Directional flows using capillary assembly of photo-deformable colloidal particles at water-air interfaces

Domain: physics
Published: 2025-12-24
Editorial outcome: major_revision

Abstract
Colloidal particles at liquid interfaces experience long-ranged capillary interactions, whose magnitude and directionality depend on the particle shapes. When particle shapes are determined by fabrication or synthesis, the resulting shape-mediated interactions are predefined and often lead to the formation of persistent interfacial structures. Here, we introduce polymer particles at water-air interfaces whose shape and, therefore, interactions can be altered by illumination with polarized light. Specifically, we selectively trigger capillary self-assembly by anisotropically deforming the particles at the interface. Intriguingly, further deformation of already assembled particles induces sustained interfacial flows with velocities of up to 90 μm/s. Benefitting from polarization-defined deformation directions, we create flow-patterns that do not simply follow the illumination intensity pattern, such as shear flows along a single rectangular illumination stripe. We anticipate that this interplay between photo-deformation and capillary interactions of particles will enable various forms of mixing, manipulation, and assembly of soft matter at liquid interfaces.

Introduction
Capillary interactions are a fundamental phenomenon at liquid interfaces. In fact, when small objects are adsorbed to an interface, they deform it. These deformations increase the surface tension and are therefore energetically unfavorable. As a consequence, lateral forces between the objects emerge to minimize the surface tension and the surface deformations. This mechanism enables the emergence of intriguing natural phenomena. For example, some insects can climb the slippery curved slopes at a pond edge by adopting quasistatic body postures at the air–water interface1. In doing so, they actively create surface deformations that interact with the external edge meniscus so that they are propelled uphill. Biological entities can also use surface deformations to interact directly with each other, for example, by means of anisotropic shapes creating anisotropic interface deformations resulting in long-ranged, oriented capillary attraction forces. Correspondingly, ordered capillary assemblies have been reported on several length scales, including oval beetle bodies2, ellipsoidal mosquito eggs3 and boomerang-shaped Ruppia maritima pollen4. Regarding artificial systems, shape-mediated capillary forces were first demonstrated on the mesoscale by guiding the ordered interfacial assembly of millimetric synthetic particles with anisotropic geometries and patterned hydrophilicity into well-defined static patterns5. Building upon this concept, tunable systems have recently been reported. Using temperature6,7, magnetic fields8, or light9,10, the mutual interaction and assembly of mesoscale objects was controlled directly at the liquid interface. In all these works, thin, sheet-like rafts were employed, with lateral sizes ranging between 50 μm and several millimeters. The rafts relied on significant contour undulations stemming from well-defined wrinkles, folds, or bending to pin the liquid interface to different heights and to induce large, tunable interface deformations.

Downscaling this shape-mediated capillary control to colloidal particles, with sizes between 100 nm and several μm, is of great interest considering the prospect of assembling and manipulating large numbers of particles simultaneously, but involves the challenge of controlling the interface deformation geometries at much smaller scales. Thus, researchers have studied the capillary interactions of interface-adsorbed particles with anisotropic shapes such as cylinders11, curved disks12, cubes13, or ellipsoids14, which can be prepared by methods involving, e.g., photolithography11,12, hematite synthesis13,15, or mechanical stretching16,17. In fact, on the scale of a colloidal particle, a smooth prolate ellipsoidal shape can be sufficient to induce a sizeable near-quadrupolar interface deformation around a particle due to the constant wetting angle18,19. Minimizing these quadrupolar deformations, particles were then reported to assemble, for example, in large-scale tip-to-tip or side-by-side stackings14,19–22. However, since these works relied on prefabricating particles with fixed shapes, the assembled particle phases were static. Versatile tunable assembly phase changes have been recently predicted in simulations using an external control mechanism based on magnetic fields to tilt magnetic ellipsoidal particles at the liquid interface, thereby tuning the induced interface distortions and particle interactions23,24. Yet, experimental realizations of tunable colloidal assemblies, based on direct control over shape-mediated capillary forces, have so far remained elusive.

Here, we experimentally introduce a 2D-confined colloidal system that permits us to directly control capillary inter-particle attraction forces and to generate sustained flow patterns. The system consists of colloidal azopolymer particles adsorbed to an air–water interface, whose shape can be altered using polarized visible light. This effect, which can be anisotropic and polarization-dependent25, has frequently been used in nanofabrication contexts to optically inscribe surface topographies in thin films26–28 or to reconfigure microscale features and particles bound to solid substrates29–32, embedded in soft matrices33–35, or within microporous films36,37. Here, we start by extending this phenomenology to the interface-adsorbed, mobile azopolymer particles, inducing both anisotropic and in-plane isotropic deformations depending on the illumination’s polarization. We then show how the resulting shape-mediated capillary effects permit local assembly and disassembly of particles. Finally, the continuous deformation of local capillary assemblies in denser particle settings is discovered to enable steady particle flows, whose intriguing properties can be controlled by simple intensity patterns with defined polarization.

Results
Shape-morphing particles at an air–water interface
We start by considering the behavior of single azopolymer particles adsorbed to a liquid interface when subjected to illumination with polarized visible light. Specifically, we show that these particles can be deformed into anisotropic shapes directly at the air–water interface by laser illumination with suitable polarization, complementing the studies that have shown this effect on dry substrates29,31,32.

The photo-deformable azopolymer particles were prepared by a solvent evaporation method, using the commercial light-responsive polymer poly[(Disperse Red 1 methacrylate)-co-(methyl methacrylate) pDR1m-co-mma (Fig. 1a). In brief, a chloroform solution of the polymer was added to an aqueous solution containing polyvinylpyrrolidone (PVP) and emulsified by sonication while the chloroform was continuously evaporated (see Methods for details). This generated a polydisperse set of azopolymer particles, sterically stabilized by PVP, with diameters up to 3 μm (Supplementary Fig. 1a). These particles were spread at the air–water interface in a sealed sample cell, where their movement was confined to two dimensions. PVP was used as a steric stabilizer to promote particle adsorption to the interface and to prevent aggregation upon adsorption. Thus, the particles were predominantly found at the interface plane (as shown by a confocal microscopy z-stack, Supplementary Fig. 2), reflecting their successful adsorption, and exhibited lateral Brownian motion in agreement with previous reports38,39. Using gel-trapping, we measured a three-phase contact angle (CA) of 104° ± 6° (Supplementary Fig. 3). Optical deformation was induced by illuminating the particles with an expanded green laser (λ = 532 nm) while observing them under an inverted optical microscope with white background illumination (Supplementary Movie 1).

When using a linearly polarized illumination beam, we were able to anisotropically stretch the particle along the polarization direction into a rod-like shape (Fig. 1b). Similar stretching behaviors have already been shown for similar azopolymer particles but on solid substrates29,31,32. Some studies also reported this transformation to be close to the uniaxial, isochoric one (i.e., the polymer being incompressible and the deformed particle being symmetric around the axis of polarization and elongation)32,34.

Next, we observed circular polarization to induce in-plane isotropic flattening of particles, leading to an axially symmetric oblate, disk-like shape (Fig. 1c), again matching with previous studies focusing on immobile microstructures30,35,40. In Fig. 1c, note that the particle becomes less visible due to its flattening, reducing the lateral differences in optical path length (i.e., distance times refractive index, integrated along the optical axis) as well as the attenuation through the flattened particle, ultimately lowering imaging contrast.

Finally, elliptical polarization can be used to produce an intermediate result, i.e., a flattened ellipsoid with lower in-plane aspect ratio (Fig. 1d). Also this intermediate has been shown previously on solid substrates30,37. We note that, even in the theoretical case, such an ellipsoid will have three independently adjusted principal axes (no axial symmetry).

In Supplementary Fig. 4, the above examples are statistically quantified based on 20 individual deformation sequences for each case. We confirm that linear polarization induces the highest aspect ratios on average, followed by elliptical polarization, while circular polarization results in an in-plane aspect ratio close to one for the whole sequence. Further, we observe that all polarizations induce considerable flattening of particles, with relative area expansions of up to a factor of five for circular polarization. In this context, note that the underlying mechanism of photo-deformation in this polymer is based on cyclic trans-cis-trans isomerization induced in the pseudostilbene-typedye Disperse Red 1 (DR1)41, which occurs due to the strong overlap of its cis and trans spectra at the employed wavelength42. While photo-thermal effects and the increase of cis isomer populations are known to accompany this effect for any polarization, the directionality of the material’s photo-deformation is linked to a polarization-sensitive average reorientation of the dyes upon prolonged isomer cycling25. Hence, the different directionality of the particles’ photo-deformation is the major change occurring when only the illumination polarization is altered in the experiments below.

Optically controllable capillary interactions and assembly
Next, we show that shape-mediated, capillary-driven self-assembly—previously achieved using anisotropic particles that were fabricated in advance and then placed at liquid interfaces11–14,19–22,43—can instead be induced in situ via light-driven deformation of initially spherical particles directly at the interface. To do so, we study sample regions where pristine spherical particles diffuse freely and in close proximity along the interface. When shining elliptically polarized light on these particles, they deform into ellipsoids, approach each other and bind in a stable side-by-side configuration (Fig. 2a, i–iii and Supplementary Movie 2).

This behavior can be attributed to the anisotropic, saddle-like interface deformations, which are known to be induced by the constant three-phase contact angle around ellipsoidal particles18,19, and are illustrated in the corresponding schemes shown in Fig. 2b, frames i–iii. The resulting long-range capillary forces, with quadrupolar symmetry, can significantly exceed the thermal energy kBT14,43,44, and lead to oriented particle assemblies. Thereby, the observed side-by-side configuration constitutes the minimum energy configuration for two ellipsoidal particles in contact3,21,39. The intermediate frames in Supplementary Fig. 5 show how the two particles rotate into this configuration upon contact44,45. The underlying capillary mechanism is overall surface energy minimization of the liquid interface, which can be achieved by superposing matching deformations, e.g., matching surface elevations or depressions43.

Interestingly, the stable capillary bond between the particles can be reversed by a subsequent illumination with circular polarization (Fig. 2a, frames iv–v). This second illumination induces a biaxial flattening of the particles, which is applied on top of the previous deformation since azopolymer deformations are plastic, superposing processes28,31,34. Although the particle cross-sections do not become perfectly circular again during this process, the particles consistently disassemble during prolonged exposure.

This is likely due to a combined effect of in-plane ellipse aspect ratio reduction, intrinsically reducing the anisotropic interface deformation, and out-of-plane particle flattening (see schemes in Fig. 2b, frames iv–v). In fact, since the interface deformation causing the capillary attraction stems from contact line undulations around the physical particle, the maximal deformation height is approximately limited by the (gradually diminishing) particle height43. By flattening the particles, the increasingly sharp edge of the flattened particle associated to a diminishing out-of-plane curvature radius, is expected to become the dominant factor and to suppress the capillary attraction when the in-plane particle anisotropy is comparingly low.

Finally, this behavior is not restricted to pair-wise particle interactions. Additional insights can be obtained by considering regions containing multiple nearby particles. In such cases, capillary assembly and disassembly can involve larger particle ensembles (Fig. 2c and Supplementary Movie 3), driven by the long-range nature of the shape-mediated capillary forces, which have been reported to act over distances up to several tens of particle diameters14,44,46. While we observe pair-wise interaction up to 20 μm, we find that particles initially separated by up to 50 μm can become part of the same capillary assembly (Supplementary Fig. 6).

Additionally, the initial deformation may be performed using linearly polarized light, which deforms the particles into higher aspect ratio rod-like shapes (Supplementary Fig. 7 and Supplementary Movies 4, 5), although the disassembly time with circular polarization tends to increase in this case. Importantly, when circular polarization is used directly for the initial deformation, no assembly is induced, since the particles expand isotropically within the interface plane (Supplementary Fig. 8 and Supplementary Movie 6). Notably, in pre-assembled structures containing multiple particles, switching to circular polarization to reduce capillary attraction can trigger dynamic rearrangements. As the particles flatten and become increasingly rounded, the assemblies typically evolve into tip-to-tip configurations—the minimum energy configuration of multiple ellipsoids with lower-aspect ratios39—before eventually disassembling (Supplementary Fig. 9 and Supplementary Movie 7). In addition, the influence of particle size on the capillary forces becomes evident. Precisely, smaller particles are known to create smaller interface deformations and thus weaker attractive forces43. Therefore, they are not only pushed aside by larger particles during multi-particle assembly but also tend to dissociate more rapidly from other particles during disassembly (Supplementary Fig. 10 and Supplementary Movie 8).

Continuously deforming capillary assemblies
We now report on the emergence of a collective, dynamic flow phenomenon arising from the combination of the previously described particle deformation and capillary assembly processes (Fig. 3 and Supplementary Movie 9). This intriguing effect was discovered when the particle density at the interface was significantly increased—from sparsely distributed particles in earlier sections (surface coverage: <5%) to a denser, near homogeneous surface coverage (Fig. 3a–c, frame i: surface coverage: 38%, see Methods), where the sterically-stabilized particles are still exhibiting Brownian motion. Upon illumination with a ~80 μm wide Gaussian laser beam profile polarized linearly along the y-axis, the particles in the entire illuminated area are stretched and start to self-assemble (Fig. 3a–c, frame ii). The assembled particles subsequently elongate further along the polarization direction and propagate their deformation along the growing capillary assembly (Fig. 3a, b, frame iii). At such high interfacial densities, both side-by-side and tip-to-tip configurations become energetically favorable, as each reduces interfacial deformation by superimposing matching surface elevations and depressions of adjacent particles21. As the deformations propagate, assembled particles are seen to be pushed in y-direction towards the upper and lower boarders of the field of view and beyond (Fig. 3a, b, frame iv). The magenta inset, magnified in Fig. 3c, traces the course of large, well-recognizable pristine particles. On subsequent frames, these deforming particles self-assemble, deform further, and are pushed towards the upper border of the field of view by the collective symmetric deformation caused by all other assembled particles. Surprisingly, instead of a finite deformation, a continuous motion is generated (Fig. 3a, b, frames v-vi). In fact, the blue inset magnified in Fig. 3c displays fresh, peripheric particles at a later stage, which get pulled toward the zone of illumination along the x-direction to compensate for assembled particles leaving the zone along the y-axis. Entering the illumination zone, the pristine particles deform, assemble and contribute to sustaining the flow, initiating a stationary process.

To quantify this behavior, we measured the y-axis velocity of outflowing particle structures in the area contained by the black/yellow square in Fig. 3b, vi, using cross-correlation and maximum overlap fitting of subsequent frames (see Methods for details). The resulting velocities were plotted as a function of illumination time in Fig. 3d. After an initial phase where the particles are illuminated, but not yet assembled, the outflow velocity slowly rises to a constant value. When the illumination is turned off, the flow almost immediately stops. Subsequently, it resumes quickly at full speed when the illumination is switched on again. This may be explained with the particles already being assembled and thus being able to propagate their deformation instantly, in contrast to the dynamics at the first illumination onset.

At first glance, the transport phenomenon described above may appear similar to free particle flows along the interface. Indeed, several optically induced flow mechanisms capable of transporting particles or larger objects along liquid interfaces have been reported—the most relevant in this context being those based on trans to cis isomerization of azobenzene molecules or on photo-thermal phenomena47,48. For example, particles or oil droplets can exhibit directional locomotion along liquid interfaces when lateral gradients of trans and cis isomers with different hydrophilicity form on their surface49,50. Thermal gradients across particles and small objects can play a similar role51,52. Furthermore, Marangoni flows may be induced anywhere on a liquid interface using photo-thermal effects53,54, or, e.g., by isomerization of azobenzene-containing surfactant molecules55–57, with the aim of displacing nearby particles.

To rule out such effects as the primary cause of the flow phenomena reported herein, several key observations can be considered. First, no locomotion is observed for sparsely distributed particles in the previous sections, although similar laser profiles were used. Therefore, flows arising from gradients across the particles themselves do not seem to drive the phenomenon. Secondly, the flow in our system stops immediately after the illumination is switched off. Yet, the relaxation of the cis population, accompanying the deformation, is known to take several seconds in the dark for the DR1-doped azopolymer42,58, a timescale over which isomerization-related flows should proceed. Thirdly, upon close inspection of Supplementary Movie 9, one can easily observe the absence of individual diffusion for deformed particles when illumination is switched off, reflecting their assembled configuration. Indeed, the assembly could even be seen to extend far beyond the field of view in the y-direction (outflow direction) after the movie was acquired (Supplementary Fig. 11). Conventional flow mechanisms would then have to break up the rigidly assembled state in the illumination zone each time illumination is resumed, to cause smooth, free particle flows. Finally, and most importantly, the y-oriented directionality of the flow, which follows the particles’ photo-deformation direction, contrasts with the rotationally symmetric illumination intensity profile (Gaussian beam). The full dependency of the local flow direction on the polarization is shown in the next section, amongst others, by freely rotating the outflow direction without modifying the illumination intensity pattern and by showing the absence of flow for circular polarization. Since photothermal and isomerization-based effects have no intrinsic directionality, this suggests a decisive role of the particles’ polarization-directed photo-deformation in driving the flows.

On the other hand, the phenomenon cannot be explained by directional photo-deformation alone either, which is apparent when comparing the presented velocity graph to the well-studied time-dependent deformation effect in fixed azopolymer structures31–33. In these works, photo-deformation is shown to start deforming with a constant rate almost immediately when illuminated. Here, the macroscopically transmitted flow displacement initially arises only after particle assembly, tens of seconds later, when the particles can propagate their individual deformations. On the other hand, the referenced azopolymer deformations consistently saturate during prolonged exposure, upon reaching a maximal deformation. A film made of a single, large azopolymer structure would therefore be expected to cease flowing once the deformation in the illumination zone has saturated. In contrast, we observe that fresh particles can freely and constantly flow in from directions orthogonal to the outflow, reach the center of the illumination zone and efficiently evacuate heavily deformed particles as the capillary assemblies are remodeled. Thus, we conclude that it is the synergy of local, illumination-triggered particle assembly and polarization-dependent particle photo-deformation itself, which drives the directional flow.

Polarization-controlled directionality and shear flows
Finally, we demonstrate how the sustained interfacial flows introduced above can be readily tuned by adjusting the illumination pattern and especially the polarization direction (Fig. 4a). This permits us not only to drive both symmetrical flows with arbitrary direction and pure shear flows, but also to thoroughly confirm the link between particle photo-deformation direction and flow behavior. For these experiments, we use azopolymer particles with a smaller average size (≤1.5 μm; Supplementary Fig. 1b, CA = 111° ± 4°, Supplementary Fig. 3d), which were observed to result in faster and more homogeneous flows. Instead of solely monitoring outflow velocity, we divide the field of view into regular tiles (Fig. 4b). This approach allows us to compute local velocities and extract entire flow fields through cross-correlation (see Methods). An entire flow field upon Gaussian illumination with y-oriented linear polarization is shown in Fig. 4c. If the polarization is x-oriented instead, an orthogonally oriented flow pattern is observed (Fig. 4d), which is a direct consequence of the polarization defining the anisotropic particle deformation direction. The original flows are shown in Supplementary Movie 10. Intriguingly, one can also alter the symmetric outflow axis dynamically during illumination, for example, by polarization rotation (Supplementary Movie 11 and Supplementary Fig. 12). Thus, not only does the flow directionality break with the rotational symmetry of the intensity pattern, but the directionality can also be changed without modifying the latter. Importantly, the same intensity pattern can even be shown without inducing any flow, when circularly polarized light is used (Supplementary Movie 12 and Supplementary Fig. 13). As shown in the previous sections, circularly polarized illumination causes in-plane isotropic, biaxial particle flattening, but no capillary assembly, which would allow the particles to propagate these deformations. We finally remark that biaxial expansion is also not compatible with the inflow of fresh, non-assembled particles along any in-plane axis on the interface, thus inhibiting persistent flows for circularly polarized illumination even in cases where the particles have previously been assembled using linear polarization (Supplementary Fig. 14). These observations corroborate that the flow profiles cannot be attributed to thermal or isomerization-driven effects, which occur also when using circular polarization, as discussed earlier.

It is also important to note that smooth and steady flows for linear polarization may not occur at any interfacial particle loading. Although the manual particle dispersion (see Methods) inhibits very precise adjustments, we highlight this by varying the parameter in coarse steps (via pre-dilution/concentration), leading to three extreme situations compared under y-oriented linearly polarized illumination (Supplementary Fig. 15 and Supplementary Movie 13, details in Supplementary Note 1). Crucially, in a fully packed particle monolayer where Brownian motion is severely hindered, the film deformation rate peaks rapidly but decays as the deformation saturates, and no flow is sustained (Supplementary Movie 13, right). This mirrors the immediate onset and saturation behavior of regular azopolymer deformation, as discussed previously. The transient velocity field for this deformation is also highly divergent, due to the lack of particle inflow. Similarly, a net positive divergence (i.e., higher total outflow than inflow) is observed when the starting situation are dense but still diffusing particles as in Fig. 4c, d. This is confirmed by explicit divergence computation (inset, Fig. 4d) and may be attributed to the particles' increasing surface area as they are stretched. Importantly, using a suitable dilution of particles with respect to this case, one can obtain situations where a steady particle flow is still occurring (Supplementary Movie 13, left), but where the contribution of divergence to the flow fields is rendered negligible (Supplementary Note 1). Such situations can be exploited to, for example, create velocity fields where the particles flow into the illumination zone faster than they exit, using a suitable illumination pattern (Supplementary Fig. 16 and Supplementary Movie 14). They can also give rise to shear patterns, as detailed below.

Shear flows were created using stripe-shaped illumination, where the linear polarization is oriented at 45 degrees relative to the stripe (Fig. 4e, f). In this configuration, the combined diagonal pushing outflow (light blue arrows) and compensating diagonal inflow of equal magnitude (orange arrows) create parallel flows in opposite directions on either side of the stripe (red arrows). Hence, the result is a pure shear flow with invertible directions for ±45 degrees offset between the polarization and the stripe axis (Fig. 4g, h and Supplementary Movie 15). Under shear flow conditions, particles traverse the entire field of view in opposite directions alongside the rectilinear illumination stripe (Supplementary Fig. 17), a behavior that, once again, cannot be explained by the illumination pattern only. Instead, both the intensity pattern (here: illumination stripe) and the polarization (here: diagonal polarization) have to be considered to explain the overall shear flow pattern. Finally, at slightly increased densities, occasional turbulence with rotational motion was observed within the stripe region (Supplementary Movie 16), and the lateral shear flow velocities reach up to 90 μm/s (Supplementary Fig. 18), corresponding to ~100 body sizes per second for the particles.

Methods
Particle fabrication
The polymer poly[(Disperse Red 1 methacrylate)-co-(methyl methacrylate) pDR1m-co-mma (Sigma-Aldrich, ~15 mol% dye monomer) was dissolved in chloroform at 10 | 25 mg/mL for samples shown in Supplementary Fig. 1a, b, respectively. 1 mL of solution was then added to 12.5 mL of deionized (DI) water containing 0.5 wt% polyvinylpyrrolidone (Sigma-Aldrich, MW: 360 kD) | polyvinyl alcohol (Sigma-Aldrich, MW: 13–23 kD, 87–89%, hydrolyzed) respectively as stabilizer. The phase-separated mixtures were sonicated in an ultrasound bath (Elmasonic P30H, 37 kHz, 100%) for up to 5 h, interrupted by sporadic manual shaking only, until appearing homogeneously emulsified upon visual inspection. Subsequently, the chloroform solvent was evaporated by transferring the emulsions to an open beaker and sonicating further, whilst slowly raising the bath temperature to the boiling point of chloroform (~0.1 °C/min, from 55 °C upwards). After passing the boiling point, the samples were sonicated for 30 more minutes at 75 °C. Finally, the solutions were filtered with a 10-μm syringe filter, and excess surfactant was removed by three times centrifugating the particles and redispersing them in DI water.

Water–air interface
Water–air interfaces were prepared inside dedicated cells, made from two glued microscopy glass sides, where the top slide figures a circular, laser-cut aperture (~5 mm in diameter). The cells were cleaned with a NaOH solution before each use and subsequently filled with 5 μL of DI water. After dilution to a suitable particle density, 0.5 μL of the particle dispersion was carefully spread at the interface, using a micropipette. The sample was left to evaporate in open air for 5 min, before it was sealed by a dedicated transparent glass slide fixed with vacuum grease, such as to limit convective and evaporative flows and permit long enough observation times.

Predominant particle adsorption at the water/air interface was verified by confocal laser scanning microscopy (Zeiss LSM980) using z-stack imaging with a 20×/0.8 NA objective, 514 nm excitation wavelength, and detection wavelength between 516–639 nm. To estimate the surface coverage for movies in sections 1–3, 20 raw frames were selected from the initial seconds of the movies, where no illumination is provided yet. These frames were then inverted, and subsequently, a particle localization with a thresholding detection algorithm was applied. After locating the center of the particle, we obtained its area as the sum of all pixels surrounding the center that differ from the background intensity level and averaged over the considered frames. Examples are shown in Supplementary Fig. 19. Notably, the measured surface coverage is based solely on the area of particles large enough for detection and does not account for the surrounding steric stabilization layer39. The actual surface coverage is therefore expected to be substantially higher.

Optical setup
The optical setup consisted of a regular inverted microscope, illuminated by an LED (Thorlabs MNWHL4) with a 10x objective as a condenser from the top and with a 40x/0.75 NA objective mounted below the sample for observation. For recordings, a CCD camera from IDS (UI-3060CP-M-GLR2) was used, which permitted reliable acquisition at fixed frame rates of 30 and 50 fps. A 532 nm wavelength continuous wave laser diode was employed for the particle deformations. The beam was introduced from below and focused into the vicinity of the back-focal plane for suitable expansion of the beam width. Intensity was adjusted by means of neutral density filters, and polarization was controlled with zero-order waveplates. For assembly experiments, a quarter wave plate’s fast axis was oriented at 0, 22, and 45 degrees with respect to the axis of the incoming x-directed polarization, to obtain linear x-axis, elliptical (2.5:1 axis ratio) and circular polarization, respectively. To rotate the linear polarization in the flow experiments, a half-wave plate was used instead. Note that in Fig. 1d, the images (as well as the underlying movie) are rotated back by 22 degrees for visual alignment with the linear polarization case. Finally, to create the stripe-shaped profile in Fig. 4e–h, the neat sides of a scribed silicon wafer were mounted on a holder in parallel, facing each other, and inserted in a plane conjugate to the sample plane, leaving a small slit defining the stripe-shaped profile. The useful intensity range exploited in flow experiments was comprised between 26 and 645 W/cm2, and intensities around 200 W/cm2 were used in sparse particle experiments.

Particle size characterization
To prepare samples for scanning electron microscopy (SEM), particles from both samples were diluted and dried on regular silicon wafer pieces. They were then sputter-coated with 10 nm of platinum-palladium. Large overview images were obtained using a standard-mode ETD detector (secondary electrons), 5 kV acceleration voltage and 0.1 nA electron current (image size 6144 × 4096 pixels, 33.7 nm/pixel). Particle outlines and sizes were detected in the program imageJ, using the following sequence: Gaussian Blur (2.5px) → Auto Local Threshold v1.11 (“mean”, 15px, P1=−15) → Convert to Mask → Fill Holes → Watershed → Analyze Particles (Circularity: 0.6–1.0) using 5 | 3 images from distinct regions for samples shown in Supplementary Fig. 1a and Supplementary Fig. 1b, respectively. Finally, the absolute particle counts were reweighed by the particle cross-section in 2D, using the following equation (which leaves the total amount of renormalized particle counts unaltered):

where ni designates the net particle count in the ith histogram interval, hi designates its reweighted value used for the histograms in Supplementary Fig. 1e, f (renormalized particle counts), and ri designates the average radius of the particles in the ith interval which is used to calculate the corresponding cross-section ci. The distributions were plotted on a logarithmic scale.

Three-phase contact angle by gel-trapping technique
The three-phase contact angle of the azopolymer particles was determined by the gel-trapping technique developed by Paunov75. 49 mg agarose (ROTH) was dissolved in 3 mL water and heated to 60 °C. After equilibration for 30 min, 100 µL of the particle dispersion in 90:10 (v:v) water-isopropanol was spread at the air–water interface using a micropipette. Following an equilibration period of 1 h, the samples were allowed to cool to room temperature to enable agarose gelation, which occurred over ~2 h. Subsequently, polymethylsiloxane (PDMS; SYLGARD 184—Dow) prepared by mixing the base and curing agent at a 10:1 mass ratio was poured over the agarose gel. The PDMS was left to cure for 5 days. Once cured, the PDMS layer was carefully peeled off the gel. Residual agarose was removed by immersion in 90 °C water followed by rinsing. Finally, the PDMS films were air-dried.

The resulting PDMS films were analyzed using atomic force microscopy (AFM; Nanoscope Icon with closed-loop, Bruker) operated in tapping mode with OTESPA tips (MikroMasch; nominal resonance frequency: 300 kHz, spring constant: 26 N/m, tip radius: <7 nm). AFM images were processed using Gwyddion. All images were leveled to remove tilt, and the minimum height value was set to zero. From cross-sectional profiles of at least 20 particles, the height (H), and arc length (S) were extracted to calculate the three-phase contact angle (θ)75.

Particle detection at interfaces
Where individual particle outlines are fitted, e.g., to obtain particle areas and positions, dedicated procedures are applied in ImageJ and post-processed in MATLAB 2021. For example, to determine the aspect ratios and areas for the single particle deformation statistics in Supplementary Fig. 4, the following sequence was applied to entire stacks after cropping them to the relevant single particle area: Auto Local Threshold v1.11 (“Phalsankar”, 15px, P1=0.1, P2=0.2) → Convert to Mask → Median (1px) → Close → Fill Holes → Median (1px) → Analyze Particles (Circularity: 0-1, Area: 100px-Inf). From the detected particles, only the largest one, generally representing the particle of interest, was kept. When another particle entered the field of view toward the end of the sequence, the area was occasionally re-cropped for this part of the movie to the particle of interest. The obtained values were then post-processed in Matlab to remove noisy outliers due to faulty detection on single frames, by automatically rejecting unphysical results (with respect to the movies), consisting of detected aspect ratios above 6, as well as relative areas below 1 and above 8. Outliers with a distance to the surrounding mean higher than the surrounding standard deviation were also removed, and finally, all detected outliers were replaced with the surrounding mean.

Similar approaches relying on local thresholding were applied for the detection of initial particle positions in Supplementary Fig. 6 and for assessing individual particle areas in Supplementary Fig. 10, without further post-processing. The exact procedures are included, together with the segmented images and extracted values, in the shared data folder. To track two prominent particles in Supplementary Fig. 17 (also upper inset in Fig. 4f), an inverted global threshold was utilized.

Flow analysis algorithm
The analysis code was written in MATLAB 2021. To analyze the flows, a total number of spatial tiles nx × ny and a temporal step length ΔT, were defined. The movie stacks were then split into spatiotemporal sub-stacks, each covering the size of one tile in space (Δx × Δy = 1 = nx × 1 = ny) and spanning one timestep ΔT in time. The code was optimized for parallel computation of subsequent timesteps to reduce the overall computation time. Eventually, each sub-stack would lead to one velocity arrow, representing the average flow at the given tile position and for the time interval [tk, tk+ΔT] where tk designates the onset time of the kth timestep. The procedure to extract this single flow arrow from its corresponding sub-stack is summarized below.

First, after subtraction of—and normalization by—the mean pixel value for each sub-stack image, the correlation between image pairs separated by a given number of frames Δf was computed and averaged. This gives a temporal autocovariance function, which is decaying for increasing Δf, and which is similar to the decay function used in e.g., Dynamic Light Scattering experiments. In the spatiotemporal correlation maps detailed below, these values correspond to the decaying central pixel. Next, all the images of the sub-stack would be shifted by -i pixels in the x-direction and -j pixels in the y-direction, constructing a second stack. The same correlation would then be computed for image pairs where the first image would be taken from the initial non-shifted stack, whilst the image delayed by Δf frames would be taken from the shifted, second one. Note that this distinction of the delayed image always being the shifted one, is crucial to avoid temporally symmetric results and to be able to extract drift directions as schematically depicted in Supplementary Fig. 20. Finally, for each value of i, j, and Δf the obtained correlation value was plotted as the pixel in position (i, j) with respect to the center on the Δf-th correlation map. Examples of the obtained correlation maps, which depict the full, averaged, spatiotemporal drift-diffusion behavior of the particles pertaining to the sub-stack, are shown in Supplementary Fig. 21.

We note that the 0th correlation map (containing the correlation between image frames with shifted versions of themselves) simply shows the spatial autocovariance, which may be anisotropic, for example, if the particles in this part of the field of view and at the given time on average are already anisotropically deformed. The Δf-th correlation map then shows the probability of image features (e.g., particle outlines) moving to new relative positions after Δf frames, on average. This spatiotemporal evolution may be influenced by diffusion, drift (with velocity dispersion), and deformation of features. Here, the only aim was to extract the average drift velocity, which was performed by tracking the average movement of the center of the spatiotemporal probability distribution. Hence, for each correlation map linked to a Δf delay, we started from the pixel with the highest correlation value and attempted to fit the exact peak position within this pixel by a 2D Gaussian fit of the whole map. Finally, the obtained peak positions were plotted against Δf, and the average drift velocity was obtained by a linear fit of motion (see Supplementary Fig. 21, bottom), followed by conversion into the final units (from pixel/frame to μm/s). The resulting arrow was then plotted, alongside the arrows from the other tiles, on the flow field pertaining to the time step tk. In Fig. 3d, we plot only the y-component of the velocity for the tile of interest.

To calculate divergence maps of entire flow fields, origins were placed in each center between four flow arrows. The area used to compute an approximation to the local divergence was chosen as a square at an angle of 45 degrees with the velocity vectors’ grid (see Supplementary Fig. 22). Then, the total outflow of the four vectors via each side of the square, divided by the total square area, was calculated to obtain the local average divergence. Note that horizontally/vertically adjacent tiles partially overlap (acting as a moving average) and that diagonally adjacent divergence tiles are not independent, since they always share one arrow. Hence, when taking the mean divergence of the whole field, as done in Supplementary Fig. 15f, in practice, one computes the outflow only through the total outer boundary of the considered tile region, since internal arrow contributions will cancel out.

Data availability
Raw data were made available on the Figshare repository https://doi.org/10.6084/m9.figshare.28067498. Specifically, the original flow movies, with full frame rate and resolution, are included, as well as raw data concerning single particle deformations and capillary interactions. Any data or relevant information is available from the corresponding authors upon request.

Code availability
The annotated correlation analysis code, and a list of code parameters used for the analysis is made available on the Figshare repository https://doi.org/10.6084/m9.figshare.28067498.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript deals with self-assembly of deformable particles at liquid interfaces, whose shape can be modulated. Authors have reported a simple method to modulate the shape of particles at the interface, studied their self-assembly at fluid interfaces and comment about interesting interfacial flows that can be generated. Overall, I see several conceptual issues and lack of new insight about interfacial assembly of colloids. I am of the opinion that the manuscript is not a adequate quality of publication in Nat Com. Following are major concerns:\n(1) The results presented in the section \"Optically controllable capillary interactions and assembly\" are not new. There have been several studies where similar interfacial arrangement or self-assembly of particles has been reported.\n(2) The shape modulation that is claimed is very limited. There are several methods for the controlled synthesis of non-spherical particles, including those of different elongation. Authors do neither demonstrate versatility of shape transformation nor the ability to create unique structures at interfaces.\n(3) Figure 3: Quality of the microscopy images is very poor. Its hard to believe if the particles are at the interface or they are in the bulk.\n(4) Authors discuss experiments at higher density where interfacial flows are generated, but there is no quantification of surface coverage, and the lack of flow in dilute systems.", "reviewer_2": "I have reviewed the manuscript NCOMMS-24-84692 titled \"Directional capillary flows induced by photo-deformable colloidal particles,\" authored by David Urban et al.. Their research focused on morphological alterations and subsequent aggregation or separation of amorphous azobenzene polymer particles dispersed on aqueous surfaces. This study revealed that when exposed to linearly polarized visible light, these azobenzene particles exhibited continuous movement along the polarization direction. This phenomenon is likely to captivate readers' interest. However, the authors' discussion that this continuous flow resulted from capillary forces generated by rod-shaped particles lacks sufficient supporting evidence. This manuscript requires additional experimental data and thorough analysis. Furthermore, there is a lack of literature research on the light-driven locomotion of nanoobjects on water surfaces. The detailed comments are as follows.\n1. To establish the novelty of this manuscript, the authors should extensively review the existing literature on the movement of powdered substances or particles on water surfaces through irradiation as well as other forms of nano-locomotion. This comprehensive review should include, but is not limited to, studies such as Norikane et al. Cryst. Eng. Commun. 2016, 18, 7225; Fujii et al. Adv. Funct. Mater. 2016, 26, 3199; and Lucchetta et al. AIP Adv. 2015, 5, 077147.\n2. What method did the authors employ to achieve stable dispersion of individual azobenzene polymer particles at the water-air interface? Typically, particles tend to aggregate on water surfaces or disperse in the water. Successful stable dispersion of azobenzene polymer particles is a key technique in this research. Consequently, the authors should provide a detailed explanation of their technique for creating a stable dispersion on the water surface, supported by experimental evidence, such as water contact angle measurements.\n3. The authors should discuss the photoisomerization of the azobenzene polymer particles more carefully.\n3.1. The authors should clarify how the laser wavelength correlates with the absorption of the azobenzene polymer. They must also include the time evolution in the UV-vis absorption spectra of the azobenzene polymer before, during, and after laser exposure. This information is crucial for analyzing the light-induced properties of azobenzene-based materials and represents one of the most fundamental datasets in this study.\n3.2. More quantitative analyses of the particle morphology changes and movements are necessary. The wavelength and intensity of the light source typically influence the light-activation properties of azobenzene-containing materials.\n3.3. The factors affecting capillary forces should be discussed more carefully. The surface free energy, as well as the shape of the particles, influence capillary forces. During n–(cid:1)* absorption, azobenzene is known to undergo trans–cis conformational interconversion. This photoisomerization process results in two notable effects, in addition to shape alterations in azobenzene materials. First, the photothermal effect occurs, where irradiation elevates the temperature of azobenzene materials. Second, there is an increase in the composition of cis-isomers, which exhibit greater hydrophilicity than trans-isomers. Both temperature changes and increased hydrophilicity can alter the surface free energy of azobenzene polymer particles. These phenomena should be addressed in the Results and Discussion sections. For instance, when a linearly polarized 532-nm laser irradiates one side of the azobenzene polymer particles, it can create a gradual difference in the surface free energy across the particle surface, resulting in nano-locomotion on water surfaces.\n3.4. To substantiate the claim of \"shape-mediated assembly and disassembly\" as discussed in the Discussion section, where the authors claimed that capillary forces resulting from rod shapes would be the sole cause of continuous locomotion, they must thoroughly rule out alternative explanations. This includes eliminating the possibility of other effects, such as Marangoni propulsion, which has been extensively researched in the field of nano-locomotion. The authors should address this issue using appropriate scientific methodologies.\n3.5. The authors should distinctly differentiate between nano-locomotion, which results from microscopic forces near particle surfaces, and macroscopic water movement. The initial part of the Results section noted that the azobenzene polymer particles aggregated together after changing from spherical to rod-shaped, even after the laser was turned off. This indicates that the capillary forces from the rod shapes promote aggregation rather than repulsion. Figure 3iii and Movie M7 provide clear evidence of rod-shaped azobenzene polymer particle aggregation even during irradiation. Concurrently, the clustered particles were drawn away from the irradiated area on the water surface. The authors suggested that water flow caused by osmotic pressure was a potential cause, inappropriately citing photoswitching of the adsorption/desorption behavior of azobenzene surfactants. They claimed that photoisomerization of azobenzene components increased hydrophilicity, creating the \"sustained pumping machinery.\" However, this effect is highly unlikely in the current system, where no azobenzene derivatives are dissolved in the aqueous phase or detached from the particles; therefore, a local concentration of cis-isomers and the resulting osmotic pressure should not be generated. Consequently, this study lacks a compelling explanation for the continuous flow observed during irradiation.\n3.6. As illustrated in Figure 3 and Movie M7, the nano-locomotion effect was the most pronounced in the central region of the scope. This observation suggests that the intensity of the laser progressively decreased from the center to the periphery of the exposed area. Such a gradient in laser power could also explain the observed continuous flow.\n3.7. Additionally, when the light-induced motion of azobenzene materials typically ceases upon turning off the light source, the photothermal effect of azobenzene groups during illumination is generally considered the primary cause of this movement. Although hydrophilic cis-isomers are transformed back into hydrophobic trans-isomers under dark conditions, this conversion does not occur instantaneously after the light source is deactivated. As previously mentioned, the time-dependent changes in UV-vis absorption spectra would likely support this gradual conformational reversal process.\n3.8. The rod-shaped particles aggregated after changing their shape, regardless of the irradiation. This suggests that deformed particles expelled from the irradiated area would aggregate together once the laser was turned off. However, Movie 7 demonstrates that the deformed particles remained stationary on the surface of the water after laser deactivation. This raises the question of what accounts for this discrepancy.", "reviewer_3": "The manuscript entitled “Directional capillary flows induced by photo-deformable colloidal particles” by Urban et al. presented very interesting assembly and disassembly of azopolymer-based shape-deformable microparticles at the air/water interface in response to polarized light. However, to precisely evaluate this work, the capillary flow-driven mechanism should be clarified.\n(1) The authors applied highly intensive polarized light to drive the shape deformation. In addition to photoisomerization, azobenzene-based aggregates would perform photothermal conversion under light irradiation, which enables driving directional movement at the air/water interface as well (e.g., CrystEngComm, 2016, 18, 7225). The authors should clarify whether there is a photothermal behavior or not. And the impact of this behavior on the directional assembly and particle flow.\n(2) Similarly, such highly intensive light is another possible source producing a thermal effect on the water, which may drive particle flow. The authors should clarify its impact on the water and strong photoabsorbing azopolymer particles.\n(3) Photoisomerization is another possible driving force for directional movement (e.g., Advanced Functional Materials, 2016, 26, 3164). Because a change of polarized light would lead to assembly and disassembly, the authors should clarify the impact of photoisomerization on directional particle assembly.\n(4) Considering the capillary effect, the mechanism of assembly and disassembly is still not very clear. The particle shape is very important in capillary assembly, but lots of research shows the spheres can also achieve capillary assembly. Why does the shape deformation here lead to a rapid disassembly? Is there an impact of interfacial interaction on stabilizing or destabilizing particle aggregates? Does changing the light from elliptical polarization to linear one or reverse operation have some impact on the assembly or disassembly? If the explanation is the variation of out-of-plane curvature radius as the authors claimed, the particle dimension should play an important role in the capillary-driven assembly and disassembly. The authors should provide information on this impact.\n(5) The effective length (or interparticle distance) of the capillary effect in driving directional particle assembly should be clarified."}, "author_response": "We thank the reviewers for their detailed comments. In particular, we observed that several reviewers raised overlapping questions regarding the fundamental working mechanism of the flow phenomenon, the influence of azobenzene isomerization or thermal effects. In response, we revised the manuscript thoroughly by providing further experimental data, relevant literature, as well as an extensive discussion clarifying the proposed flow mechanisms and the intended message of the work. We hope that these clarifications address the reviewers’ concerns and help to convey the significance and originality of our findings more clearly. For simplicity in referring to manuscript modifications, we refer to the result sub-sections in the following way:\n“Section 1” for “Shape-morphing particles at an air-water interface”\n“Section 2” for “Optically controllable capillary interactions and assembly”\n“Section 3” for “Continuously deforming capillary assemblies”\n“Section 4” for “Polarization-controlled directionality and shear flows”\nSupplementary Figures and Movies are numbered with respect to their appearance in the revised manuscript and the attribute “new” Supplementary Figure/Supplementary Movie labels items that were not yet included in the initial submission."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The revised manuscript has been enhanced and is now much clearer than the original version. The authors have meticulously addressed my comments one by one. This version effectively clarifies that the continuous flow was not a direct result of traditional nano-locomotion due to photoisomerization, but rather from the ongoing self-assembly of ellipsoids when exposed to a linearly polarized light. These self-assembling movements then consistently expelled water in the same direction as the long axis of the self-assembled clusters. The concept of a novel driving force for particle flows proposed in this study may engage readers.\nHowever, concerns have emerged regarding the adaptability of this strategy due to several limitations. Furthermore, the discussion in the concluding paragraph lacks persuasiveness in its assertions about the strategy's impact.\nFirst, the functionality of the particle is notably constrained. The range of applicable materials is predominantly confined to DR1 polymers, characterized by a substantial overlap of the trans-cis bands. In the absence of this overlap, conventional nano-locomotion mechanisms are likely to be activated. This limitation in material applicability restricts the functional diversity of the particles. Additionally, the functional modification of particle surfaces is impeded because the balance between hydrophilicity and hydrophobicity on the particle surfaces is vital for achieving a dense distribution on the water surface while simultaneously preventing the initial formation of aggregates. The functional limitation constrains the potential application of this strategy.\nSecond, the lack of correlation with light intensity, which was stated in the rebuttal, hinders the precise quantitative control of directional flows. Although the authors suggest the potential application of various light properties, controlling directional propulsion by intensity gradients remains unlikely.\nMoreover, the nonspherical shapes of the particles are insufficient for promoting diverse particle flows, as the generation of capillary forces requires one-dimensional deformation of the particles, irrespective of their initial shape. Nonetheless, the authors have proposed the potential application of buckling particles. Additionally, the use of Janus particles would interfere with the one-dimensional stretching of the particles.\nThe findings of this study must demonstrate substantial potential for future advancements that surpass the objectives delineated by the authors in the Discussion section.\nThe following are additional minor comments:\n1. Although stretched particles predominantly self-assemble in a side-by-side manner, the formation of end-to-end configurations is also essential for the development of elongated assemblies. The end-to-end configurations are clearly illustrated in Figure 3c, panels iii and iv, along with the side-by-side configurations. The mechanism underlying the formation of the end-to-end configurations must be elucidated.\n2. The head-tail configuration of the DR1 main chain structure depicted in Figure 1 is inverted. The sequence -C(CH3)-CH2- needs to be altered to -CH2-C(CH3)-.\n3. The section headings should be revised. Most of the discussion is detailed in the Results section, while the Discussion section primarily summarizes this manuscript.\n4. Considering the title and the focus outlined in the Introduction, it is inappropriate to conclude this manuscript by emphasizing the relevance of tiled incidence illumination to conventional nano-locomotion systems in the closing paragraph.", "reviewer_3": "The reviewer thanks the careful response and additional experiments for the revision. The response answers some questions. However, some content still sounds confusing.\n1. Photoisomerization has shown a crucial effect on particle deformation. And photothermal conversion would influence the surrounding flow. The authors did not do the characterization. The UV-vis spectra and photothermal curves should be given to reflect photo-responsive behaviors.\n2. If the reviewer understands correctly, the authors insist that there is a similar photothermal effect and photoisomerization in response to different polarization lights, so they would not give different influences on the flow. The change of polarization light would induce particle deformation into different shapes. The photothermal conversion within different-shaped particles would significantly influence the surrounding temperature distribution and flow direction (e.g., Lab Chip, 2012, 12, 3707). The authors should clarify that on particle locomotion at the interface.\n3. Because the particle shape would influence the surrounding flow direction, the particle assembly into aggregates may further intensify this effect on the flow, leading to directional flow. The authors should clarify that.\nIn addition, I have also looked over the responses to the comments from Reviewer 1.\n4. I agree with Reviewer 1. The current microscopy images cannot accurately localize the particles at the interface. And the authors did not give direct evidence for that in the response. It is better to use another characterization instrument (e.g., confocal microscopy with z-stacking scan) to give the particle distribution in the solution. That would also rule out the possible influence of the thermo-flow induced by the dispersed particle underwater.\n5. The authors discussed the influence of surface coverage on particle assembly and disassembly in the revision. According to Reviewer 1's comments, the flow phenomenon of these dilute systems should be explored. Normally, there should be a thermal Marangoni effect to propel photothermal particles at the interface. In terms of high-intensity light used in this study, it is very surprising that the authors’ response indicated there was no flow observed for the diluted systems. The authors should explain this phenomenon. That would be a good control in this study."}, "author_response": "Rebuttal letter 02/07/2025\nWe thank the reviewers for their detailed comments. In particular, we observed that several reviewers raised overlapping questions regarding the fundamental working mechanism of the flow phenomenon, the influence of azobenzene isomerization or thermal effects. In response, we revised the manuscript thoroughly by providing further experimental data, relevant literature, as well as an extensive discussion clarifying the proposed flow mechanisms and the intended message of the work. We hope that these clarifications address the reviewers’ concerns and help to convey the significance and originality of our findings more clearly. For simplicity in referring to manuscript modifications, we refer to the result sub-sections in the following way:\n“Section 1” for “Shape-morphing particles at an air-water interface”\n“Section 2” for “Optically controllable capillary interactions and assembly”\n“Section 3” for “Continuously deforming capillary assemblies”\n“Section 4” for “Polarization-controlled directionality and shear flows”\nSupplementary Figures and Movies are numbered with respect to their appearance in the revised manuscript and the attribute “new” Supplementary Figure/Supplementary Movie labels items that were not yet included in the initial submission."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have comprehensively addressed all my concerns, thereby enhancing both the manuscript and the Supporting Information. They showed that their findings regarding particle flows are not attributable to conventional mechanisms but rather to the deformation of particles, which induces capillary forces. Compelling data and discussions support this explanation. This approach holds significant promise for advancing novel technologies for photomechanical energy conversion. I recommend that this manuscript be suitable for publication.", "reviewer_3": "The authors have addressed the reviewer's concern. This version of the manuscript is recommended for publication."}, "author_response": "Rebuttal Letter 04/11/2025\nReviewer #2 (Remarks to the Author)\nThe revised manuscript has been enhanced and is now much clearer than the original version. The authors have meticulously addressed my comments one by one. This version effectively clarifies that the continuous flow was not a direct result of traditional nano-locomotion due to photoisomerization, but rather from the ongoing self-assembly of ellipsoids when exposed to a linearly polarized light. These self-assembling movements then consistently expelled water in the same direction as the long axis of the self-assembled clusters. The concept of a novel driving force for particle flows proposed in this study may engage readers.\nHowever, concerns have emerged regarding the adaptability of this strategy due to several limitations. Furthermore, the discussion in the concluding paragraph lacks persuasiveness in its assertions about the strategy's impact.\nREPLY: We thank the reviewer for the positive assessment of the improved clarity of the manuscript. Regarding the adaptability of the findings, we added a broader perspective in response to the specific points raised below.\nFirst, the functionality of the particle is notably constrained. The range of applicable materials is predominantly confined to DR1 polymers, characterized by a substantial overlap of the trans-cis bands. In the absence of this overlap, conventional nano-locomotion mechanisms are likely to be activated. This limitation in material applicability restricts the functional diversity of the particles. Additionally, the functional modification of particle surfaces is impeded because the balance between hydrophilicity and hydrophobicity on the particle surfaces is vital for achieving a dense distribution on the water surface while simultaneously preventing the initial formation of aggregates. The functional limitation constrains the potential application of this strategy.\nREPLY: We realize that the variety of effects shown in this work, which can be controlled by comparatively simple optics, may have sparked the reviewer’s curiosity about adaptability to other materials. Traditionally, the azopolymers used for polarization-dependent photo-deformation indeed often contain DR1, although similar pseudo-stilbene-type azobenzene dyes such as DR19, Disperse Orange 3 and others have also been used (see e.g., Yin, X. et al., Macromolecular Chemistry and Physics 2018 219, 1800113, Jo, W. et al., ACS Appl. Mater. Interfaces 2020 12, 5058–5064 and Pirani, F. et al., Scientific Reports 2016 6, 31702). In the case the reviewer’s interest is directed towards more conventional azobenzene-type dyes (without strong overlap of the bands), the simultaneous use of two wavelengths may be considered to achieve enhanced cycling between the isomers (a strategy utilized e.g., in Liu, D. & Broer, D. J., Nat Commun 2015 6, 8334). In this case, a trans-to-cis wavelength (e.g., UV) and a cis-to-trans wavelength (e.g., blue light) are applied simultaneously to effectively induce isomer cycling also for such dyes. We believe that the trans-to-cis irradiation should then be polarized, if re-orientational effects are to be studied.\nIn the context of this work, since all the effects ultimately rely on the anisotropic photo-deformation of particles, employing anisotropic photo-deformable particles is the minimum criterion for adaptations. We point out that numerous other approaches to obtaining anisotropic photo-deformable particles exist. They do not necessarily rely on molecular re-orientation through isomer cycling and, in some cases, do not even require the presence of azobenzene molecules. Examples include liquid crystal elastomer (LCE) particles (see e.g., B. Braun, L., Hessberger, T. & Zentel, R., Journal of Materials Chemistry C 2016 4, 8670–8678), as mentioned in the Discussion section. LCEs are directionally deforming materials, whose photo-deformation in some cases can also be polarization-dependent (Yu, Y., Nakano, M. & Ikeda, T., Nature 2003 425, 145–145), particularly if dichroic dyes are included (Li, Y., Liu, Y. & Luo, D., Adv. Optical Mater. 2020 9, 2001861). Other polymeric materials, for example hydrogels doped with anisotropic platelets, can also be photo-deformed anisotropically (Zhu, Q. L. et al., Advanced Materials 2024 36, 2314152) and may therefore be used for similar concepts in future studies.\nFinally, the particles need to remain colloidally stable and efficiently adsorb to the liquid interface. In this work, we employed steric stabilization, as it simultaneously ensures colloidal stability and promotes interfacial adsorption (Rey, M. et al., Nat Commun 2022 13, 2840). The energy gain upon colloidal particle adsorption to a liquid interface is on the order of millions of kBT; therefore, at this length scale, the balance between hydrophilicity and hydrophobicity can almost be ignored, and particles generally adsorb (Pieranski, Pawel. Physical review letters 1980 45, 569). Nevertheless, kinetic barriers can impede monolayer formation, and various additives have been reported to facilitate particle adsorption (Vialetto, J. & Anyfantakis, M., Langmuir 2021 37(31), 9302–9335). Moreover, several other strategies exist to maintain colloidal stability once particles are adsorbed at the interface (Vogel, N. et al., Chemical reviews, 2015, 115(13), 6265–6311). A widely used approach involves charge-stabilized colloids. Depending on the balance between attractive van der Waals and capillary interactions and repulsive dipole–dipole and electrostatic interactions, stable non-close-packed monolayers can be obtained (Menath, J. et al., Advanced Materials, 2023, 35, 2206593.) In summary, also with respect to functional modifications, we see no fundamental reason why the reported results could not be extended to other colloidal particle systems.\nSecond, the lack of correlation with light intensity, which was stated in the rebuttal, hinders the precise quantitative control of directional flows. Although the authors suggest the potential application of various light properties, controlling directional propulsion by intensity gradients remains unlikely.\nREPLY: We are not entirely certain if we understand the reviewer’s concern correctly. What we stated in the rebuttal letter and pointed out additionally in the manuscript, is that the intensity pattern does not define the flow alone.\nSpecifically, different flow scenarios can be created by changing polarization while keeping the intensity pattern constant. For example, using the same Gaussian laser profile, one can obtain no flow (circular polarization), weak directional flow (elliptical polarization), and strong directional flow (linear polarization), where the directionally axis can be rotated for the latter two.\nIf the polarization is kept constant instead, and the intensity pattern is altered, this provides an additional means to control and alter the flow. For example, a 45-degree linear polarization of a Gaussian beam intensity profile leads to the symmetric 45-degree oriented outflow in Supplementary Movie M11. In contrast, when a stripe-shaped intensity pattern is used with the same polarization, a pure shear flow is created (Supplementary Movie M15), demonstrating that combinations of intensity and polarization patterns can be deterministically exploited to control particle flows. In addition, higher nominal intensities – with otherwise identical patterns – create faster flows, since the particles’ deformation is accelerated (see example in the Figure below).\nHence, in contrast to flows driven by intensity patterns only, where each point on the interface can, in theory, be attributed a given intensity, here each point on the interface can be attributed both an intensity and a polarization, together defining the strength and the directionality of the locally created flow contribution. This allows the flow patterns to be altered through modification of either intensity patterns or the polarization. Considering this, a mere correlation of light intensity with the “quantitative control of directional flow”, would not fully capture the complexity of the effect observed. We have added a clarifying sentence towards the end of result section 4 in the manuscript to highlight this aspect more explicitly and further elaborated on it in the revised Discussion section.\nMoreover, the nonspherical shapes of the particles are insufficient for promoting diverse particle flows, as the generation of capillary forces requires one-dimensional deformation of the particles, irrespective of their initial shape. Nonetheless, the authors have proposed the potential application of buckling particles. Additionally, the use of Janus particles would interfere with the one-dimensional stretching of the particles.\nREPLY: This comment appears to reflect a slight misunderstanding, and we apologize for any lack of clarity in our original explanation. The aim of that paragraph was not to suggest that our system could be combined with these other approaches (buckling particles, Janus particles), but rather to illustrate that any directional flow needs a symmetry breaking element (making the flow directional). In different systems, different light properties (such as intensity gradients, propagation direction, or polarization states) can serve as this symmetry-breaking factor. We have rephrased this second-last Discussion paragraph accordingly.\nThe findings of this study must demonstrate substantial potential for future advancements that surpass the objectives delineated by the authors in the Discussion section.\nREPLY: We appreciate the reviewer’s encouragement to emphasize the broader potential of this work. While we agree that it would be highly interesting to demonstrate \"substantial potential for future advancements\", we believe that this cannot be convincingly demonstrated a priori. Instead, we have aimed to outline promising development directions based on the newly observed effect and proposed application domains in which these findings may prove beneficial. It should be noted that further advancements may rely both on the capillary assembly mechanism itself and on the ensuing flow phenomenon (addressed in separate Discussion paragraphs). Potential routes toward improved and novel behavior may involve different functional materials (such as e.g., LCEs for reversible photo-deformation; see the second Discussion paragraph) and/or refined experimental scenarios (such as e.g., polarization patterns or passive objects interacting with the flows; see final Discussion paragraph).\nThe following are additional minor comments:\n1. Although stretched particles predominantly self-assemble in a side-by-side manner, the formation of end-to-end configurations is also essential for the development of elongated assemblies. The end-to-end configurations are clearly illustrated in Figure 3c, panels iii and iv, along with the side-by-side configurations. The mechanism underlying the formation of the end-to-end configurations must be elucidated.\nREPLY: We thank the reviewer for drawing attention to this detail. For ellipsoidal particles at liquid interfaces, both side-by-side and end-to-end (tip-to-tip) configurations are energetically favorable, since each reduces the overall interfacial deformation by superimposing matching surface elevations and depressions of the adjacent particles. In contrast, configurations such as side-to-tip are energetically disfavored. In the case of core–shell particles, such as the colloidal particles with a PVP shell investigated here, the energy gains associated with the two assembly modes are comparable and depend on the particle aspect ratio and the core-to-shell size ratio (Eatson, J. et al., Journal of Colloid and Interface Science 2025 683, 435–446).\nFor particles with a high aspect ratio, the side-by-side configuration yields a greater energy reduction than the tip-to-tip configuration and is therefore typically the preferred configuration when the interfacial particle density is low (as in the experiments of the first two result sections). At higher interfacial particle densities, additional energy can be minimized by forming tip-to-tip contacts between particles already arranged side-by-side, a process that has been described both experimentally and theoretically (Luo, A. M. et al., Journal of Colloid and Interface Science 2019 534, 205–214). Qualitatively, we observe the same trend of more tip-to-tip assembly in our experiments at higher interfacial particle density (see Figure 3).\nIn addition, we note that the capillary interactions between anisotropic particles are strongly attractive, and thus the assembly process can easily become kinetically trapped in local minima when many particles are involved. Together with particle size polydispersity in our system, this likely explains the large structural variability observed at high particle density and the frequent occurrence of tip-to-tip bonds in the elongating assemblies. We have added a sentence mentioning this observation in result section 3.\n2. The head-tail configuration of the DR1 main chain structure depicted in Figure 1 is inverted. The sequence -C(CH3)-CH2- needs to be altered to -CH2-C(CH3)-.\nREPLY: We thank the reviewer for the careful reading and have corrected the graphical typo.\n3. The section headings should be revised. Most of the discussion is detailed in the Results section, while the Discussion section primarily summarizes this manuscript.\nREPLY: The reviewer correctly notes that the technical discussion of the different effects is presented directly in the result sections. This structure was chosen to avoid confusion between the different novel effects shown in the different sections and not to leave the reader with too many open questions along the way.\nIn the final Discussion section, we try to contextualize the results more broadly, including a concise summary and several outlook perspectives. According to our understanding of the journal’s formatting guidelines, this final section should indeed be labeled as “Discussion”. In either case, we would ultimately prefer to consult the editor regarding this stylistic decision, if possible.\n4. Considering the title and the focus outlined in the Introduction, it is inappropriate to conclude this manuscript by emphasizing the relevance of tiled incidence illumination to conventional nano-locomotion systems in the closing paragraph.\nREPLY: As outlined above, the aim of this section is not to directly compare different strategies in terms of performance (which we believe depends on application scenarios and on potentially refined systems), but rather to show that any directional flow system requires an effective strategy for symmetry breaking. The referenced articles are some of the most elegant and impressive examples of different optical symmetry-breaking mechanisms that rely on various properties of light (for example, the incidence direction). We then point out that polarization has not been used frequently as a symmetry breaking mechanism, yet strategies based on this approach—or similar ones—may hold significant potential and could be adapted to many other systems.\nStrategies relying on polarization and polarization-directed deformation may differ substantially from the specific one presented here and might not even rely on capillary forces to collectively propagate deformation. This realization, as well as the possibility to further combine intensity and polarization patterns to obtain more complex flow fields, has been added to the Discussion section (last two paragraphs), to broaden the adaptability perspective before mentioning possible applications of the flow concept."}]

Decision letter