When to Rotate, When to Vibrate?
I’ve been working on very tangible models of both solid spherical crystals of lignin nanotubules, as well as spherical liquid crystals of the same lignin nanotubules, when suspended in a suitable reagent. My latest animation of the coupled rotation of “A Liquid Crystal Sphere” depicts quantum pressure in action, where the motion on the surface of a spherical object is transferred through the whole volume of the object. While I’ve talked about the differences between solids and liquids and the influence of pressure, I realize that there is an additional phenomenon that’s just as important, but which I still haven’t talked about: that of the inertia of the rotating cylinders. In this post I’m going to correct this.
So, what is inertia? According to Wikipedia:
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes its velocity to change.
Inertia in solids is quite well defined. However, the theory of quantum pressure, which I’m still working on crystallizing, changes how inertia is perceived in liquids and gases. While a solid experiences inertia as a macroscopic object, liquids are a bit more complicated. Forgetting gases for a while, liquids consist of quantized objects, mostly coupled to their environment, but still exist as separate entities that can decouple (at least partially) in certain conditions.
I think I must backtrack a bit more. What is this elementary quantized object? Well, in the case of liquid crystal lignin sphere, the elementary object is a single crystallized nanotubule. some of these are long (possibly over 100 nm) and some very short (ca. 8 nm) depending on their location within the spherical liquid crystal. And the inertia of the whole spherical liquid crystal is the sum of the inertias of the individual cylinders.
In a liquid the rotational inertia of a quantized object is retained. Also, the angular momenta of neighboring quantized objects have opposite signs. However, if the cylinders rotate at the same angular velocity, the absolute quantities of neighboring objects are not the same, unless they are of identical length, which most times is exactly the case.
So, when is inertia not retained within the quantized object? When a liquid freezes or in the case of lignosphere liquid crystals, when a solvent is removed from the liquid solute. Or when there is a chemical reaction and the reaction product cannot exist in the liquid state in the same conditions.
Let’s consider freezing first. When the temperature of the liquid drops, the speed of individual quantized objects drops reducing their inertia. And when the inertia drops sufficiently, it is no longer sufficient to retain the rotational motion and the object locks in place. The inertia itself is retained, but the rotational motion converts into the back-and-forth vibration of the locked object.
And the case with solutes is similar. The solvent traps the solute within it, allowing it to rotate freely, without interlocking with its neighbors. In the case of the self-assembly of lignospheres, lignin dissolved in a solvent (such as tetrahydrofuran) is free to rotate, either as individual molecules, or small clusters of molecules. But when this solution is introduced into water, much of the solvent that was dissolving lignin diffuses into the water phase, dissolving water in the very same way (although water can dissolve itself above its freezing temperature). When the solvent composition is kept sufficiently high, the lignin doesn’t crash uncontrollably out of the solution but begins to crystallize into about 8 nanometer long nanotubules that in turn crystallize into longer nanotubules, forming spheres, mostly comprised of water (very roughly about three fifths), lignin (about a fifth) and solvent (about a fifth). To understand why, I would have to explain a quite a bit about chemistry, but trust me in saying that I’ve worked on the general process for 12 years and the industrial process for 8 years.
Modeled with animated hollow cylinders, the process looks like this:
The internal pressure of the cylinders keeps them in rotational motion, while the internal pressure of the rounded rhombuses is insufficient, forcing the same thermal motion to be expressed as vibration. This pressure is close to, but not necessarily the same as vapor pressure.
Once the spherical crystal has been locked into place, it’s not a big problem redissolving the lignin, but to do so while maintaining the crystal structure is trickier. One of the problems is purely figuring out whether this has been accomplished or not. My current hypothesis is that if anything is added into lignin spheres that convert them from anything between a powder to a hazy brown dispersion into a viscous transparent liquid, this liquid at least begins as a liquid crystal. The viscosity limitation is that if there’s enough solvent to break the spheres apart, it’s impossible to say whether the solution is comprised of something smaller than the original sphere, or whether the sphere retains its shape. However, if the concentration of the liquid is sufficiently large, there is basically no external volume for the spheres to dissolve in. Or the spheres could only form smaller spheres upon dissolution.
It’s relatively easy to convert the spheres into a liquid that remains liquid for a short time but then solidifies or gels. However, nowadays we can make liquids in the lab that have a shelf-life of over a month at room temperature and much longer than that when cooled down. Probably if we were to intentionally aim for extremely long-lived liquids, a shelf-life of years at room temperature would not be a problem, but as we want to make reactive formulations for coatings and adhesives, too much stability isn’t always the goal. An adhesive needs to react at some point.
One might ask, if the rotating quantized objects in liquids and solutions conserve their inertia, wouldn’t this be akin to perpetual motion? The short answer, if one considers elementary particles of energy, is yes. Everything is made of elementary particles of energy that are constant motion at the speed of light (or the speed of energy, as I like to call it). But the longer answer is, no because of black-body radiation. The generation of torque/pressure requires there to be a constant radiation of thermal radiation that is mostly being absorbed by the body, keeping up the temperature/pressure, but unless the system is being bombarded with more radiation, it will inevitably cool down and the rotation stops. Luckily, we people are good at maintaining such a temperature. But if we didn’t, things would eventually freeze. Especially here in Finland.
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