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How to Make a Surface Act as a Micropump

In this paper, the phenomenon of light‐driven diffusioosmotic (DO) long‐range attractive and repulsive interactions between micro‐sized objects trapped near a solid wall is investigated. The range of the DO flow extends several times the size of microparticles and can be adjusted to point towards or away from the particle by varying irradiation parameters such as intensity or wavelength of light. The “fuel” of the light‐driven DO flow is a photosensitive surfactant which can be photo‐isomerized between trans and cis‐states. The trans‐isomer tends to accumulate at the interface, while the cis‐isomer prefers to stay in solution. In combination with a dissimilar photo‐isomerization rate at the interface and in bulk, this yields a concentration gradient of the isomers around single particles resulting in local light‐driven diffusioosmotic (l‐LDDO) flow. Here, the extended analysis of the l‐LDDO flow as a function of irradiation parameters by introducing time‐dependent development of the concentration excess of isomers near the particle surface is presented. It is also demonstrated that the l‐LDDO can be generated at any solid/liquid interface being more pronounced in the case of strongly absorbing material. This phenomenon has plenty of potential applications since it makes any type of surface act as a micropump.


Introduction
Generation of liquid transport with spatio-temporal control has drawn tremendous attention over the past few decades due to a large number of microfluidic based applications such as improvement of biochemical assays, generation of highly portable diagnostic devices, microfluidic synthesis, sorting and focusing mechanism for cells and colloids, and many others. [1][2][3][4][5][6][7][8][9][10][11][12][13] To force liquid flow one can either pump it externally or utilize different types of surface bound phenomena such as electro-or diffusioosmosis. [14][15][16][17] In the former case a design of The same mechanism is responsible for the so-called local-light driven diffusioosmotic (l-LDDO) flow generated by a single colloid possessing a large solid/liquid interface. [39] When porous silica particles are immersed in a water solution containing surfactants in the trans-state, the surfactant molecules are absorbed by the particles. [40][41][42] Under irradiation with UV light that promotes trans-cis isomerization, the more hydrophilic cis-isomers diffuse out the particles. The emergence of a laterally inhomogeneous excess of cis-molecules around the particle close to the solid-liquid interface leads to a local generation of DO flow (l-LDDO flow). The l-LDDO flow strength (defined as flow velocity and extent) and direction depend on the intensity and irradiation wavelength. For instance, if blue light is used at the photo-stationary state, the ratio of trans to cis isomers is 67% to 33% in solution. This results in a continuous flow of cis isomers out of the particles and trans isomers into the particle; leading to the continuous, local, and radially directed flow around a single colloid making it act as a "micropump" (see scheme in Figure 1).
The duration of this flow is defined only by irradiation time and can proceed over hours till the light is simply switched off. [43] Under exposure to UV light, at some point most of the isomers will be in the cis-state, the continuous exchange of isomers is very low and the flow stops. Moreover, at the beginning of irradiation with UV light of low intensity, the colloid may experience long-range diffusioosmotic attraction. [44] This process is transient and is reversed with increasing irradiation time.
Here we discuss a mechanism of the transient diffusioosmotic (DO) attraction and permanent DO repulsion by expanding the analysis of the l-LDDO flow proposed elsewhere. [39] For this, we introduce the time dependence of the concentration excess of isomers during the irradiation process. Assuming that the trans-cis photo-isomerization kinetics is slower in the particle in comparison to the bulk, we have calculated the inversion of the concentration excess during irradiation with UV light, while exposure to blue light builds concentration excess of the same sign. We confirm this experimentally using tracer particles to probe the l-LDDO flow generated at different surfaces such as hair, sand corn, wood stick, and so on. In this way, we demonstrate that surfaces capable of absorbing large amounts of photosensitive surfactant can act as a micropump.

Materials
Light responsive surfactant. The azobenzene containing trimethyl-ammonium bromide surfactant (C 4 -Azo-OC 6 TMAB) was synthesized as described elsewhere. [45] The surfactant (Figure 2a) Figure 1. Scheme of generation of local-light driven diffusioosmotic flow (l-LDDO) during irradiation with blue light. Under light exposure the cisisomers leave the particle, while the trans-isomers present in solution enter it continuously. The excess of the cis-isomers around the colloid generates a concentration gradient (shown by black dashed line), which in turn results in an osmotic pressure gradient (depicted by white arrows and letter "P") near the wall. As a consequence, local diffusioosmotic flow is established pointing out of the particle, in this particular case. The profile of the DO velocity near the wall is shown by the white arrows.
consists of a spacer of 6 methylene groups between the positively charged trimethyl-ammonium bromide head group and the azobenzene unit with butyl tail attached. A stock solution of surfactant of 10 mM concentration was diluted to the required concentrations ranging from 0.1 to 2 mM. Water (Milli-Q system) with a specific resistance larger than 18 MΩcm was used to prepare aqueous solutions. Figure 2b shows characteristic UV-vis absorption spectra of the surfactant recorded at photo-stationary state under exposure to light of different wavelengths. The trans-isomer (denoted as dark) had a characteristic absorption band (π−π* transition) with a maximum at 351 nm. The spectrum of the cis-isomer was characterized by two absorption bands with Figure 2. a) Chemical structure of the photo-sensitive surfactant (C 4 -Azo-OC 6 TMAB) and the two isomers of the azobenzene group. b) UV-vis absorption spectra of azobenzene containing surfactant at photo-stationary state recorded during irradiation with light of different wavelength as indicated in the legend. c) Cartoon of dynamic exchange of both isomers under illumination. d) Scheme of the l-LDDO flow of velocity v (green horizontal arrows) generated around single particle; concentration of the cis-isomers near the particle interface, c C,P , and in bulk, c C,B ; green arrow indicates the isomer concentration gradient; red circular arrows demonstrate dynamic exchange, i.e., adsorption/desorption of the surfactant molecules; blue arrows depict osmotic pressure, P. e) Scheme of the plain and porous particles with effective area contributing to net isomer exchange. maxima at 313 nm (π−π* transition) and 437 nm (n-π* transition). The lifetime of the metastable cis-isomer in the dark or in red light (λ = 625 nm) is ≈48 h at 23 °C.
The aqueous dispersion of all particles was mixed with surfactant solution at different concentrations and kept at least 1 h for equilibration. A chamber with a volume of 40 µl was used in order to provide a closed environment. When an aqueous dispersion of azobenzene containing surfactant and porous or non-porous silica colloids was placed on a chamber, the colloids sediment down to a glass surface. All samples were kept in the dark or in red light to prevent unwanted photo-isomerization. The measurements were conducted at room temperature of T = 23 °C.

Methods
An inverted microscope Olympus IX73 equipped with a light source of various wavelengths was used for the measurements. The global irradiation was performed with LED lamps from Thorlabs of different wavelengths: UV (λ = 365 nm, M365LP1), blue (λ = 455 nm, M455D2 and λ = 491 nm, M490L3), green (λ = 532 nm, M530L4). Red LED (λ = 625 nm, M625L1-C1, Thorlabs GmbH) was used for imaging as it does not affect the photo-isomerization of the azobenzene molecule. The illumination power was directly measured at the sample position prior to each measurement using an optical power meter PM100D with a sensor S170C (Thorlabs GmbH, Germany). The intensities between 0.2 mW cm −2 and 20 mW cm −2 were applied in the experiments. The optical path length was 0.5 mm. Time-resolved micrographs were recorded with a CCD camera (Hamamatsu ORCA-Flash4.0 LT (C11440)) at 1 or 2 frames per second and were analyzed using the software Fiji ImageJ with an implemented tracking algorithm (Mosaic Plugin) by Koumoutsakos. [46]

Theoretical Background
An estimate of the velocity of l-LDDO flow has been derived in our previous publication: [39] · · 4 · · · · · LDDO B 0 where Δc C is the local excess of cis-isomer concentrations near the particle, η is the viscosity, k B is the Boltzmann constant, T is the temperature, l B is the Bjerrum length, / 0 e k T B  φ = Φ is the dimensionless wall electrostatic potential, D is the diameter of the particles, I is the ionic strength in the bulk. Δc C can be understood as the cis-isomer concentration difference between the area near the particle and the bulk: where c C,P and c C,B are the cis isomer concentration near the particle interface and in the bulk, respectively ( Figure 2d). In Equation 1 Δc C is assumed to be constant over time, which was true only for the case of the photo-stationary state. The latter was not achieved instantaneously and requires some time of irradiation ranging between seconds and minutes (intensity and wavelength dependent). It has recently been shown that the photo-isomerization rate of the surfactant in bulk and at the interface (such as surfaces, polymers, aggregates) differs. [47,48] Here we expand the analysis of Δc C to give an estimation of the fluid flow direction and strength for the l-LDDO velocity by considering the change in the excess of concentration with the irradiation time as a consequence of isomerization rate, which was especially important for the first few seconds of irradiation till the photo-stationary state was achieved: where dc C,P /dt and dc C,B /dt are time-dependent changes in the cis-isomer concentrations at the particle interface and in bulk solution. Inserting rate equations of isomerization at interface, dc C,P /dt, and bulk, dc C,B /dt, [50] one gets: and dc C,B /dt: and finally: where k TC , k CT are the isomerization rate constants of trans-cis and cis-trans in bulk, I is the light intensity, A eff is the effective area for surfactant adsorption, θ T (c T,B ) is the trans isomer surface coverage, c T,B and c C,B are the trans and cis isomers concentration in bulk, k TC,I the isomerization rate constant of trans-cis process at the interface. Here we include the fact that the interface was effectively covered only by the trans isomers (surface coverage θ T >> θ C ), since the desorption rate of cis-isomers was much faster compared to trans-isomers, k d,C >> k d,T . [47] It means that, at the interface, the isomerization rate was one-directional, i.e., from trans to cis, and was not compensated by the reverse isomerization as observed in bulk solution (equilibrium between trans and cis isomers). Details concerning the derivation of Equation 6 were presented in the Supporting Information (Sections 1-3). By integrating the Equations 4 and 5, the time-dependent concentration of cis isomers near the particle was calculated, c C,P : and in bulk, c C,B : Inserting Equations 7 and 8 into Equation 2, one gets the Δc C as a function of irradiation time, intensity, and effective area for isomer adsorption, A eff (size and porosity of the particles). A positive value of Δc C , i.e., when c C,P > c C,B corresponds to an outgoing flow near planar substrate (pointing out of the particle) and was inverted by the negative sign. The time-dependent Δc C correlates well with the experimentally measured change in sign of velocity as will be shown in Figure 3. So it can now be stated that, in a first approximation the velocity at a point fixed in space scales with the current value of Δc C .
It should be mentioned that the time-dependent change in the concentration gradient should also be altered by the kinetic of surfactant adsorption and desorption on a surface. However, since both the processes have different time scales, i.e., net concentration change of isomers from photo-isomerization (tens of seconds to get a photo-stationary state) [49] and adsorption/desorption (few seconds), the influence of the adsorption kinetic was neglected. Considering the porous particle, one should additionally take into account that the diffusion coefficient of azobenzene inside porous glass (D = 4.2 µm 2 s −1 ) was much lower than that in bulk (D ∼ 2.4 × 10 2 µm 2 s −1 ). [50] Here, the calculated values of k TC,I indicate that the average isomerization rate constant was smaller for the entire particle, basically resulting from the reduced diffusion ability of the surfactant molecules inside the pores as well as due to steric hindrance within the pores; similar to molecules located in micelles. [49] This effect was much more pronounced for big porous particles (d = 20 µm, t D = 11.9 s → k TC,I /k TC = 0.15) than for the small porous particle (d = 5 µm, t D = 0.7 s → k TC,I /k TC = 0.95). Values of k TC,I were obtained for d = 20 µm and 5 µm from approximating the experimental data in Figure 4 and Figure S4, Supporting Information. Figure 3a,b shows the values of time resolved concentration difference of cis-isomers, Δc C , during irradiation with light of different wavelength blue (λ = 455 nm) and UV (λ = 365 nm) as calculated using Equations 2, 7, and 8. For calculations we use c T,0 = 1 mM, k TC,I = 0.0045 cm 2 (mW s) −1 for 20 µm particle diameter or k TC,I = 0.030 cm 2 (mWs) −1 for 5 µm particle diameter. [49] As can be seen, under irradiation with blue light the Δc C is always positive implying outgoing DO flow, while in the case of UV light temporal attractive and repulsive DO flow can be generated. This is possible because the isomerization rate constant at the interface of the particles, k TC,I , is smaller than  Figure S4, Supporting Information, [44]  in bulk, k TC . [49] Indeed, during exposure to UV light, since the value of k CT << k TC , [49] the Equation 5 can be approximated by:

Results and Discussion
therefore, the cis-trans photo-isomerization at the beginning of irradiation is neglected. Under consideration that k TC,I < k TC , temporally negative gradient of Δc C appears followed by positive one developed over isomerization time (see Equations 2, 7, 8 and Figure 3a,b). The intensity of UV light alters the position of the maximum attractive flow (Figure 3b). At the time where the flow changes from attractive to repulsive (see, e.g., the green dashed line at ca. 240 s in Figure 4f and violet dashed lines in Section 5, Figure S4, Supporting Information), the Δc C = 0. This experimentally measured time is then used to set boundary conditions for solving Equations 2, 7, and 8, i.e., we calculate the value of k TC,I (the inverted time at which the DO flow changes its sign from attraction to repulsion). Values for concentration, c T,0 = 1 mM, intensity I, and isomerization rate constants k TC and k CT are obtained experimentally and taken from our previous publication. [49] Under irradiation with blue light (455 nm) according to Equation 8 the forward isomerization, i.e., trans-cis, is compensated by a reverse isomerization, cis-trans, resulting in a constant amount of the trans-and cis-isomers (photo-stationary state). As can be seen from the plot, small negative values of Δc C can be observed also for irradiation with blue light at the very beginning of light exposure, which is in comparison to irradiation with UV light is, however, small (≈0.004 mM), and most probably is not enough to generate inwards flow, since experimentally, we observe the l-LDDO flow to point only out of the particle generating repulsive DO flow.
To visualize the temporal attractive and repulsive DO flow under UV exposure, we analyze the process by acquiring the motion of small tracer particles around one large porous colloid. At the small intensity of the UV light (I = 3 mW cm −2 ), the tracer particles are first attracted to the porous colloid during the initial 230 seconds of irradiation (Figures 4a and 3b), afterwards, the repulsive DO flow sets on and the tracer particles are removed in a radial direction out of the porous one (Figure 4c,d). The repulsive DO flow decays within the next 4 min of irradiation followed by the l-LDDO flow and thermal motion of the tracer particles (Figure 4e). The decay of the l-LDDO flow under UV exposure is explained by the conversion of a majority of isomers into cis-state, i.e., consumption of fuel stored in the particles. [44] The change in time dependent normalized nearest particle distance of tracer colloids, NPD/NPD 0 (NPD 0 is calculated for Brownian motion of the particles, i.e., without irradiation) (see black squares in Figure 4f) correlates with the sign of the cis-isomers excess concentration, Δc C , near the porous particle (red curve in Figure 4f): Δc C < 0 corresponds to inwards directed flow, Δc C > 0 indicates the outwards flow. The minimum of the Δc C value at t ≈ 25 s marks the maximal attractive flow, followed by deceleration and inversion.
In our previous publication, we have described similar behavior of an ensemble of porous particles of 5 µm in diameter ( Figure S4 in Supporting Information), where at high intensity of UV light only DO repulsion between the particles have been observed, while low intensities generate transient DO attraction and repulsion. [44] Applying the introduced analysis here, we have reconstructed the time-dependent development of the concentration excess, Δc C , and have found an excellent agreement with the experimental results (see red curves in Figures S4f-j,  Supporting Information).
To demonstrate experimentally the persistence of the repulsive DO flow under blue light exposer, we analyze the motion of the tracer particles (non-porous colloids of d = 1.5 µm) around large porous particles of different diameters (Figure 5a). Under illumination with blue light (λ = 455 nm) the l-LDDO flow generated around each porous particle pushes the tracer colloids out in radial direction over distances up to several tens of micrometers and the flow maintains during the whole illumination time (see Figure 5 and corresponding Video S2, Supporting Information). The extent of the DO flow depends on the diameter of the porous particle, i.e., the amount of stored surfactant, as illustrated for four porous particles of 5, 18.3, 21.7, and 26.9 µm in diameter (Figure 5b). The radius of the cleaned area at saturation, R C,max (Figure 5c), as well as the DO velocity (slope of the curves at the beginning in Figure 5a) increases linearly with particle diameter, i.e., with the effective area available for adsorption of trans-surfactant depicted according to Equation 6 ( Figure 5c, details of calculations are reported in Supporting Information, Section 4).
The dependence of the extent of the l-LDDO flow on irradiation intensity is shown for one selected porous particle of 20 µm in diameter (Figure 6, see also Videos S3 and S4 in Supporting Information). The average velocity of the tracer   , and as log-log plot c). The wavelength of incident light is 455 nm, the particle diameter is 5 µm. Corresponding raw data are provided in Figure S3 (see Supporting Information, Section 5). Corresponding videos are provided for porous (Videos S5, S6, and S7, Supporting Information) and none-porous (Videos S8,S9 and S10, Supporting Information) silica particles. particles increases from 0.1 µm s −1 to 1.5 µm s −1 with increasing the intensity from 0.16 to 10 mW cm −2 (see red circles in Figure 6f).
We should mention that since the surfactant molecules adsorb also on a surface of plain particles, the l-LDDO flow is generated at the non-porous colloids as well, however, the extent of flow is significantly less. Figure 7 depicts the difference between the DO repulsion of porous and non-porous particles at other parameters fixed (c azo = 2 mM, λ = 455 nm). We have found that the separation rate increases with intensity for Figure 8. a) Nearest particle distance as a function of time for porous silica colloids (d = 5 µm) calculated from Videos S11 -S14 (Supporting Information). b) Separation rate κ and photo-isomerization rate, k TC , taken from published in our recent work [49] as a function of the wavelength obtained from fitting the data with Equation 10. Note, that the data for 365 nm are fitted with delayed time due to the existence of the attractive flow at the beginning of irradiation. Dashed lines in red and dark illustrate the data trend. both types of particles and shows more than 30 times smaller values for non-porous colloids (Figure 7b,c). The analysis is based on the calculation of using NPD values as a function of irradiation time: where NPD 0 and NPD e are the nearest particle distance at the initial state and equilibrated during irradiation, respectively, κ is the separation rate of two adjacent particles and t is the time.
Expanding the analysis of the l-LDDO flow over more wavelength, i.e., 365, 490, and 532 nm (I = 1 mW cm −2 is kept constant for all wavelength) (Figure 8a) we have found that with increasing irradiation wavelength, the separation rate, κ (see Equation 10), decreases (Figure 8b). In the case of blue and green light, the continuous generation of cis-isomers in steady state is low (20% and 10%, respectively) resulting in a weak DO flow (Figure 8a,b, its effective dynamic isomerization rate is illustrated in Figure S5a, Supporting Information). For UV (365 nm) light, although, the initial separation rate is fast (the rate of isomerization is fast), during further continuous irradiation, the amount of trans isomers drops down to 10% in the steady state (effective surfactant exchange displayed in Figure S5b, Supporting Information) and thus the cis isomer gradient decays with Brownian motion of the particles overtaking the DO repulsion (see details in Supporting Information, Section 6).
With the knowledge gained, we would like to show that as long as the dynamic exchange of trans-and cis-isomers at a surface of an object exists, any kind of interface can generate l-LDDO flow. Here we demonstrate it by using different micro-sized objects (see Figure 9) such as human nail (a) and hair (b), dust (c) earth soil (d), sand corn (e) and a small part of a wood sting (f). During illumination with blue light (λ = 455nm, I = 10 mW cm −2 ) all micro-sized objects show an outgoing l-LDDO flow of different strength, i.e., different cleaned areas of tracer particles. This can be explained by the roughness of the objects as well as the different affinity of both isomer to the surface of these objects (see details in Supporting Information Section 7).
For instance, one can see from the SEM micrograph (inserted in the optical micrographs), that the sand corn has quite a rough surface, i.e., larger A eff , in addition to the negative charge of the surface due to the presence of the silica oxide and thus exhibit stronger l-LDDO flow.

Conclusion
Here we demonstrate that objects dispersed in an aqueous solution of photosensitive surfactant can generate local-light driven diffusioosmotic (l-LDDO) flow and thus act as a micropump. The driving mechanism of the DO flow is based on the photo-isomerization of the surfactant molecules during exposure to light of an appropriate wavelength. Two states of the surfactant, trans-and cis-, have dissimilar photo-isomerization rates and different affinity to a solid/liquid interface providing a continuous exchange of both isomers between the interface and the bulk. This yields a concentration gradient of cis isomers and a consequent gradient in the osmotic pressure around the particles generating local DO flow along the solid surface. The radially directed flow can be adjusted to point towards or away from the particle by variation of the irradiation wavelength making the particle active with respect to interaction potential. It means that by generation of the DO flow at single colloids we introduce diffusioosmotic repulsive (outwards directed flow) or attractive (inwards direction) interactions, the range of which is determined by the extent of DO flow. We have shown that the strength of l-LDDO flow depends on the amount of the surfactant molecules absorbed by the particle as well as irradiation parameters. We extend the analysis of the mechanism of LDDO flow formation by introducing the time dependency of the concentration excess near the particle utilizing recently reported kinetics of surfactant photo-isomerization. The increase in intensity results in stronger DO flow, while variation of the wavelength has a more complex influence on the l-LDDO flow. Indeed, we have demonstrated that under UV light at low intensity, the DO flow can change its direction during light exposure from temporal attractive to repulsive, while irradiation with blue light results in continuously repelling flow. The fact, that any object capable to absorb selectively one of the isomers and thus generate l-LDDO flow can be used in many practical applications such as removal of contaminating particles out of an active surface, local pumping of a solute, or local mixing near the active object, as well as adjustment of the interaction strength and sign between active particles by generating DO repulsion or attraction flows.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.