Sunday, June 26, 2022

How did the Chemical Elements form?

The absolute majority of chemists know immediately what to do with the chemical elements. They know their symbols by heart, they know by heart their atomic number, their mass, some densities. They are adept at mixing their compounds under different conditions to create molecules and give the compound formed a noble use. In the end, atoms are the raw material of chemistry. But where did these fundamental units come from? How were chemical elements formed?

 This is a question that is not very common, or even necessary, in the conversation circles of chemists in general. After all, when we colonized this world, all the natural chemical elements were already here and will certainly be around long after we leave. To begin to answer the question that gives title to this text, it is important, first, to quantify these elements. We know that on Earth we find, to a greater or lesser extent, 90 chemical elements represented in the Periodic Table, from hydrogen to uranium, skipping Technetium and Promethium, which do not exist naturally here, but which have already been detected in stars. The other elements, called transuranic, are obtained artificially in particle accelerators. Although these 90 elements form the entire framework of our planet and even our organism, they were not created on Earth.

It would be interesting, then, to know how these elements are distributed outside our planet. The Standard Cosmological Model tells us that the Universe is made up of 68.3% of dark energy (energy that has not yet turned into matter – E=mc2 – but which is very little known), 26.8% of its structure is composed by cold dark matter (matter identifiable by its gravity, but which is not visible, since it does not emit light) and 4.9% of baryonic matter, which is matter composed of protons, neutrons and electrons, that is, atoms of our chemical elements.

In turn, these 4.9% of baryonic matter are distributed as follows: hydrogen and helium gas from the primordial formation of the Universe, 4%; hydrogen turning into helium in the cores of stars, 0.5%; neutrinos, 0.3%; the remaining 88 natural elements heavier than helium represent only 0.1% of the Universe's composition. It is little, very little, but considering that these elements are concentrated in clouds that, in the end, will give rise to the planets, including the Earth, that 0.1% is of fundamental importance!

This entire formation process began in a unique and singular moment, called the Big Bang. The Big Bang model was proposed by a Belgian priest, mathematician, philosopher and astronomer named Georges Lemaître. This model proposes that, at a given time zero, all the mass that makes up our Universe was concentrated in a single point of negligible volume and maximum density. The four forces that govern the interactions of the Universe – electromagnetism, gravity and the strong and weak nuclear forces, responsible for the stability of the nucleus of atoms – were united. In that initial moment, the temperature reached the colossal mark of 1032 K.

What happened between moment zero and 10-43 seconds after the Big Bang, no one knows for sure, because, in that interval, the theories of Quantum Mechanics and General Relativity do not understand each other (and it is the establishment of the relationship between these theories in this singular moment that Theory of Everything, or Theory of Grand Unification – TGU, seeks to unify mathematically). This first moment is called the Planck Era and the Universe was the size of the Planck Length (1.6 x10-35 m).

Contrary to what most people believe, the Big Bang was not a big explosion. In an explosion, matter is thrown out from somewhere. On the contrary, in an expansion there is no idea of ​​“outside”, since neither space nor time existed outside the Universe. Therefore, in the moments following the Big Bang, the entire Universe expands, including the space (and time) between its constituents. Think of a raisin cake baking and rising. If the Universe is the cake, there is no cake outside the cake and all the dough expands, decreasing its density and pushing all the raisins away from each other.

Like the cake, as the Universe expanded, its density decreased, and with it the temperature. After 13.7 billion years from the initial moment, the average temperature of the Universe dropped from 1032 K to 3 K and the density plummeted from maximum to about 2×10-29 kg.m-3.

 10-36 seconds after the Big Bang, the period known as the Inflation of the Universe begins. At that time, the Universe was composed of an extremely hot and dense soup formed only by elementary particles, among them, quarks and gluons, which constitute protons and neutrons. This soup, called “Quark and Gluon Plasma”, therefore presented the subatomic particles necessary for the creation of atoms.

At 10-11 seconds after the Big Bang, the individualization of the weak nuclear and electromagnetic forces begins and, with this, the aggregation of subatomic particles occurs. The temperature reaches 1015 K. Obeying Einstein's equation: E=mc², matter and antimatter are created and annihilated at a frantic pace. At 10-9 seconds, the excess quarks unite to form the first stable protons and neutrons.

After the 1st second after the Big Bang, when the Universe registered a temperature of 10 million degrees Celsius, nucleosynthesis begins. The protons and neutrons bonded together to form the nuclei of deuterium (1 proton and 1 neutron), tritium (1 proton and 2 neutrons), helium (2 protons and 2 neutrons) and some lithium and helium 3. This initial nucleosynthesis ended when a few minutes had elapsed from the Big Bang. The result of the current proportion of these elements in the Universe is from that time: 75% hydrogen 25% helium.

By the time the Big Bang completed its 10,000th anniversary, the temperature of the Universe had dropped enough for matter to prevail over energy, and as a result, gravity became the dominant force. The matter produced (nuclei of H and He) was concentrated in clusters that, millions of years later, would give rise to galaxies.

During the next 100,000 to 300,000 years, the photons possessed enough energy to prevent electrons from stabilizing around the nuclei. It was only after the Universe reached a temperature of 3,000º C that the power of the photons decreased, allowing the stabilization of electrons. At that moment, the first stable atoms of hydrogen and helium appeared.

 Between 300,000 and 1 billion years, despite the very low average density of the Universe, the atoms of H and He agglomerate to form denser points, the so-called primordial clouds. It was between 1 Billion years and the present that cosmic structures, such as galaxies and galaxy clusters, acquired their current form, originating from the evolution of these primordial clouds. The microphysics of this phase is very well known.

The density of primordial clouds, about 1012 particles per m3, is high enough to allow hydrogen atoms to coalesce into stable H2 molecules. Despite the high density, the temperature is low, around 10 K. At this temperature, gravity becomes predominant, allowing the primordial clouds to collapse under a central point. It is at this moment that the nuclear fusion reactions begin that will ignite the stars, the furnaces that will forge all the natural chemical elements present in our periodic table.

 In the Universe, there are stars of all sizes and their classification is based on the mass of the Sun, which is 2 × 1030 kg. Low-mass stars are stars that weigh less than 8 times the mass of the Sun. Stars larger than 8 times the mass of the Sun are called massive stars. These two types of stars have distinct evolutionary cycles.

Low-mass stelae, when they run out of their nuclear fuel, H, initially expand and then shrink and fade, keeping their mass in a dense, cold, carbon-rich core called a white dwarf. In turn, massive stars, at the end of their nuclear fuel, start an expansion movement followed by a collapse where all their gigantic mass precipitates on their core, causing a gigantic explosion. This catastrophic moment is called a supernova.

Very low mass stars produce practically only He from the fusion of H by the mechanism called “Proton Cycle”:

p + p —> 2H + e+ + νe

p + 2H —> 3He + γ

3He + 3He —> 4He + p + p

In the Proton Cycle, the first two reactions occur twice. Six protons go in and the product is a helium nucleus, two protons, a positron, a neutrino and energy.

In addition to the proton-proton cycle, stars can also produce energy through the CNO cycle. In this cycle, atoms of carbon, nitrogen and oxygen, which were already present in the stellar nucleus, act as the catalysts in chemical reactions: their composition does not change along the chain of reactions. In the CNO cycle, there is consumption of protons and production of helium atoms. The other elements remain unchanged.

               CNO

In most low-mass stars, the process of nucleosynthesis proceeds only until the carbon core forms, in a process called the alpha-process.

 3 4He —> 12C + e+ + e– + γ

In massive stars, this process continues through nuclear fusion until the formation of the iron core. Continuing the alpha process, helium combines with carbon to produce heavier elements, but only those with an even number of protons. Combinations happen in this order:

Carbon fuses with helium to produce oxygen.

Oxygen fuses with helium to produce neon.

Neon fuses with helium to produce magnesium.

Magnesium fuses with helium to produce silicon.

Silicon fuses with helium to produce sulfur.

Sulfur fuses with helium to produce argon.

Argon fuses with helium to produce calcium.

Calcium fuses with helium to produce titanium.

Titanium fuses with helium to produce chromium.

Chromium fuses with helium to produce iron.

Each element forms a concentric layer around the star's core, ordering itself in decreasing order of density, from the center outward. When low-mass stars begin to form iron, the gravitational energy outweighs the expansion energy generated by nuclear fusion. Initially, there is an expansion (red giant), ejecting its "shell" into space, in a phase called "planetary cloud". Then your core contracts. It is at this moment that the star extinguishes in the form of a white dwarf.

In massive stars, gravity compresses the elements formed in the respective layers in such a way that the stellar core falls under itself, turning into a neutron star, which then explodes as a supernova. During this explosion, as in the phase of the planetary cloud of less massive stars, all the elements formed until then are ejected into the surrounding space. But more than that. During the process of supernova formation, all other elements heavier than iron are formed.

And why is iron the edge line for a star's sustenance? The answer lies in the difference in the energy of internuclear bonds. The graph below shows that energy generated in nuclear fusion to form nuclei is increasing up to iron. This energy competes with the energy of gravity and maintains a stable equilibrium in the star. The process of forming the nuclei of elements larger than iron generates less energy in proportion to the mass of the element. The release of smaller energies therefore breaks the balance, allowing gravity to be the predominant force on the star, causing it to collapse.

This internuclear energy difference is also responsible for the change in the formation process of elements larger than Fe. While elements smaller than iron are produced only by nuclear fusion, the heavier elements are formed by a process that involves neutron capture and subsequent radioactive decay. This process is called Process S (S for slow):

56Fe +n —> 57Fe

57Fe +n —> 58Fr

   58Fe + n —> 59Fe —> 59Co

                                                                                                                                                                     59Co + n —> 60Co —> 60Ni

The Process works until the 209Bi element core is formed. Elements more massive than Bi are only produced in environments where the neutron flux is very high (on the order of 1022 neutrons per cm² per second). This process is called Process R (R for rapid). In stars, Process R occurs only in the seconds flanking the supernova explosion. During the explosion, there is an intense collision process of electrons and protons resulting in the formation of the gigantic amounts of neutrons needed in Process R.

Once ejected into the surrounding space, these clouds formed after supernova explosions possess all the elements that we know on our planet today. These elements are now available to be used in the formation of new generations of stars and, consequently, the new planets that will orbit them. This is the raw material that originated our solar system about 4.5 billion years ago and this will also be the process that will lead to the end of our Sun and, with it, our planet, predicted to occur in 5 or 6 billion years. Who lives will see…

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