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Does a phase transition occur as a gas is heated to create a plasma? If so, is this a first or second order phase transition?

Also, does the presence of a phase transition depend on the pressure or composition? It seems to me that in the dilute limit (i.e. low pressures), no phase transition should occur because the fraction of atoms that are ionized will follow a Boltzmann distribution, which is a smooth function of temperature. However, the presence of phase transitions in Debye-Hückel theory seems to suggest that a gas-plasma transition could occur at higher pressures.

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  • $\begingroup$ Yea - this is an adequate explanation of what a phase transition is: en.wikipedia.org/wiki/Phase_transition. From gas to plasma you have ionization; from plasma to gas you have recombination. $\endgroup$
    – astromax
    Commented Nov 6, 2013 at 19:48
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    $\begingroup$ What would be the order parameter? $\endgroup$ Commented Nov 6, 2013 at 19:58
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    $\begingroup$ @astromax: really? If you created a plasma in a calorimeter would you see discontinuities? I suspect there would be no obvious transition. $\endgroup$ Commented Nov 6, 2013 at 20:00
  • $\begingroup$ @JohnRennie, if you could define an order parameter that becomes finite once the constituents start to dissociate then you could identify the critical point. However, whether you could call it a phase transition as in the phenomenological theory may be another question because I am unfamiliar with plasmas in general. You may be stuck calling it a crossover... $\endgroup$ Commented Nov 6, 2013 at 20:04
  • $\begingroup$ @MaxGraves I would imagine that the density of the fluid could be an order parameter, as in a liquid-gas transition. The fraction of molecules that are ionized might work as well. $\endgroup$
    – Max Radin
    Commented Nov 6, 2013 at 20:14

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The short rough answer is no. The transition between gaseous state and plasma is continuous and gradual. Phase transition typically happens at constant temperature for given pressure, which doesn't happen for plasma. Have a look here.

Some references classify the transition from gaseous state to plasma as a special type of phase transition called second order phase transition.The difference between the second order and first order (standard well known phase transition) is that second order is gradual while first order is sudden. Have a look here.

So if you are referring to standard definition of phase transition, the answer is no.

Hopefully that helped

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    $\begingroup$ Why the downvote? I know nothing about plasmas - if there is a flaw in this answer, I'd like to know what it is. Downvoting without leaving an explanation means no-one learns anything. $\endgroup$ Commented Nov 6, 2013 at 23:41
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    $\begingroup$ Thanks for your answer. I wasn't the one who downvoted, but I would say that the "standard" definition of a phase transition includes second order transitions. $\endgroup$
    – Max Radin
    Commented Nov 7, 2013 at 16:45
  • $\begingroup$ As long as the difference between liquid turning into gas and gas turning into plasma is clear, that is great!! It doesn’t really make a big difference to say yes or no as long as the concept is clear $\endgroup$ Commented Nov 7, 2013 at 16:48
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    $\begingroup$ @MaxRadin Your question became vague after you edited it. I am doing my PhD in plasma and people in plasma field talk about phase transitions either for plasma crystallization or dense plasma like quark-gloun plasma. No body really argues about phase transition when creating plasma. I feel your question is about creating plasma and its pressure dependence rather than classifying its creation into phase transition or not, am I right? $\endgroup$ Commented Nov 7, 2013 at 18:02
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The obvious order parameter is something like the fraction of atoms or molecules ionized, say "x'. Simple stat mech says that at any finite temperature that will be in the range (0,1). The question is whether, for some density of particles, there's a discontinuity as a function of T in either x (first order) or dx/dT (second order). There's a reason some such discontinuity could happen. As more ions form, the Debye screening cloud lowers the free-energy of ion formation. That cooperative phenomenon, like many others, e.g. spin-spin interactions in magnets,can in principle lead to runaway feedback to a new phase. It's a quantitative question. A very quick first calculation indicates that unless the density of ions becomes larger than ~(kT/e^2)^3 (in cgs units), there won't be a phase transition. (Here k is Boltzmann's constant, T is temperature, and e is the ion charge.) Since x doesn't get large until T is pretty high, (Boltzmann factor), and since you don't have a gas to start with unless the overall concentration is pretty low, I think you typically don't get a phase transition. Somebody with more detailed knowledge should check that. Of course, the quantitative comparisons are completely different for say quark-gluon matter, etc.

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  • $\begingroup$ Hi mike, and welcome to Physics Stackexchange! This isn't a bad answer, but you may want to break up long posts into more than one paragraph for readability. Also, you can typeset math with Latex-style MathJax on this site. (If you're not familiar with the notation, here is a very complete reference.) $\endgroup$
    – user10851
    Commented Feb 12, 2015 at 23:56
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The plasma properties already become palpable at a low degree of ionization. On the other hand the degree of ionization never reaches 100% in a macroscopic plasma (where thermal collisions occur): there will always be some electrons and ions recombining somewhere (equilibrium). So it seems like the 'perfect' plasma state is only asymptotic as $T\rightarrow\infty$. For practical purposes, a plasma with a high degree of ionization is considered fully ionized.

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This is a very interesting question and since I have thought before about it, I would like to share my answer.

As far as I am concerned, there has been no empirical evidence of coexistence between a fully ionized plasma and a neutral gas as separated phases in contact such as ice and water at $0^{\circ}$C. As @Gotaquestion correctly pointed out, the transition between gaseous and plasma state is continuous and gradual.

However, the heat capacity at constant volume, $C_{V}$, and also the heat capacity at constant pressure, $C_{p}$, exhibit peak values in some temperature intervals where atom/molecule ionization due to energy exchange gets more probable. In the figure below, extracted from an old paper form Phys. Fluids by Drellishak et al, $C_{V}(T)$ and $C_{p}(T)$ curves were calculated using thermodynamics principles and the partition function of diatomic nitrogen and diatomic oxygen.

enter image description here
enter image description here

In these figures, the peaks show the effect of very strong increase in the specific heats mainly due to energy loss by electron ionization. After each peak, the curve decreases to a minimum which is always higher than the previous. This happens because after a peak occurs, the corresponding ionized electrons are introduced in the system, giving their own contribution to the specific heat by increasing the degrees of freedom of the system.

Note that as the peaks get narrower they should resemble more and more a second order phase transition. Second order phase transitions are characterized by continuous $G(T, P), S(T,P), V(T,P)$, but discontinuous constant pressure heat capacity $C_{p}(T,P)$ (a good reference may be find here).

Finally, I must point some caveats in this answer. Here I considered what is called "classic plasma", which uses classical statistical mechanics in the treatment of Debye-Hückel.

I am not a specialist in quantum mechanical plasmas, but maybe in such systems other kind of phase transition may occur.

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Plasma as an ionized gas
Naïvely, plasma results from ionization of gas molecules. In this sense transition to plasma with increasing temperature is no different from, e.g., thermal dissociation of molecules or activation of vibrational degrees of freedom at higher temperatures. This regime is similar to chemical equilibrium, and is described in case of plasmas by Saha ionization equation - i.e., the equilibrium between the charged particles and neutral atoms, where the former recombine, while the latter may become ionized.

Plasma with radiation
Things may become more complicated, if we consider different mechanisms of ionization and different particle densities. Indeed, besides collisional ionization, there may be photoionization and Compton ionization. Photoinization requires extending the definition of plasma to include the radiation field (alongside the ions), and one cannon exclude possibility of phase transition, like the superradiant transition in Dicke model.

Plasma in phase diagrams
Despite the ambiguity about whether plasma is a separate thermodynamic phase, its inclusion in phase diagrams is of substantial practical interest, although no clear prescription exists. This article provides one example by simply connection two critical points by what the authors call "ionization equilibrium curve":
enter image description here

Remark
The answer by @mike provides a good discussion of what could be an order parameter for plasma phase transition.

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