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:
- Molecular Solids,
- Covalent Solids,
- 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’.
Also, the amount of tension which is required to cause a spring to break, does not need to cause one bond between its fundamental particles to reach the point, of having particularly strong force. It only needs to cause that bond, to switch to forming a different bond. I.e., the amount of hypothetical force required to pull two atoms apart, is likely to be much greater than the force required, that will simply cause their electron-pairs – charge-droplets – to form some new bond, which was not there before, and to let go of the particle which is trying to separate.
This can be observed directly, in the fact that a surface which is freshly-exposed – due to a fracture – does not have any anomalies with respect to Physics or Chemistry. A fresh surface has intact bonds between its atoms, to the same degree with which the original solid had. It doesn’t suddenly have unpaired electrons standing out along its normal-vector, where before it had covalent bonds… What is observed about freshly-exposed surfaces however, is that erosion that normally affects the substance in question, has not had time to set in, if the new surface is examined shortly after having been formed.
And finally, even if a solid strongly resembles a covalent solid, it’s rarely present in its mono-crystalline form. The macroscopic bodies often tend to form microscopic crystals, which cannot be seen, but which are larger than one molecular unit, yet smaller than the body. This degree of poly-crystallization can progress to the point of giving rise to an amorphous solid, in which the covalent bonds traverse in every random direction. And then, their contribution to mechanical strength diminishes. I.e., window-glass is as brittle as it is, mainly because this is a most-famous amorphous form of matter. And I would estimate that Human bone-matter, is also closer to being amorphous, then it would be, to being crystalline.
It’s really a recent development in Human Technology, that we can manufacture mono-crystalline – i.e., monolithic – solids, such as for example semiconductor-grade silicon, or propeller-blades for aircraft, that can by now be made mono-crystalline as well ! And in the latter case, the advantage this brings to mechanical strength, seems obvious.
Therefore, the main point along which my earlier account fails, is to assume that the main force holding together a macroscopic solid, is in fact the covalent bond. This force can just as easily be the Van der Walls attraction, or Hydrogen-Bonds. And it can be modified strongly, by thermal vibrations in the solid.
I feel that the WiKiPedia’s Quantum-Mechanical adaptation of Heat, has a basic flaw. They state, that the discrete states which a molecule can occupy, do not need to have a net difference in potential energy, to contribute to specific heat.
This description suggests a poor distinction between Heat and Entropy.
Entropy is thought to be a statistical function, of how much information a substance can store thermally, while Heat is thought to be a function, of how much energy it can store.
Changes in state which do not represent much net difference in potential energy, should not contribute much to Specific Heat, but still contribute to Entropy.