What are liquid crystals?

Once you accept the idea that the simple, microscopic interactions between bits of matter can lead to the emergence of dramatic collective properties when large numbers of particles are concerned, it's not surprising to realize that there are many different ways that large ensembles of particles end up organizing.  As mentioned previously, a true liquid is a system where the average distance between the particles is comparable to the particle size, but the particles are in constant motion and there is no particular long-range order to the way the particles are arranged.

New possibilities present themselves if the particles have some kind of "internal degree of freedom".  For example, think of the particles not as little featureless billiard balls, but as elongated objects.  Now we can consider having the orientation of all the particles have some long-range correlation.  A liquid crystal is an emergent phase when the particles are close together and there is not 3d spatial order in the arrangement of particle positions, but there is order in the orientations of the particles.  In nematic liquid crystals, the centers of mass of the particles are completely spatially disordered, but there is long-range order in their orientation. For example, they could all be pointing the same direction, indicated by the not-so-cleverly-named vector, the director.  Cholesteric liquid crystals have some twist or chirality to the particle orientation.  In smectic liquid crystals, the particle centers of mass are actually spatially ordered in one direction, but not in the other two (i.e., you can think of stacks of layers of particles, with particles free to move within each layer).  The wiki page about liquid crystals gets into the history of these systems, and here is a nice webpage that classifies them.  Liquid crystals are very useful because their directed nature gives them anisotropic optical properties, and if the objects in question are polar molecules, it is possible to reorient them electrically.  This combination enables many technologies, almost certainly including the display device you're using to read this.

There was a time when I was somehow skeptical that all these phases were "real" thermodynamic phases.  I was used to solids, liquids, and gases, and I'd learned about "hard" condensed matter phases like ferromagnets and superconductors that dealt with emergent properties of the electron gas.  Somehow these liquid crystal things didn't seem like the same sort of thing to me.  Then I read the really great book by Chaikin and Lubensky, and saw things like the figure at right (from G. S. Iannacchione and D. Finotello, Phys. Rev. E 50, 4780 (1994)).  The figure shows the specific heat of a liquid crystal (in some nanopores) as it goes through a thermally driven transition between the nematic and isotropic phases, as a function of scaled temperature, \(t \equiv (T/T_{\mathrm{c}})-1\).  This kind of sharp, divergent feature and scaling as a function of temperature are hallmarks that show these phases and their transitions are every bit as real as any other thermodynamic phase, even though the materials are squishy.

Java applets for physics - a great resource being strangled by security?

As many of my readers know, starting in the late '90s, many clever, creative people around the world wrote cute (and sometimes very sophisticated) Java applets to demonstrate certain physics and engineering concepts.  Examples include this great site by the University of Buffalo, a virtual lab by the University of Oregon, this resource by UCLA, this outstanding site from the University of Barcelona, etc.  Many of us owe a real debt of gratitude for these resources, as they have been great educational tools. 

A problem has arisen, however.  You will notice that none of the applets linked above actually run.  Because of security concerns about Java, the latest versions of Java require applets to have been compiled, authenticated, and certified (via electronic security certificates), or the applets simply won't be run by the virtual machine.   For actively maintained sites (such as the excellent "physlet" effort from Davidson), the authors and maintainers have thoughtfully recompiled and updated their code.  Others (the University of Colorado) have rewritten everything (!) in Flash or HTML5.  Unfortunately, these are the exceptions, and many other cool sites are orphaned, with clever code that can't be run.

If anyone knows a work-around (some kind of emulator that would run the code in a walled-off way?), please describe it in the comments.  It would be a real shame if the accumulated excellence of all those older sites was wiped out.  Thanks.

Several items, including interesting reading

• Celebrity scientist Lawrence Krauss has written an article (pdf) about whether celebrity scientists are good for society, and noting that celebrity \(\ne\) greatest scientific researcher, necessarily.  In response to the title ("Celebrity scientists:  Bad for science or good for society?") it's tempting to be snarky and respond "Why not both?". Note that this guy is conspicuously absent from the article.
• Hat tip to the Angry Physicist for pointing out this article about the US military academies.  I found it genuinely shocking.  I'd always had the impression growing up, based on anecdotes I guess, that West Point and Annapolis in particular were incredibly selective and could be very academically demanding.  The academy graduates I've met over the years had only reinforced this idea by being very impressive people.  I was very dismayed to read about the apparently low academic standards.
• I was dismayed by two NSF-related issues in the last week.  First, NSF has gotten increasingly rigid about enforcing minutia of their guidelines over the last couple of years.  This is particularly frustrating when combined with guidelines that are themselves ambiguous (e.g., saying that a preproposal must include certain items, but not saying whether other items like collaboration letters are desired, or worse, forbidden because adding extra material can be grounds for getting bounced without review), and then being hard to reach for clarification.  This is a further sign that they are understaffed and overwhelmed.
• Second, in the Major Research Instrumentation call, NSF no longer allows grant funds to pay for technical staff.  That means that an approach that had previously been extremely helpful (have NSF pay for 75% of a staff person the first year, 50% the second, and 25% the third, so that a university can taper in technical staff support over time) is no longer possible. 
•  An old friend of mine does an excellent podcast, and he spent some time talking with me - it was really fun.

What is a phase (of matter)?

Defining "a phase of matter" for a popular audience is a tricky business, with choices ranging from the overly simplistic and therefore vacuous (a collection of matter that has homogeneous, uniform, well-defined physical properties that are distinct from other such phases), to the very technical, to sophistry (like the famous definition of obscenity).

A critical ingredient missing from the simple definition above is the deep, profound point that phases of matter only make sense as emergent from the collective behavior of many constituents (the dynamics of which are often governed by simple rules).  A single water molecule is not a solid, a liquid, or a gas - it is just a single molecule, with a structure and some mechanical, electronic, and optical properties that can be calculated with pretty good accuracy through "ab initio" techniques like density functional theory and its relatives.  (Note:  Even doing that is bloody hard, given that ten electrons is actually a lot from the standpoint of quantum chemistry.)

However, if you take a collection of \(N\) water molecules and stick them in a box of a fixed volume \(V\), with a certain amount of kinetic energy \(E\), and let them bounce around and do their thing, interacting with each other via van der Waals and longer-ranged (dipolar, since water is a polar molecule) forces, something interesting will happen.  To avoid difficult conceptual issues about reversibility, let's imagine you have a whole bunch of boxes like this, all prepared with the same \(N, V\) and \(E\) but with the microscopic initial conditions like molecular positions and velocities scrambled.  (This is the "microcanonical ensemble", for experts.)  Wait an unspecified long while. What you will find is that as \(N\) increases from 1 to a large number, at some point you will start being able to classify the emergent, "coarse-grained" properties of these boxes.  For a sufficiently low \(E\), you will find that the vast majority of the boxes contain a blob of water molecules that have arranged themselves in a spatially ordered way, with spatially periodic positions and orientations.  There will be a few leftover molecules bouncing around, and the blob will have a certain amount of jiggling going on.  If you shook the box, you would see that the blob moves rigidly, exhibiting some resistance to deformation, though the molecules at the edges would move more easily, and would be constantly exchanging with the few leftover molecules bouncing around the rest of the box.  Somehow, the molecules in those boxes have spontaneously broken a bunch of symmetries (picking out spatial locations that exhibit some periodicity and rotational symmetry), and what we think of as "bulk" properties have emerged, like density, some kind of elastic modulus, a speed of sound, etc.  There is now some interface as well, between the solid and the mostly unoccupied void. 

For higher \(E\), you will probably find that the vast majority of boxes contain a blob of water molecules that are very close together, bumping into each other all the time, but tumbling around with no particular relative orientation.  This blob of water has an interface with the remaining "gas", and does not respond rigidly if it bumps into a wall of the box.  If you could look at all the molecules, you could add up how much energy it takes to expand the surface of that blob - this is proportional to the surface tension.

At still higher \(E\), you will find that the water molecules are roughly homogeneously distributed throughout each box, bumping into each other and the walls.  You could still think about an average density for this gas, and if you banged on the wall of the box to impart momentum to the molecules that happen to be hitting that wall, you could watch the propagation of a density wave (sound!) through the molecules.   In the really high \(E\) limit, the molecules decompose and the constituent atoms ionize - this is a plasma.

Each of these arrangements that you would find in a very large percentage of such imaginary boxes, with its emergence of well-defined "bulk" physical properties (including more subtle ones I haven't mentioned, like magnetic order or electrical conductivity) as \(N\) grows to a statistically large value, is a thermodynamic phase of matter.    Why are these the particular ones that occur?  Why do water molecules tend to form particular solid structures?  Why don't we see the spontaneous appearance of phases that look very different, like long 1-d chains of water molecules, for instance?  It's not at all obvious!  That's the fun of condensed matter physics:  The answer somehow lies in the microscopic properties of the molecules and their interactions - it's latent in there as soon as you have one molecule, but somehow cannot emerge and be realized except through the collective response of a large ensemble.  More soon.

More posting soon.

Sorry for the brief hiatus.  Many urgent tasks (e.g., proposal deadlines, prep for semester, grad admissions).  Suggestions for forthcoming topics are always appreciated.  Coming up in future installments:  "When does water become wet?", "What is a phase?", "What are liquid crystals?", and "Centers, Institutes, and all that".