X-Message-Number: 3751
Subject: SCI.CRYONICS Molecular Mobility, Hydrogen Bonds, etc.
From:  (Ben Best)
Date: Thu, 26 Jan 1995 04:20:00 -0500

     Over a week ago I posted a reply to Keith Lynch in which I reported
a rough extrapolation of his vapour pressure/temperature table to lower
temperatures of interest. To my great embarrassment I must admit that my
extrapolation was "rough" to the point of inexcusable sloppiness. I have
now very carefully drawn a semilog plot and I find that the figures vary
with log10 very well indeed -- virtually forming a straight line (with
values quite different from the ones I posted previously):

 Celcius T   Kelvin T   mm Hg                  Reference
  -130        143      0.000 000 6           Near Tg (water/glycerol)
  -196         77      0.000 000 000 18      Liquid nitrogen boiling pt.
  -268          4.2    0.000 000 000 000 056 Liquid helium boiling pt.

    I have also decided that I was wrong about RMS velocities of an
ideal gas being a better proxy than vapour pressure of molecular
mobility in low temperature vitreous solutions. It is well-known that
temperature is inversely proportional to log10 viscosity for glasses --
which matches the decline in vapour pressure with temperature.

   What irritated me about Keith's assertion, however, was that it
merely alluded to an answer, while claiming to be an answer, and in
a misleading way. I wanted to show that a presumably small quantity
in terms of a macroscopic property like vapour pressure could still
correspond to a large quantity on a molecular scale. For example,
if the decline with temperature of RMS velocity of a water vapour
molecule is comparable to the decline in vapour pressure, then from
273 Kelvin, 4.6 mm Hg and RMS velocity 615 m/s we get RMS velocity
of 2400 nm/sec at 77 Kelvin and 7.5 nm/millisec at 4.2 Kelvin. Since
a water molecule is in the order of 0.1 nanometer, this is a
considerable mobility.

   I was also irritated by Keith's refusal to acknowledge the difference
between a crystal and a vitrified solid -- his use of vapour pressure of
*ICE* being one example. He even went so far as to say "The hydrogen
bonds in water and in ice are the same." In fact, H-bond enthalpies
in ice I vary from 4.7 to 8.2 kcal/mole, whereas H-bond enthalpies in
water vary from 1.3 to 2.8 kcal/mole. A water H-bond has an average
life of about 2x10*-13 second. At 0 Celcius water molecules experience
10*11 to 10*12 reorientational and translational movements per second,
whereas ice molecules at the same temperature experience 10*5 to 10*6
reorientational and translational movements per second. This makes me
think that ice is more fluid that I had thought.

    At 135 Kelvin (-138 Celcius) vitrified water has a vibrational
energy of 17.91 KJoule/mole and a bending energy of 1.93 KJoule/mole
as opposed to ice I which has 18.55 and 0 KJoule/mole, respectively.
All-in-all I am ready to agree that the translational motion difference
between a crystal and vitreous solid at liquid nitrogen temperature is
probably less than an order of magnitude. Nonetheless, I still wish
I had some *quantitative* sense of molecular mobility at 143K, 77K
and 4.2K. I had hoped that some physical chemist would enter the
discussion and enlighten us.

   By the way, it is a common convention for physical chemists to omit
the hydrogen atoms when drawing and discussing the tetrahedral hydrogen
bonds between oxygen atoms in an ice lattice. I agree that this is
misleading and I will try to avoid the practice in the future.

                  -- Ben Best ()

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