Track of the Brownian motion of a 50 nanometre diameter particle in a fluid.
Nanoparticles are being used in a myriad of applications including sunscreen creams, sports equipment and even to study the stickiness of snot! By definition, nanoparticles should have one dimension less than 100 nanometres, which is one thousandth of the thickness of a human hair. Some nanoparticles are toxic to humans and so scientists are studying the interaction of nanoparticles with human cells. However, a spherical nanoparticle is smaller than the wavelength length of visible light and so is invisible in a conventional optical microscope used by biologists. We can view nanoparticles using a scanning electron microscope but the electron beam damages living cells so this is not a good solution. An alternative is to adjust an optical microscope so that the nanoparticles produce caustics [see post entitled ‘Caustics’ on October 15th, 2014] many times the size of the particle. These ‘adjustments’ involve closing an aperture to produce a pin-hole source of illumination and introducing a filter that only allows through a narrow band of light wavelengths. An optical microscope adjusted in this way is called a ‘nanoscope’ and with the addition of a small oscillator on the microscope objective lens can be used to track nanoparticles using the technique described in last week’s post entitled ‘Holes in liquid‘.
The smallest particles that we have managed to observe using this technique were gold particles of diameter 3 nanometres , or about 1o atoms in diameter dispersed in a liquid.
Image of 3nm diameter gold particle in a conventional optical microscope (top right), in a nanoscope (bottom right) and composite images in the z-direction of the caustic formed in the nanoscope (left).
‘Scientists use gold nanoparticles to study the stickiness of snot’ by Rachel Feldman in the Washington Post on October 9th, 2014.
J.-M. Gineste, P. Macko, E.A. Patterson, & M.P. Whelan, Three-dimensional automated nanoparticle tracking using Mie scattering in an optical microscope, Journal of Microscopy, Vol. 243, Pt 2 2011, pp. 172–178
Patterson, E.A., & Whelan, M.P., Optical signatures of small nanoparticles in a conventional microscope, Small, 4(10): 1703-1706, 2008.
Out-of-focus image from optical microscope of 10 micron diameter polystyrene spheres in water
The holes that I wrote about last week and the week before (post entitled ‘Holes‘ on October 8th)were essentially air-filled holes in a solid plate. When an in-plane load is applied to the plate it deforms and its surface around the hole becomes curved due to the concentration of stress and light passing through the curved surfaces is deviated to form the caustic. If you didn’t follow that quick recap on last week then you might want flip back to last week’s post before pressing on!
The reverse situation is a solid in a fluid. It is difficult to induce stress in a fluid so instead we can use a three-dimensional hole, i.e. a sphere, to generate the curve surface for light to pass through and be deviated. This is quite an easy experiment to do in an optical microscope with some polystyrene spheres floating in distilled water with the microscope slightly out of focus you get bright caustics. And if you take a series of photographs (the x-y plane) with the microscope objective lens at different heights (z-value) it is possible to reconstruct the three-dimensional shape of the caustic by taking the intensity or greyscale values along the centre line of each image and using them all to create new image of the x-z and, or y-z plane, as shown in the picture.
Well done if you have got this far and are still with me! I hope you can at least enjoy the pictures. By the way the particle in the images is about the same diameter as a human hair.
Image in optical microscope of polystyrene particle in water (left), series of images at different positions of microscope objective (centre) and artificial image created from greyscale data along centre-lines of image series (right).
Patterson, E.A., & Whelan, M.P., Tracking nanoparticles in an optical microscope using caustics, Nanotechnology, 19(10): 105502, 2008.
White light caustic of 4mm diameter hole in 6mm (PMMA) plate subject to 3kN tension
As children many of us have burnt a hole (yes, tenuous link to last week’s post on ‘Holes’) in a piece of paper by focussing the sun’s rays with a magnifying glass. If you move the glass up or down and tilt it slightly then the sun’s rays will not be focussed on a spot and instead you see a complex spiralling pattern of light. This pattern is caused by the rays being bent by their passage through different sections of the curved glass. The same type of pattern, known as a caustic, appears on the bottom of your bath when you let (clean) water run out down the plug-hole if you have spotlights above the bath. This caustic is produced by the light rays from the spotlight being bent by varying degrees depending on where they pass through the vortex formed by the water spinning down the hole. Caustics can also be produced when light passes through a glass of water or on the bottom of an outdoor swimming pool in bright sunlight.
The top picture shows the caustic formed by light passing through a transparent plate with a hole when the plate is stretched in the vertical direction. The load in the plate has to flow around the hole where it ‘bunches up’ or concentrates (see last week’s post entitled ‘Holes’) which causes high levels of local deformation with the plate thinning non-linearly at the intersection of the hole circumference and horizontal diameter. When the light passes through the deformed region it is deviated by amount dependent on the local thinning and forms the pattern shown.
This is not a totally abstract phenomenon because the same mechanism of thinning occurs at the tip of cracks as a result of the very high stress concentration at the sharp crack tip, as shown schematically in the diagram below. So we can evaluate the stress concentration by measuring the caustic it generates; it is even possible to predict in which direction the crack will grow next.
Schematic diagram of transparent plate with a crack loaded vertically in tension (left), light ray tracings through the cracked region (centre) and caustic formed on a screen (right).
Carazo-Alvarez, J.D., Patterson, E.A., 1999, ‘A general method for automated analysis of caustics’, Optics & Lasers in Engng., 32: 95-110.
Holes, little circular ones. There are billions of them in engineering machines and structures. There are more than a million in a jumbo jet alone. Some of them are filled with fasteners, such as bolts and rivets, others are empty to allow fluids to flow through a surface. Load passing through a structure has to flow around holes, especially when they are empty, and the contours of stress bunch up around a hole to form a stress concentration. For a small hole in a very large plate, the stress on the circumference of the hole is three times the level found in the absence of the hole. This concentration increases for bigger holes or smaller plates, so that holes are a potential source of failure – that’s why sheets of stamps are perforated with lines of holes.
A hole can also stop a failure. For instance a crack extending under repeated loading will often stop when it grows into a hole because the ‘sharpness’ of the crack tip is blunted by the roundness of the hole. Engineers sometimes deliberately drill a hole at a crack tip to arrest its progress. So, holes can be both an engineer’s friend and foe.
Origami wings in the roof-box?
A few weeks ago I was fascinated by the competitors’ bikes tessellated on top of the team support cars during the Tour of Britain [see my post entitled ‘Tessallating bikes‘ on September 10th, 2014]. What if instead of tessellating bikes we could use origami to fold away a set of wings? Many people have dreamed of escaping the frustration and congestion of traffic on the road with a convertible. Not the classic convertible but a car that converts to a plane. One small company from Massachusetts, Terrafugiama has already flown a prototype flying car with self-folding wings and is working on an advanced prototype capable of vertical take-off and highway driving. Vertical take-off with wings is difficult so as an alternative a group of universities in Europe is studying the feasibility of a Personal Air Transportation System (PATS) based on a helicopter, known as MyCopter.
These convertibles are difficult to design in practice due to the space constraints for a flying car to take-off and land, the need for two propulsion or at least two transmission systems, the different type of suspension required for comfortable driving compared to landing, the current approach to crashworthiness in cars, and the overwhelming requirement for a light-weight system if there is any hope of getting airborne. If you add to this list the desire for an environmental-friendly vehicle then perhaps there is no hope, unless we can cross a Tesla with the Airbus prototype electric plane, the E-plane! [See my post entitled ‘Are electric cars back?‘ on May 28th, 2014]
‘Why we’re not driving the friendly skies‘ by Stuart F. brown in the New York Times on August 22nd, 2014
‘If cars could fly‘ by Nick Bilton in the New York Times on June 30th, 2010