When Does Particle Population Size Shift from Microscopic to Macroscopic?

[BillTre]

In biology and optics, macroscopic and microscopic are distinguished by being large enough (or not) to be seen by the unaided eye (or almost), vs. requiring a microscope rather than just a hand lens (or macrolense).
Fairly small things (like paramecia) can be easily seen without a microscope, depending on the lighting and other aspects of the setting.

In physics (as I understand it) these terms are used to distinguish between the thermodynamically driven behavior of large populations of particles (like a population of gas molecules) vs. the detailed behavior of each individual particle (microscopic; very data intensive).

What are the considerations with respect to this thermodynamics view, on when an increasing number of particles (particle population size) result in it being more appropriate to consider them as a population of particles rather than a collection of several single particles, each with its own distinguishable behavior?

Not expecting a sharp cut-off.

 

[Borek]

Back in eighties a friend of mine as part of his MSc thesis in quantum chemistry tried to calculate how some selected property changed with the size. Sadly the only thing I remember is that the conclusion was "for this particular substance, for this particular property, for this particular approach crystal larger than made of 100 units can be considered bulk".

So at least the question isn't new

 

[Haborix]

I suppose one way that has been taken is to ask about the magnitude of finite-size effects. Calculations in this vein are usually done in increasing powers of inverse volume. Sort of a power series around the thermodynamic limit.

 

[gmax137]

normal engineering thermodynamics (tanks of gas, heat engines built with cylinders and pistons) consider collections of ~10^23 molecules. That's why it works: the numbers are so inconceivably large that no individual effects remain.

 

[Ygggdrasil]

This concenpt gets discussed in chemistry in the context of nanotechnology (and how at small enough size scales, the properties of substances can be very different from the bulk material). For example,

Nanoscale gold illustrates the unique properties that occur at the nanoscale. Nanoscale gold particles are not the yellow color with which we are familiar; nanoscale gold can appear red or purple. At the nanoscale, the motion of the gold’s electrons is confined. Because this movement is restricted, gold nanoparticles react differently with light compared to larger-scale gold particles.

https://www.nano.gov/nanotech-101/special

Perhaps the site cited above and other similar texts on nanotechnology could be good sources to consult on this issue.

 

[Lord Jestocost]

What are the considerations with respect to this thermodynamics view, on when an increasing number of particles (particle population size) result in it being more appropriate to consider them as a population of particles rather than a collection of several single particles, each with its own distinguishable behavior?

A rough criterion takes into account the size of fluctuations in the thermodynamic properties of interest that follow from the statistical-mechanical approach: http://farside.ph.utexas.edu/teaching/sm1/lectures/node8.html