# Why do discrete states of matter exist as opposed to a continuous spectrum?

Why is it that bonds are broken at certain temperatures (melting and boiling points) only, that thermal energy is converted to kinetic energy at all other temperatures (and not potential energy)? This is evidenced by heating and cooling curves. I haven't been able to find out how chemistry explains this observation.

I am asking if there is any theoretical model in chemistry that yields the result that states of matter are discrete as opposed to continuous.

Would be really grateful if you could point me towards some related literature to go through. I am studying for my A-levels currently, so you may need to reference basic concepts.

• What do you mean by "potential"? Do you mean potential energy, if so which kind? or electric potential (as in voltage)? Bonds are broken at energy levels rather than "temperatures". It's why water can 'boil' at ambient temperature if the pressure if low enough, you need less energy to drive the phase change. Overall, there is no "continuous spectrum" because particles have the required energy for a given state or they don't. I'd recommend a book on chemical thermodynamics.
– STOI
Commented Jul 13 at 19:37
• Above the critical point the discontinuous transition between liquid and gas phases disappears, so the behavior you describe is not obligatory. The discontinuous phase transitions are a particular type of phase transition. Also, are you familiar with phase diagrams, phases, and coexistence lines? Commented Jul 13 at 20:03
• I am not familiar with phase diagrams, phases, or coexistence lines.
– Sak
Commented Jul 13 at 20:25
• I am simply asking if there is any theoretical model in chemistry that yields the result that states of matter are discrete as opposed to continuous.
– Sak
Commented Jul 14 at 6:28
• @Sak About the simplest model of a phase transition is the 2D Ising model. You can model a number of systems with it, one traditional example is a system which acts like a magnet at low temperatures, but above a certain specific temperature the magnetism is destroyed (see Curie Temperature ). At A level with a bit of hand holding a good student could probably get the essence of the ideas behind this, especially if they know a little programming - "solving" it on a computer is a nice exercise. Commented Jul 14 at 15:19

In general, the intermolecular interactions that lead to solids and liquids can be broken at any temperature.

When a liquid boils, molecules completely lose these interactions as they transfer into the gas phase (because they are too far away from their interaction partners). When a liquid slowly evaporates, the same process happens at the molecular level. However, most of the liquid remains liquid, and there might be molecules going from the gas phase back to the liquid phase, reforming intermolecular interactions.

For melting, you can have supercooled liquids or superheated solids. They change phase at a temperature different from the melting point (as a supercooled liquid freezes rapidly or a superheated solid melts rapidly, it does undergo a temperature change in the direction of the melting point). There is also a process called surface melting, where molecules or atoms on the surface start melting at a lower temperature than the molecules in the bulk phase. You can rationalize this by considering how these surface particles have fewer neighbors, i.e. fewer interactions that have to be broken for melting the surface layer.

The reason why the bulk of a sample melts or freezes at a specific temperature is that the process is a feedback loop. You put some thermal energy in, which would normally raise the temperature, but some particles melt, using up that energy. Or you remove some thermal energy, but then some particles freeze, releasing energy to make up for it. If the heat exchange with the environment is sufficient slow, it looks like the temperature never changes.

Would be really grateful if you could point me towards some related literature to go through.

You should find more about intermolecular interactions, supercooled liquids, evaporation, and surface melting either in textbooks or by looking for educational videos on these topics.

• A drop of water can completely evaporate A system under reflux can hopefully never evaporate., and boiling is certainty at the molecular level. Phase changes are an energy-entropy paso doble. The reason pure substances have a constant MP is the solid and liquid have constant activities [Gibbs phase rule] . All these properties change smoothly with temperature when there is sufficient matter. Commented Jul 13 at 23:05
• I don't understand how there is a feedback loop at certain temperatures. Could you please elaborate?
– Sak
Commented Jul 14 at 6:41
• @jimchmst Don't all pure substances (gases too) have constant activity at some given T,p and composition? How are liquids and solids special? Also, you are welcome to post your own answer. Commented Jul 14 at 7:19
• When you write 'molecules completely lose these interactions' what you mean is that there is now sufficient energy to overcome these interactions and that because they decrease with distance they become unimportant or some such wording. Commented Jul 14 at 8:00
What prevents continuity in the solid phases is the emergence of long-range order in such phases, which limits the crystal phases to a countable (and thus discrete) set even if quasilattice structures are included. Even so, on some occasions there are distinct solid phases with the same crystal structure that merge into each other under pressure. In cerium at ambient pressure there are two fcc phases with different densities and apparently different electronic structures (the lower-temperature, denser phase is distinguished by having the $$4f$$ electrons participate in the metallic bonding). But at about 2 GPa pressure a critical point appears between these phases and they merge like a liquid and gas phase would.