Why the inter-atomic world only approximates the macroscopic properties of matter.

In a previous posting, I wrote that the microscopic world, in this case implying inter-atomic distances, generates an approximation of the macroscopic, mechanical properties of matter.

What any alert reader should notice, is that in order for this theory to be true, it actually needs to lead to an exact result at some point, and not just to approximate results. And so the question which should follow is, ‘Why only an approximation, the way it was described?’

There is a family of answers to that question, which starts with the fact that not all solids are covalent solids. I was taught that there exist essentially three types of solids:

  1. Molecular Solids,
  2. Covalent Solids,
  3. Ionic Solids.

I feel that the WiKiPedia article I linked to in this list, gives a good explanation for what Molecular Solids are, and also gives links to the other types of solids. If the reader has serious questions, I recommend he read that WiKi next; they explain certain details better than I can.

At the same time, solids which I was taught were covalent solids, are really just a combination of molecular and covalent solids, due to the way molecules could be linked in certain directions, but not linked in other directions, in 3D. This is why the WiKi describes those types of solids as ‘mesh-solids’.

Organic polymers are extreme examples of meshes, while certain structural materials such as beryllium are completely different, being highly covalent, and being much stronger therefore, than organic polymers.

Another reason for which my first description is only an approximation, is the existence of thermal agitation. This means that individual nuclei are always in motion, even if the macroscopic body is not noticeably in motion. Furthermore, due to the involvement of Quantum Mechanics, heat can take the form of transitions between discrete states, instead of all the heat being stored, just as the continuous agitation of the nuclei. Hence, molecules which have a greater number of QM states to occupy, at any given temperature, will also store more heat, as their temperature changes, and will therefore also have greater specific heat. If heat was just the kinetic energy of the nuclei, we should find that all matter have very predictable properties of specific heat, just a function of atomic density, when in fact this is not so.

And, the velocities associated with thermal agitation at room temperature, are often underestimated. They can be enough to break the bonds between molecules by themselves, which is also a reason ‘why ice melts at room temperature’.

Continue reading Why the inter-atomic world only approximates the macroscopic properties of matter.

Elastic Bodies. Force.

A certain person named Francis used to ask me repeatedly,

“When my arm pushes against a wall, or when anything pushes against my arm, what causes the force?”

I always answered his question exactly the same way.

When we think of the bone inside the arm, or of components used to build houses and walls, we think of those as ‘rigid bodies’. But in reality, rigid bodies are just special cases of ‘elastic bodies’, and one needs to understand why elastic bodies exist, in order to understand rigid bodies, in the way He asked.

The molecules that make up an elastic body, generally consist of atomic nuclei that are separated by electron-pairs, or chemical bonds. These bonds act as ‘microscopic springs’.

When the distance between two nuclei that are part of a molecule is at its neutral distance, the electrostatic repulsion between the nuclei equals, or cancels with, the electrostatic attraction caused by the electron-pair itself.

If the distance between the nuclei decreases slightly, then the electrostatic repulsion increases, but the attraction caused by the electron-pair – i.e. caused by the chemical bond – stays about the same. And so a net repulsive force results, that tries to restore the distance between them to their neutral distance.

If the distance between the nuclei increases slightly, then the electrostatic repulsion decreases, but the attraction caused by the electron-pair – i.e. caused by the chemical bond – stays about the same again. And so a net attractive force results, that tries to restore the distance between them to their neutral distance.

One reason why the folly is still undertaken today, to teach Newtonian Bodies to Students, prior to teaching more-advanced concepts, is the fact that what happens on the macroscopic scale in Newtonian Mechanics, also tends to approximate what happens on the microscopic scale, and vice-versa. With Quantum-Mechanics, Relativity, etc., this can no longer be guaranteed. And it helps explain why Newton was able to ‘understand his world’ so well, even though the subatomic world wasn’t known yet, in his era.

Elastic bodies are made out of a huge number of atoms, but their macroscopic behavior derives from their microscopic behavior, in that If the distance between their end-points decreases slightly, from its neutral distance, a net repulsive force results, while if the distance between their end-points increases, a net attractive force results. This latter, net attractive force is also due to their ‘tensile strength’.

When such elastic bodies are only modeled as having two end-points, then they are also simplified as ‘springs’. And springs have a so-called ‘force-modulus’, which is a linear factor, by which a small change in distance, results in some change in force. If a spring has a very low force-modulus, then it is very ‘soft’ or elastic. If it has a very high force-modulus then it is very ‘stiff’ or inelastic.

Beyond some amount of compression the spring will fracture, and this behavior is known as ‘brittleness’. If the spring is very brittle, then it won’t compress much, before it breaks.

The fact to understand about rigid bodies, is that they are just elastic bodies, whose force-modulus is so high, that we don’t humanly observe them deform. And the brittleness is also so weak, that to try to apply enough force to them to make them (appear to) deform, is impractical and just results in their breaking.

Continue reading Elastic Bodies. Force.