Home > optical tweezers, physics, Uncategorized > Optical tweezers and sizing nanoparticles

## Optical tweezers and sizing nanoparticles

I thought I’d write something more linked to my day job (or one of them at least), and discuss a nice new paper on the application of optical tweezers by my colleague Peter Reece who works at the University of New South Wales in Sydney. In case you are unaware, optical tweezers are a tool in which a highly focused laser beam can be used to pick up and manipulate microscopic particles. In fact there is a lot of interest in trying to use them to work with much smaller nanoscopic particles. Of particular interest are metallic nanoparticles, since by illuminating them you can excite what are called surface plasmons. These are a special kind of excitation of electrons on the surface of the metal, and result in a enhanced electric field appearing around the metal nanoparticle. This can be used in a variety of applications, particularly in spectroscopy (called surface enhanced Raman spectroscopy).

In many experiments to date a suspension of particles is used, and these have lots of different sizes. The particuar properties of the surface plasmons are size dependent however and are avergaed out in the suspension experiments. One of the nice things about optical tweezers is that they are able to localise particles and then move them to a desired point. So in this way, one could imagine making use of the size specific properties and tailoring them to the experiment at hand.

The main problem with this approach is that it is difficult to know before hand the exact size of the particle you will be trapped, and in fact once you have trapped your particle, it’s still a challenge to size it. In the paper “Dark-ﬁeld optical tweezers for nanometrology of metallic nanoparticles*.” by Kellie Pearce**, Fan Wang and Peter Reece (Opt. Express 19 25559 (2011)) a technique is described to overcome this problem by sizing the particle directly in the optical tweezers. The particles trapped are gold and range in size from 60nm – 200nm.

Optical trapping setup and images of trapped nanoparticles. From: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-25-25559

The technique relies on the idea that a particle in an optical trap acts like a mass on the end of a spring, and obeys Hooke’s Law:

$F = -\kappa x$

Here F is the force on the particle, $\kappa$ is called the spring constant and x is the displacement of the particle form the centre of the beam. The equation tells us that if the particle is moved away from the centre of the beam there will be a force acting on it directing it back to the equilibrium position at the centre of the beam (where the force will be zero). This is the same idea if you have a mass on a spring: pulling the mass will extend the spring and it will then act to pull the mass back to the place where it was at rest. The spring constant is a measure of how stiff the spring is, and is related to how ‘springy’ the spring is, and hence to with how much force a particle will be pulled back to equilibrium (and hence how quickly).

In an optical tweezers system we can measure the spring constant a number of ways. In the paper the authors compare two different methods and since these should be the same, and one depends explicitly on the size of the particle, the particle size can be determined. The first method is called the ‘Power Spectrum’ method and relies on measurments of the position of the trapped particle and transforming these position measurements into the frequency response of the particle. This can be mapped to the equation of motion for the particle in the trap. The trap stiffness in this case is related to the damping on the particle due to the water in which it is immersed, and it is this that is particle size dependent.

The second method isa called the ‘Gaussian method’ and makes use of the idea that the particle must be displaced in a particular way within the trap (explicitly the trapping potential defines the particle displacement probability). This is on the dependent on the drag or size. It is possible to make both the measurments at the same time, and hence work out the particle size.

The particle size can then be related to the surface plasmon resonance curves that can be collected for the particles, and these then show an explicit size dependence. Further, with all this information at hand, it is straightforward to tell if you have more than one trapped particle, or are looking at a single particle only.

The final nice part of this paper is that the imaging is done via a technique called darkfield in which the background of the image is dark. This is usually difficult in optical tweezers due to the constraints on the microcope objective used in both techiques being incompatible. However this is overcome by imaging the backscattered light from the particles rather than a conventional transmission image. This darkfield imaging then allows the scattering spectra from the particles to be collected simultaneously with the sizing information, enabling direct correlation between the two.

This is a really nice paper, demonstrating a few novel techniques and combining them all into a powerful tool which will hopefully find use in the control of nanoparticles in tweezers and their application as single particle emitters and sensors.