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I am reading the book Computer Simulation of Liquids[1] where on multiple occasions it says MD is valid as long as the conditions simulated are away from phase transition. For example, at the beginning of section 2.3 (emphasis mine):

Since the ensembles are essentially artificial constructs, it would be reassuring to know that they produce average properties which are consistent with one another. In the thermodynamic limit (for an infinite system size) and as long as we avoid the neighbourhood of phase transitions, this is believed to be true for the most commonly used statistic ensembles [Fisher 1964][2]

In the literature there are many MD studies of phase transitions. In fact there are some YouTube videos showing simulated MD system experiencing phase transition (for example here)

My question is, what is the problem that makes simulating phase transition in MD non-trivial (if any)?

References:

  1. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids. Oxford Scholarship Online 2017. DOI: 10.1093/oso/9780198803195.001.0001.
  2. Fisher, M. E. The free energy of a macroscopic system. Arch. Ration. Mech. Anal. 1964, 17 (5), 377–410. DOI: 10.1007/BF00250473.
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  • $\begingroup$ Since the ensembles are essentially artificial constructs, it would be reassuring to know that they produce average properties which are consistent with one another. In the thermodynamic limit (for an infinite system size) and as long as we avoid the neighbourhood of phase transitions, this is believed to be true for the commonly used statistical ensembles (Fisher, 1964). -It does not mention MD simulations at all (at least at the beginning of chapter 2.3), no?! $\endgroup$
    – Jakob
    Nov 2, 2021 at 11:42
  • $\begingroup$ My concern is always with the fact that force fields (in general) don't work forming/breaking bonds. $\endgroup$
    – Camps
    Nov 2, 2021 at 14:06
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    $\begingroup$ @Jakob Aren't finite size ensembles the essence of MD? Another statement on the same issue in the same book in page 37: "periodic boundary conditions have little effect on the equilibrium thermodynamic properties and structures of fluids away from phase transitions and where the interactions are short-ranged. It", my interpretation of this statement was that typical MD simulations domain are small to capture nucleation of gas bubbles in a liquid for example, but a quick search on YouTube suggests this is not an issue (phase transition can be capture on molecular level) $\endgroup$ Nov 2, 2021 at 17:48
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    $\begingroup$ @Camps why would you need to form or break bonds at a phase transition? $\endgroup$
    – B. Kelly
    Dec 7, 2021 at 1:51

2 Answers 2

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Off the top of my head, I can think of two reasons to be concerned about simulations near a phase transition, although I'm only really well-qualified to talk about one of them in detail.

The one I know less about is finite size effects. There are many cases where the limited size of the system prevents it from behaving as it would at the thermodynamic limit. My recollection is that phase transitions are one of these, but better to hear from someone who remembers the details. I expect this is actually what A&T were thinking about in this context.

The one I know more about is time scale limitations. Quite simply, a phase change is frequently an example of a rare event -- that is to say, it takes a long time for it to spontaneously occur. So ergodic sampling is impossible because there is a kinetic barrier large enough that kinetic trapping keeps you stuck on the "wrong" side for longer than simulations can explore.

This may seem surprising, but in many cases, a "long time" here can even be long on human timescales. Some standard examples are superheating, supercooling, and supersaturation. (Search YouTube for "sodium acetate supersaturation" for some nice videos; here's one). We can experimentally create metastable states on a multi-mole size scale and multi-second (or hour!) time scale, where the more thermodynamically stable state is only found upon perturbation. The experimental physics shows that these transitions don't spontaneously occur on human-relevant time scales, so what chance would MD have to sample ergodically?

Note that many simulations you'll find of "melting" or whatnot are done at temperatures far from the equilibrium conditions. It's one thing to study the phase equilibrium of ice and water at 0°C, it's another to say, "look, my ice melts if I simulate it at 75°C!"

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    $\begingroup$ Thanks very much for the great answer. Would you say that there is a difference between going from more orderly phase to less ordered phase? I mean is freezing different from melting from MD perspective? $\endgroup$ Jan 3, 2022 at 21:11
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Thermodynamics

There is no problem with simulating a phase transition. There is only a problem with calculating thermodynamic averages during a phase transition.

Short simple answer: I don't know anyone who has ever had a use for a property that corresponds to part one phase, part another phase. There are plenty of needs for the properties of mixed phase systems, but you need to know the pure phase properties, and mix these together, with a lever rule, essentially. One does not calculate the heat capacity of a fluid that is half liquid, half vapor. one calculates the heat capacity of a pure liquid and pure liquid, and then finds what a mixture that is 50/50 or X/(100-X) is. This is just thermodynamics, and stat mech is just microscopic thermodynamics, and simulations are just stat mech i.e., thermodynamics.

If it isn't useful thermodynamically, then an ensemble average of something won't be useful(or relevant) computationally.

If your simulation is at a phase boundary, your results will be strange. You will lose sleep, nothing will make sense, until you realize you aren't simulating a single phase. I know, I have done this, more than once, unfortunately.

Another thing to realize (or perhaps just a different way of looking at the same problem) is you must manage your Degrees of Freedom(the following depends on a pure fluid. Refer to Gibbs phase rule for general case of multiple components) in a simulation. When you start a simulation, you must set what is constant i.e., T and P is common, but also, T and V. However, at a phase transition, you can only choose one degree of freedom. So you can't be simulating at a chosen T and P and a phase transition. That is purely unphysical.

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