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I was studying a book about thermodynamics of nanosystems and I got stuck with this question in my mind which I couldn't find an answer for.

For instance, does a single water molecule have a state, like being liquid or something? Or is one molecule of TiO2 solid or gas? I would appreciate if anyone could clarify this.

I should state that I am not considering a macromolecule in my case.

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    $\begingroup$ Thermodynamics typically arises when there's a lot of something. For a fluid, you'll need a lot of constituent particles, molecules. However, a single molecule that is made up of a lot of atoms can have states; For example a single polymer (e.g. DNA) can be in a coiled state, or in a helix state. $\endgroup$ – alarge Jan 16 '15 at 13:46
  • $\begingroup$ @alarge:You should make an ans with some more details $\endgroup$ – Paul Jan 16 '15 at 14:13
  • $\begingroup$ also en.wikipedia.org/wiki/Liquid_crystal $\endgroup$ – Phoenix87 Jan 16 '15 at 14:30
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You can't build a liquid from a single molecule. Neither you build ice with a single molecule.

A single particle (in your case, molecule) has no state. A water molecule isolated from the rest of the water, "doesn't know" anymore that it belonged to a liquid state or a solid state, or to vapors.

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  • $\begingroup$ I don't understand why this is downvoted!? $\endgroup$ – Hritik Narayan Jan 16 '15 at 15:20
  • $\begingroup$ @HritikNarayan , I suppose you ask about answers. Then, of which one of the answers you ask? $\endgroup$ – Sofia Jan 16 '15 at 15:25
  • $\begingroup$ The answer you posted is correct so I can't think of any reason why people have downvoted it. $\endgroup$ – Hritik Narayan Jan 16 '15 at 15:27
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    $\begingroup$ @HritikNarayan I can only thank you. Anyway, I enhanced the explanation a bit. $\endgroup$ – Sofia Jan 16 '15 at 15:29
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    $\begingroup$ @HritikNarayan: Someone also flagged it as low quality/not an answer. I think it may be the shortness of the answer before the recent edit that prompted that, though it was a complete answer even before that. $\endgroup$ – ACuriousMind Jan 16 '15 at 15:29
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Traditionally, for proper phase transitions, and thus phases, to exist, you must in statistical mechanics take a thermodynamical limit, i.e. make the system infinitely large. In actuality this is a bit more involved (not to even start with nonextensive systems), but let's start working from this assumption.

  1. Given that you need a lot of particles (mathematically, infinite) to define a phase, it is then clear that one particle does not a phase make. This is to say that a single molecule is not solid or gas.

  2. That said, a single molecule that is made up of many atoms most certainly can have phases and phase transitions of its own: The molecule is a system of its own and if it has enough atoms, we can approximate as if it had an infinite amount. As an example, polymers can undergo the helix-coil transition.

  3. Finally, consider the question of whether by looking at just a single molecule in a phase A, it is possible to identify the phase as A. Turns out that in practice it often is. In this sense a molecule does have a state identical to the macroscopic state. For example, the lipid bilayer has a gel-fluid phase transition. The gel is kind of a solid, where the molecules are packed in a rather ordered fashion, whereas in the fluid state the system is, in a sense, a 2D fluid. Now instead of looking at packing and symmetry at this scale, one could also measure the order parameters of the individual molecules: In the gel state the tails of the lipids are straight and in the fluid state they flap around more freely. This is to say that the molecules do have internal states that often correspond to the phase at the macroscale.

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  • $\begingroup$ But this is a nonextensive system, isn't it? And let me point out that I didn't mean a macromolecule ( I should have stated that) $\endgroup$ – psychob Jan 16 '15 at 17:53
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From Wikipedia:

The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice) or irregularly (an amorphous solid such as common window glass).

A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds.

Gas particles are widely separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles.

We see that a phase state is defined by the bonds between atoms/molecules rather than the particles themselves. (Although historically they were defined by more empirical properties, a solid retains its shape, etc.)

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  • $\begingroup$ what if, then, a single molecule is in all the states of matter, since there is no violation to any of the above definitions? $\endgroup$ – Phoenix87 Jan 16 '15 at 14:27
  • $\begingroup$ How can a single molecule be held together by "intermolecular" forces? $\endgroup$ – Kieran Hunt Jan 16 '15 at 14:32
  • $\begingroup$ en.wikipedia.org/wiki/Vacuous_truth this is what I was referring to $\endgroup$ – Phoenix87 Jan 16 '15 at 14:33
  • $\begingroup$ If an item cannot physically possess a property, it surely cannot be a member of a set that requires that property. $\endgroup$ – Kieran Hunt Jan 16 '15 at 14:37
  • $\begingroup$ if I tell you that the single molecule is tightly bound to all the other molecules, would you be able to provide a counterexample to disprove this? $\endgroup$ – Phoenix87 Jan 16 '15 at 14:39
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A single molecule doesn't have a state of matter. Single or individual molecules (when observed in Ion Traps) are considered to be "Gas". It requires a minimum of n(unknown to me) number of molecules to define the state of matter.

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  • $\begingroup$ Single molecules have no state. You can't answer another question than what was asked. It wasn't specified in the question that the molecule is in an ion trap. I that case the molecule is in a structure, it is not single. A single particle has no state, whatever is the word you use for "defining" it, and whatever is the means by which you watch it. See what you wrote - It requires a minimum of n(unknown to me) number of molecules to define the state of matter. $\endgroup$ – Sofia Jan 16 '15 at 13:47

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