Tag Archives: bonding

The Rainbow of Bonds

Now that we have looked at the broader picture of what a bond is, we can go a little deeper. Bonds can be easy or hard to break, they can involve particle exchange between atoms, they can be the result of transient forces, and they can react in a variety of ways. There is a rainbow of bond types to explore, but we can focus on a few primary examples.

We’ll start with the stronger sort of bonds: those that involve direct transfer of electrons between atoms. For example, say we have two neighboring atoms, one with an empty low-energy state and one with an outer electron that’s all alone at a high-energy state. If the states are similarly shaped, both atoms can lower their overall energy when the extra electron moves to the low-energy state. The atom that gave up the electron is now positively charged, and the atom that accepted the electron is negatively charged, so there is an electrostatic force attracting them. Charged atoms are also called ions, so we say that these two atoms have an ionic bond. And it’s possible to have ionic bonds involving more than one electron, if an atom has two or three electrons to donate which another atom can accept. A common example of ionic bonding is table salt, which has a sodium atom donate an electron to a chlorine atom.

It’s also possible for two atoms to share a pair of electrons, so that the electron cloud overlaps with both atomic nuclei. If the electrons in question have oppositely aligned spins, they can have the same energy without being in the same quantum mechanical state. This is called covalent bonding. It happens most often when the two atoms in question are comparably attractive to electrons, for example if they are the same type of atom. Graphite, or pencil lead, is one form of carbon that has covalent bonds. So is graphene, the atomically thin version of graphite whose discovery (and extraordinary properties) recently garnered a Nobel prize in physics.

Ionic and covalent bonds tie atoms together very tightly, and can be linked together to form complexes with many bonded atoms. These complexes are known as molecules. But large numbers of atoms can also share electrons diffusely, so that the electrons aren’t localized to a single atom or a pair of atoms. This is called metallic bonding, so-called because delocalized electrons are found in metals. The free electrons move around the atomic nuclei like a sea moving around rocks, only weakly bound to them. The mobility that electrons have in metals is why we say that metals have high ‘electrical conductivity’: it is easy to pass an electrical current, which just consists of individual electrons, through a metal. As a special case of metallic bonding, it’s also possible to have partially delocalized electrons in small molecules, which is the basis of organic chemistry.

Another way to weakly bind atoms comes from the fact that charge is separated in an atom, between the positively charged nucleus and the negatively charged electron cloud. Imagine that the cloud is slightly distorted, by a passing electrical field or by a random fluctuation. If the electron cloud is not symmetric around the nucleus at that moment, there will be a distance between the center of the positive charge and the center of the negative charge, and a force because of the opposite charges. This is called a dipole in electromagnetism, because of the two oppositely charged poles. And if you have two next to each other, they will try to align so that the negative side of one dipole is near the positive side of the other. What starts as a small fluctuation can cause a slight reordering over a large material, because of the dipoles attempting to align. This dipole-dipole interaction is another weak form of bonding. It can happen with induced dipoles, as I’ve described, or between permanent dipoles which are common in molecules.

There is also a lone form of chemical bonding which doesn’t rely solely on electrons. The hydrogen atom, with its single proton and single electron, is pretty small and pretty reactive. So it’s actually possible for two atoms to share a third atom, hydrogen, which means that both the electron and the proton are in energy states that minimize the total system energy. The hydrogen bond is partly covalent, since the hydrogen electron is usually paired with a second electron. But the separation of the proton and electron also induces a dipole, making hydrogen bonding a dipole-dipole interaction. Hydrogen bonding may sound like a strange beast, and it is, but it is an important factor in the chemical behavior of water which is essential to life as we know it.

Electrons, Bonding, and the Periodic Table

The structure of the periodic table of elements is a bit weird the first time you see it, like a castle or a cake. If we just read the periodic table top to bottom and left to right, we are reading off the elements in order of increasing number of protons. However, if this were the only useful ordering on the periodic table, it could be a simple list. The vertically aligned groups on the periodic table actually represent the chemical properties of the elements. Dmitri Mendeleev developed the table in 1869 as a way to both tabulate existing empirical results, and predict what unexplored chemical reactions or undiscovered elements might be possible. It was revolutionary as a scientific tool, but the mechanism behind the periodicity was not understood until decades later. As it turns out, the periodicity of chemical behavior corresponds to the bonding type of the outer electrons in different atoms.

To understand what that means, we can start by looking at the elements on the left side of the periodic table. Hydrogen has only one proton, so the electrically neutral form of hydrogen has only one electron. This single electron is a point particle, jumping around the nucleus. The electron exists in a probability cloud, whose shape is given by the lowest energy solution to the quantum mechanical equations describing the system. These quantum states can be distinguished by differing quantum numbers for various quantities like spin and angular momentum, and we will talk about these in more depth later on. When we add additional electrons, they all want to be in the lowest energy state as well. Sadly for electrons but happily for us, no two electrons are able to occupy the same quantum state: they must differ in at least one quantum number. This is known as the Pauli exclusion principle, and was devised to explain experimental results in the early years of quantum mechanics. So while the single electron in hydrogen gets to be in the lowest energy state available for an electron in that atom, in an atom like oxygen, its eight electrons occupy the eight lowest energy states, as if they are stones stacked in a bucket.

But what’s really interesting about these higher energy electron states is that they have different shapes, as we can see by the mathematical forms that describe the possible probability distributions for electrons. So while the electron cloud in a hydrogen atom is a sphere, there are electron clouds for other atoms that are shaped like dumbbells, spheres cut in two, alternating spherical shells, and lots of other shapes.

The electron cloud shape becomes important because two atoms near each other may be able to minimize their overall energy via electron interactions: in some configurations the sharing of one, two, more, or even a partial number of electrons is energetically preferred, whereas in other configurations sharing electrons is not favorable. This electron sharing, which changes the shape of the electron cloud and affects the chemical reactivity of the atoms involved, is what’s called chemical bonding. When atoms are connected by a chemical bond, there is an energy cost necessary to separate them. But how atoms interact depends fundamentally on the shape of the electron cloud, determining when atoms can or can’t bond to each other. So the periodic table, which was originally developed to group atoms with similar chemical properties and bonding behaviors, actually also groups atoms by the number and arrangement of electrons.

Now, there is a lot more that can be said about bonding. You can talk about the inherent spin of electrons, which is important in bonding and atomic orbital filling, or you can talk about the idea of filled electron shells which make some atoms stable and others reactive, or you can talk about the many kinds of chemical bonds. It’s a very deep topic, and this is just the beginning!

Since every real world object is a collection of bonded atoms, the properties of the things we interact with, and what materials are even able to exist in our world, depend on the shape of the electron cloud. Imagine if the Pauli exclusion principle were not true, and all the electrons in an atom could sit together in the lowest energy state. This would make every electron cloud the same shape, which would remove the incredible variety of chemical bonds in our world, homogenizing material properties. Chemistry would be a lot easier to learn but a lot less interesting, and atomic physics would be completely solved. Stars, planets, and life as we know it might not exist at all.

The Attraction of Low Energy

One of the tricky things about learning, science or other topics, is that so many things are interconnected. You can take separate courses on literature and history, and maybe separating those two things is a reasonable way to categorize information, but really you might have understood the literature better with the historical context, or you might have learned historical motivations better by reading some relevant literature. Until the day comes when we can learn everything at once, we have to learn topics separately and then later on, look back for connections. I mention this because what I am about to talk about is relevant to huge swathes of physics, chemistry, and biology, and can be discussed in a wide variety of ways, and is difficult to really get to the bottom of. But it’s a really useful thing to have in the back of your mind while looking at a lot of scientific ideas.

I am talking about energy minimization.

When we discussed the forces due to electromagnetic and gravitational fields earlier, forces that draw oppositely charged objects together or two objects with mass together, we were talking about energy minimization. This is because, in each of those fields, there is a potential energy associated with sitting at a high field value. Imagine a rock perched on a high precipice, feeling a large gravitational force pulling it downward. Unless it is being supported in a way to counteract that force, it will fall, because it is seeking to minimize its energetic state. Oppositely charged objects drawing together are minimizing their electromagnetic potential energy with respect to each other, by moving toward each other.

At the atomic scale, energy minimization is also a factor, but in a different way. Within a single atom, electrons can be in many states, the equivalent of the rock choosing different positions on the precipice. If there is only one electron, it will go to the lowest energy state. But in atoms with many electrons, additional electrons are required to take higher energy states because the lowest ones are occupied; you can imagine a pile of rocks growing up the side of the precipice. And if an atom had no electrons at all, free electrons nearby would see that atom as very attractive, because atomic states are lower energy than free states.

If you consider multiple atoms coming together, the electrons are still looking to minimize their energy. In some cases this may mean sharing an electron with a neighbor, lowering the energy of both atoms and forming a chemical bond. But for other configurations of electrons, bonds do not lower overall energy, and so these atoms are unlikely to form bonds. In other words, for some atoms, bonding is energetically favorable, and for some atoms it isn’t. We’ll get more into the nuts and bolts of this later on, but you can imagine a whole energy landscape that determines what things bond or don’t, what chemical reactions happen or never start, and thus what macroscopic phenomena are commonplace.

Processes that are more energetically favorable are the ones we see in nature, also called “naturally occuring”. Energy minimization is at the heart of many of these processes, but in such a wide variety of ways that the more you learn, the more you see it around you.

Thinking About Collections of Atoms

On a basic level, science is about asking why the world is the way it is, and engineering is about asking, how can we use that to better our condition? There is certainly a lot of interplay between the two; they inform each other and rely on each other. And in my mind, a good scientist should always be a reasonable engineer, and vice versa. So if we want to understand what the science is that underpins a lot of our current technology, we first have to ask a lot of “why” questions about the world around us. Such as, why do different objects and materials have different properties? Why are there different forms that matter can take? Why do some forms appear on Earth and some don’t? Then, once we know what makes materials different from each other, we can start talking about how to use that to do something useful.

So what is the difference between the atoms in a metal table, the atoms in a cup of coffee, and the atoms in our hands? There are two major differences that are relevant: first, the atoms themselves come in a wide variety of types, and second, they can be arranged with other atoms in many unique ways that affect the property of the resultant material. The image below shows how we can arrange the same silicon and oxygen atoms in a random way or an ordered way, to get either silica or quartz. This change in ordered affects the physical properties of the resultant material.

We touched on the many types of atoms before when we discussed the number of protons in an atom. Proton number affects electron number, because of the attractive force between protons and electrons due to their opposite charge. So, for a given number of protons, an atom will end up with a similar number of electrons. How many electrons an atom has is very important, because the cloud of electrons is much larger than the compact nucleus which contains the neutrons and protons, so electrons are the primary means by which an atom interacts with the world.

What “the world” means here is primarily other atoms. So to assemble a solid, we have lots of atoms whose electron clouds are interacting with each other. Atoms can share electrons, they can be attracted to each other if they have opposite charges, and they can form three-dimensional structures to allow many atoms to interact . These interactions are all based around electronic forces, which stem from charge as we discussed earlier. Different kinds of atoms will experience different forces in different environments, so we end up with a whole slew of ways to assemble atoms. We can pack carbon into sheets and get pencil lead, we can jam it together with no ordering and get charcoal, we can compress it until it has a dense, flawless periodic structure and get diamond, or we can mix it with hydrogen to get the long hydrocarbon chains that crude oil is made of. And that’s just carbon!

Now, the obvious question to ask here is why atomic species and ordering vary, and why those variations lead to different material types. We’ll get into the first question shortly, but the second will take a lot longer to answer.