X-Message-Number: 33230
Date: Fri, 14 Jan 2011 16:51:49 -0500
From: "Perry E. Metzger" <>
Subject: Glass vs. Crystal transitions
References: <>

It is rare that a topic comes up here that is actually of direct
interest to improving cryopreservation quality. However, as
Mike Darwin has had the temerity to interrupt the usual chatter around
here by discussing actual experiment, I thought I'd chime in:

> From: 
> Date: Thu, 13 Jan 2011 21:56:09 EST
> Subject: Intracellular Freezing & Vitrification
> vitrify. A potential problem arises, especially when ice growth
> inhibiting  molecules are also present, in that such tissues will
> tend to supercool far below their true freezing point,

One side note here. (I'm sure Mike is aware of this, but others may
not be.) A uniform idealized substance (and sometimes a uniform
idealized mixture) can have a single definable freezing point, but
non-uniform substances do not. Biological tissues and individual cells
are nearly the definition of a non-uniform substance -- if they were
uniform, they would not function.

Furthermore, not every substance has a well defined freezing point
even when it is perfectly uniform. A good everyday example (just for
purposes of illustration) is paraffin.

Why mention this? Because even in idealized conditions, getting an
entire cell or block of tissue to undergo a phase transition at the
same time may be a bit of a challenge, and because things one learns
from uniform systems may warp when applied to non-uniform systems like
biological tissues.

> What Brian pointed out to me is that a
> 7.5 M solution of glycerol has a melting point of ~ -50 deg C.Thus,
> even if tissues containing 7.5 M glycerol solution nucleated
> perfectly upon passing below their melting point during cooling,
> all the  ice growth would take place at deep subzero temperatures
> where the mobility of water (and cell membrane permeability to
> water) is putatively low. An added complicating factor is that 7.5
> M glycerol solutions are virtually certain  to supercool well below
> their thermodynamically ideal freezing point - and indeed to do so
> by tens of degrees.

Supercooling is common across most substances. Extremely pure water
with no nucleation sites can be cooled to below -40C before it will
undergo spontaneous "homogeneous nucleation". Crystal formation itself
is a fairly complicated process, and without a nucleation center the
transition can be disfavored even if the final crystal would be
perfectly stable.

The specific issue, as I understand it, is this. (If someone
understands the process better than I do, please chime up -- I know a
bunch of physical chemistry but it is not my area of expertise.)

Forming an interface between the two phases requires energy, which is
proportional to the size of the surface area at the interface. Now,
there is a source of energy available, to whit, the energy liberated
by the formation of the crystal itself (the crystal necessarily has
lower free energy than the liquid), which is proportional to the
volume of the forming crystal. However, the smaller an object is, the
larger the ratio of its surface area to its volume. Thus, a very small
spontaneously formed crystal will not liberate enough energy to
account for the energy of the interface. Assuming a spherical nucleus,
one can calculate a critical radius below which a spontaneously formed
crystal is unstable. (A very similar process happens in water
droplet formation in clouds, where below a critical radius the
droplets are disfavored.)

However, as the temperature becomes lower and lower, the critical
radius itself lowers (one can model this mathematically though it has
been some years since I knew the details), until finally you hit a
point where the critical radius is small enough that spontaneously
formed crystals are larger than it and you get homogeneous nucleation
followed by a spontaneous phase transition throughout the liquid.

> This will be even more true of glycerol
> solutions at these temperatures because of their very high
> viscosity and  the resultant decreased mobility of water in the
> solution.

I know little about the physical chemistry of glycerol undergoing this
transition. Are the crystals formed pure water? If so, the
concentration of glycerol of the surrounding liquid would rise during
crystal formation, inhibiting further growth if diffusion was slow
enough. That would tend to explain the phenomenon you describe below:

> As Brian points out, if you carefully examine a vial of
> such a solution being slowly cooled to well below its freezing
> point,  what you  notice first is the presence of a few scattered
> large ice balls in the  solution. These are the points in the
> solution where nucleation and  subsequent ice growth first began,
> and they will typically have formed and begun  growing at between
> -50 deg C and -60 deg C; at the warmest temperatures  that ice can
> form in a 7.5 M glycerol solution.

The "sentinel" ice balls you describe may fail to grow faster
precisely because their formation alters nearby concentration of
glycerol, a self limiting process especially since the formation of
pure water ice requires energy since it is entropically disfavored. It
would be interesting to learn if this is true. However, with time, as
the liquids diffuse, they should grow until the overall concentration
is sufficient to impede further change. The phenomenon, as you
describe it, is self limiting even in a slowly cooled solution, which
is slightly puzzling.

> These sentinel ice balls almost certainly occur as a result of the
> presence of bacterial ice nucleating proteins that are present just
> about everywhere in the environment.

That may or may not be the case. It should be straightforward to
determine which, however, if it proved to be important.

> Brian further notes that these initial ice balls (several
> millimeters in diameter) grow as large as they do because they have
> lots of time to do so during slow cooling.

That would seem on its surface to be correct, but what limits them to
a few millimeters?

> However, what is easy to miss, or at least not to
> understand, is that as the rest of the rest of the 7.5 M glycerol
> solution is further cooled, it will grow cloudy. This cloudiness is
> due to the  formation of millions of microscopic tiny ice balls
> that refract the light.  Those microscopic ice balls were areas in
> the solution that nucleated  LONG after those few big ice balls
> formed, in fact, tens of degrees C later,  when the solution was
> much more viscous. As a result, those tiny ice balls  couldn't grow
> much before the glass transition temperature (Tg) of the  solution
> was reached, which in the case of 7.5M glycerol, is ~ -100 deg  C.

Again, that seems reasonable, but are you sure of the details? One
would tend to believe that an abrupt change in optical characteristics
has to be associated with a partial phase change, but the exact nature
of the phase change is of interest.

In particular, can you be sure these are not formed of some sort of
organized glycerol-h2o crystals or small particles of glassy solid and
are instead pure water? I would tend to agree that pure water seems
most plausible, but mere plausibility isn't enough, and this actually
may be important. Also, can you be sure the crystals grow no larger
because they have no time to do so, or could it be because the overall
concentration of glycerol has gone up enough to impede growth, or for
some other reason? It seems to me that this would require some

> In other words, the ice that makes the solution milky which  is
> most of the ice that will form in a 7.5 M glycerol solution - is
> ice  that formed in a deeply supercooled state.This happens even in
> the absence of  ice blockers because this is how concentrated
> cryoprotectant solutions behave  when cooled slowly to below their
> freezing point. Thus, ice formation in  supercooled solutions in
> cryonics patients is not a new phenomenon that began  with
> vitrification.

Yes, that last sentence (which is one of the punchlines in your note)
is almost certainly true.

> As Brian points out: "It should also be clear from
> this that idea of nucleating high molarity glycerol solutions
> externally would not have achieved anything because such nucleated
> ice, like those ice balls in the flask formed near Tm, could only
> have  grown a few millimeters into the solution before cooling was
> complete. The  same goes for any ice that nculeated at higher
> temepratures inside the patients  in poor perfused areas.

Well, this sounds plausible, but I don't have a well validated model
here of what's going on in a uniform solution, and biological tissues
are very different from a uniform solution, so it is hard to know how
well that applies in tissues. It is, I think, a mistake to believe you
understand something simply because you have a plausible but
unvalidated model. Experiments would probably be needed to determine
the answers for real.

> In parts of the brain that experienced good equilibration with the
> high concentration solution, the penetration of ice from other areas
> would be minimal, and most of the ice that formed in well-perfused
> areas would be formed under conditions of deep supercooling.

Presuming that the explanation of the opacity in the cooled solutions
is indeed homogenous nucleation of some sort, this is again
potentially plausible. Of course, tissues are very different from a
uniform solution -- some components of the tissues might promote
nucleation at much higher temperatures, might impede nucleation, etc.,
and in any case, the contents of cells and tissues are very

> You
> can bet whatever "blasted areas" or ice holes were seen  in your
> 7.5 Molar 1995 canine brains were areas hit by ice that started
> growing  in a very supercooled state." What I take away from this
> is that ice will still form and grow extracellularly under
> conditions where the colligative CPA concentration is very  high
> and the solution is very viscous. Where nucleation and ice growth
> occur close to the melting point of the solution (Tm), the ice
> formed will be 'large mass' ice, and likely mechanically
> disruptive. Where ice forms well below Tm, it will likely be in
> microscopic domains that still begin forming (nucleate)  outside of
> cells and consequently do little damage.

Again, extremely plausible, but this is a question which actual
experiments could answer, and in fact very quickly.

Now, going beyond all that we've discussed up to here, this whole
topic brings to mind a very basic question: has anyone in the cryonics
world or cryobiology world done a deep exploration of the physical
chemistry literature on the formation of glasses at low temperatures?

I have to admit that until a few years ago I wouldn't have even
thought to ask if such a literature existed, but I'm now no longer so
ignorant. My suspicion is that the pchem guys know a whole lot more
about this topic than most of us, and have a lot of understanding
about the competition between crystal and glass formation and what
shifts the equilibrium one way or the other.

I'm unsure as to whether we would learn anything valuable by exploring
that topic in depth, but there is a good chance we would. Knowing what
things are like in most of science, I suspect that the pchem guys and
even conventional cryobiology types have never really talked, though
of course I could be entirely wrong on this.

Anyway, it doesn't hurt to ask...

Perry E. Metzger		

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