We demonstrate a method for the optical trapping of solid aerosol particles. Suspension of silica particles in ethanol allows their delivery to the trapping volume using a commercial medical nebulizer. The ethanol quickly evaporates, leaving the solid particles trapped in air. We use the technique to make comparisons between aerosol and colloid tweezing through power spectra analysis of the particle’s positions fluctuations for identical particles trapped in a water or air suspending medium.
© 2008 Optical Society of America
Optical tweezers  have become an important tool in a wide range of applications, [2, 3] and offer convenient non-contact manipulation and measurement techniques across the spectrum of the physical, biological and chemical sciences. One of the emerging niche roles for such tools is in the study of airborne aerosols [4, 5]. This work has grown out of a body of work making use of optical radiation pressure based optical levitation [6, 7, 8] to study aerosol properties [9, 10, 11]. The advantages that optical tweezers, making use of high numerical aperture (NA) microscope objectives, offer over optical levitation  include improved particle localization, better particle control and movement, the ability to control multiple particles  and integration with the wide range of powerful analysis techniques developed for optical tweezers as well as the ability to sample smaller particle sizes.
To date work using optical tweezers to trap aerosols has largely focused on liquid aerosols  and as much of the aerosol content in the atmosphere is solid there is clearly an interest in developing techniques for trapping solid particles. Previous methods of optically tweezing  and optically levitating  solid aerosol particles used a piezoelectric element to vibrate a microscope slide covered with silica spheres. Particle oscillation forced the particles into a trap, using a conventional non-inverted optical tweezers, focused just above the sample plane. This method suffers from issues associated with particles sticking to each other, appears difficult to replicate reliably, and is not suited to environmental sampling.
Building on our previous work looking at nebulized liquid aerosols  we show that by nebulizing solid particles using ethanol as a suspending medium [16, 17] we are able to trap the solid aerosols in an inverted single beam gradient force trap. This provides a simple method of introducing solid aerosol into the trapping volume and can be used for nearly any optical tweezers geometry (unlike the oscillating surface methods). The interaction of optical tweezers with colloidal particles in liquid is well understood but this is not true of gas phase systems . Here we take the opportunity, for the first time, to directly compare trapping parameters in air to that of particles suspended in water using a back focal plane interferometry technique to precisely monitor the particles position . Based upon work by Ghislain, et al.,  a photodiode is used to measure amplitude changes in transmitted light from the trapping beam, corresponding to particle displacements in the optical plane of the laser trap. Such displacement measurements can be converted into a power spectrum, characteristic of the particle and trap.
An optically trapped particle can be treated as a damped harmonic oscillator whose position is described by the Langevin equation ;
where m is particle mass, γ 0=6πηR the stokes drag, κ the optical trap stiffness, η, the medium’s dynamic viscosity, R, the particle radius and λ, the Brownian stochastic force.
For the particles studied here the characteristic time for loss of kinetic energy through friction, tinert=m/γ0, for a particle in water, is a lot shorter than our experimental time resolution . However, when trapping in air this timescale is longer than or equal to the resolution, so we must carefully choose the form of Langevin equation we use in each case. For an optically trapped particle in air we must retain the full Langevin equation giving
which when solved gives the power spectrum of position fluctuations, where inertial effects can be observed, to be
where Ω=(κ/m)0.5, Γ=γ0/Ccm, and Cc is the slip correction factor to the drag coefficient. When trapping in water the inertial term is neglected to give the simplified Langevin
giving the power spectrum for a particle trapped in an environment neglecting inertia to be 
where ωc=κ/γ0, the angular corner frequency. The gradient of the power spectrum tail is characteristic of the degree of damping in the system, falling off with ω -4 for an under-damped system and ω -2 for an over-damped system .
Initial development of the sample chamber, aerosol delivery, and tweezing methods were conducted with a 1064nm tweezers system (see Fig. 1) , without a position detection system. A 2W c.w. Ytterbium fibre laser provided a Gaussian beam attenuated to a maximum of 100mW with power control supplied by a polarizing beamsplitter and half-wave plate. We used silica spheres as aerosols with diameters of 1.86µm and 3.01µm (Bangs Labs).
To carry out more quantitative measurements a 532nm tweezers equipped with a quadrant photodiode detector (QPD) system was employed. The method of aerosol delivery remained the same for both wavelengths but we also performed measurements on colloidal particles trapped in water at 532nm. As illustrated in Fig. 1 the Gaussian beam from a 532nm c.w. 4W Laser Quantum Finesse laser was focused with a 100x Nikon E Plan oil immersion microscope objective (NA=1.25) having been expanded using a Keplerian telescope to ensure its back aperture was slightly overfilled . The chamber within which the aerosols were trapped was placed on a thickness one cover slip on top of the objective, with the focus formed approximately 10 microns above. The samples were imaged from below using the same microscope objective, with tube lens, to transmit the image through a dichroic mirror onto a Basler A602f Firewire camera. A Mitutoyo long working distance (LWD) 100x objective (NA=0.55) was used to image light from the trapping plane onto the QPD (Hamamatsu Silicon Photodiode Array) via a 4f imaging system. A higher numerical aperture collecting lens would have been desirable  but from those available, this provided the best compromise between NA and allowing enough space (working distance=13mm) for our chamber design. The small currents produced by the QPD were sent, via shielded cables to reduce any interference from external sources, to amplification electronics containing a 50 kHz anti-aliasing filter. In order to reduce the background noise further the laser was always used at greater than 30% capacity with control over the power achieved with a half wave plate and polarizing beam cube.
The method of generating solid aerosol particles and introducing them into the trap is an extension to our liquid aerosol system , using an Omron MicroAir NE-U22 nebulizer. This nebulizer uses a vibrating ultrasonic mesh with holes approximately 3µm in diameter to generate droplets with a mass median aerodynamic diameter (MMAD) of 4.9µm: thus it is possible to pass solid particles of similar or smaller size. We suspend silica spheres in ethanol as it is easily nebulized and can act as a liquid carrier for the solid aerosol. The sample chamber is designed to be relatively open to the environment, allowing the ethanol component of the aerosol to rapidly evaporate either by the time they arrive at the trap, or within a few seconds of being trapped.
The design of the sample chamber is critical to the successful trapping of spheres as there is a competition between evaporation rates and isolation from disruptive air currents. The most successful chamber design, shown in Fig. 2(a) consisted of a well in the centre to shield the region nearest the trapping site. A microscope slide was placed on top of the lower section, with 5mm spacers to provide central vents, and to allow scattered light from the sample to be collected by the long working distance objective above.
As with other aerosol trapping experiments  the ‘conditioning’ of the aerosol flow is important and we tested a range of nozzle attachments aiming to provide a useful sample flow rate. For our particular nebulizer, the most effective nozzle is shown in detail in Fig. 2(b). The solid component of the flow also had to be considered. Through observing the number of solid particles deposited on a cover slip over a given time interval we found that longer tubes or sharp angles in the flow conditioner restricted the number of solid particles contained in the final aerosol. In our preliminary efforts to extend the size range beyond the 3µm limit set by the vibrating mesh nebulizers, pneumatic nebulizer designs seemed to be the most promising for generating larger solid aerosol. To keep the solid particles separated whilst in suspension the samples were placed in an ultrasonic bath for five minutes before each experimental session. This helped prevent clogging the ultrasonic mesh with larger particles and gave a higher proportion of isolated silica spheres in the resulting aerosol.
Silica spheres of 1.86µm and 3.01µm diameter were successfully tweezed and held for several minutes in the sample chamber at constant trapping powers. The axial trapping efficiency for such a tweezers, Q, is a measure of the efficiency of the optical trap . We measured the Q using the IR tweezers by first trapping the spheres, then reducing the optical power until the particles fell out. These values were found to be in agreement with previously measured trapping efficiencies in air (see Table 1). Silica spheres of diameter 4.32µm were produced using a pneumatic nebulizer using compressed air (CompAir NE-C28-E) and were trapped for several seconds at 3mW. However, the airflow generated by this nebulizer model made trapping unstable and detailed Q measurements impractical – this indicates a limitation of the production of the aerosol rather than of the technique.
Silica spheres of diameter 0.97 µm and 2.47 µm were similarly tested, but we were unable to trap these stably (i.e. for more than 10s). The reason for this is unknown to us at present, but may be possible with an improved nebulizer or sample chamber design.
For the colloidal measurements, only the sample chamber differed. Dilute samples of the spheres in de-ionised water were placed in spacers sandwiched by thickness one cover slips. Care was taken to ensure only one particle was being tweezed at a time.
For all the following results the diode signal was sampled at 50 kHz for 4 seconds with the data binned into units of 50. For the airborne samples, a least squares fit was performed between 18 Hz and 10kHz and in water the data was fit between 18Hz and 5kHz.
Fluctuations in particle position are output as voltage fluctuations from the amplification electronics. The relationship between voltage and displacement is governed by the detection system sensitivity, β, with units Vm-1, where the true physical displacement, x(t)=xvolts(t)/β. This sensitivity will differ when trapping in an air medium as opposed to a water medium, as well as for particles of differing properties, so to make comparisons between the dynamics of the two systems we must calibrate the detector signals for each individual experiment. Conventional methods could be very difficult to implement in air. For example, moving a fixed bead over a known distance through the laser beam waist is clearly not a good replica of experimental conditions . Oscillation of the sample stage to produce a known drag force on the trapped particle would also be difficult to implement in an air due to its more complex flow . There are techniques that use AODs to produce known oscillations of the trapping beam to calibrate the system for a given trapped particle which could be implemented in future airborne trapping systems.
Here we are not concerned with high precision and for simplicity we calculate the detector sensitivity, β, from an uncalibrated voltage power spectrum SVover(ω)=β2Sover(ω) by use of the plateau reached for ω≫ωc in the function ω2SVover(ω) . For the under-damped case, where inertia is included, it is clear we must multiply the voltage power spectrum by ω4 to obtain a similar plateau in ω4SVinert(ω). For clarity such a plot is inset in Fig. 4 where the plateau value Pv is indicated. The over-damped detector sensitivity, βover, is given in by Allersma, et al.,  and we find the under-damped detector sensitivity, βinert, to be,
We find βinert or βover for each individual power spectrum allowing us to calibrate the spectrum into the familiar nm2Hz-1 units. Examples of the calibrated spectra for silica particles in both water and air media are shown in Figs. 3 and 4.
In order to make direct comparisons between the airborne and non-airborne cases, attempts were made to trap beads in water using the small amount of power needed in air. Although tweezing was possible the corner frequencies were so low they resided in the region of mechanical noise and provided “poor fits”. Instead, the particles were tweezed with 100 times the power used in air and hence Table 2 gives κnorm, which is κ normalized to units of pNµm-1mW-1.
Our technique for particle delivery into an optical trap appears to be robust and should be extendible to other types and sizes of particles, provided they can be placed in a suspension that can be nebulized and is able to rapidly evaporate. However we obviously encounter limitations. The majority of interest in examining solid particles from an atmospheric science point of view lies in the sub-micron range and is predominately made up of irregularly shaped particles. Our data suggests that trapping smaller particles appears to be difficult but whether this is a physical limitation or, at this point, purely an engineering issue remains to be investigated. The broad issues that impact upon carrying out more extensive studies lie in the slight differences between trapping in air and trapping in liquid, which our results highlight. For example, unlike colloidal based tweezers simply increasing the power does not allow aerosols to be ‘caught’ more easily. To trap in air the laser power must be carefully selected. As such, only a small region exists over which an aerosol can be tweezed from the air, hence the seemingly arbitrary powers shown in Table 2. So, to trap particles of another size is a trial and error process until the optimum power range is discovered.
It is worth noting some of the issues associated with producing comparative power spectra. At frequencies greater than 10 kHz it was at times difficult to obtain a power spectrum with an amplitude larger than the background level. In the same frequency region there were also spikes in the background signal due to laser noise. The use of a second probe laser was considered but, clearly, even the small powers involved (minimum trapping powers of the order of 100µW) could significantly alter the shape and size of the potential at the trap site. At low frequencies mechanical noise can dominate resulting in a non-flat plateau despite using a floating optical bench and where possible working solitarily in the laboratory. For these reasons we only plot between 10 Hz and 10 kHz in our results.
Fitting to above 5 kHz for colloidal particles inhibits the theoretical fits quality because the Lorentzian description, Eq. (3), does not fit the system perfectly, as seen in Figs. 3 and 4. The reason for this is the neglected hydrodynamic correction to the friction felt by the microspheres which can become significant for the particle sizes studied here . The correction in air is low in comparison for the sizes considered here which is evident from the good quality fits to the airborne data. In any future investigations this discrepancy needs to be taken into account to increase precision and accuracy.
Once calibrated power spectra have been obtained they can be used to infer much about the system under study. Figures 3 and 4 show both 1.86µm and 3.01µm silica spheres trapped with the powers used in our experiments oscillate with larger amplitude at all frequencies plotted. This is expected when tweezing in air with 1/100th the power used to tweeze in water. However, looking at Table 2 we see the trap stiffness per milliwatt is over twice as large in air as in water, indicating that for a given power (assuming linear trap stiffness dependence) the airborne particle would, counter-intuitively, oscillate in a more confined volume. It is believed this confinement is attributed to the higher refractive index contrast between the particle and medium. Obviously the environment through which the beam is focused is very different for water and air based systems so there is uncertainty in the quality of the comparison between airborne and colloidal tweezing. A full investigation of the optical forces involved is complex  and beyond the scope of this work but will be described in future . It is known that due to a higher spherical aberration induced when crossing the glass to air interface the focus quality will be poorer in air. This indicates that if one were to use a beam of the same quality within colloidal tweezers the trap stiffness would be even lower than measured here.
Finally, we note that pairs of spheres could be trapped for short periods of time (<5s) in the trap. This could be interpreted as a disadvantage when carrying our environmental sampling, for example, but as the pairs are short lived in the trap and inevitably give spurious results for any monitoring method we might use on the spheres this should not be a problem. One possibility for this observation is that the particles are stuck together.
In conclusion we have presented a method to introduce solid aerosols into an optical trap and have quantitatively studied the particle behavior within the trap. We have compared the particle dynamics with colloidal particles in solution and found that trap stiffness is higher in air. However we have found that there may be limitations in the size of particle which can be controllably trapped in air using optical tweezers which may have physical reasons to do with the optical forces produced on airborne particles through a layered interface (which we are currently investigating). In tandem with this, an improved sample chamber design should lead to better environmental control and improved trapping.
Much of our current work [13, 15, 22] is based on studying how airborne particles interact with optical fields. One of the key issues with using liquid aerosols, although interesting from an applications perspective, is that for basic studies examining optical forces and particle behavior the size of liquid droplets is ill defined. Here we are able to trap particles of known size which allows easier integration with models where the particles size is assumed: easily trapping solid particles will be important in carrying out quantitative studies of particle behavior in optical traps more robustly.
In addition, we hope that this method of solid aerosol trapping will make the study of solid aerosols more accessible for atmospheric chemistry applications. This could include nucleation studies  and kinetic and product analysis  in addition to more basic particle dynamics.
We thank Jonathan Reid of Bristol University for helpful discussions. MDS thanks the Royal Society of Chemistry/EPSRC Analytical Trust for support. DM is a Royal Society Research Fellow.
References and links
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