Hydrophobic-substrate based water-microdroplet manipulation through the long-range photovoltaic interaction from a distant LiNbO<sub>3</sub>:Fe crystal

Zuoxuan Gao; Yuhang Mi; Mengtong Wang; Xiaohu Liu; Xiong Zhang; Kaifang Gao; Lihong Shi; E. R. Mugisha; Hongjian Chen; Wenbo Yan

doi:10.1364/OE.417225

1. Introduction

Microfluidic techniques with an ability to control cellular micro-environments have been playing an increasingly important role in biological applications. Various mechanisms have been employed to manipulate microfluids efficiently and swiftly, e. g. magnetic [1], acoustic [2], electrical [3], optical [4]. Magnetic technique is for manipulating microfluids susceptible to magnetic fields and thus it requires magnetic beads to be pre-dispersed inside the microfluids. Surface acoustic wave (SAW) carries momentum so that they can exert force on microfluids, and but it requires interdigitated electrodes (IDT) patterned on a piezoelectric substrate. Electric potential can be utilized to manipulate microfluids through the electrowetting-on-dielectric (EWOD) effect, but it also requires the complicated electrode fabrication in advance. Optical tweezers, which employs the radiation pressure or gradient of the light, is capable to manipulate a micro-object in a non-contact way. However, the force provided by the conventional optical tweezer is usually in the level of pN which is apparently smaller than that provided by other means.

Lithium niobate (LN) is regarded as a potential material for many bio-photonics applications such as biological analysis, clinical diagnostics and drug discovery [5–8]. As a key technique for these applications, manipulating aqueous microdroplets on LN has attracted broad interests [9–15]. Recently, photovoltaic actuating and splitting of water microdroplets were successively realized on a hydrophobic LN:Fe crystal [9,11]. This technique for manipulating water utilizes the photovoltaic property of LN:Fe crystal and employs the electrostatic interaction of the photo-generated charges. Thus, it can avoid the usage of the external beads required by the magnetic technique and the electrode fabrication required by the acoustic and electrical techniques [1–3], and permits the massive parallel manipulation of micro-objects [16,17]. The force employed by the photovoltaic manipulation originates from the photo-generated charges on the LN:Fe surface [17–25]. Under the illumination of the visible light, the electrons are easily photo-excited from Fe^2+/3+ traps in the crystal, forming the current toward the -c surface of the LN crystal (i.e., photovoltaic current). In virtue of the inhomogeneous electrostatic field produced by the charges accumulated on the surface, water microdroplets were manipulated in multimode with high efficiency.

Despite the progress made on the photovoltaic manipulation of water microdroplets [9–15], there is still an obvious limitation on the flexibility of this technique, that is, the microdroplet has to be supported by the LN:Fe crystal. It is because the photovoltaic field employed by the microdroplet manipulation was generally considered to be a kind of evanescent field that can only work quite close to the LN surface [17]. Using the LN:Fe crystal to support the microdroplet can guarantee the close contact between the microdroplet and the crystal surface. However, a hybrid sign of microfluidics is often required in many biological applications, i.e. other kinds of biomaterials instead of the LN:Fe crystal are required to support the microdroplet [26–28], and this limitation is not beneficial to the development of biological lab-on-chips. As the matter of fact, the electrostatic field generated on the LN:Fe surface can reach a value as high as 10⁷ V/m [29], and it was found recently that this field is capable to extend from the crystal surface to the nearby space and exert on the ultrasonically atomized water-vapor in air [10] or the water-microdroplets at air/oil interface [13] through a long-range electrostatic interaction. However, so far no successful water-microdroplet manipulation was reported on a non-LN substrate through this long-range photovoltaic interaction from a distant LN:Fe crystal. Moreover, the issues regarding the manipulating distance and velocity, which are quite crucial for the practicalization of the technique of long-range photovoltaic water-microdroplet manipulation, have never been studied both experimentally and theoretically.

As compared to the recent works on the water microdroplets, those on dielectric microdroplets were more intensive. By using the electrostatic field generated on LN surfaces, various fantastic manipulations on dielectric microdroplets including dispensing [30,31], guiding [23,32], actuating [18,33] and splitting [19,20,34] were reported. Pyroelectric rather than photovoltaic effect was utilized in some manipulations using nominally pure LN crystals [30–35]. Ferraro et al. invented a pyroelectro-dynamic shooting system for dispensing dielectric micro-droplets [30], and then this technique was further developed by Grilli et al. to detect biomolecules below femtomolar range [31], write microfluidic footpaths [32], and print high viscous microdots [34]. Recently, Tang et al. realized a remote manipulation of a water microdroplet on a hydrophobic surface by utilizing optically induced pyroelectric effect on a pure LN wafer bonded with a high-absorption film [33]. By this way, they demonstrated a desired lossfree manipulation of water microdroplets, functioning as a “magic” wettingproof hand to navigate, fuse, pinch, and cleave fluids on demand [35]. In spite of the great progress in the pyroelectric manipulation, the temperature rise (usually several tens of centigrade) required by the pyroelectric process [33,35] is not suitable for the biomedical applications of LN-based lab-on-chips. It is because this temperature rise may accelerate the evaporation of the aqueous microdroplet which has a very high saturated vapor pressure even at the room temperature. Moreover, this huge temperature rise is fatal to the cells who are quite temperature sensitive. The photovoltaic process in LN:Fe crystals does not need the aid of the temptation rise, and therefore it is a more suitable way for manipulating biological aqueous microdroplets [9–12]. Although the photovoltaic microfluidic manipulation avoids the huge temperature rise, there is still a unneglectable heating effect [10] due to the laser absorption of the LN:Fe crystal. Since LN:Fe crystal is used to support the microdroplets in the conventional way, the heat generated on the LN:Fe crystal may transfer into the microdroplet through the contacting area which is possibly harmful to the fragile cells. If the water microdroplets can be manipulated on a non-LN substrate through the long-range photovoltaic interaction generated at a distance, then the close contact between the microdroplets and the LN:Fe surface can be avoided and the heating effect will be suppressed substantially by the distance and become negligible during the manipulation.

Very lately, A. Puerto et al [13] reported a successful long-range (∼1 mm) photovoltaic manipulation on the water-microdroplets hanging at the air-oil interface, and the guiding, trapping, merging, and splitting of aqueous bio-droplets was demonstrated in a contactless way and the heating effect can be suppressed by this mm-thick oil layer. In their work the water microdroplets are required to be almost totally immersed in oil and hung at air-oil interface through the compensation of the microdroplet gravity with a drag force arising from the surface tension. However, this balance requirement of the water microdroplet is not convenient to fulfill in some biological applications, as the values of the surface-tension coefficient, oil density, the microdroplet volume and the thickness of the oil layer have to be adjusted carefully to prevent the instability of the manipulation, which may result in the detachment of the water-microdroplet from the air/oil interface and its permanent immobilization on the naked LN:Fe surface. Thus, developing other modes of long-range photovoltaic manipulation for water microdroplets are quite urgent. For a better adaptability and integratablity of this technique, contactless manipulation modes based on a solid substrate has to be explored.

In this paper, we demonstrate a successful hydrophobic-substrate based manipulation of a water microdroplet by utilizing the long-range photovoltaic interaction from a distant LN:Fe crystal. It will be shown that the maximal distance for manipulating the water microdroplet (i.e. maximal manipulation distance, MMD) can be tuned, by increasing the laser-illumination intensity, up to a sub-centimeter level (∼4 mm). We will establish an analytic model to describe the force balance during the microdroplet manipulation under a long-range photovoltaic interaction. An unusual behavior of the water microdroplet under a strong photovoltaic interaction will be reported and explained from the viewpoint of electrostatic interaction mechanism. The technique reported here has a potential to solve the practical problems existing in the relevant biological applications.

2. Experiments

A c-cut congruent LN:Fe crystal doped with 0.03 wt% Fe₂O₃ is responsible for producing the long-range photovoltaic interaction. The sample thickness is 1.05 ± 0.01 mm and its absorption at 405 nm is about 7.9 cm^-1. A common glass slide (substrate) is used for supporting the water microdroplets. To lower the resistance of the microdroplet when it is manipulated, a porous Polytetrafluoroethylene (PTFE) membrane infiltrated with transformer oil (dielectric constant of ∼2.1) was bonded onto the glass slide [11]. The LN:Fe crystal was fixed on a sample holder while the glass slide was mounted onto a XYZ motorized linear stage (KOHZU) with the distance between them being adjustable. This stage can translate in three dimensions with a repeatability of ±0.3μm, and thus the precision of all positioning actions, including setting the droplet or adjusting the distance, could be guaranteed to be in a high level. The water microdroplet is produced by a volume controlled micro-pipette driven by a micro-positioning unit. The volume of the droplet was fixed to be 0.45 ± 0.02 μL for all experiments.

The experimental setup for recording the behavior of the water microdroplet under a long-range photovoltaic interaction is shown in Fig. 1(a). The 405 nm laser (CniLaser) was normally focused by an objective (NA=0.5, 25×) onto the LN:Fe sample from the top. The power of the laser beam was adjusted from 4 to 140 mW. The diameter of the beam waist at the focal plane (i.e. the bottom surface of the LN:Fe crystal) is measured to be ∼60 μm. A camera was used to capture the behavior of the water microdroplet at a lateral position. Figure 1(b) shows the geometry configuration of the long-range photovoltaic manipulation on the water microdroplet. The -c surface of the LN:Fe crystal was set toward the water microdroplet. The inhomogeneous electrostatic field creates a trapping force on the microdroplet below, and the long-range photovoltaic manipulation of the water microdroplet on the glass substrate can be realized by utilizing this trapping force. To demonstrate the photovoltaic manipulation, we create relative displacement between the microdroplet and the supporting substrate through moving the substrate instead of moving both the laser position and the LN:Fe substrate.

Fig. 1. a) Setup for recording the behavior of a water microdroplet during a long-range photovoltaic manipulation; b) Geometry configuration of the long-range photo-voltaic manipulation on the microdroplet. Note that the vertical distance from the microdroplet to LN:Fe surface is considered to be approximately equal to the distance (D) from the Glass substrate to the LN:Fe surface. The yellow dot represents the illumination point, i.e. the crossing point of the laser beam and the Glass substrate. The parameter d represents the distance from the illumination point to the balance position of the water microdroplet.

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3. Theoretical background and analysis

The photovoltaic and pyroelectric effects in LN crystals are both a consequence of the polar structure of the crystalline lattice [5–25,30–37]. Providing a z-cut crystal face is under a uniform illumination with an intensity I, the photovoltaic current can be described by:

(1)$${J_{pv}} = KI[{F{e^{2 + }}} ]$$

Where K is the bulk photovoltaic coefficient and [Fe²⁺] the density of donor Fe²⁺. Under an open-circuit condition (see Fig. 2(a)), the appearance of photovoltaic current leads to the accumulation of negative and positive charges at the + c and -c surfaces of the LN:Fe crystal, respectively. As a result, a space charge field (photovoltaic field E_pv) is developed across the crystal bulk with a Maxwell relaxation time:

(2)$${\tau _{pv}} = \frac{{\varepsilon {\varepsilon _0}}}{{e\mu n}} = \frac{{\varepsilon {\varepsilon _0}\gamma [{F{e^{3 + }}} ]}}{{e\mu sIF{e^{2 + }}}}$$

Fig. 2. Schematic diagram of surface charge generation. (a) Photovoltaic and (b) pyroelectric charges are generated solely. (c)-(e) Superposition of the photovoltaic and pyroelectric charges. (f)-(h) The compensation of the bounded pyroelectric charges by the moving photovoltaic charges.

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Where ε is the dielectric constant of the crystal. When a steady state is reached, the surface charge density σ_pv due to the photovoltaic effect can be given by:

(3)$${\sigma _{pv}} = \varepsilon {\varepsilon _0}{E_{pv}}$$

(4)$${E_{pv}} = \frac{{{J_{pv}}}}{{e\mu n}} = \frac{{KI[F{e^{2 + }}\left] \gamma \right[[F{e^{3 + }}]}}{{e\mu sI[F{e^{2 + }}]}} = \frac{{K\gamma [F{e^{3 + }}]}}{{e\mu s}}$$

The response time τ_pv is dependent on the illumination intensity while the photovoltaic surface charge density σ_pv is not. The pyroelectric effect is connected with the surface charge due to the spontaneous polarization P_s, σ_s=n·P_s. Normally, this polarization surface charge σ_s is fully compensated by external charges. However, upon a sudden temperature change ΔT the rapid variation of P_s induces a uniform uncompensated surface charge σ_py (see Fig. 2(b)):

(5)$${\sigma _{py}} = {P_c}\Delta T$$

As mentioned in the introduction, both of the photovoltaic and pyroelectric effects can be utilized to create the surface charges for the optoelectronic manipulation of nano- or micro-objects on LN crystals. In Ref. [13], [22–25], the surface charges were generated by illuminating Fe-doped LN crystals with a visible laser beam or light patterns with very low intensities. In these cases, the optically induced thermal effect is negligible and only the photovoltaic current contributes to the accumulation of surface charges (see Fig. 2(a)). In Ref. [30–35], the surface charges were created by applying a thermal stimulus on nominally pure LN crystals, i.e. hot-tip contact, illuminating LN wafers with a high-intensity IR laser and indirect heating through the IR illumination on the LN wafers bonded with a high-absorption film. In these cases, LN crystals were not truly photo-activated even sometimes the illumination was applied, because the IR photons are not capable to excite the electrons and generate photoconductivity in LN crystals. Therefore, the pyroelectric effect solely contributes to the accumulation of surface charges here (see Fig. 2(b)). In Ref. [19] and [36], both the visible illumination and the temperature variation were applied to LN:Fe crystals, and the superposed effect of the photovoltaic and pyroelectric charges on the optoelectronic manipulation was observed (see Fig. 2(c)-(e)). In particular, it was proved experimentally that, the temperature variation of 10-20°C can generate the surface charges equivalent to that normally induced by the photovoltaic current [36]. However, we have to emphasize here that the simple superposition of the photovoltaic and pyroelectric charges is valid only when the visible illumination and the temperature variation were applied step by step as reported in Ref. [19] and [36]. In the present work, the LN:Fe crystal will be illuminated by a visible laser beam with a high intensity, and a heating effect due to the laser absorption of the LN:Fe crystal may company the laser illumination. Thus, it should be a case where the visible illumination and the temperature variation are applied synchronously. In this situation, the presence of bulk photoconductivity may cause the compensation between the bounded pyroelectric charges and the moving photovoltaic charges (see Fig. 2(f)-(h)), making impossible the superposition of the photovoltaic and pyroelectric charges. Considering the compensation caused by the bulk photoconductivity, we can write the temporal evolution of the pyroelectric surface charges as [37]:

(6)$${\sigma _{py}}(t )= \frac{{I[{1 - exp({ - \alpha d} )} ]}}{{{C_p}\rho d}}{P_c}{\tau _h}\left[ {1 - exp \left( {\frac{{ - t}}{{{\tau_h}}}} \right)} \right]exp \left( {\frac{{ - t}}{{{\tau_{pv}}}}} \right)$$

where I is the illumination intensity, α the absorption coefficient, ρ the crystal density, d the crystal thickness, C_p the specific heat capacity, τ_h the heat-relaxation time constant, and τ_pv the Maxwell relaxation time. Note that τ_pv is inversely proportional to the photoconductivity if the dark conductivity is negligible. Equation (6) reveals that the bounded pyroelectric surface charges exist transiently and they decay exponentially with the Maxwell relaxation time τ_pv of the LN:Fe crystal. The time for the full compensation of the pyroelectric surface charges depends on the photoconductivity of the LN:Fe crystal, and the time t_m that is necessary to reach the maximum of the pyroelectric charge density can be derived from Eq. (6) to be:[37]

(7)$${t_m} = {\tau _h}In\left( {1 + \frac{{{\tau_{pv}}}}{{{\tau_h}}}} \right)$$

Considering the low heat conductivity of the LN:Fe crystal, the heat-relaxation time constant τ_h is estimated to be at least serval seconds. By contrary, the Maxwell relaxation time τ_pv should be in the level of ms as a high intensity of 10⁷ W/m² will be adopted for the illumination in the present work. Thus, the time t_m is estimated to be nearly zero according to Eq.6, which indicates that the pyroelectric charges are negligible in spite of the presence of the photothermal heating effect in our case. As the matter of fact, the pyroelectric effect is negligible in the majority of cases of optoelectronic manipulation based on LN:Fe crystals as long as the photoconductivity is large enough for the timely compensation of the bounded pyroelectric surface charges.

Now, let’s establish a model involved with the photovoltaic charge accumulation, the long-range electrostatic interaction, and the force balance during the microdroplet manipulation. Theoretically, the accumulation of photovoltaic charge happens on both the + c and –c surfaces and thus the source of the electrostatic field should be treated as a dipole (see Fig. 2(a)). However, in the present model we simplify the source of the electrostatic field as a unipolar, point-like source for two reasons. First, the photovoltaic charge accumulation at the -c surface was reported to be more efficient to generate a strong electrostatic field than at the + c surface experimentally [16,20]. Second, in the experiment the -c surface of the LN:Fe crystal was set toward the water microdroplet while the + c surface is on the crystal back which is far from the water microdroplet. Therefore, the photovoltaic charge accumulation at the + c surface does not play an important role on the microdroplet manipulation [13,33] and it could be neglected in the model. According to the one-center charge-transport model [24], the temporal accumulation of the photovoltaic charges on the -c surface follows an exponential function: σ₋=σ_PV[1-Exp(-t/τ)] = σ_PV[1-Exp(-tβI)], where the σ₋ is the surface charge density and τ is the time constant. However, if the accumulation duration (some seconds in our case) is far beyond the time constant τ (in the level of ms for the illumination intensity I of 10⁷ W/m²), then the photovoltaic charge accumulation will reach a steady state (σ_PV = εε₀kγ[Fe³⁺]/(eμs), derived from Eq. (3) and 4), which is no more related to the illumination intensity.

Beside the conventional model, a two-center model was also proposed to describe the light-induced charge transport in LN:Fe crystal [38]. This model is quite suitable for the cases of high illumination intensity, i.e. under the illumination of a focused laser beam. According to this model, the surface charge density at the steady state can be written as a function of the illumination intensity:

(8)$$\sigma = \frac{{\varepsilon {\varepsilon _0}({{I_c}{l_{02}}{v_{02}} + {l_{12}}{v_{12}}I} )}}{{{\mu _1}{\tau _{10}}{v_{02}}{I_c} + {\mu _2}{\tau _{21}}({{v_{02}}{I_c} + {v_{12}}I} )}}$$

where ε is the permittivity of LN, I_c the critical illumination intensity, l₀₂ and l₁₂ the photovoltaic drift length from the Fe energy level to the CB and from the intermediate energy level to the CB, μ₁ and μ₂ the electronic mobility in the intermediate energy level and CB, τ₁₀ and τ₂₁ the recombination time from the intermediate energy level to the Fe energy level and from the CB to the intermediate energy level, ν₀₂ and ν₁₂ the photoionization cross section from the Fe energy level to the CB and from the intermediate energy level to the CB.

Here, some relationship between the parameters could be used to simplify the equation: (i). ν₁₂/n₀₂=2 (ii). l₁₂/l₀₂=3 [38]. In addition, we also set that: μ₁τ₁₀= Nμ₂τ₂₁, μ₁τ₁₀+μ₂τ₂₁∼10⁻¹⁷ m²/V and l₀₂∼10⁻¹⁰ m [38]. Here, the parameters of N and the critical intensity I_c in Eq. (8) are unknown and could be obtained from a fitting analyses.

In our case, the spot size (i.e. the diameter of the laser beam waist, 60 μm) is much smaller than the size (∼1.2 mm) of the water microdroplet and the distance D (1.5∼4 mm) between the substrate and LN:Fe surface, and thus two simplifications could be accepted in our case. (i) The inhomogeneity of illumination intensity inside the spot is neglected. (ii) The accumulated photovoltaic charges at the illumination point are treated as a point charge. Under these simplifications, the laser spot can be considered as a homogeneous illumination with the spot size, and the accumulated photovoltaic charge amount can be simply written as:

(9)$$Q = \frac{{\pi {r^2}\varepsilon {\varepsilon _0}{l_{02}}}}{{{\mu _2}{\tau _{21}}}}\frac{{({{I_c} + 6I} )}}{{({N + 1} ){I_c} + 2I}}$$

Where I is the average light intensity and r (30 μm) is the radius of the laser beam waist.

The DEP force exerting on the water microdroplet is derived by calculating an integral over the Kelvin polarization force density, i.e. all dipoles in the fluid volume [23].

(10)$$F = \frac{1}{2}{\varepsilon _0}\smallint ({{\varepsilon_l} - {\varepsilon_m}} )\nabla {E^2}dV$$

Where ε_l is the permittivity of water microdroplet, ε_m the permittivity of the surrounding medium (air), V the volume of water microdroplet.

To simplify the calculation, we assume that ∇E² does not change too much over the entire water micro-droplet. The above assumption is accepted when the water is considered as a fluid with a high permittivity rather than a high conductivity. In addition, we adopt the spatial electrostatic distribution of a point charge (accumulated photovoltaic charge), the DEP force exerting on the water microdroplet can be written as:

(11)$${F_{DEP}} = \frac{1}{2}{\varepsilon _0}({{\varepsilon_l} - {\varepsilon_m}} )\nabla {E^2}V$$

Where V (0.45 μL) is the volume of the water microdroplet. The horizontal component of the DEP attraction force (F_DEP-x) along the sliding plane (hydrophobic substrate) is responsible for the actuation during the microdroplet manipulation. Under the approximation (Sin θ_P=Tan θ_P, R = D) for a small projection angle θ_p, the actuation force F_DEP-x can be written as:

(12)$${F_{DEP - x}} = Fsin{\theta _p} = \frac{{{\varepsilon _0}({{\varepsilon_l} - {\varepsilon_m}} )4{k^2}V{Q^2}}}{{2{D^5}}}\frac{d}{D}$$

Where k is the Coulomb constant, D the distance from the substrate surface to the LN:Fe surface, and d the distance from the balance position to the illumination point.

If the actuating force F_DEP-x and the friction force f are balanced, we obtain the following equation for the microdroplet manipulation:

(13)$${F_{DEP - x}} = f$$

Considering the friction force f as a constant, we get a nonlinear relationship between the illumination intensity and the distance for a critical microdroplet manipulation:

(14)$$D = H\sqrt[3]{{\frac{{({{I_c} + 6I} )}}{{({N + 1} ){I_c} + 2I}}}}$$

{\textrm {with}}\; H = \sqrt[6]{{{{\left( {\frac{{\pi {r^2}\varepsilon {\varepsilon_0}{l_{02}}}}{{{\mu_2}{\tau_{21}}}}} \right)}^2}\frac{{{\varepsilon _0}({{\varepsilon_l} - {\varepsilon_m}} )4{k^2}Vd}}{{2f}}}}

4. Results

In the cases of manipulating microdroplets directly on naked LN:Fe substrates [18–20], the object is often dielectric liquid. By contrast, the microdroplet in our case is settled on another substrate rather than LN:Fe crystal, thus the manipulation of the conductive liquid becomes possible because the gap between the substrate and LN:Fe isolates the photovoltaic charges accumulated on the LN:Fe surface and prevents the charge compensation through the liquid. The induced electrostatic field traps the water microdroplet towards the illumination point. As F_DEP-x is essentially an electrostatic interaction provoked by the laser illumination, its magnitude is expected to be dependent on the illumination intensity (I, an average intensity defined as the total laser-illumination power divided by the area of the laser spot) and the distance (D) from the substrate to the LN:Fe surface.

To quantitatively study the trapping process, two manipulation modes, i.e. static and kinetic modes, will be adopted in the experiments. In the static mode the substrate supporting the water microdroplet was kept static, while in the kinetic mode the substrate was translated continuously in order to create a displacement of the microdroplet with respect to the substrate. The different states of the force balance in the static-mode trapping of the microdroplet are shown in Fig. 3(a). It should be noticed that the initial position of the water microdroplet on the substrate is quite important to the trapping effect. Generally, for a certain distance D and illumination intensity I, the initial position of the water microdroplet could be classified into three cases. In Range1, the microdroplet was too far from the illumination point (marked by the yellow dot in Fig. 3(b)), F_DEP-x cannot overcome the static friction force (f_s), and the microdroplet keeps stationary in this case. In Range 2, F_DEP-x exceeds the static friction force f_s, and the microdroplet moves toward the illumination point till it entering Range 3. In Rang 3, F_DEP-x is below the kinetic friction force f_k due to the reduction of projection angle θ_p, and the microdroplet slows down and stops again. If the deceleration process of the microdroplet is ignored, then the microdroplet can be considered to stop at a critical position where F_DEP-x and f_k is just balanced. It should be noticed that the division of Range 1-3 depends highly on the distance D and the illumination intensity I. In addition, the static friction force f_s is usually a little bit larger than the kinetic friction force f_k.

Fig. 3. (a) The different states of the force balance during the static-mode trapping and manipulation: (b) D = 2.65 mm; (c) D = 2.82 mm; (d) D = 2.97 mm; The arrows in (b)∼(c) indicate the direction of microdroplet movement, and the yellow and red dots represent the illumination points and the reference marks on the substrate, respectively. The scale bar equals to 1 mm.

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Figure 3(b)-(d) show the experimental results about the static-mode trapping of the microdroplet. In the experiments, different distances but the same illumination intensity was used, the initial position of the microdroplet was set about 1.2 mm from the illumination point, and the substrate was kept static once the adjustment of the distance D has been done. When D > 2.82 mm, the microdroplet is almost motionless because it is located in the Range 1 (Fig. 3(d)). However, when D ≤2.82 mm, the microdroplet falls into the range 2, and thus the trapping motion of the microdroplet toward the illumination point were observed (Fig. 3(b) and (c)). It is found experimentally that the microdroplet stops at ∼0.6 mm to the illumination point, indicating that ∼0.6 mm to the illumination point (named as P_0.6 here and after) is the critical position where F_DEP-x and f_k is just balanced. Thus, P_0.6 will be fixed as the initial position of the water microdroplet in the following kinetic-mode trapping experiments for studying the relationship between the distance D and the illumination intensity I.

We fix the illumination intensity and try to find the maximal distance for trapping a water microdroplet in the kinetic mode. During the kinetic-mode manipulation, we first put the microdroplet at P_0.6 and then translate the substrate and see if the microdroplet is trapped in this position. By repeating the kinetic-mode trapping experiment at a varied distance D, we can find a maximal manipulation distance (MMD) for a critical trapping at a fixed illumination intensity. Under the critical trapping condition, the actuating force F_DEP-x is equal to the kinetic friction force f_k, a little bit lower than the static friction force f_s. Therefore, under this condition we often observed a transient microdroplet movement with respect to the substrate at the beginning of the substrate translation. However, the deviation of the microdroplet from P_0.6 may result in the increase of F_DEP-x. Once F_DEP-x exceeds f_s then the relative movement between the microdroplet and the substrate will be triggered and the microdroplet will go back to P_0.6 where F_DEP-x and f_k are balanced. Here, it should be emphasized that the standard for the successful kinetic-mode manipulation is that the microdroplet is trapped at P_0.6. To judge whether the microdroplet can be trapped at P_0.6, we follow the experimental procedures as below: First, the position of P_0.6 was electrically marked on the video window of the manipulation monitor program. Second, translate the substrate and check the response of the microdroplet. If it finally stays at P_0.6, then we know it is really trapped. Otherwise, the microdroplet will be carried away by the translating substrate.

We measure the maximal distance (MMD) for trapping a water microdroplet in the kinetic mode at different illumination intensities (see Fig. 4). During the continuous manipulation the microdroplet is almost kept at the balance position (P_0.6) from the illumination point (see the sequential frames of the microdroplet manipulation in the inset of Fig. 4). It is found that the maximal manipulation distance (MMD) follows a nonlinear function of the illumination intensity, and in particular, it can be tuned up to a value of ∼4 mm in the intensity range available in our experiments. Note that exceeding the maximal manipulation distance (MMD) the local inhomogeneous electrostatic field cannot provide sufficient trapping force to overcome the friction force.

Fig. 4. The dependence of the maximal manipulation distance (MMD) on the illumination intensity. The red curve is a nonlinear fit to the data according to Eq.14. The inset shows three groups of sequential frames during the microdroplet manipulation under different illumination intensities. The arrows indicate the direction of the microdroplet movement with respect to the substrate, and the yellow and red dots represent the illumination points and the reference marks on the substrate, respectively. The scale bar equals to 1 mm.

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In the case of the critical microdroplet manipulation the actuating force is just enough for overcoming the kinetic friction force f_k, thus only a low velocity (∼120 μm/s, see Fig. 4) of the microdroplet movement is allowed during the manipulation. If a higher manipulation velocity is applied to the water microdroplet in this case, a pronounced deviation of the microdroplet from the initial position P_0.6 will be observed due to the unbalance friction force f_k, and eventually it may make the water microdroplet out of control. This unbalanced effect is straightforward because the friction force f_k usually increases with the velocity of the relative movement between the water microdroplet and the hydrophobic substrate. Even though the dependence of the friction force on the microdroplet velocity is unknown for a hydrophobic substrate, it is clear that sufficient actuating force has to be provided for the microdroplet manipulation at a higher velocity. By gradually increasing the translation velocity of the substrate in the kinetic-mode trapping experiment and see if the microdroplet can be trapped at P_0.6 without any deviation, we can obtain the maximal velocity for the photovoltaic manipulation at each distance and illumination intensity. Figure 5(f) and 6(f) show the dependence of the microdroplet velocity on the manipulation distance and the illumination intensity, respectively. According to the nature of photovoltaic interaction, either shortening the manipulation distance or increasing the illumination intensity can enhance the actuating force and increase the manipulation velocity. In the available range of the manipulation distance and illumination intensity in our experiments, the maximal velocity is found to be roughly linear with the two parameters. The sequential frames of the microdroplet manipulation in Fig. 5(a)-(d) and 6(a)-(d) are corresponding to the data points in Fig. 5(f) and 6(f), respectively. In particular, Visualization 1 shows a stable water-microdroplet manipulation with a high velocity of 220 μm/s.

Fig. 5. (a)-(d) The sequential frames of the microdroplet manipulation with a fixed illumination intensity I (1.18×10⁷ W/m²) but a varied distance D (2-2.8 mm). (e) The unusual behaviors of the microdroplet when too short manipulation distance D (< 2 mm) is applied. (f) The dependence of the microdroplet velocity on the manipulation distance D. The low, moderate and high zones are classified based on the strength of the long-range photovoltaic interaction. Visualization 2 corresponds to the sequential frames plotted in (e).

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Fig. 6. (a)-(d) The sequential frames of the microdroplet manipulation with a fixed distance D (2.33 mm) but a varied illumination intensity I (0.67-1.7×10⁷ W/m²). (e) Unusual microdroplet behaviors when too high illumination intensity I (>1.7×10⁷ W/m²) is applied. (f) The dependence of the microdroplet velocity on the illumination intensity I. The low, moderate and high zones are classified based on the strength of the long-range photovoltaic interaction. Visualization 1 corresponds to the sequential frames plotted in (c).

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All measurements mentioned above, including the static and kinetic manipulation of the microdroplet, were repeated at least three times, and the results were reproducible if the experimental conditions such as the vibration, temperature and humidity were controlled well. The uncertainties of the MMD and speed data have been given by the error bar, and the correlation coefficient R² of the fitting is 0.9940 in our work. It should be emphasized that these behavioral data about the microdroplet can be influenced by the parameters such as the volume of the microdroplet and the initial position of the microdroplet. It is reasonable because the actuating force is highly associated with the volume and initial position of the microdroplet. However, due to the limitation of the pages, only the cases of the fixed volume (0.45μL) and initial position (P_0.6) of the microdroplet were studied in this work, and more details will be published in the future.

5. Discussions

The dependence of MMD on the illumination intensity plotted in Fig. 4 cannot be predicted by the one-center model, but it can be well fitted by Eq. (14) indicating that the analytic model based on the two-center model is valid. We obtain the fitting value of parameter I_c (4×10⁶ W/m²), which matches the threshold reported for LN:Fe crystals [38]. Based on the fitting parameter N (42) μ₂τ₂₁ is estimated to be 10⁻¹⁹ m²/V under the restriction condition μ₁τ₁₀+μ₂τ₂₁∼10⁻¹⁷ m²/V. During the kinetic manipulation the actuating force F_DEP-x and the kinetic friction force f_k are balanced. Therefore, the kinetic friction force f_k (1.1 μN) can be calculated from the fitting parameter H (0.00386). We also measure the sliding angle of the water microdroplet in order to calculate the actual friction force on the hydrophobic layer (see Fig. 7). For a water microdroplet with a volume of 0.45 μL, the sliding angle is found to be in the range of 10∼20 degrees. Thus, considering the force balance between the microdroplet gravity and the static friction force f_s, we obtain the value of f_s, which is in the range of 0.8∼1.5 μN and a little bit higher than the value of the kinetic friction force f_k given by the fitting analysis.

Fig. 7. Schematic and experimental diagrams for measuring the sliding angle of a water microdroplet (0.45 μL) on a hydrophobic Glass.

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As described by Eq. (9) and Eq. (12), the actuation force F_DEP-x is determined by the accumulated charge amount Q which depends on both the illumination intensity I and the radius r of the laser spot. For a fixed laser beam, if we modify the focusing ability of the objective, both I and r may change and so does the actuation force F_DEP-x. However, we emphasize that Eq. (9) and Eq. (12) are derived under the assumption that the laser beam is highly focused and a spot radius is sufficient small. Therefore, the above analytical equations are not suitable for the loosely focused laser beam. Experimentally, if we use the loosely focused laser beam, the illumination intensity will be at a low level and the intensity dependence of MMD will be absent according to the conventional one-center model.

Based on the obtained friction force, we simulate the static-mode trapping (Fig. 3(c)) of the water microdroplet through a finite-element method. The evolution of the water microdroplet during the critical trapping at the illumination intensity of 1.18×10⁷ W/m² is plotted. (see Supplement 1, Fig. S1). It is found that the distribution of the electrostatic field produced by the accumulated photovoltaic charges roughly resembles that of a point charge, and the DEP force exerting on the water microdroplet has a horizontal component towards the illumination point. (see Supplement 1, Fig. S1(a)). The sequential frames correspond to the evolution of the microdroplet movement in 5 seconds, which is in line with the experimental observation (Fig. 3(c)). (see Supplement 1, Fig. S1(b)). We integrate the horizontal component of the DEP force over the whole microdroplet, and plot the total actuating force F_DEP-x as a function of time. (see Supplement 1, Fig. S1(b)). It can be seen that the actuating force is higher than the friction force f_k (1.1 μN) at the start-up of the microdroplet movement, but a little bit lower than 1.1 μN when the microdroplet almost stops. The temporal curve of the actuating force reveals the acceleration and slow-down of the microdroplet movement. Although these effects are neglected in deriving Eq. (14), the analytic method based on Eq. (14) is still accepted as the actuating force in simulation is basically around 1.1 μN and could be considered as a quasi-balance.

In Fig. 5(f) and 6(f), the whole range can be divided into three zones: low, moderate and high zones, based on the strength of the long-range photovoltaic interaction. The actuating force is not enough to overcome the friction force in the low zone, and it becomes sufficient for the microdroplet manipulation with a variable velocity in the moderate zone. However, with the further enhancement of the long-range photovoltaic interaction an unstable situation may happen. More exactly, too short manipulation distance or too high illumination produces a strong electrostatic field, which may induce the instability of the microdroplet water/air interface at the balance position and cause the jet of tiny droplets ejected from the main water microdroplet [39]. This phenomenon could be understood considering the well-known Rayleigh jets from electrified droplets when the water/air interface is charged beyond the Rayleigh limit in an electrostatic field. In fact, the jet occurring at the water/oil interface due to the photovoltaic field on the LN:Fe surface was observed by Muñoz-Cortés et al [12]. As mentioned in Ref. [39], the microdroplet undergoes a shape change after the jet because the ejected tiny droplets may carry a large amount of charges. In Fig. 5(e) and 6(e), we show the unusual behaviors of the microdroplets when too short manipulation distance and too high illumination are applied, respectively. There is first an abrupt change of the microdroplet shape, then followed by a fast repelling movement (with an average velocity of several mm/s) of the microdroplet (see Visualization 2). Although we cannot capture the moment of jet due to both the too fast process and the too small sizes of the tiny droplets, we still can attribute these behaviors to the jet from the water microdroplet for two reasons: one is the abrupt microdroplet shape change which agrees well with the feature of the jet; the other is a fast repelling movement of the microdroplet, which indicates the microdroplet that is initially neutral becomes positively charged due to the loss of the negative charges carried by tiny jetting droplets. Note that the charging of the microdroplet results in an instantaneous transition of the electrostatic interaction from the dielectrophoretic (DEP) to electrophoretic (EP) mechanism [25], which leads to the repulsive behavior and makes the microdroplet out of control in the present experiment.

Lately, J. F. Muñoz-Martínez et al. reported the time evolution of the photovoltaic charge density generated on a z-cut LN: Fe surface [29]. Under the laser illumination, the profile of photovoltaic charge density was found to evolve from a simple Gaussian one to a quite complicated profile. In our work, the time evolution of the photovoltaic charge density is neglected because the illumination intensity (∼10⁷ W/m²) used here is at least two orders magnitude higher than in their work, thus the photovoltaic charge density reaches the saturation in a very short time. In addition, the profile of the photovoltaic charge density is also neglected due to the small size of the laser spot as compared to that of water microdroplet. Nevertheless, the effect reported by J. F. Muñoz-Martínez et al. is still quite important to the long-range photovoltaic interaction in the case of patterned illumination where relatively low intensities are used.

In this work, DI (deionized) water microdroplets were selected as manipulating objects. As compared with normal dielectric liquid (∼10⁻¹³ S/m), DI water (∼10⁻⁶ S/m) can be considered definitely as liquid with higher conductivity. However, for biological use of the presented technology, the manipulating microdroplets are often the medium employed for cellular culture, which usually contains a large amount of ions and has a much higher conductivity. To demonstrate the effectiveness of the presented technology on these employed medium, we try the long-range photovoltaic manipulation on microdroplets made of normal saline solution (0.9%), which is a typical medium (∼1.6 S/m) employed for cellular culture. The long-range photovoltaic manipulation is still valid on these aqueous microdroplets. (see Supplement 1, Fig. S2). We also perform the manipulation on microdroplets with much higher NaCl concentrations, and find that the high conductivity only affects a little bit on the illumination-intensity beyond which the Rayleigh jetting of electrified droplets may happen.

By using the long-range photovoltaic interaction, we avoid the close contact between the microdroplet and the LN:Fe crystal, and therefore the heat transfer from the LN:Fe crystal to the microdroplet can be suppressed substantially. During the long-range photovoltaic manipulation, the balance position of the microdroplet always deviates from the illumination center of the transmitted laser beam. This deviation (P_0.6) avoids the direct illumination of the transmitted laser beam on the microdroplet and reduces the illumination intensity suffered by the microdroplet. We measure the laser-induced temperature rise during the long-range photovoltaic manipulation. In Fig. 8, we compare the thermal images of the LN-microdroplet-gap before and after 3-min laser illumination with intensity of 10⁷ W/m². The laser illumination causes a local temperature rise of ∼ 4°C on the LN:Fe crystal while the microdroplet almost shows no temperature increase due to the existence of the air gap between the crystal and the microdroplet. Since the laser illumination has no obvious influence on the microdroplet temperature, the resultant microdroplet evaporation is negligible. At the humidity of 50% and the room temperature, the complete evaporation of a water microdroplet with a volume of 0.45 μL usually takes 30 minutes during the long-range photovoltaic manipulation, which is longer than in a normal case of microdroplet evaporation [40]. The slow evaporation rate of the water microdroplet can be attributed to the two features of the present configuration: one is the suppression of the heat transfer owing to LN-microdroplet-gap, the other is the super-thin oil layer inclosing the microdroplet, which often occurs on the oil-infused membrane and is capable to prevent the microdroplet from evaporation [41].

Fig. 8. Comparison of the thermal images of the LN-microdroplet-gap before (laser off) and after 3-min laser illumination with intensity of 10⁷ W/m² (laser on). The laser illumination causes a local temperature rise of ∼ 4°C on the LN:Fe crystal while the microdroplet almost shows no temperature increase.

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In this work, we used an oil-infused hydrophobic coating, rather than an oil-free super-hydrophobic coating, to support the water microdroplet for two reasons. First, as mentioned above, the super-thin oil layer inclosing the microdroplet can prevent it from evaporation [41]. Second, the direct friction between the water microdroplet and an oil-free super-hydrophobic surface often charges the microdroplet through the contact-electrification (CE) effect, resulting in two possible states (Onsite/Offsite) of the microdroplet under an electrostatic field [42]. Since the Onsite state of the microdroplet has a very low adhesion on the oil-free super-hydrophobic substrate, the microdroplet may be attracted away from the substrate surface due to the vertical component of the electrostatic field, which is definitely unfavorable to the stability of the long-range photovoltaic manipulation. By contrast, on the oil-infused hydrophobic substrate the oil lubrication makes the microdroplet moving always in a slippery mode where no charging can happen. Moreover, the drag force of lubricating oil to the water microdroplet is sufficient to prevent it from being attracted away vertically. With a super-hydrophobic coating to reduce frictional force the performance of the system could be better, but it takes a risk of unstable or failed manipulation. It should be noted that in the theoretical analysis of the force balance we did not consider the influence of the vertical DEP force (F_DEP-v) on the manipulation of the microdroplet. This is because in our case where the weight (W) of the water microdroplet is negligible as compared to the electrostatic force [20] the frictional force acting on the microdroplet originates mainly from the fluid friction and skin friction and it is more sensitive to the fluid viscosity [43] rather than the applied load, i.e. W-F_DEP-v. As shown in Fig. 5, the gap between the glass slide and the LN substrate may influence on the performance of microdroplet manipulation, but the relevant mechanism is more connected with F_DEP-x than F_DEP-v.

For LN:Fe crystals, the photovoltaic charges induced by the laser illumination remains in the material for a long time. If only the photovoltaic charges are considered, it is impossible to make the microdroplet untrapped in a short time by stopping the laser illumination. As mentioned in the theoretical section, the pyroelectric charges are negligible as long as the photoconductivity is sufficient large. However, upon the stop of the laser illumination (the photoconductivity is absent at this moment) the pyroelectric charges may take an effect. In fact, we always observed a fast decay (in several seconds) of the photovoltaic field after we stopped the laser illumination, which can be attributed to the rapid compensation between the photovoltaic charges previously accumulated during the laser illumination and the pyroelectric charges newly generated during the sudden cooling (usually a few centigrade) of the LN:Fe crystal upon the stop of the laser illumination. This fast decay of the electrostatic field may result in a significant decrease of the maximal manipulation distance (MMD), making the current microdroplet untrapped immediately. Besides, there are another two ways to untrap the microdroplet more quickly. One is to lower the substrate, i.e. to increase distance (D) till it exceeds the value of MMD and the trapping becomes non-effective. The other one is to speed up the decay of photovoltaic charges by either increasing the dark conductivity of the crystal bulk [5] or enhancing the external charge compensation from the ambient air [10]. As the super-fast decay of the photovoltaic charges is quite important for lab-on-chip applications that require time-to-time manipulation of microdroplets, the further tuning of the photovoltaic properties of LN:Fe crystals is necessary in the future [5,44,45].

The force provided by the photovoltaic interaction is generally in the level of μN, which is consistent with the result of Puerto et al [13]. The level of this optoelectronic force is much higher than that (∼pN) of radiation pressure or gradient employed by the conventional optical tweezer [46], and it is thus an advantage of the present technique in manipulating μL-level microdroplets where the viscous or drag forces in the μN-level usually have to be overcome. In addition, the high illumination intensity of 10⁷ W/m² is used to achieve the long-range (4 mm) photovoltaic manipulation in this work. If we decrease the intensity to a low level, for example, 10⁴∼10⁶W/m² [13], then the distance for a stable photovoltaic manipulation will be decreased to about 1 mm. Note that the high intensity of 10⁷ W/m² might be not suitable for the configuration in Ref. [13], because too strong photovoltaic field could induce a violent convention in the oil media and makes the microdroplet manipulation at air/oil interface unstable.

6. Conclusion

In this paper, we demonstrate a successful manipulation of a water microdroplet on a hydrophobic substrate by utilizing a long-range photovoltaic interaction from a distant LN:Fe crystal. It is found that the maximal distance for a critical manipulation follows a nonlinear function of the illumination intensity at the LN:Fe crystal, and in particular, the manipulation distance can be tuned up to a sub-centimeter level (∼4 mm) in the intensity range (∼10⁷ W/m²) available in our experiments. Either shortening the manipulation distance and increasing the illumination intensity can enhance the photovoltaic interaction and increase the velocity of the microdroplet being manipulated. In addition, an abrupt shape change followed by a fast repelling movement of water microdroplet is observed under a strong photovoltaic interaction, and it is attributed to an instantaneous transition of the electrostatic interaction from the dielectrophoretic (DEP) to electrophoretic (EP) mechanism. The reported technique has a potential to solve the practical problems existing in the relevant biological applications, and is of great importance to the hybrid and heating-avoided design of various complicated biological lab-on-chips.

Funding

Natural Science Foundation of Hebei Province (No. F2020202037); National Natural Science Foundation of China (No. 11874014).

Acknowledgment

We thank Prof. Yongfa Kong for his help on sample preparation, and we also thank the reviewers for their valuable comments.

Disclosures

The authors declare no conflicts of interest.

Supplemental document

See Supplement 1 for supporting content.

References

1. L. Metzler, U. Rehbein, J. N. Schonberg, T. brandstetter, K. Thedieck, and J. Ruhe, “Breaking the Interface: Efficient Extraction of Magnetic Beads from Nanoliter Droplets for Automated Sequential Immunoassays,” Anal. Chem. 92(15), 10283–10290 (2020). [CrossRef]

2. N. T. Nguyen and T. D. Luong, “Surface Acoustic Wave Driven Microfluidics – A Review,” Micro Nanosyst. 2(3), 217–225 (2010). [CrossRef]

3. P. Y. Keng, S. P. Chen, H. J. Ding, S. Sadeghi, G. J. Shah, A. Dooraghi, M. E. Phelps, N. Satyamurthy, A. F. Chatziioannou, C. J. Kim, and R. M. Van Dama, “Micro-chemical synthesis of molecular probes on an electronic microfluidic device,” Proc. Natl. Acad. Sci. U. S. A. 109(3), 690–695 (2012). [CrossRef]

4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288 (1986). [CrossRef]

5. Y. Kong, F. Bo, W. Wang, D. Zheng, H. Liu, G. Zhang, R. Rupp, and J. Xu, “Recent Progress in Lithium Niobate: Optical Damage, Defect Simulation, and On-Chip Devices,” Adv. Mater. 32(3), 1806452 (2020). [CrossRef]

6. P. Minzioni, R. Osellame, C. Sada, S. Zhao, F. G. Omenetto, K. B. Gylfason, T. Haraldsson, Y. B. Zhang, A. Ozcan, and A. Wax, “Roadmap for optofluidics,” J. Opt. 19(9), 093003 (2017). [CrossRef]

7. T. Yang, P. Paiè, G. Nava, F. Bragheri, R. M. Vazquez, P. Minzioni, M. Veglione, M. D. Tano, C. Mondello, R. Osellame, and I. Cristiani, “An integrated optofluidic device for single-cell sorting driven by mechanical properties,” Lab Chip 15(5), 1262–1266 (2015). [CrossRef]

8. A. Blázquez-Castro, A. García-Cabañes, and M. Carrascosa, “Biological applications of ferroelectric materials,” Appl. Phys. Rev. 5(4), 041101 (2018). [CrossRef]

9. B. Fan, F. Li, L. Chen, L. Shi, W. Yan, Y. Zhang, S. Li, X. Wang, X. Wang, and H. Chen, “Photovoltaic Manipulation of Water Microdroplets on a Hydrophobic LiNbO₃,” Phys. Rev. Appl. 7(6), 064010 (2017). [CrossRef]

10. K. Gao, X. Zhang, Z. Zan, Z. Gao, E. Mugisha, L. Shi, Y. Ma, F. Li, C. Liang, M. Ren, H. Chen, and W. Yan, “Visible-light-assisted condensation of ultrasonically atomized water vapor on LiNbO₃:Fe crystals,” Opt. Express 27(26), 37680–37694 (2019). [CrossRef]

11. X. Zhang, K. Gao, Z. Gao, Z. Zan, L. Shi, X. Liu, M. Wang, H. Chen, and W. Yan, “Photovoltaic splitting of water microdroplets on a y-cut LiNbO₃: Fe crystal coated with oil-infused hydrophobic insulating layers,” Opt. Lett. 45(5), 1180–1183 (2020). [CrossRef]

12. E. Muñoz-Cortés, A. Puerto, A. Blázquez-Castro, L. Arizmendi, J. L. Bella, C. López-Fernández, M. Carrascosa, and Á García-Cabañes, “Optoelectronic generation of biological aqueous solution femto-droplets based on the bulk photovoltaic effect,” Opt. Lett. 45(5), 1164–1167 (2020). [CrossRef]

13. A. Puerto, A. Méndez, L. Arizmendi, A. García-Cabañes, and M. Carrascosa, “Optoelectronic Manipulation, Trapping, Splitting, and Merging of Water Droplets and Aqueous Biodroplets Based on the Bulk Photovoltaic Effect,” Phys. Rev. Appl. 14(2), 024046 (2020). [CrossRef]

14. Á García-Cabañes, A. Blázquez-Castro, L. Arizmendi, F. Agulló-López, and M. Carrascosa, “Recent Achievements on Photovoltaic Optoelectronic Tweezers Based on Lithium Niobate,” Crystals 8(2), 65 (2018). [CrossRef]

15. W. S. Yan, D. F. Zhao, L. Zhang, R. Jia, N. K. Gao, D. D. Zhang, W. Y. Luo, Y. L. Li, and D. Liu, “Optically induced reversible wettability transition on single crystal lithium niobate surfaces,” Appl. Phys. Lett. 111(9), 091603 (2017). [CrossRef]

16. C. Sebastián-Vicente, E. Muñoz-Cortés, Á García-Cabañes, F. Agulló-López, and M. Carrascosa, “Real-Time Operation of Photovoltaic Optoelectronic Tweezers: New Strategies for Massive Nano-object Manipulation and Reconfigurable Patterning,” Part. Part. Syst. Charact. 36(9), 1900233 (2019). [CrossRef]

17. M. Carrascosa, A. García-Cabañes, M. Jubera, J. B. Ramiro, and F. Agulló-López, “LiNbO₃:A photovoltaic substrate for massive parallel manipulation and patterning of nano-objects,” Appl. Phys. Rev. 2(4), 040605 (2015). [CrossRef]

18. L. Chen, S. Li, B. Fan, W. Yan, D. Wang, L. Shi, H. Chen, D. Ban, and S. Sun, “Dielectrophoretic behaviours of microdroplet sandwiched between LN substrates,” Sci. Rep. 6(1), 29166 (2016). [CrossRef]

19. L. Chen, B. Fan, W. Yan, S. Li, L. Shi, and H. Chen, “Photo-assisted splitting of dielectric microdroplets in a LN-based sandwich structure,” Opt. Lett. 41(19), 4558–4561 (2016). [CrossRef]

20. F. Li, X. Zhang, K. Gao, L. Shi, Z. Zan, Z. Gao, C. Liang, E. R. Mugisha, H. Chen, and W. Yan, “All-optical splitting of dielectric microdroplets by using a y-cut-LN-based anti-symmetrical sandwich structure,” Opt. Express 27(18), 25767–25776 (2019). [CrossRef]

21. M. Gazzetto, G. Nava, A. Zaltron, I. Cristiani, C. Sada, and P. Minzioni, “Numerical and Experimental Study of optoelectronic Trapping on Iron-Doped Lithium niobate Substrate,” Crystals 6(10), 123 (2016). [CrossRef]

22. X. Zhang, J. Wang, B. Tang, X. Tan, R. A. Rupp, L. Pan, Y. Kong, Q. Sun, and J. Xu, “Optical trapping and manipulation of metallic micro/nanoparticles via photorefractive crystals,” Opt. Express 17(12), 9981–9988 (2009). [CrossRef]

23. M. Esseling, A. Zaltron, W. Horn, and C. Denz, “Optofluidic droplet router,” Laser Photon. Rev. 9(1), 98–104 (2015). [CrossRef]

24. J. F. Muñoz-Martínez, I. Elvira, M. Jubera, A. García-Cabañes, J. B. Ramiro, C. Arregui, and M. Carrascosa, “Efficient photo-induced dielectrophoretic particle trapping on Fe:LiNbO₃ for arbitrary two dimensional patterning,” Opt. Mater. Express 5(5), 1137–1146 (2015). [CrossRef]

25. J. F. Muñoz-Martínez, J. B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Electrophoretic versus dielectrophoretic nanoparticle patterning using optoelectronic tweezers,” Phys. Rev. Appl. 7(6), 064027 (2017). [CrossRef]

26. T. C. Sung, H. C. Su, Q. D. Ling, S. S. Kumar, Y. Chang, S. T. Hsu, and A. Higuchi, “Efficient differentiation of human pluripotent stem cells into cardiomyocytes on cell sorting thermoresponsive surface,” Biomaterials 253, 120060 (2020). [CrossRef]

27. N. P. Williams, M. Rhodehamel, C. Yan, A. S. T. Smith, A. Jiao, C. E. Murry, M. Scatena, and D. H. Kim, “Engineering anisotropic 3D tubular tissues with flexible thermoresponsive nanofabricated substrates,” Biomaterials 240, 119856 (2020). [CrossRef]

28. J. Friguglietti, S. Das, P. Le, D. Fraga, M. Quintela, S. A. Gazze, D. Mcphail, J. H. Gu, O. Sabek, A. O. Gaber, L. W. Francis, W. Zagozdzon-Wosik, and F. A. Merchant, “Novel Silicon Titanium Diboride Micropatterned Substrates for Cellular Patterning,” Biomaterials 244, 119927 (2020). [CrossRef]

29. J. F. Muñoz-Martínez, A. Alcázar, and M. Carrascosa, “Time evolution of photovoltaic fields generated by arbitrary light patterns in z-cut LiNbO₃: Fe application to optoelectronic nanoparticle manipulation,” Opt. Express 28(12), 18085–18102 (2020). [CrossRef]

30. P. Ferraro, S. Coppola, S. Grilli, M. Paturzo, and V. Vespini, “Dispensing nano–pico droplets and liquid patterning by pyroelectrodynamic shooting,” Nat. Nanotechnol. 5(6), 429–435 (2010). [CrossRef]

31. S. Grilli, L. Miccio, O. Gennari, S. Coppola, V. Vespini, L. Battista, P. Orlando, and P. Ferraro, “Active accumulation of very diluted biomolecules by nano-dispensing for easy detection below the femtomolar range,” Nat. Commun. 5(1), 5314 (2014). [CrossRef]

32. S. Coppola, G. Nasti, M. Todino, F. Olivieri, V. Vespini, and P. Ferraro, “Direct Writing of Microfluidic Footpaths by Pyro-EHD Printing,” ACS Appl. Mater. Interfaces 9(19), 16488–16494 (2017). [CrossRef]

33. X. Tang and L. Q. Wang, “Loss-Free Photo-Manipulation of Droplets by Pyroelectro-Trapping on Superhydrophobic Surfaces,” ACS Nano 12(9), 8994–9004 (2018). [CrossRef]

34. L. Mecozzi, O. Gennari, S. Coppola, F. Olivieri, R. Rega, B. Mandracchia, V. Vespini, A. Bramanti, P. Ferraro, and S. Grilli, “Easy Printing of High Viscous Microdots by Spontaneous Breakup of Thin Fibers,” ACS Appl. Mater. Interfaces 10(2), 2122–2129 (2018). [CrossRef]

35. W. Li, X. Tang, and L. Q. Wang, “Photopyroelectric microfluidics,” Sci. Adv. 6(38), eabc1693 (2020). [CrossRef]

36. A. Puerto, J. F. Munoz-Martin, A. Mendez, L. Arizmendi, A. Garcia-Cabanes, F. Agullo-Lopez, and M. Carrascosa, “Synergy between pyroelectric and photovoltaic effects for optoelectronic nanoparticle manipulation,” Opt. Express 27(2), 804–815 (2019). [CrossRef]

37. X. Yue, S. Mendricks, T. Nikolajsen, H. Hesse, D. Kip, and E. Kratzig, “Transient enhancement of photorefractive gratings in lead germanate by homogeneous pyroelectric fields,” J. Opt. Soc. Am. B 16(3), 389 (1999). [CrossRef]

38. B. Sturman, M. Carrascosa, and F. Agullo-Lopez, “Light-induced charge transport in LiNbO3 crystals,” Phys. Rev. B 78(24), 245114 (2008). [CrossRef]

39. D. Duft, T. Achtzehn, R. Muller, B. A. Huber, and T. Leisner, “Coulomb fission: Rayleigh jets from levitated microdroplets,” Nature 421(6919), 128 (2003). [CrossRef]

40. S. Dash and S. V. Garimella, “Droplet evaporation on heated hydrophobic and superhydrophobic surfaces,” Phys. Rev. E 89(4), 042402 (2014). [CrossRef]

41. J. P. Cao, Q. An, Z. P. Liu, M. L. Jin, Z. B. Yan, W. J. Lin, L. Chen, P. F. Li, X. Wang, G. F. Zhou, and L. L. Shui, “Electrowetting on liquid-infused membrane for flexible and reliable digital droplet manipulation and application,” Sens. Actuators, B 291, 470–477 (2019). [CrossRef]

42. H. Y. Dai, C. Goo, J. H. Sun, C. X. Li, N. Li, L. Wu, Z. C. Dong, and L. Jiang, “Controllable High-Speed Electrostatic Manipulation of Water Droplets on a Superhydrophobic Surface,” Adv. Mater. 31(43), 1905449 (2019). [CrossRef]

43. Y. Guan and A. Y. Tong, “A numerical study of microfluidic droplet transport in a parallel-plate electrowetting-on-dielectric (EWOD) device,” Microfluid. Nanofluid. 19(6), 1477–1495 (2015). [CrossRef]

44. J. Sun, Y. Hao, L. Zhang, J. Xu, and S. Zhu, “Brief review of lithium niobate crystal and its applications,” J. Synth. Cryst 49(260), 947–964 (2020).

45. L. Xue, H. Liu, D. Zheng, S. Shahzad, H. Yu, S. Liu, S. Chen, L. Zhang, Y. Kong, and J. Xu, “Study on photorefractive properties of near-stoichiometric lithium niobate crystals doped with molybdenum,” J. Synth. Cryst 49(255), 21–26 (2020).

46. K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5(6), 491–505 (2008). [CrossRef]

Hydrophobic-substrate based water-microdroplet manipulation through the long-range photovoltaic interaction from a distant LiNbO₃:Fe crystal

Abstract

1. Introduction

2. Experiments

3. Theoretical background and analysis

4. Results

5. Discussions

6. Conclusion

Funding

Acknowledgment

Disclosures

Supplemental document

References

Supplementary Material (3)

Cited By

Figures (8)

Equations (15)

Optics Express

Name	Description
Supplement 1	Supplemental document
Visualization 1	Long-range photovoltaic manipulation of a water microdroplet
Visualization 2	Abrupt shape change and fast repelling movement of water microdroplet under a strong photovoltaic interaction