Science from An Old Bucket of Water

wallpaper-mountains-1366x768
Trees’s growth  ignore the slope. Picture Source: https://previews.123rf.com/images/waldru/waldru1303/waldru130300029/18594282-Trees-on-the-mountain-slope-Winter-without-snow-Stock-Photo.jpg

If you climb a hill, you will notice that the trees are not perpendicular to the slope. With some variations due to wind, tree trunks generally meet the horizon at a right angle. Similarly, if you are collecting rain water with an old bucket on a slanted driveway, you will notice that the water level is not parallel to the asphalt. More water leans against the walls of the bucket facing downslope.

bucket

If you wait for more rain to fall into the bucket it will look like the second illustration. Wait longer and liquid water will not reach point C.  Instead it will overflow at point A. The bucket never fills with liquid.

All this is a reminder that gravity neither acts from the surface just below trees, nor from the surface below the driveway. It acts from the center of the Earth. We know from geometry that any radius is perpendicular to a line tangent to the circle. The horizon is equivalent to a tangent line, hence the reason for the alignment of trees and for the fact that points A and B in the bucket are at the same height above the horizon. (see green arrows in the diagram) It’s at those positions that they have the same potential energy, the product of weight and distance from the plane’s center.

If you leave the bucket out in late autumn, you will be in for a more pleasant surprise. After I knocked the bucket down, here’s what slid out along with the water that had not yet frozen.

icebucket
Two views of the same hollow cylinder of ice from a bucket. My keys are at the base for a sense of scale.

The ice is in the form of a hollow cylinder, one that eventually would have filled the whole bucket. The sight is a little deceiving. Unfrozen water is not the only thing missing from the picture. On its way out, the unfrozen water broke through a thin layer of surface-ice, which formed first because it’s the only part of the water that was directly in contact with the cold air. But why was the core of the liquid left unfrozen? The inner plastic walls not only cooled off faster than the subsurface water due to the lower specific heat of plastic, but the impurities and imperfections on its surface also provided nucleation sites for ice crystals to form. Even at the very beginning, one observes a crescent of thin ice on the colder surface, not coincidentally resting on the side of the bucket with more plastic exposed.

If we had waited long enough, why would the entire bucket have been filled with ice, something liquid water is incapable of doing when the bucket is sitting on a slope? On average, in liquid water, each molecule is hydrogen-bonded to about 3.4 neighboring molecules that constantly break and reform. But in ice each each molecule is hydrogen-bonded to 4 other molecules in a more stable fashion. This spreads out the H2O molecules in the ice structure, lowering its density. It’s the reason ice expands as it freezes into a hexagonal network, one that’s 3 kJ/mole stronger than that of a non-supercooled liquid network. It’s also the reason ice can’t flow like liquid water.

ice2
Text and image modified from a combo of AP Biology and chemguide.co.uk diagrams.

So after the ice starts to form on top and then along the internal walls of the bucket, the frozen base and the circular rim begin to thicken. The rest of the forming crystals grow until they reach the middle of the bucket. With molecules that are more tightly bound, the ice at point A cannot flow out of the bucket as it did when it was in a liquid state. But the air space in the bucket above the slant will be occupied as the ice from the freezing core expands and pushes upwards. The bucket, as a result, even though on a slant, gets completely filled with ice, which also expands against the bottom, deforming the plastic base.

If you slide the ice back into the bucket and wait for a warm day to melt it, water will reveal its intrinsic color. Most glass containers aren’t large enough for water to absorb enough red light to reveal a perceptible hue of greenish blue. Too often we get the false impression that water is transparent. But the white walls of the bucket will provide enough internal reflection to increase the path length, and water’s color becomes noticeable. I’ve ventured a little deeper into that idea in this blog entry. If you’re not interested, hopefully I’ve nevertheless shown that there are some side-benefits to saving water and energy while collecting rain.

Advertisements

Life at the End of Quantum Tunnels

Recently a biochemistry student told me that her classmates looked like they had seen a ghost when their professor seemingly took a left turn from a lecture on cellular respiration and started to discuss quantum tunnelling. But this 90-year discovery keeps surfacing in different contexts, reminding us that without the tunnelling effect, there would be no life in the universe.

Part of the lecture focused on iron–sulfur clusters, which play a role in the oxidation-reduction reactions of mitochondrial electron transport. The clusters are part of four protein complexes that sequentially shuttle electrons. The latter are ultimately gained from the breakdown of food molecules and are destined for oxygen. In so doing, protons are consumed inside the mitochondrial membrane while others are pumped out, creating a potential difference that helps motor the synthesis of adenosine triphosphate (ATP). Then ATP goes on to facilitate a host of energy-requiring reactions that keep an organism alive.

ElectronFlow
Each green arrow represents an electron jump due to quantum tunnelling.   http://www.pnas.org/content/107/45/19157/F2.large.jpg

But each time an iron cluster transfers an electron, it does so against a potential energy barrier. How does it do it? Because of the wave-like properties of a tiny particle like the electron, when it’s up against a thin-enough barrier, such as the 2.2 to 3.0 angstrom gaps (0.22 to 0.30 nanometers) shown in the diagram, there is a small but non-zero probability that the electron will be in the gap, and more importantly, also beyond it.  The best way to convince yourself that quantum tunnelling is physically possible is to go through the math and physics, and if you’re interested, it’s found here.  The author does not show every tedious algebraic step, but if you get stuck, I will gladly help in the comments section. It’s great fun while the laundry is being done.

Life involves a struggle against entropy made possible by a continuous energy source. For the planets and presumably moons that harbour life, the most important energy source is fusion from the sun. If you are like me in that you once assumed that the prodigious gravitational force at the core of a sun could provide hydrogen atoms with sufficient energy to overcome Coulombic repulsion and bring about fusion,

5-13-Nuclear-Fusion.jpg
Image credit: E. Siegel

then you were also incorrect. It turns out that the kinetic energies are too small by a factor of 1000. So how does fusion take place? Like electrons in iron clusters, hydrogen atoms, although more massive, are small enough, and thanks to gravity, close enough to overcome the thousandfold barrier working against them. So quantum tunnelling is ultimately working with gravity to make stars shine.

The fact that tunnelling probability decreases steeply with lower thermal velocities extends the duration of smaller stars, those weighing less than 1.5 solar masses. This is important in that it gives life enough time to evolve in solar systems with appropriate conditions. One of the prerequisites of life, we imagine, is the presence of water on the surface of a moon or planet. Whether water is out-gassed or brought in via a comet or asteroid, it has to be first synthesized in molecular clouds according to this reaction between molecular hydrogen and hydroxyl radicals:

OH + H2  →  H + H2O

The extremely cold temperatures combined with adsorption on dust particles create boundaries small enough for quantum tunnelling to allow the production of molecular hydrogen from its atomic counterparts. There is even evidence that the hydroxyl reaction itself benefits from the same phenomenon.

From deep space back to our bodies, can tunnelling cause unwelcome changes in the DNA molecule? In the double helix or “twisted ladder” of DNA, each nucleotide of one strand of the ladder is attracted to its complement on the other strand by means of a hydrogen bond. A hydrogen bond consists of a lone pair of electrons from one nucleotide attracted to the hydrogen bonded to an oxygen or nitrogen atom of the nucleotide on the other side of the strand.

c5cp00472a-f1_hi-res.gif
from Modelling Proton Tunnelling in the Adenine–Thymine Base Pair
A. D. Godbeer , J. S. Al-Khalili * and P. D. Stevenson

But there is a small possibility that the proton (hydrogen without electrons) can overcome the potential energy barrier and end up bonded to the hydrogen-less atom on the other strand. If the effect would be common enough, it could lead to a mutation. It should be noted that this a very active area of research and these authors have concluded that, at least in the adenine-thymine base pair, tunnelling does not occur. Less controversial is the ideas that quantum tunnelling plays a key role in the repair of DNA from ultraviolet damage, specifically in the electron-transfer needed to undo the dimerization of pyrimidines.

If those shocked biochemistry students read this blog, I am not sure that it would erase the “seen-a-ghost” expression from their faces. As educators we don’t often empathize enough with their survival-mode of trying to focus on the “essentials” that will get them through a given course. Quantum tunnelling and quantum phenomena are central ideas, but grasping them rests on an above average foundation of mathematics, physics and chemistry concepts. Is it realistic to assume that most biochemistry freshmen have already acquired that? We have to be patient, fuel them with enthusiasm and make sure that we don’t muddy the waters of key concepts with too much content in our courses.

Other Sources:

WordPress.com.

Up ↑