Control and characterisation of a single aerosol droplet in a single-beam gradient-force optical trap

Optical tweezers are used to control aerosol droplets, 4–14 μm in diameter, over time frames of hours at trapping powers of less than 10 mW.

When coupled with cavity enhanced Raman scattering (CERS), the evolution of the size of a single droplet can be examined with nanometre accuracy.

Trapping efficiencies for water and decane droplets are reported and the possible impact of droplet heating is discussed.

We demonstrate that the unique combination of optical tweezing and CERS can enable the fundamental factors governing the coagulation of two liquid droplets to be studied.

Heterogeneous atmospheric aerosol chemistry is an experimentally challenging area of research.

Measurements often must be made on an ensemble of particles, characterised by distributions of particle size and composition, and complicated by indeterminacy of mixing state, phase and morphology.1

With heterogeneous chemistry often governed by the surface-to-volume ratio, interfacial composition and phase, the fundamental factors governing the chemical and physical transformation of aerosols may be obscured or at best averaged.

To complement measurements made on ensembles of particles, measurements made on a single particle may provide detailed information on the mechanisms of heterogeneous chemistry, the factors governing mixing state, and the processes that lead to the physical transformation of the particle through phase transformation and growth.

In this Communication, we demonstrate for the first time that single-beam gradient force optical trapping,2,3 or optical tweezing, can be used to trap a single water or decane droplet, 4–14 μm in diameter, for timescales of hours, affording the prospect of characterising the mechanisms of chemical and physical transformations of a single droplet.

When coupled with cavity enhanced Raman scattering (CERS), the size of the droplet can be determined with nanometre precision.4,5

By creating two optical traps, two droplets can be manipulated simultaneously, providing the unique opportunity to study the coagulation of two droplets directly.

The interplay of scattering and gradient forces must be considered when a dielectric sphere is illuminated with a Gaussian laser beam.3,6

The scattering force acts in the direction of propagation of the laser and is proportional to the light intensity, ultimately acting to displace the particle from the beam focus.

Conversely, the gradient force acts to draw the dielectric sphere towards the beam focus and is proportional to the gradient of the light intensity.

When the gradient force dominates the scattering force, a restoring force with a magnitude of piconewtons acts to confine the particle to the most intense region in the laser beam and a stable trap is created.3

Such a scenario can be achieved with a tightly focussed laser beam using a microscope objective, forming a three dimensional trap with the particle position constrained both in the horizontal plane and on the vertical axis.

Tweezers have found widespread application in the biological and colloidal sciences, but have not been developed to address key issues in aerosol science.3

Tweezing has been applied to trapping solid glass spheres in air6 and scattering forces have been used to levitate particles,7–13 but there has been little success in tweezing liquid aerosols and no reported entrapment of water droplets.14

A schematic diagram of the experiment is shown in Fig. 1(a).

Trapping is achieved with a cw argon ion laser operating at 514.5 nm.

Not only is the complex refractive index of water near a minimum at this wavelength,1 minimising droplet heating, but the size parameter, x, is larger than it would be at the more usual longer wavelengths chosen for tweezing.3

This is extremely important for recording a CERS fingerprint from the trapped droplet.4,5

The size parameter is defined as the ratio of the circumference of the droplet, radius a, to the wavelength of the light, λ (x = 2πa/λ).15

The tweezing instrument has been described in a previous publication and will be outlined only briefly here.16

The trapping beam is passed through two sets of beam expansion optics, reflected from a holographic notch filter (HSPF-514.5, Kaiser Optical Systems) and directed into a Leica DM IRB microscope.

Two microscope objectives are compared in this work: a 63× water immersion objective (NA of 1.2), and a 60× oil immersion objective (NA of 1.4).

The backscattered Raman light from the trapped droplet is collimated by the objective lens, passed through the filter, and focussed onto the entrance slit of a 0.5 m spectrograph (1200 g/mm grating) coupled with a CCD, with a spectral resolution of 0.05 nm.

The trapped droplet is imaged onto a CCD camera using conventional brightfield microscopy.

The aerosol was generated with an Omron NE-U07 Ultrasonic Nebuliser, introduced into an aerosol cell mounted on the translation stage of the microscope (Fig. 1(a)), along with a flow of humidified nitrogen using a mass flow controller in order to regulate the humidity in the aerosol cell.

To achieve stable trapping in the aerosol cell, which is always at a relative humidity of less than 100%, the water aerosol was doped with sodium chloride at a concentration of ∼40 mM.

Köhler theory enables the equilibrium droplet size to be estimated at a particular relative humidity and for a given dry particle diameter.1

Doping the water droplets with sodium chloride reduces the vapour pressure of the droplet so that an equilibrium size is rapidly attained, and enables the droplets to be trapped for timescales of hours.

The aerosol trap was loaded by providing a brief dose of aerosol from the nebuliser.

A stable trap was achieved for water droplets and decane droplets 4–14 μm in diameter, with laser trapping powers of 5–15 mW (Fig. 1(b)).

The axial trapping efficiency of a droplet, Q, can be determined by measuring the minimum incident laser power, P, required to counterbalance the gravitational force experienced by the particle, F6,14,17.The refractive index of the surrounding medium is denoted by n, the speed of light by c, the particle density by ρ and the gravitational acceleration by g.17

The minimum power required to trap a droplet is estimated by systematically reducing the laser power until a droplet falls out of the trap.

Q was measured as 0.07 ± 0.02 and 0.1 ± 0.04 for water droplets trapped using the water and oil immersion objectives, respectively, and 0.45 ± 0.12 for decane droplets with the oil immersion objective.

The trapping efficiencies are comparable to those measured for particles in liquids, allowing the prolonged trapping and manipulation of droplets for timescales of hours.3

In previous publications we have shown that CERS can be used to probe dynamic changes in the size and the composition of aerosol droplets.4,5,18

A spherical droplet behaves as a high finesse optical cavity at wavelengths commensurate with whispering gallery modes (WGM).19

Such modes occur when an integer number of wavelengths, n, form a standing wave around the circumference of the droplet, providing a mechanism for optical feedback.

A CERS fingerprint can result, with amplification of the Raman scattering only occurring at wavelengths commensurate with WGMs.

This leads to stimulated Raman scattering, which is apparent as structure superimposed on the spontaneous Raman bands.

The fingerprint of resonant wavelengths can be used to determine the droplet size with nanometre precision.4,5

Fig. 2 illustrates three CERS spectral fingerprints obtained from optically trapped water droplets of different sizes.

The spectra are comprised of the spontaneous Raman scattering envelope arising from the O–H stretch of water, with resonance structure superimposed from stimulated Raman scattering at wavelengths matching WGM wavelengths.

Successive modes of the same scattered polarisation, as indicated by the brackets, correspond to sequential integer values of the mode number, n.

The trend in resonance wavelengths illustrates the increase in mode spacing with diminishing droplet size.

Mie scattering calculations are performed to determine the droplet radius with an estimated error of ±2 nm, limited primarily by the spectral resolution of the spectrograph.5

All sizes should be assumed to have this associated error.

As a further illustration of the sizing capability of CERS, Fig. 3 illustrates the variation in the trapped droplet size when equilibrating with the local relative humidity in the aerosol cell, each spectrum corresponding to 1 s of signal integration.

This demonstrates that dynamic size changes at the nanometre level can be investigated by CERS.

Perhaps the most important issue to address is the influence of the laser on the droplet temperature through absorption.20

Fig. 4(a) illustrates that varying the laser power by a factor of three over a period of ∼10 min leads to droplet size fluctuations of <±2 nm.

Indeed, the invariance of the resonant wavelengths with power also suggests that the refractive index of the droplet is constant, reinforcing the conclusion that there is no significant change in temperature.5

A shift to shorter wavelength of 0.047 nm/K would be apparent if heating were occurring, reflecting the change in refractive index with temperature.5

The magnitude of this shift is comparable to the experimental resolution of the spectrograph and it can be concluded that any droplet heating must correspond to a temperature change of <1 K.

Assuming an absorbance of 0.005, the upper limit of the absorbance in the visible of the HPLC grade water used in this work, the complex refractive index can be calculated15 to be less than 1 × 10−8.

Mie scattering calculations of the absorption efficiency4 indicate that Qabs ∼2 × 10−7.

By applying the procedure adopted by Popp et al., this correlates with an increase in droplet temperature due to heating of 0.01 K under steady state conditions, consistent with the temperature invariance inferred from the experimental data.21

It should be noted that a droplet resonant with the incident laser field will show enhanced heating and this would lead to an enhancement in Qabs of two orders of magnitude and a temperature rise of the order of 1–10 K. The low density of WGMs for the droplet sizes considered in this work and the invariance of the refractive index and resonant wavelengths suggest this does not occur.21

However, a final caveat should be added.

The intensity of the CERS signal shows a strong inverse correlation with laser power (Fig. 4(b)), suggesting that the droplet cavity losses increase with increasing laser power, and this may be symptomatic of enhanced absorption losses in the droplet.4,19

Studies of this will be undertaken to examine further any role that laser induced heating may play.

The nature of the optical trap enables 3D manipulation of the aerosol droplets, an advantage over purely levitating the droplet with the scattering force.

A beam splitter was inserted into the laser path between the two sets of expansion optics, creating a second optical trap and allowing two aerosol droplets to be trapped simultaneously.

The position of each droplet could be controlled independently enabling the coagulation of the two droplets to be studied.

Two water droplets were trapped simultaneously and their radii monitored until stable by examining the CERS fingerprint from each droplet (radii of 3.014 μm and 4.038 μm), as illustrated in Fig. 5.

Following controlled coagulation, a final CERS fingerprint was recorded to determine the size of the coagulated droplet (4.533 μm).

The results from the coagulation measurement shown in Fig. 5 illustrate that the additive volumes of the two individual droplets and the volume of the coagulated droplet are in agreement to within ±3 × 10−19 m3.

By coupling optical tweezers with CERS, a wide range of aerosol dynamics can now be explored.

We have performed preliminary measurements of the growth of water droplets through the uptake of ethanol and water and are exploring further the fundamental factors that govern aerosol coagulation.

Not only can accurate measurements be made of droplet size, but the evolution of the chemical composition can be monitored by spontaneous and stimulated Raman scattering.