# Minimal quantity of substance to reveal its physical state properties

What is minimal quantity of matter required to reveal its physical state properties? I.e. number of particles/atoms when their collection can be considered as liquid, solid, gas or plasma.

I am aware about environment parameters: gravity, EM fields, atmospheric pressure, etc. No matter whether exists a generic form solution or sets of special cases (models). I'm interesting from where to start the quantity estimations.

I guess thermodynamics could answer this, but this part of physics is so huge and I beg for answers (or clues) from more experienced users which as expert could save tons of time by one line.

I know that some physical properties can be deduced from one particle of the system. I consider collection of particles as a black box which we could analyse as substance to reveal its properties (viscosity, density, etc). So how to obtain a sufficient (representative) number of particles for this case.

• In formal terms, what you're looking for is the onset of collective behavior in a material. Though I'm personally not an expert in this field, one thing that I do know is that the point at which this occurs differs in materials with different interactions. You can see this quite prominently in e.g. heavy ion collisions, where, due to the strength of interactions between constituents, collective behavior occurs with only a few thousand nucleons, which is not something that one could say about something like water. Feb 1 '19 at 16:30

Funny thing is, there is actually not a single correct answer.It's a very interesting question really! It actually depends on the particular physical property you would be interested in studying.

For example, if you would try to figure out why a substance is in a particular state at a particular temperature, all you need to know is how strong the bond is between two molecules of the substance.

If you wanted to figure out the pressure exerted by a fluid on the walls of the container, you would think about only one molecule and then derive the pressure for the entire volume of fluid.

If you wanted to figure out the mean free path of a gas (the average distance between two molecules in a given gas), you would have to consider N number of molecules of the gas.

So as you can see, there is no single answer to your question. But this number game, so to speak, only happens when you try to derive these physical properties using theoretical methods. If you were to find these properties experimentally, then taking a good amount of the substance wouldn't hurt you. Anywhere from a few milliliters to a few thousand kilograms may be used during experiments!

Hope this helps!

• I thinking about when collection of particles becomes an liquid or crystal so we can start to analyse it to figure out some physical properties, e.g. viscosity, solubility, density, temperature, etc. Collection of particles kind of black box
– rook
Feb 1 '19 at 16:55
• Well, in that case, what you are interested in is how we define terms like liquid or crystals. One would require at least two molecules of the substance to figure any of the properties you are interested in. This is because all physical properties are bulk properties and require us to know both the inter-molecular as well intra-molecular interactions (more important being the inter-molecular interactions) in order to understand them well. Feb 1 '19 at 17:01