away from the Ag colloid.A negatively charged tracer nearby reacts to this electric field by electrophoretically migrating toward the Ag colloid under the influence of an electrophoretic force F EP .In addition, the electric field causes an electroosmotic flow from the negatively charged bottom substrate that advects the tracer via an electroosmotic draf force F EO .F EP dominates over F EO , so that tracers are attracted to Ag colloids.(B) Fluorescence photograph of SiO 2 -Ag in 0.01 wt% H 2 O 2 .Stronger green fluorescence indicates higher pH values.A pH-sensitive fluorescent dye Solvent Green 7 was used at a concentration of 100 μmol L −1 .Blue light of 475 nm and ~75 mW cm −2 was used to excite fluorescence.

Figure 3
Figure 3 Phase separation of Ag colloids under different H 2 O 2 concentrations.From top to bottom: the kinetics and an optical micrograph (t = 50 s) of the phase separation of Ag colloids (dark) of φ = 17% in 0.001 wt%, 0.01 wt%, 0.1 wt% H 2 O 2 aqueous solutions, respectively.Solid lines are linear fits.Both x and y axes are in log10 scales.

Figure 4
Figure 4 Phase separation of oscillating Ag colloids under intermittent UV illumination.(A) SiO 2 -Ag colloids repel each other when light is on, but attract each other when light is off.(B) Clustering process of non-oscillating (top) and oscillating (bottom) Ag particles.Top row: photograph of Ag particles (φ = 7.9%) aggregating in 200 μmol L −1 KCl and 0.25 wt% H 2 O 2 aqueous solution.Bottom row: in 200 μmol L −1 KCl and 0.25 wt% H 2 O 2 aqueous solution, Ag particles (φ = 8.1%) aggregated upon switching UV on and off at 0.5 Hz (i.e., 1 s light on+1 s light off = one cycle).Note that Cl − is not necessary for the non-oscillating sample to cluster, but was added only to ensure the same solution composition for both samples.(C) Optical micrographs of the phase separation of oscillating Ag colloids (φ = 17%) at a UV trigger frequency of 0.5 Hz (405 nm, ~126 mW cm −2 ) at different time instances.

Figure 5
Figure 5 Phase separation at different frequencies of switching light on/off (the "trigger frequency").(A) The change in the interparticle interaction force during one cycle at different trigger frequencies.F t is the time-averaged interparticle forces of the intermittent attractionrepulsion during one cycle.Positive forces are attractive, and the half-cycles of the darkness and illumination are colored in green and red, respectively.See Supplementary information for measurement of these interparticle forces.(B) Optical micrograph (top) and Brownian dynamics simulations (bottom) of the evolution of the phase separation of Ag colloids of φ = 17% at different trigger frequencies.(C), (D) Characteristic lengths of the patterns in (B).Experiments were carried out in 0.25 wt% H 2 O 2 and 200 μmol L −1 KCl aqueous solutions, using 405 nm light of ~257 mW cm −2 .See Supplementary information for simulation details.

Figure 6
Figure 6 Spatial control of the phase separation of Ag colloids via structured light.(A) Two adjacent regions where Ag colloids (φ = 14%) formed clusters of different sizes under two light patches of a trigger frequency of 1 (left) and 0.25 Hz (right), respectively.(B) Phase separation under light patches of different sizes.(C) Phase separation under light patches of different aspect ratios.(D) Writing letters of NANO using Ag colloidal clusters with light patches.(E) Phase separation under light patches of different shapes.In (B)-(E), the particle density is 28% and the trigger frequency is 1 Hz.These experiments were carried out in 0.25 wt% H 2 O 2 and 200 μmol L −1 KCl aqueous solutions.The light patches are shown in the top panels of each figure, where the white area is irradiated by 405 nm light of ~257 mW cm −2 .