Stretched Water

The physics of water is endlessly fascinating. The phase diagram of water at positive temperature and pressure is already remarkably complex, as shown in this diagram by Martin Chaplin:

Click for a larger version. And read this post of mine for more:


But it turns out there’s more: water is also interesting at negative pressure.

I don’t know why I never wondered about this! But people study stretched water, essentially putting a piston of water under tension and measuring its properties.

You probably know one weird thing about water: ice floats. Unlike most liquids, water at standard pressure reaches its maximum density above the freezing point, at about 4 °C. And for any fixed pressure, you can try to find the temperature at which water reaches its maximum density. You get a curve of density maxima in the pressure-temperature plane. And with stretched water experiments, you can even study this curve for negative pressures:

This graph is from here:

• Gaël Pallares, Miguel A. Gonzalez, Jose Luis F. Abascal, Chantal Valeriani, and Frédéric Caupin, Equation of state for water and its line of density maxima down to -120 MPa, Physical Chemistry Chemical Physics 18 (2016), 5896–5900.

-120 MPa is about -1200 times atmospheric pressure.

This is just the tip of the iceberg. I’m reading some papers and discovering lots of amazing things that I barely understand:

• Stacey L. Meadley and C. Austen Angell, Water and its relatives: the stable, supercooled and particularly the stretched, regimes.

• Jeremy C. Palmer, Peter H. Poole, Francesco Sciortino and Pablo G. Debenedetti, Advances in computational studies of the liquid–liquid transition in water and water-like models, Chemical Reviews 118 (2018), 9129–9151.

I would like to learn about some of these things and explain them. But for now, let me just quote the second paper to illustrate how strange water actually is:

Water is ubiquitous and yet also unusual. It is central to life, climate, agriculture, and industry, and an understanding of its properties is key in essentially all of the disciplines of the natural sciences and engineering. At the same time, and despite its apparent molecular simplicity, water is a highly unusual substance, possessing bulk properties that differ greatly, and often qualitatively, from those of other compounds. As a consequence, water has long been the subject of intense scientific scrutiny.

In this review, we describe the development and current status of the proposal that a liquid−liquid transition (LLT) occurs in deeply supercooled water. The focus of this review is on computational work, but we also summarize the relevant experimental and theoretical background. Since first proposed in 1992, this hypothesis has generated considerable interest and debate. In particular, in the past few years several works have challenged the evidence obtained from computer simulations of the ST2 model of water that support in principle the existence of an LLT, proposing instead that what was previously interpreted as an LLT is in fact ice crystallization. This challenge to the LLT hypothesis has stimulated a significant amount of new work aimed at resolving the controversy and to better understand the nature of an LLT in water-like computer models.

Unambiguously resolving this debate, it has been shown recently that the code used in the studies that most sharply challenge the LLT hypothesis contains a serious conceptual error that prevented the authors from properly characterizing the phase behavior of the ST2 water model. Nonetheless, the burst of renewed activity focusing on simulations of an LLT in water has yielded considerable new insights. Here, we review this recent work, which clearly demonstrates that an LLT is a well-defined and readily observed phenomenon in computer simulations of water-like models and is unambiguously distinguished from the crystal−liquid phase transition.

Yes, you heard that right: a phase transition between two phases of liquid water below the freezing point!

Both these phases are metastable: pretty quickly the water will freeze. But apparently it still makes some sense to talk about phases, and a phase transition between them!

What does this have to do with stretched water? I’m not sure, but apparently understanding this stuff is connected to understanding water at negative pressures. It also involves the ‘liquid-vapor spinodal’.


The liquid-vapor spinodal is another curve in the pressure-temperature plane. As far as I can tell, it works like this: when the pressure drops below this curve, the liquid—which is already unstable: it would evaporate given time—suddenly forms bubbles of vapor.

At negative pressures the liquid-vapor spinodal has a pretty intuitive meaning: if you stretch water too much, it breaks!

There’s a conjecture due to a guy named Robin J. Speedy, which implies the liquid-vapor spinodal intersects the curve of density maxima! And it does so at negative pressures. I don’t really understand the significance of this, but it sounds cool. Super-cool.

Here’s what Palmer, Poole, Sciortino and Debenedetti have to say about this:

The development of a thermodynamically self-consistent picture of the behavior of the deeply supercooled liquid that correctly predicts these experimental observations remains at the center of research on water. While a number of competing scenarios have been advanced over the years, the fact that consensus continues to be elusive demonstrates the complexity of the theoretical problem and the difficulty of the experiments required to distinguish between scenarios.

One of the first of these scenarios, Speedy’s “stability limit conjecture” (SLC), exemplifies the challenge. As formulated by Speedy, and comprehensively analyzed by Debenedetti and D’Antonio, the SLC proposes that water’s line of density maxima in the P−T plane intersects the liquid−vapor spinodal at negative pressure. At such an intersection, thermodynamics requires that the spinodal pass through a minimum and reappear in the positive pressure region under deeply supercooled conditions. Interestingly, this scenario has recently been observed in a numerical study of model colloidal particles. The apparent power law behavior of water’s response functions is predicted by the SLC in terms of the approach to the line of thermodynamic singularities found at the spinodal.

Although the SLC has recently been shown to be thermodynamically incompatible with other features of the supercooled water phase diagram, it played a key role in the development of new scenarios. The SLC also pointed out the importance of considering the behavior of “stretched” water at negative pressure, a regime in which the liquid is metastable with respect to the nucleation of bubbles of the vapor phase. The properties of stretched water have been probed directly in several innovative experiments which continue to generate results that may help discriminate among the competing scenarios that have been formulated to explain the thermodynamic behavior of supercooled water.

17 Responses to Stretched Water

  1. Wyrd Smythe says:

    I think it’s wonderful how, the more we look at good old water, the more interesting it is. Thanks for some very interesting links to pursue!

  2. macbi says:

    You could also extend the graph in the direction of negative temperatures, although they would be placed on the right of the graph since they’re really hotter than infinity!

    • John Baez says:

      Yes, for some crystals you can effectively get negative temperatures—actually in a metastable state, not true thermodynamic equilibrium—but I haven’t heard of it being done with water.

  3. John Baez says:

    This site stole my blog post but turned it into gobbledygook.

    For example it changed this:

    At negative pressures the liquid-vapor spinodal has a pretty intuitive meaning: if you stretch water too much, it breaks!

    There’s a conjecture due to a guy named Robin J. Speedy, which implies the liquid-vapor spinodal intersects the curve of density maxima! And it does so at negative pressures. I don’t really understand the significance of this, but it sounds cool. Super-cool.

    into this:

    At destructive pressures the liquid-vapor spinodal has a aesthetic intuitive that manner: whereas you occur to stretch water too powerful, it breaks!

    There’s a conjecture attributable to a man named Robin J. Presently, which implies the liquid-vapor spinodal intersects the curve of density maxima! And it does so at destructive pressures. I don’t truly understand the importance of this, however it certainly sounds chilly. Gargantuan-chilly.

    Any reason why someone would bother doing this, except as a joke? I can see why someone might want to change words to avoid some crude plagiarism-detection algorithms, but what’s the point if you create a bunch of ridiculous bullshit?

    • Toby Bartels says:

      It sounds as if it’s been sent on a round trip through a computer translator. People do this for humour, but sometimes it happens on accident too. Here’s a YouTube channel that does this to popular songs:

    • John Baez says:

      Maybe some people build software that goes around grabbing blog articles and translating them into other languages. If a loop gets created, all hell would break loose as an article gets translated into mush. But presumably such software gets aimed mainly at real blog articles, not translations.

  4. Supernaut says:

    Fascinating stuff; who would have thought that ‘simple’ water would exhibit such complexity?

    • John Baez says:

      Water is a very unusual liquid – it breaks a lot of the usual rules. Besides getting less dense as you cool it below 4 ° C and even less dense when it freezes, its viscosity decreases at higher pressures. It also has an unusually high specific heat, and an unusually high melting and boiling point compared to similar molecules.

      Going up one row of the periodic table we have:

      hydrogen telluride (H2Te) – melting point -49 °C
      hydrogen selenide (H2Se) – melting point -64 °C
      hydrogen sulfide (H2S) – melting point -84 °C
      water (H2O) – melting point 0 °C

      Lighter molecules tend to have lower melting points… but water breaks this pattern!

  5. Harvey Brown says:

    Thanks John for this interesting post. Stretched water is ubiquitous in Nature, but hidden in tall trees and not fully appreciated until the end of the 19th century. The story is told in my ‘The theory of the rise of sap in trees; some historical and conceptual remarks’, Physics in Perspective, 15, 320-358 (2013); An updated version of this paper is at

    • John Baez says:

      Hello, Harvey! I hadn’t thought about that. What sort of negative pressures are typical in the sap of tall trees?

      • Harvey Brown says:

        I was wrong to single out tall trees; certain plants of modest stature are even more impressive in terms of negative pressure. Recalling that positive atmospheric pressure is roughly 0.1MPa, I quote from a 2014 review paper by John Sperry:

        “Gravity actually exerts a relatively trivial influence on xylem [pressure]. … [A]bout 1,000 kPa of pressure is required to move water from soil to leaves against friction, a value that does not appear to be markedly size-dependent. Overcoming friction and gravity requires a 10-m tall tree at mid-day to have a xylem pressure of about … -1.1 MPa. The other significant determinant of xylem pressure is the soil water potential. Because of the reverse osmosis at the root, the xylem must extract water not only from the soil pore space, but also against the osmotic strength of the soil solution. A 10 m mangrove rooted in seawater must pull against ca. -2.4 MPa of osmotic potential, which added to -1.1 for gravity and friction, comes to -3.5 MPa. In deserts, plants have to pull against soil water potentials of -5 MPa or lower. The lowest xylem pressure the author is aware of is -13.1 MPa (mean value) in a shrub from the California chaparral (Ceanothus cuneatus) during the dry season …”

      • John Baez says:

        Nice! -13.1 megapascals in the California chaparral! The ‘liquid-vapor spinodal’ — the negative pressure at which liquid water ‘breaks’ — looks to be between -120 and -200 megapascals at room temperature. That’s taken from Figure 1b here:

        • Stacey L. Meadley and C. Austen Angell, Water and its relatives: the stable, supercooled and particularly the stretched, regimes.

        Elsewhere they say it’s about -150 megapascals.

        • Harvey Brown says:

          Yes, metastable sap in the xylem will not break in this sense in plants, but the threat is bubble nucleation or cavitation, triggered by gas bubbles in the sap, and which blocks transmission to the leaves. Trees have interesting ways of minimising the threat.

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