X-Message-Number: 3690
Subject: SCI.CRYONICS: Mobility in a Semi-Vitreous Solid
From:  (Ben Best)
Date: Sun, 15 Jan 1995 00:06:00 -0500


   Keith Lynch's claim that vapour pressure is a good indicator of
mobility of H20 molecules in water or ice got me playing with some
numbers -- which turned-out to be a lot of fun. 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. I did a rough extrapolation of his figures on a semi-log
plot and got the following values:

     Celcius T    Kelvin T    mm Hg      Reference
      -130          143     0.00018      Near Tg (water/glycerol)
      -196           77     0.0000025    Liquid nitrogen boiling point
      -268            4.2   0.0000001    Liquid helium boiling point

Using the fact that 1 atm = 760 mm Hg and that there are 101.3 Joules
per litre-atm, I get that a litre of sublimated water vapour will have
about 0.018, 0.00025 and 0.00001 Joules at 143K, 77K and 4.2K,
respectively. Using      PV
                     n = -- , these samples will have 200, 5.2 and 3.8
                         RT
x10*-10 moles of atoms, respectively. (I am using * for exponentiation.)
Since water has a mass of approximately 0.018 kg/mole, since
Joule = (kg x m*2)/(sec*2) and using Kinetic Energy = 0.5 x m x (v*2)
I get average molecular velocities of 10,021 m/s, 7,353 m/s and
1,717 m/s at 143K, 77K and 4.2K.

    But I think that Keith overstates molecular mobility by using vapour
pressure, because only the most energetic molecules will escape into a
vapour. A better proxy for molecular mobility might be molecular
velocities for an ideal gas approximation. In this case, I calculate
root-mean-square velocity:

                V (RMS) = (3RT/M)*0.5

         where  R = 8.314 Joule/(Mole x degrees Kelvin)
                T = Kelvin Temperature
                M = molecular weight x 0.001 (to give kilograms/mole)

This gives me 445, 327 and 76 meters/second for each atom at 143K, 77K
and 4.2K. 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?

    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
and very capable of dissolving other substances -- which is precisely my
concern. All hydrogen-bonds are not created equal. The hydrogen-bonding
in liquid water makes the molecules adhere lightly to each other, but
does not prevent their mobility. 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. Water is a random network of bendable, interchangeable
hydrogen bonds. An ethanol solution is even more highly hydrogen-bonded
than water -- 98% -- but it is still fluid. Which returns me to my
original concern about the mobility -- and dissolution capabilities --
of molecules in a semi-vitreous solid (like a cryonics patient). Nothing
Keith or I have said gives a good quantitative sense of what the
mobility (or immobility) really is for molecules not bound-up in a
rigid lattice. A vitrified solid could simply be a "slow liquid".

    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."
But I would still like to see a more quantitative description of
diffusion than the word "insignificant". Mazur does at least say
"there is no confirmed case of cell death ascribable to storage at
-196C for some 2-15 yr and none even when cells are exposed to levels
of ionizing radiation some 100 times background for up to 5 yr."

      My comment about superconductivity and superfluidity was a token
for unexpected weirdness at liquid helium temperature, not specifically
a reflection of concern about using helium. Whether solid silica is
"normally" crystalline depends on what you mean by "normal". Silica
forms a crystal or glass depending on cooling rate -- and for geologic
processes cooling rates have been slow. For commercial glass 15% soda
is typically added to silica to lower the melting point, and 10% lime
is added to make the glass more chemically stable. This is tangential
to the basic points I was making. Silica is the prototypic glass-forming
substance. Its viscosity at melting temperature is 10*7 Poise, in
contrast with water, which is 0.02 Poise -- and this is a critical
factor for glassification.

                     -- Ben Best (ben.best%canrem.com)

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