I recently learned a little about the history of the discovery of liquid crystals, stimulated by Soft Matter: A Very Short Introduction by Tom McLeish. Besides being a fascinating story there are lessons about the importance of curiosity-driven research, interdisciplinarity, serendipity, and the long road to technology.
Friedrich Reinitzer (1857 - 1927) was a botanist and chemist who worked at the Institute of Plant Physiology in Prague. He was studying cholesterol with the aim of determining its molecular weight. He produced crystals of cholesteryl benzoate and measured their heat capacity as a function of temperature. Aside: For chemists today this measurement is known as differential scanning calorimetry (a constant source of heat is added and the temperature measured as a function of time).
The sorites paradox (/soʊˈraɪtiːz/; sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?
What is the minimum number of gold atoms needed to produce shininess?
How large must a grain of tin be for it to superconduct?
When spontaneous symmetry breaking is involved there are subtleties. Strictly, speaking it only occurs in the thermodynamic limit, i.e. for an infinite system. However, for a finite system, one can observe some properties associated with symmetry breaking such as rigidity. These issues can be addressed in the laboratory with ultracold atoms and with metallic grains of superconductors, both of which can be produced with controlled numbers of particles, ranging from a few hundred to billions. There also are some resonances with the problem of trying to identify the quantum-classical boundary.
Finally, piles of sand were central to the discovery of self-organised criticality.
I believe that there is one verb that describes the mission of universities (think) and that teaching a discipline means teachings students how to think in accord with that discipline.
But, what about high school? What are the key critical thinking skills that all students should learn? In particular, what is needed they can become engaged citizens who play a constructive role in a democracy.
I wonder if the most essential skill is to be able to consider an issue and critically evaluate different perspectives on the issue. Consider issues that are often topics of public debate (and acrimony): taxation, immigration, government regulation, freedom of speech, funding health care, covid lockdowns, capitalism, socialism, ...
These are all complex issues and there is a wide range of perspectives on each of them. First, a student (citizen) should be able to acknowledge the existence of different perspectives. Second, objectively identify (or at least understand) the essential content of the different perspectives. Third, identify (or at least understand) the strengths and weaknesses of each of the perspectives, including acknowledging the level of evidence including its uncertainty. Fourth, compare and contrast these strengths and weaknesses. Fifth, be able to make the case for the perspective they may prefer. This may be too ambitious. But, it is a desirable goal.
I should point out that I am not at all proposing something postmodern/relativist along the lines of "all views are equally valid" or that "all views should get equal air time." Rather, such exercises and skills should lead to the ability to see why extremist and crackpot views should not get the attention or credibility that too often they do.
How does one achieve this? A concrete example is provided by an Indian newspaper presents opinion columns with Left, Right, and Centre views on specific issues.
There is a related but distinct skill that all citizens should desirably have, empathy, i.e. the ability to put oneself in the shoes of another (their context, background, and life experience) and see why they hold the views they do. This is more of an emotional skill, rather than an intellectual one. This skill enables one to understand and communicate better with those who have wildly different views than our own.
What do you think? What critical thinking skills do think should be promoted? What is realistic?
What is soft matter?
Soft Matter: A Very Short Introduction by Tom McLeish has just been published.
McLeish identifies six characteristics of soft matter.
1. Thermal motion
They exhibit large local spatial rearrangements of their microscopic constituents under thermal agitation. In contrast, "hard" materials experience only small distortions due to thermal motion.
2. Structure on intermediate length scales
There are basic units ("fundamental" structures), typically involving a very large number (hundreds to thousands) of atoms, that are key to understand soft matter behaviour. These basic units are neither macroscopic nor microscopic (in the atomic sense), but rather mesoscopic (meso from the Greek word for middle). The relevant scales range from several nanometres up to a micrometer. An example of these length scales is those associated with (topological) defects in liquid crystals, such as those shown below.
Image is from here.
3. Slow dynamics
The mesoscopic length scales and complex structures lead to phenomena occurring on time scales of the order of seconds or minutes.
4. Universality
The same physical properties can arise from materials with quite different underlying chemistries.
This characteristic is of significant practical relevance. Solving a problem for one specific material can also solve it for whole families of materials. This universality is also of deep conceptual significance as understanding a general phenomenon is usually more powerful than just a specific example.
5. Common experimental techniques
The dominant tools are microscopy, scattering (light, x-rays, neutrons), and rheometers which measure mechanical properties such as viscosity (rheology).
6. Multi-disciplinarity
Soft matter is studied by physicists, chemists, engineers, and biologists.
The chapter titles in the book are
Milkiness, muddiness, and inkiness [Colloids]
Sliminess and stickiness [Polymers]
Gelification and soapiness [Foams and Self-assembly]
Pearliness [Liquid crystals]
Liveliness [Active matter]
I highly recommend the book. Hopefully, later I will write a review.
One of the most common and reliable indicators of a phase transition into a new state of matter is anomalies (e.g. discontinuities or singularities) in thermodynamic properties such as specific heat capacity. This is how the superfluid phases of helium 4 and helium 3 were both discovered. Further transport experiments were required to show that the new states of matter were actually superfluids. This point was highlighted at the end of my last post.
In 2014, I wrote about the puzzling magnetoresistance of graphite and some experiments that were interpreted as evidence of a metal-insulator transition when the electrons are in the lowest Landau level of the graphene layers. This interpretation was partly motivated by theoretical predictions of charge density wave (CDW) transitions in this regime. I expressed some caution and skepticism about this interpretation, highlighting problems in other systems where magnetoresistance anomalies were given such interpretations. I suggested that thermodynamic measurements should be performed.
In 2015, I highlighted similar issues, suggesting there is no metal-insulator transition in extremely large magnetoresistance materials, contrary to claims in luxury journals. Within two months my claim was shown to be correct.
I was delighted to recently learn from Benoit Fauque that he and his collaborators have now performed measurements of the specific heat of graphite in high magnetic fields.
Wide critical fluctuations of the field-induced phase transition in graphite
To what extent Landau valued ... connexion with experiment is revealed by the following. His theoretical department at the Institute was small (there were no more than ten research workers and aspirants). Although I suggested that the Academy might set up a special Institute of Theoretical Physics on as large a scale as he wished, Landau not only declined, but even refused to discuss the matter. He said that size was not important and he was extremely happy to be classed as a staff member of the experi mental institute.
But Landau’s greatest contribution to physics was the theory of quantum liquids. Its significance continues to increase and undoubtedly during recent decades it has also had a revolutionary effect on other fields of physics— solid state and even nuclear physics.The theory of superfluidity was stated by Landau in 1940-41 soon after the discovery in 1937 by P. L. Kapitza of this basic property of helium-II....The discovery and explanation of superfluidity is also remarkable for its truly constructive interaction between experiment and theory. The research of Kapitza and Landau was carried out in close scientific co-operation and there is no doubt that results of the wide experimental research into processes of heat transfer in liquid helium carried out by Kapitza in 1939-41, had a stimulating effect on theoretical constructions. For his part, Landau formulated his theories while these experiments were still in progress, which made it possible to interpret the results of new experiments immediately.The basis of Landau’s theory is the notion of ‘quasi-particles’ (elementary excitations) which compose the energy spectrum of liquid helium. Landau was the first to put the question of the energy spectrum of a macroscopic body in this most general form, and he also found the character of the spectrum for a quantum liquid of the type to which liquid helium (the 4He isotope) belongs;
The concept of quasi-particles is arguably one of the most important in quantum many-body theory and condensed matter.
Aside: I had forgotten this and tended to think quasi-particles were introduced by Landau in his Fermi liquid theory paper fifteen years later.
The comments above follow the common narrative of the discovery of superfluidity, which as Sebastien Balibar argues is debatable. This narrative exclusively focuses on Kapitsa and Landau. The new state of matter, Helium-II, associated with a singularity in the specific heat of liquid 4He at the lambda temperature, was discovered in 1927 by Willem Keesom in Leiden. Superfluidity was independently discovered in 1937 by Allen and Misener. Theories of superfluidity, including the two-fluid model, by Laszlo Tisza and Fritz London, were developed before Landau's.
Nevertheless, the main point remains clear. It is highly likely that Landau and Kapitsa had a significant influence on one another. Such synergy between experiment and theory is at the heart of condensed matter physics. Kapitsa was definitely following the integrated approach of Kammerlingh Onnes: development of experimental techniques, careful measurements, addressing fundamental questions, and interaction with theorists.
Condensed matter physics aims to understand different and describe states of matter. Each state (phase) is associated with a particular type of order and phase diagrams encode the external parameters (temperature, pressure, chemical composition, magnetic field,...) that are necessary for each of the possible orderings to be stable.
Phase diagrams of even the simplest systems, such as binary alloys, can be quite rich, with many competing phases. Nevertheless, in many cases, simple microscopic models, with just a few degrees of freedom and a few parameters can describe these rich diagrams. Often a key is for the model to involve competing interactions, which can arise from different forces or from geometric frustration. Earlier, I wrote about how an Ising model on a hexagonal close-packed lattice could describe the plethora of distinct orderings that are observed in binary alloys. There the orderings are defined by the ordering wave vector and the composition of the unit cell. Another example occurs in spin-crossover materials and is described in recent work by my UQ colleagues.
Structure–property relationships and the mechanisms of multistep transitions in spin crossover materials and frameworks, Jace Cruddas and Ben J. Powell
A 2016 chemistry paper was First Step Towards a Devil's Staircase in Spin‐Crossover Materials
Another rich example is where there are two different spatial scales associated with interactions between the components of the system. In a lattice system, this can lead to ordering wavevectors that are incommensurate with the lattice. About forty years Per Bak wrote a nice series of papers that explored this situation.
Ising model with solitons, phasons, and "the devil's staircase", Per Bak and J. von Boehm
This is an elegant and clear study of a simple Ising model in three dimensions with a frustrating interaction J_2 in the vertical direction. This is an example of an ANNNI model.
A paper by Bruinsma and Bak considers an AFM Ising chain with 1/n^2 interaction, in a magnetic field, at zero temperature.
Note: In the figure below q is NOT the wavevector but rather the ratio of up to down spins.
The magnetisation vs field curve has a fractal structure.
Bak also wrote a Physics Today article (that compares the phenomena to frequency mode locking) and a general review that includes examples of experimental realisations, ranging from magnets to atoms on surfaces.
This illustrates an important point that is often made in complexity science. Simple rules (theoretical models) can produce complex behaviour.
This also illustrates characteristics of emergent phenomena. A wide range of physical systems can exhibit the same phenomena. Many of the details do not matter.
The devil is not in the details.
The statement "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement" has been widely misattributed to Kelvin since the 1980s, either without citation or stating that it was made in an address to the British Association for the Advancement of Science (1900).[86] There is no evidence that Kelvin said this,[87][88] and the quote is instead a paraphrase of Albert A. Michelson, who in 1894 stated: "… it seems probable that most of the grand underlying principles have been firmly established … An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals."[88]
“The time has come to close the book on infectious diseases. We have basically wiped out infection in the United States.”Wow, that sure was wrong. There are now 9 million covid-19 cases and more than 200,000 deaths in the USA. I was going to write a blog post about this. But, then I discovered these two nice articles.
I have just rewritten chapter 1 of Condensed Matter Physics: A Very Short Introduction. I obtained very helpful feedback on my first version from a freelance editor. This has given me fresh eyes for the whole manuscript, which I am now rewriting. She suggested moving some strong material from later chapters into the first chapter, particularly the fact that CMP is all about emergence. I have also benefited from other readers and blog commenters. For example, David Sholl's asked about how CMP is different from other approaches to materials science.
Here is the new version.
I welcome comments. But, again you are probably not my intended audience. Rather, it is your family, undergraduates, or colleagues in biology or social sciences.
Some progress is being made in understanding the structure and dynamics of the SARS-CoV-2 virions (virus particles) that are responsible for the pandemic. A nice starting point for the non-expert is a recent article in The New York Times.
A fundamental question is what is the structure and symmetry of the virion? In particular, does it have the icosahedral symmetry possessed by many virions, as discussed in a talk I gave earlier this year and in a recent review (with lots of nice pictures). As far as I am aware, there are still no definitive results on the overall structure and symmetry.
This preprint has some really nice images and videos such as the video below.
SARS-CoV-2 structure and replication characterized by in situ cryo-electron tomography
The paper below shows that the nucleocapsid protein (N) is similar to that for SARS-CoV and MERS. The protein can form dimers and tetramers, steps in the self-assembly of the whole virion.
Specific viral RNA drives the SARS CoV-2 nucleocapsid to phase separate
Some nice soft matter physics is in the preprint below. It argues that the N protein can undergo liquid-liquid phase separation with the viral genome. Aside: even before covid, liquid-liquid phase separation was quite a hot topic in cell biology, as recently discussed by Tom McLeish.
Architecture and self‐assembly of the SARS‐CoV‐2 nucleocapsid protein
Qiaozhen Ye, Alan M. V. West, Steve Silletti, Kevin D. Corbett
Finally, the paper below combines molecular dynamics simulations with experiments to argue that the stalk of the spike protein has three hinges giving the head of the spike unexpected orientational freedom so it can scan the host cell surface.
