Saturday, 28 September 2013

Relativistic Chemistry- Why Mercury is Liquid

Mercury is a periodic anomaly. It's liquid at room temperature, but why? Traditionally, the answer has always been its low melting point, but how? The marriage of quantum chemistry and relativity allows us to demystify many deviations of the periodic table, let's begin by comparing some of its next-door neighbours. Au and Hg are similar and distinct in many ways: with melting points of 1,064 °C and -38.83 °C densities of 19.32 and 19.30 g·cm−3 respectively. Their entropies of fusion are quite similar as opposed to their enthalpies. And regarding their crystalline structures: Au, Ag and Cu are cubic while Zn and Cd are hexagonal; Hg is rhombohedrally distorted Finally, Hg is a poor conductor with weak metal-metal bonding as opposed to Au, despite their similar electron configurations. Looking beyond the rare earth elements, some surprising periodic deviations arise; Hf and Zr have an uncanny resemblance. To explain this phenomenon, the lanthanide contraction is invoked. This involves the filling of the 4f orbital (unlike s, p or d electrons, here the electrons poorly shield the nuclear charge). As we move along the rare earths, 14 protons are added and the lesser penetration of the 4f orbitals means they are partially shielded by the 14 4f electrons; causing the electron cloud to contract. But other questions remain unanswered by the lanthanide contraction: 1. why is Ag coloured gold? why not silver? 2.what is the reason for the high electron affinity of Au? One may be tempted to introduce the idea of an inert 6s pair, but this fails to address the liquid nature of mercury. Relativity dictates that the mass of an object increases with its velocity, hence we can derive 3 main relativistic effects relevant to Hg and Au.

Firstly, the p3/2 orbital contracts to a lesser degree as opposed to the s1/2 and p1/2 orbitals (which contract a lot). Secondly, such causes an outward augmenting of the d and f orbitals (in relation to the s and p orbitals). And thirdly, the relativistic splitting of the p, d and f orbital energies manifests itself as spin-orbit coupling. These 3 effects cause the energy gap (difference) between the 5d5/2 and 6s1/2 orbitals to shrink. More importantly, we may explain away the colours of Au and Ag; the colour of Au is caused by the absorption of blue light causing 5d electrons to be excited to the 6s level, however silver appears colourless when it absorbs UV. The relativistically contracted 6s orbital in Hg is filled and hence, unlike Au, the 2 6s electrons don't play that much a role in metal-metal bonding, which is why it is liquid at room temperature.

Sunday, 8 September 2013

Universal Common Ancestry- A Test

Are Americans, Archaea, Amoeba and bacteria all genetically related? The notion of a 'universal common ancestor' (UCA) is central to evolutionary biology. Much of the traditional arguments have been confined to 'local' common ancestry (of particular phyla) as opposed to the totality of life; let's overcome this assumption and test the hypothesis using probability theory and phylogenetics. The problem of UCA has been compounded by horizontal gene transfer (transduction, transformation and conjugation) where early genetic material passed on between entirely different species is thought by some to challenge the 'tree of life' pattern by creating reticulated lineages. The qualitative evidence for UCA spans the congruence of biogeography and phylogeny; the mutual agreement between the fossil record and  phylogeny, the nested hierarchy of forms and the correspondence between morphology and molecular genetics. Such arguments boil down to 2 premises: (1) the nearly-universal nature of the genetic code and (2) critical similarities on molecular level (L-amino acids, fundamental polymers, metabolic intermediates). Since these arguments are merely qualitative, they do not rule out conclusively, the possibility of multiple independent ancestors. We can examine UCA quantitatively by model selection theory (without the presumption that sequence similarity implies a genealogical relationship) and a set of highly-conserved proteins. Also, we can model our test on Bayesian and likelihoodist probability (as opposed to the classical frequentist null hypotheses). Keep in mind that sequence similarity is the most likely consequence of common ancestry but this alone is not enough to support homology (similarity may be due to convergence). It is the nested, hierarchical relationship between sequences that necessitates the inference of common ancestry (because some similar sequences produce a conflicting phylogenetic structure which forces the conclusion of uncommon descent).

So are the three superkingdoms of life (archaea, bacteria, eukarya) united by a common ancestor? Douglas Theobald recently performed a test where 23 conserved amino-acids across the three domains had evolutionary networks (or trees) build around their sequences. Then contrasting the probability values for a range of ancestry hypotheses. But does this imply that life originated only once around 3.5 BYA? Not at all! It just implies that one of the primordial (original) forms of life has extant descendants; however it is possible for life to arisen more than once but the whole conclusion necessitates that all life has at least once common ancestor: a last universal common ancestor (LUCA). A problem however is that a phylogenetic tree can be build on virtually any set of data; we need to demonstrate an agreement between trees for the exact set of data spanning different datasets. And this agreement can also be explained in terms of other biological processes so the Akaike Information Criterion (AIC) may be applied to compare and contrast a range of hypotheses.So what signature feature of sequence data allows us to give qualitative evidence for UCA? In a nut-shell, the site-specific relationships in the amino-acids across a range of species; such relationships fade away as we go back in time through a lineage and species converge back (but with enough data, the progressive accumulation of relationships becomes statistically significant). On the other hand, if a pair of extant species have absolutely distinct origins, the relationships between the site-specific amino acid correlations (in the two species) disappear.

Friday, 6 September 2013

Graphene- One Carbon Thick

This carbon flatland is one wonder material. Graphene is a two-dimensional sheet of crystalline carbon just one atom thick; it is the 'mother' of all carbon-based structures: the graphite in pencils, carbon nanotubes and even buckminsterfullerene. The behaviour of electrons in the honey comb lattice as massless Dirac fermions gives graphene its unique properties. One signature effect of graphene is its distinct Hall effect, in the original Hall effect, an electric current (in the presence of a transverse magnetic field) causes a decrease in potential perpendicular to both the current and magnetic field. Near absolute zero, the Hall resistivity (ratio of decrease in potential to current flowing) in a 2-D electron gas becomes discrete (or quantised), taking integer values h/ne^2. But in graphene, a Berry phase means that the Hall resistivity is only quantised as odd integers (π), hence if you spin the wave-function of the Dirac fermions in graphene (about a circle), there is no symmetry and the state ends up in a different phase then what it began with. Moreover, the quantum Hall effect in graphene can occur at room temp. and can distinguish between layers (due to cyclotron energy of electrons). Graphene could give insight into relativistic effects on the bench-top, since the velocity of light for Dirac fermions is 300 times less in graphene, it should have a larger value for its fine structure constant (around 2). Zitterbewegung (the jerky motion that arises when its impossible to locate the wave function of a relativistic particle) is yet another frontier for graphene, the path of a relativistic electron jitters when it interacts with a positron. This type of motion occurs too quickly to be observed directly in materials like solids but when Dirac fermions are restricted to graphene sheets, they can be interpreted as mixing of states.

The Klein paradox in QED is when a potential barrier allows relativistic particles to move through freely, yet the probability that an electron tunnels through decreases at an exponential rate with the height of the barrier. Paradoxical enough, the probability for relativistic particles increases with barrier height (since a potential barrier that acts to repel electrons will also attract positrons). Chiral symmetry breaking may also be illuminated by graphene; in graphene the right and left-handed fermions behave the same unlike neutrinos which are strictly left-handed. But graphene is too conductive and to lower its conductivity we can take advantage of carbon's adaptability. In diamonds, each carbon is bound to four others (involving all electrons) in contrast to graphene, where one electron is left over (making it a good conductor). The most basic way of achieving this is to add a hydrogen (just like conversion of ethane to ethane) to make graphene into graphane. The σ-electrons that bind carbon atoms in graphene make a band structure with an energy gap between the final occupied and vacant states. But the delocalised π-electrons cause fully occupied and vacant bands to touch one another. In graphane, the π-electrons are strongly attached to hydrogen atoms, making an energy gap between the lowest vacant band and the highest occupied band. Bizarrely, annealing causes the hydrogen to disperse leaving the graphene backbone whole.