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We present an experimental study on oscillation of absorbing particles at the water-air interface. The oscillation is induced by laser tweezers, which are generated with a high numerical aperture objective. When the laser beam is tightly focused at the water-air interface, the optical gradient force attracts the particles to the spot center, and the laser heating of particles results in a strong thermal gradient that drives the particles to leave the spot center. Under the action of thermal and optical gradient force together, the absorbing particles oscillate at the water-air interface.
© 2017 Optical Society of America
1. Introduction
Optical tweezers are used to trap and manipulate microparticles in different surrounding media, such as in aqueous solution, in air or within living animals [1–8]. When the laser beam is focused weakly by a low numerical aperture (NA) microscope objective, it can form a two- dimensional (2D) optical trap at the liquid-liquid interface. Besides optical gradient force, the focused laser beam also bring thermal gradient induced by optical absorption of particles or surrounding medium. The resulting thermal gradient is a matter of concern, and is also widely applied in manipulating dispersed particles [9–15].
For most of 2D optical trapping at the interface, either the optical trapping force, or heat absorption dominates the particles' behavior. When a transparent particle is located at the interface, the optical forces govern the particles' behavior and attract the particles to the trap center similar to 3D trapping [16–18]. When the laser absorbing particles are located at the interface, the optical gradient forces are weak and the motions of particles are intensively affected by the interfacial properties. It is surprising that the absorbing particle behaves as a microswimmer orbiting around the axis of laser beam at the interface [19]. However, there is little information about the both strong thermal and optical gradient force on particles at the water-air interface. The lack of information can be attributed to the short working distance (WD) of high NA objective. It is difficult to reach the water-air interface for a high NA objective because the WD is generally limited. When the laser beam is tightly focused at the interface, both the thermal and optical gradient forces have intensive influence on the behavior of the particles. The motions of particles will be different from that in the previous investigation [16–19] under the action of two forces.
In this paper, we investigate the behavior of absorbing particles at the water-air interface under the cooperative action of strong thermal and optical gradient forces from tightly focused laser beam. The strong thermal gradient force is induced by high laser power and the strong absorption properties of the particles. In addition, the strong optical gradient force is generated by a high NA objective with long working distance, which can reach the water-air interface.
2. Experiment method
Our optical tweezers setup is based on an inverted universal infinity-corrected microscope, as shown in Fig. 1. A continuous-wave (CW) laser (linearly polarized, 1064-nm, Amonics, Hong Kong, AFL-1064-37-R-CL) is used as the trapping laser source. The laser power is controlled by adjusting the input current, and the laser power are measured at the pupil of the objective in the paper. The laser beam is expanded by a beam expander (BE) to full fill the pupil of microscope objective. Lens L1 focuses the laser beam to the conjugate point of the microscope objective as shown in Fig. 1 after the beam is reflected by mirrors M1 and M2. The laser beam is then directed into the microscope and reflects upward by a dichroic mirror, and refocuses into the sample after passing through lens Ltube (Ltube is the tube lens inside the microscope) and a microscope objective (LUMFLN, water immersion, 60 × , NA = 1.1, WD = 1.5 mm, Olympus, Japan). The transmittance of the objective is about 60% at wavelength of 1064-nm. The images are recorded by a CMOS camera (7 frames per second), and acquired by movie capture software.
Fig. 1 Optical tweezers setup. Instrument layout showing optical paths for 1064 nm trapping laser and halogen lamp for bright-field imaging. BE, beam expander; L1, lens; M1-M2, mirrors; DM, dichroic mirror; Ltube, tube lens; MO, microscope objective; CMOS, CMOS camera. Inset: side view of the circular trough.
The samples are a diluted suspension of particles. The core-shell magnetic microspheres (PSC, polystyrene@Fe3O4, 4.0-5.0 μm in diameter, BaseLine Company) are used in the experiment. The beads are suspended in aqueous solution. The water-air interface is prepared using a homemade circular trough with an inner diameter of 10 mm and height of 1 mm. 40μL of diluted suspension is injected into the trough and sealed with two coverslips. The height of the water-air interface is about 500 μm, in which the microscope objective can work at. In our experiment, the particles in water are trapped to the water-air interface by the optical tweezers at low power firstly. Upon reaching the interface, the particles are located by surface tension. The experiments are performed at room temperature.
3. Results and discussion
3.1 Unstable 3D-trapping at high power
The optical tweezers can trap a single PSC microparticle stably in three dimensions with low laser power [20]. When the laser power is larger than 200 mW, the laser induced thermal effect becomes very serious, and the PSC particle escapes from the optical trap. As shown in Fig. 2(a), a PSC particle is initially trapped in the aqueous solution at power of 110 mW. When the laser power is increased to 200 mW, the particle leaves the optical trap. The particle is pushed above the image plane at first as shown in Fig. 2(b), and then pushed away from the trap center quickly in as shown in Fig. 2(c). The optical tweezers cannot trap any PSC particles in water solution when the power is larger than 200mW. When the particles are attracted and gradually moving to the trap center by the optical gradient force, they are repelled to leave the trap center by the laser heating and consequent flow quickly.
Fig. 2 (a-c) Images of a trapped PSC particle escaping from the 3D-trap at high power. (d) Laser induced thermal damage to surface of the particle. Scale bar, 5 μm; ' + ' indicates the optical trap center.
Particles can be stably trapped in water by optical tweezers at low power because the optical gradient force is larger than the thermal gradient force. There may be two main reasons can be responsible for no longer trapping the particles at large laser power. First, there is laser induced thermal damage to the particle. After the particle in Fig. 2(a) leaving the optical trap, we adjust the position of objective to watch the particle. It can be seen that the thermal damage has changed the particle shape, as shown in Fig. 2(d), which results in the decreasing of optical force. The axial optical force is insufficient to balance the thermal gradient force again, so the particle escapes from the trap in axial direction. Second, the gas adsorbed at the surface of particles is heated to form bubbles when the particles is close to the trap center. The volume of bubbles is increasing rapidly, which destroys the stability of the liquid environment around the optical trap. The strong perturbation makes the trap unable to hold the particles stably in three-dimension. The particles leave the trap center quickly in aqueous solution while the bubble is small, so the bubble formation is not observable. When the particles are held at a 2D interface, the processes of the bubbles formation can be observed because the particles are restricted in axial direction and always at the image plane. As shown in Fig. 3 and Visualization 1, the bubble volume is quickly increased at high laser power. In our experiment, the gas bubbles are always adhered to the PSC particles during the bubbles formation. We think that the bubbles are mainly from gases at the surface of particles due to the high temperature at particles’ surface. Furthermore, the laser heating can also induce gas bubbles in the solution, which will affect the stable optical trapping. However, these bubbles will leave the optical trap due to the buoyancy and it is difficult to observe the bubble formation in the solution.
Fig. 3 Bubble volume increasing because of laser absorption of particle at the water-air interface (see Visualization 1). The white arrows mark the bubble. Scale bar, 5 μm; ' + ' indicates the optical trap center.
3.2 Oscillation at the water-air interface
At low power, the PSC particles are trapped at the position very close to the spot center at water-air interface. However, the particles oscillate at the water-air interface when the power is large. The oscillation process can be described as following briefly. At first, the particle moves towards the trap center from the position outside the beam waist. The particle is attracted by the optical gradient force, which can attract the particles from the distance much larger than the beam waist of focus spot [21–23]. With the thermal gradient force increasing, the velocity gradually decreases to 0 at the first oscillation peak close to the spot center. And then, the particle moves in the direction opposite to the temperature gradient with a large velocity. Under the action of optical gradient force and viscous drag force, the particle velocity is reduced to 0 again at the other oscillation peak. The particle is attracted by the optical force and moves toward the spot center again. The particles are repeatedly attracted and repelled at the interface.
It is important for the particles to be held in two-dimension against the water-air interface to prevent them from escaping the trap in axial direction. If the particle is in immersed in water, the particles will leave the action range of optical tweezers axially and will not oscillate without the blocking of interface. As shown in Figs. 4(a)-4(e) and Visualization 2, the particle moves at a velocity of about 3.5 μm/s towards the trap center at first, and stops moving at a distance of about 0.5 μm from the trap center. Then the particle is repelled away from the trap center at a velocity of about 25.5μm/s, and stops moving at a distance of about 6 μm from the trap center. The motion trajectory of the particle has been shown in Fig. 4(f). It can be seen that the oscillation period is about 1.3 seconds.
Fig. 4 Oscillation of an absorbing particle at the water-air interface. The laser power is 200 mW at the pupil of the objective. (a-e) Video sequences showing movement of the particle (see Visualization 2). The black arrows indicate the direction of particle movement. Scale bar, 5 μm; ' + ' indicates the optical trap center. (f) Motion trajectory of the particle. Rin and Rout are the two oscillation peaks.
In the experiment, some particles do not oscillate at the power 200 mW. However, when the laser power is creased to 600 mW, most of the particles behave as oscillators and few particles do not oscillate. We check the non-oscillation particles by focusing laser beam on them, and find that they cannot be repelled away from the spot center. We think the non-oscillation particles have been adhered to the water-air interface.
3.3 Particle parameters
The particle with density 1.463 g/cm3, is a spherical polystyrene core, surrounded by an absorbing spherical shell. The core is made of pure polystyrene (ps), of density ρps and the shell is made of pure iron oxide. With ρps = 1.05 and ρps = 5.24 g/cm3, the volume fraction of the polystyrene X is 0.9 according to the particle structure. With nps = 1.59 and nox = 2.20 + 0.60i, the effective refractive index of the particle is neff = nps·X + (1-X)nox = 1.65 + 0.06i [19].
The scattering cross-section determines the radiation pressure force pushes the particle out of the trap in the direction of beam propagation. The absorption cross-section determines the amount of light absorbed by the particle and the consequent light-induced heating that a trapped particle undergoes [24]. The scattering cross-section is equal to the absorption cross-section of the particles, 5 × 10−13 m2, calculated by the definition of scattering and absorption cross-section and Clausius-Mossotti relation [24]. It means that the optical attracting force and thermal gradient force are in the same order of magnitude because the optical gradient force is equal to the scattering force for stable optical trapping. The PSC particles oscillate at the interface under the optical and thermal gradient force.
The volume fraction of the iron oxide may affect the laser heating. For the particles with small volume fraction of the iron oxide, it is necessary to increase the laser power to increase the thermal gradient forces because their absorption cross-sections are small. In addition, the oscillations of the particles are affected by the interface stability. The particles are difficult to oscillate when the water at the interface flows fast. Furthermore, we think that the oscillations of PSC particles are dependent on the size of particles. When the size of the particle is very small, the volume fraction of iron oxide is large due to surface effect. The absorption cross-section is much smaller than scattering cross-section, and the thermal gradient force is much smaller than optical gradient force, which will repel the particles moving away from the trap center and the oscillation will be not observed.
3.4 Model for particle's oscillation
The laser induced thermal damage presumably happens when the temperature at the surface of particle reaches about 100 °C, which is close to the glass transition temperature of polystyrene [19], so we think that the temperature is about 100 °C at the trap center, and the temperature rise is about 75 °C induced by laser heating of particle. The temperature at the beam waist is equal to the room temperature since the temperature rise is linear to laser intensity. The temperature rise induced by water absorption is estimated using the method investigated by Mao and associates [25], is about 3 °C when the laser power is 200 mW, which is negligible compared to the temperature rise by laser heating of the PSC particle.
The thermal motions of particles at the interface are mainly caused by the laser heating of the particles. What we believe to be the geometry for the modeling of the oscillation of absorbing particle, is sketched in Fig. 5(a). The spot center is set as the ordinate origin. The laser beam is assumed to have a Gaussian intensity distribution at the focused spot:
where I0 is the intensity at the center of the beam and ω0 is the beam waist of laser beam at the focal point, is 0.6 μm. The laser absorption is assumed to happen when the edge of the particle crosses the beam waist. A particle at the position of Rout is exerted by the trapping force Fo, and begin moving to the trap center. Before the particle arrives at the waist of laser beam, the particle is exerted by the trapping force and viscous drag force Fs. When the particle crosses the beam waist, the velocity is gradually decreased to 0 at the position of Rin due to the action of thermal gradient force FT and viscous drag force. The absorption difference at the particle surface induces a strong thermal gradient force, which accelerates the particle to a large velocity vT in a very short time. The heat induced by the particle's absorption is transformed into kinetic energy, which drives the particle flowing out of beam waist. The particle's velocity in the position Rout decreases to 0 under the action of the optical force and viscous drag force.Fig. 5 (a) Schematic view of oscillation of a PSC particle (not same scale). The beam has a Gaussian intensity distribution. (b) Relation of the two distance peaks of oscillation.
A particle drifts along the temperature gradient at speed [26]
where DT is the coefficient of thermal diffusion, ST is the Soret coefficient, is on the order of 10 K−1 for micrometer-sized particles [27], D0 is the diffusion coefficient of the particle, can be given by the Stokes-Einstein relation , with kB the Boltzmann constant, a the radius of particle. The velocity given by Eq. (2) is negative, which means that the particle moves in the direction opposite to the temperature gradient. With the parameters of water at 100 °C [28], η = 2.8 × 10−4 Pa·s, and 30 K/μm, the vT is about 100 μm/s. The experimental velocity about 20 μm/s at the interface may be accounted for the missing of correction factor on the Stokes drag resulting from the presence of the interface.Because the optical stiffness is linearly increased with laser power, we measure the optical stiffness at low power with viscous drag method [29], which can be used to evaluate the optical force at high power. The transverse optical stiffness kop is about 0.08 pN/(μm·mW). For the particle at Rin = 0.5 μm in Fig. 4(f), the optical force Fo = kop·P·Rin = 4.8 pN, and the thermal gradient force can be calculated by [27], is about 28 pN. The particle will be accelerated to a large velocity in a short time because FT is much larger than Fo at the position of Rin.
The relation of Rout and Rin for each repulsion has been shown in Fig. 5(b). It can be seen that Rout decreases drastically with increasing Rin. For a rough approximation, we assume that the laser is strongly absorbed only by the particle when it cross the beam waist. At the position of Rin, the heat energy is transformed into kinetic energy of the particle. At the position Rout, the heat absorbed energy at Rin is transformed into the potential energy of optical trap,, so Rout can be written as
which is proportional to . Because the temperature rise ΔT is proportional to the light intensity I, Rout is proportional to light intensity I according to Eq. (2) and Eq. (3). The relationship between Rout and Rin can be fitted using the Gaussian distribution function. The fitting curve in Fig. 5(b) shows that our proposed explanation is basically consistent with the actual situation, and confirms that the thermal motion of the particles is mainly due to the thermal gradient resulting from the laser absorbing of PSC particles.The precise model is highly complicated and our model is only a rough approximation. The heating is not a continuous one but accidental only when the particle will cross the beam waist. The acceleration is at maximum at some distance from the heating event, and then drag force, ST dependency on the absolute temperature and bead’s inertia decide about the real velocity which is time and position dependent. Furthermore, because the water surface tension is decreased with temperature increasing, there is a combined buoyant-Marangoni flow at the surface of water, which will affect the velocity [30]. Due to the complexity of interfacial properties, it is necessary to record more details of the particle motion with a fast camera. If more displacement information is recorded, more thermal parameters of located region could be obtained by analyzing the repelled process by thermal gradient force.
4. Conclusion
In conclusion, we present the oscillations of absorbing particles induced by laser tweezers at the water-air interface in this paper. In general, laser tweezers trap and manipulate the micrometer-sized particles at the water-air interface with a low numerical aperture objective. Here we trap the absorbing particles with a high numerical aperture objective. The results show that the absorbing particles can be trapped three-dimensionally in water at low laser power, but the three-dimensional trapping of absorbing particles in aqueous solution becomes unstable at high power. Furthermore, when the absorbing particles are located at a water-air interface, the strong absorption of particles will induce strong thermal gradient forces, which propel the particles to leave the trap center. Under the action of thermal and optical gradient force together, the absorbing particles oscillate at the water-air interface. In the oscillation process, the velocity repelled from trap center at the interface is 10 μm/s scale. The smaller entrance distance Rin, the larger following repulsion distance Rout from trap center for each oscillation. The dependency of Rout on Rin can be deduced to the difference of absorbing power at Rin from the laser beam with Gaussian intensity distribution. The results in this paper are useful for optical trapping of absorbing particles, which can be employed to detect the thermal and mechanical properties at a local region.
Funding
National Natural Science Foundation of China (NSFC) (11302220, 61535011 and 11374292).
Acknowledgments
The manuscript has been greatly improved by addressing the constructive comments and suggestions made by two anonymous reviewers, whom we would like to thank for their time and efforts.
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