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) Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=3690