```X-Message-Number: 3708
Date: Thu, 19 Jan 1995 21:14:56 -0500
From: "Keith F. Lynch" < var s1 = "kfl"; var s2 = "access.digex.net"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
Subject: Re: SCI.CRYONICS Mobility in a Semi-Vitreous Solid

Ben Best writes:
> Keith listed vapor pressure in mm-Hg for water at various
> temperatures, but did not give values for temperatures relative to our
> discussion -- simply saying that vapour pressure is "very, very small"
> at liquid nitrogen temperature.

Unfortunately, the table I have doesn't go below -100 C.  I suspect the
vapor pressure is effectively immesurable at temperatures much below
that, as we're no longer in the range of millimeters of mercury, but
of Angstroms of mercury!

Your extrapolations can't possibly be right, as you list a pressure 18
times higher for -130 than I did for -100.  Since -100's was about 1/7
of -90's, and -90's was about 1/6 of -80's, etc, I would make a rough
guess that -130's would be somewhere around 1/(8*9*10) of -100's,
or about 0.00000001 mm, which is about 13,000 times lower than your
estimate.  (Note that this is much less than the diameter of a single
mercury atom!)  Similarly, I expect that the -196 number ought to be
at least six orders of magnitude smaller yet, rather than the <2 orders
of magnitude you estimate.  I will try to find a table that goes down
that far.

As for the speeds of molecules, the relevant formulas are that the RMS
velocity of a molecule of mass M at absolute temperature T will be
sqrt(3kT/M), where k is Boltzmann's constant of 1.38E-23 joule-degrees.
And the proportion of the molecules with a velocity greater than V
will be exp(-MV^2/2kT).  Of course these are really true only for
unconstrained molecules.

> But I think that Keith overstates molecular mobility by using vapour
> pressure, because only the most energetic molecules will escape into
> a vapour.

Only the most energetic molecules will break free of their hydrogen
bonds.

> A better proxy for molecular mobility might be molecular velocities
> for an ideal gas approximation. ...  This gives me 445, 327 and 76
> meters/second for each atom at 143K, 77K and 4.2K.

Right.

> In molecular terms, at 143K or 77K a single water molecule has an
> RMS velocity great enough to traverse trillions of times its length
> every second. But what is the molecular mobility in a solid or liquid?

That's a much harder question.

> Keith refers to the fact that water molecules are 90% hydrogen-bonded,
> but then argues that water molecules are still bound-together despite
> the hydrogen-bonding being only 1/30th the strength of covalent bonds.
> Keith seems to be forgetting that although 90% of liquid water
> molecules are hydrogen-bonded, they are very mobile

I'm not forgetting that.  Partial mobility can equate to total
fluidity or to concrete-like rigidity.  Here's an analogy:

Suppose there was an immense building consisting of an enormous number
of identical square rooms.  There are no hallways.  Every room has a
door in each of its four walls, each of which leads into an identical
room.  The building is full of hyperactive people who are all constantly
trying the doors, and going through them if they can.  The doors are
hard to open.  When it's warm, each person will be able to open a door
about 10% of the time.  The colder it gets, the lower this number gets.

If you simulate this, you'll see that the mobility of the people does
not gradually decrease as you might expect.  Instead, it freezes out at
some temperature.  And the expected amount of time it takes for a person
to travel a reasonable distance through the building will increase
hyper-exponentially with decreasing temperature below that point.

> and very capable of dissolving other substances

This isn't relevant, since there shouldn't be anything soluble in a
patient that isn't already dissolved.  Not that anything can dissolve
in sufficiently cold ice.  I think that 0 degrees Fahrenheit was
originally defined as the lowest temperature at which a mixture of
salt and ammonium chloride would dissolve in ice.  (Either material
alone would cease dissolving at an even higher temperature.)

> The hydrogen-bonds holding an ice-crystal lattice together are
> primarily those between the oxygen atoms, with each oxygen bonded
> to four neighbouring atoms in a tetrahedron. These O--O--O bonds are
> nearly as strong as covalent bonds, in contrast to the O-H--O bonds
> that account for so much of the hydrogen bonding in water.

No.  The hydrogen bonds in water and in ice are the same.  The only
difference is what proportion of them are broken at any one time.  They
are all between O (which is slightly negative) and H (which is slightly
positive).  None are between O and O, which repel each other.  If they
didn't, the bonds between them certainly wouldn't be called "hydrogen"
bonds.

There can be a weak covalent bond between two oxygen atoms, but this
doesn't occur in water.

Water molecules are electric dipoles, which is why water is called a
polar liquid.  This is why ionic compounds dissolve in water.  The
hydrogens face toward negative ions such as chloride, while the oxygens
face toward positive ions such as sodium.

> Water is a random network of bendable, interchangeable hydrogen bonds.

It's highly structured with the same basic small-scale structure as ice.
The way in which it differs from this lattice is indeed random.  In
other words, to record the instantaneous position and orientation of
molecules in water would take much less information than if they were
completely and utterly random in their distribution, since you can start
with the pattern that ice has, and merely keep track of the "defects".

> A vitrified solid could simply be a "slow liquid".

All solids are.  But in most cases, this "slow liquid" is *extremely*
slow.  Fossils of single-celled animals that lived three billion years
ago still haven't blurred, although even one micron of random motion
would have smeared them out.  The covalent bonds in fossil-bearing rock
are no more real than the hydrogen bonds in ice.  They're just stronger,
which is why rocks melt at a higher temperature than ice.  Both have
some internal motion.  Both have some non-zero vapor pressure.

> Brian Wowk referred to Peter Mazur's classic article [AM. J. PHYSIOL.,
> 247:C125-C142, 1984], so I had another look at it. Mazur says that
> below -130C "viscosity is so high (>10*13 Poises) that diffusion is
> insignificant over less than geological time spans."

This sounds right to me.

I held off on sending the above for a few days, hoping Ralph Merkle or
another expert would step in.

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