I had been reading about bulk properties, but was confused what should the minimum amount of matter be for these properties to hold. For eg: Intensive thermodynamic variables will not remain intensive (or maybe lose their meaning overall) if I just take a very tiny part of the system into consideration. The question is how "tiny" the part can be?

  • $\begingroup$ Depends how accurate you want to be. $\endgroup$ – knzhou Mar 29 '19 at 21:20
  • $\begingroup$ I would say that it is the minimum amount of matter such that the "bulk effects" of the matter "somewhat" dominate the "surface effects" of the matter. This means that there must be some point where the bulk starts looking like expectations and surface effects become less important. I would expect the answer to depend on the particular substance involved. $\endgroup$ – David White Mar 30 '19 at 1:10

I would rephrase the problem connected to small samples as the problem that every observable which could be obtained as an average, would suffer from the consequences of its small size.

One obvious consequence is the larger size of the relative instantaneous fluctuations around the average values. But there are also other consequences. Surface effects become increasingly important and the contribution to the average from atoms close to the surface , hence experiencing a different local environment, is not negligible.

Thus, how big has to be size of a cluster before typical bulk properties could emerge? This has been and it is still an active field of research. The main message seems to be that the answer depends on the property one is interested in and on the specific material clusters are made of.


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