Science, culture, complexity

Tag: electrical conductivity

  • Part light, part matter

    Consider a bunch of molecules that have been trapped between two mirrors facing each other very closely. In this ‘box’ the light can’t move around freely; it can only exist in certain fixed patterns, somewhat like sound inside a finely tuned musical instrument. Even when all light has been removed from this box, quantum physics causes small flickers of light to pop in and out of existence in fractions of a second. These immutable flickers of the electromagnetic field are sometimes collectively called the vacuum field.

    Now, what would happen if the natural motion of matter inside molecules and these confined light patterns become strongly linked?

    This isn’t an esoteric thought experiment. Over the last decade, physicists have shown in experiments that when this link is strong, new hybrid states appear that are part light and part matter — and these states can spread over many molecules at once. And in this condition, physicists have found that the materials in which these states occur suddenly have very different properties, all without changing the chemical formulae of their constituent molecules.

    A new paper by PhD scholar Subha Biswas and assistant professor Anoop Thomas — both at the Department of Inorganic and Physical Chemistry of the Indian Institute of Science — brought the many findings in this area of research together and argued that the confined vacuum field reshapes the weak forces between molecules, which is the same force that determine how the molecules arrange themselves and how easily energy and charge can move between them. And the duo has shown that this explanation can account for a wide range of surprising findings. Their findings were published in ACS Applied Optical Materials on November 11.

    The paper isn’t a single experiment; instead the authors read and compared many published papers about experiments in which other scientists placed molecules inside small mirror cavities and forced them to interact strongly with the trapped light.

    Thus, the duo reported, energy could travel quite differently in these cavities. Normally, when energy passes from one molecule to the next, it does so through a series of short hops if the material is disordered. A simple example is an ordinary piece of glass. In a crystal, atoms or molecules sit on a tidy 3D grid, like seats in a stadium. In glass however they’re more like people milling around in a crowd: there’s some short-range order but no long-range one.

    When motion inside the molecules is strongly coupled to the trapped light, however, the new light–matter states can extend over many molecules, creating a sort of highway that energy travel on faster, more efficiently, and across much larger regions than physicists generally expect in disordered materials.

    For another, the duo reported that some organic materials, especially plastics that usually conduct electricity very poorly, are suddenly able to conduct a lot better when certain internal motions of their molecules are strongly coupled to the trapped light. In some experiments scientists had found that protons also moved faster through water, suggesting the cavity could in some way alter the network of hydrogen bonds in water.

    Based on analysing these and other examples, the duo arrived at a central conclusion: that by modifying how light is confined around a material, scientists can influence how its molecules ‘feel’ each other and thus alter its bulk behaviour, even when it’s in its lowest-energy state. (Usually materials become capable of unusual things when they’re imparted more energy.) Put another way the cavity isn’t just a passive container but an active design tool that can reshapes the background electromagnetic field, and with that the landscape of intermolecular forces.

    This is interesting because it’s a new way to control molecules in chemistry. Usually when scientists need to change the way a chemical reaction happens, they change the molecules that are in play. For instance they alter the molecules’ structure, add side groups, and/or ‘mix in’ new components. But the new study has found what seems to be an additional handle: scientists may be able to leave the molecules as they are but just place them in a carefully designed optical environment. And by carefully choosing the spacing between the mirrors, the materials that make up the apparatus, and how the cavity resonates with specific molecular motions, they can adjust the reaction rate, favour one crystal form over another, stabilise certain structures, shift the balance between different reaction products, and guide how large molecules assemble into various shapes, etc.

    The implications are similarly broad for materials science, where physicists can use these cavities to improve energy transport in thin films, enhance conduction in soft or flexible materials, guide how polymers and other large molecules arrange themselves in devices, and tune how materials crystallise as they’re fabricated. Because the effect comes from light and matter coupling together over a longer range, it might be especially useful in systems that are otherwise disordered and where conventional design tools struggle.

    For instance, the molecules of polystyrene are arranged in a messy, haphazard way. This disorder makes it very hard for scientists to ‘engineer’ clean paths within the material through which electrons can flow, so polystyrene is usually an excellent insulator. However, when scientists place thin films of such plastics in a carefully tuned optical cavity, experiments have shown that their ability to conduct electricity increases drastically even though the material’s chemical makeup hasn’t changed.

    A simple salt solution, like of table salt dissolved in water, offers another good example. Here the water molecules and the salt ions move around in an incessantly shifting and disordered fashion, and chemists typically control them by changing how much salt or what additives there are. But when the solution is strongly coupled to the confined light, the way water molecules surround and move around the ions changes and the ions travel more easily through the liquid.

    The authors have stressed that these effects are selective — which is to say not every material will change dramatically. Instead scientists will have to select details such as how molecules pack together and which internal motion is coupled to the light in the cavity all matter. This in turn means this new vacuum-field engineering won’t altogether replace chemical design but could in fact complement it. In fact the authors have sketched a future in which chemists and materials scientists routinely think together about what molecules to build and the kind of electromagnetic environment to place them in to coax new or improved properties out.

  • The awesome limits of superconductors

    On June 24, a press release from CERN said that scientists and engineers working on upgrading the Large Hadron Collider (LHC) had “built and operated … the most powerful electrical transmission line … to date”. The transmission line consisted of four cables – two capable of transporting 20 kA of current and two, 7 kA.

    The ‘A’ here stands for ‘ampere’, the SI unit of electric current. Twenty kilo-amperes is an extraordinary amount of current, nearly equal to the amount in a single lightning strike.

    In the particulate sense: one ampere is the flow of one coulomb per second. One coulomb is equal to around 6.24 quintillion elementary charges, where each elementary charge is the charge of a single proton or electron (with opposite signs). So a cable capable of carrying a current of 20 kA can essentially transport 124.8 sextillion electrons per second.

    According to the CERN press release (emphasis added):

    The line is composed of cables made of magnesium diboride (MgB2), which is a superconductor and therefore presents no resistance to the flow of the current and can transmit much higher intensities than traditional non-superconducting cables. On this occasion, the line transmitted an intensity 25 times greater than could have been achieved with copper cables of a similar diameter. Magnesium diboride has the added benefit that it can be used at 25 kelvins (-248 °C), a higher temperature than is needed for conventional superconductors. This superconductor is more stable and requires less cryogenic power. The superconducting cables that make up the innovative line are inserted into a flexible cryostat, in which helium gas circulates.

    The part in bold could have been more explicit and noted that superconductors, including magnesium diboride, can’t carry an arbitrarily higher amount of current than non-superconducting conductors. There is actually a limit for the same reason why there is a limit to the current-carrying capacity of a normal conductor.

    This explanation wouldn’t change the impressiveness of this feat and could even interfere with readers’ impression of the most important details, so I can see why the person who drafted the statement left it out. Instead, I’ll take this matter up here.

    An electric current is generated between two points when electrons move from one point to the other. The direction of current is opposite to the direction of the electrons’ movement. A metal that conducts electricity does so because its constituent atoms have one or more valence electrons that can flow throughout the metal. So if a voltage arises between two ends of the metal, the electrons can respond by flowing around, birthing an electric current.

    This flow isn’t perfect, however. Sometimes, a valence electron can bump into atomic nuclei, impurities – atoms of other elements in the metallic lattice – or be thrown off course by vibrations in the lattice of atoms, produced by heat. Such disruptions across the metal collectively give rise to the metal’s resistance. And the more resistance there is, the less current the metal can carry.

    These disruptions often heat the metal as well. This happens because electrons don’t just flow between the two points across which a voltage is applied. They’re accelerated. So as they’re speeding along and suddenly bump into an impurity, they’re scattered into random directions. Their kinetic energy then no longer contributes to the electric energy of the metal and instead manifests as thermal energy – or heat.

    If the electrons bump into nuclei, they could impart some of their kinetic energy to the nuclei, causing the latter to vibrate more, which in turn means they heat up as well.

    Copper and silver have high conductance because they have more valence electrons available to conduct electricity and these electrons are scattered to a lesser extent than in other metals. Therefore, these two also don’t heat up as quickly as other metals might, allowing them to transport a higher current for longer. Copper in particular has a higher mean free path: the average distance an electron travels before being scattered.

    In superconductors, the picture is quite different because quantum physics assumes a more prominent role. There are different types of superconductors according to the theories used to understand how they conduct electricity with zero resistance and how they behave in different external conditions. The electrical behaviour of magnesium diboride, the material used to transport the 20 kA current, is described by Bardeen-Cooper-Schrieffer (BCS) theory.

    According to this theory, when certain materials are cooled below a certain temperature, the residual vibrations of their atomic lattice encourages their valence electrons to overcome their mutual repulsion and become correlated, especially in terms of their movement. That is, the electrons pair up.

    While individual electrons belong to a class of particles called fermions, these electron pairs – a.k.a. Cooper pairs – belong to another class called bosons. One difference between these two classes is that bosons don’t obey Pauli’s exclusion principle: that no two fermions in the same quantum system (like an atom) can have the same set of quantum numbers at the same time.

    As a result, all the electron pairs in the material are now free to occupy the same quantum state – which they will when the material is supercooled. When they do, the pairs collectively make up an exotic state of matter called a Bose-Einstein condensate: the electron pairs now flow through the material as if they were one cohesive liquid.

    In this state, even if one pair gets scattered by an impurity, the current doesn’t experience resistance because the condensate’s overall flow isn’t affected. In fact, given that breaking up one pair will cause all other pairs to break up as well, the energy required to break up one pair is roughly equal to the energy required to break up all pairs. This feature affords the condensate a measure of robustness.

    But while current can keep flowing through a BCS superconductor with zero resistance, the superconducting state itself doesn’t have infinite persistence. It can break if it stops being cooled below a specific temperature, called the critical temperature; if the material is too impure, contributing to a sufficient number of collisions to ‘kick’ all electrons pairs out of their condensate reverie; or if the current density crosses a particular threshold.

    At the LHC, the magnesium diboride cables will be wrapped around electromagnets. When a large current flows through the cables, the electromagnets will produce a magnetic field. The LHC uses a circular arrangement of such magnetic fields to bend the beam of protons it will accelerate into a circular path. The more powerful the magnetic field, the more accurate the bending. The current operational field strength is 8.36 tesla, about 128,000-times more powerful than Earth’s magnetic field. The cables will be insulated but they will still be exposed to a large magnetic field.

    Type I superconductors completely expel an external magnetic field when they transition to their superconducting state. That is, the magnetic field can’t penetrate the material’s surface and enter the bulk. Type II superconductors are slightly more complicated. Below one critical temperature and one critical magnetic field strength, they behave like type I superconductors. Below the same temperature but a slightly stronger magnetic field, they are superconducting and allow the fields to penetrate their bulk to a certain extent. This is called the mixed state.

    A hand-drawn phase diagram showing the conditions in which a mixed-state type II superconductor exists. Credit: Frederic Bouquet/Wikimedia Commons, CC BY-SA 3.0

    Say a uniform magnetic field is applied over a mixed-state superconductor. The field will plunge into the material’s bulk in the form of vortices. All these vortices will have the same magnetic flux – the number of magnetic field lines per unit area – and will repel each other, settling down in a triangular pattern equidistant from each other.

    An annotated image of vortices in a type II superconductor. The scale is specified at the bottom right. Source: A set of slides entitled ‘Superconductors and Vortices at Radio Frequency Magnetic Fields’ by Ernst Helmut Brandt, Max Planck Institute for Metals Research, October 2010.

    When an electric current passes through this material, the vortices are slightly displaced, and also begin to experience a force proportional to how closely they’re packed together and their pattern of displacement. As a result, to quote from this technical (yet lucid) paper by Praveen Chaddah:

    This force on each vortex … will cause the vortices to move. The vortex motion produces an electric field1 parallel to [the direction of the existing current], thus causing a resistance, and this is called the flux-flow resistance. The resistance is much smaller than the normal state resistance, but the material no longer [has] infinite conductivity.

    1. According to Maxwell’s equations of electromagnetism, a changing magnetic field produces an electric field.

    Since the vortices’ displacement depends on the current density: the greater the number of electrons being transported, the more flux-flow resistance there is. So the magnesium diboride cables can’t simply carry more and more current. At some point, setting aside other sources of resistance, the flux-flow resistance itself will damage the cable.

    There are ways to minimise this resistance. For example, the material can be doped with impurities that will ‘pin’ the vortices to fixed locations and prevent them from moving around. However, optimising these solutions for a given magnetic field and other conditions involves complex calculations that we don’t need to get into.

    The point is that superconductors have their limits too. And knowing these limits could improve our appreciation for the feats of physics and engineering that underlie achievements like cables being able to transport 124.8 sextillion electrons per second with zero resistance. In fact, according to the CERN press release,

    The [line] that is currently being tested is the forerunner of the final version that will be installed in the accelerator. It is composed of 19 cables that supply the various magnet circuits and could transmit intensities of up to 120 kA!

    §

    While writing this post, I was frequently tempted to quote from Lisa Randall‘s excellent book-length introduction to the LHC, Knocking on Heaven’s Door (2011). Here’s a short excerpt:

    One of the most impressive objects I saw when I visited CERN was a prototype of LHC’s gigantic cylindrical dipole magnets. Event with 1,232 such magnets, each of them is an impressive 15 metres long and weighs 30 tonnes. … Each of these magnets cost EUR 700,000, making the ned cost of the LHC magnets alone more than a billion dollars.

    The narrow pipes that hold the proton beams extend inside the dipoles, which are strung together end to end so that they wind through the extent of the LHC tunnel’s interior. They produce a magnetic field that can be as strong as 8.3 tesla, about a thousand times the field of the average refrigerator magnet. As the energy of the proton beams increases from 450 GeV to 7 TeV, the magnetic field increases from 0.54 to 8.3 teslas, in order to keep guiding the increasingly energetic protons around.

    The field these magnets produce is so enormous that it would displace the magnets themselves if no restraints were in place. This force is alleviated through the geometry of the coils, but the magnets are ultimately kept in place through specially constructed collars made of four-centimetre thick steel.

    … Each LHC dipole contains coils of niobium-titanium superconducting cables, each of which contains stranded filaments a mere six microns thick – much smaller than a human hair. The LHC contains 1,200 tonnes of these remarkable filaments. If you unwrapped them, they would be long enough to encircle the orbit of Mars.

    When operating, the dipoles need to be extremely cold, since they work only when the temperature is sufficiently low. The superconducting wires are maintained at 1.9 degrees above absolute zero … This temperature is even lower than the 2.7-degree cosmic microwave background radiation in outer space. The LHC tunnel houses the coldest extended region in the universe – at least that we know of. The magnets are known as cryodipoles to take into account their special refrigerated nature.

    In addition to the impressive filament technology used for the magnets, the refrigeration (cryogenic) system is also an imposing accomplishment meriting its own superlatives. The system is in fact the world’s largest. Flowing helium maintains the extremely low temperature. A casing of approximately 97 metric tonnes of liquid helium surrounds the magnets to cool the cables. It is not ordinary helium gas, but helium with the necessary pressure to keep it in a superfluid phase. Superfluid helium is not subject to the viscosity of ordinary materials, so it can dissipate any heat produced in the dipole system with great efficiency: 10,000 metric tonnes of liquid nitrogen are first cooled, and this in turn cools the 130 metric tonnes of helium that circulate in the dipoles.

    Featured image: A view of the experimental MgB2 transmission line at the LHC. Credit: CERN.