Proton mobility vs. conductance in ice

[WarpedWatch]

Greetings,

I'm trying to understand how protons might move through solid water ice. More specifically this concerns how deuterium/hydrogen ratios are used to date ice core samples drilled into glaciers.

On one hand I am told that, once it is deposited from the atmosphere in the form of snow, deuterium diffuses through glacier ice very very slowly, so the examination of H/D ratios in glacial layers provides a fairly sharp delineation of environmental conditions that tend to fractionate H and D in the atmosphere.

But on the other hand, I read that the proton has a mobility in solid ice that is about 100 times what it is in liquid water at the same temperature due to the Grutthuss mechanism in ice and maybe tunneling, etc. For example, in Modern Electrochemistry, Vol. I by Bockris and Reddy, 2nd edition page 581, states "... in pure ice the proton's mobility (not its conductance) is approximately 100 times greater than it is in water at the same temperature."

I have heard that the deuterium from a liquid drop of D₂O will very quickly diffuse into a parcel of liquid water, and result in a bunch of HDO molecules. This is because the H bonds in water allow the H's and D's to freely exchange. As I understand it, the spread of D's throughout the water is a diffusion-like process and happens very quickly.

And yet I've heard that if you put a cube of frozen D₂O into normal water, it will sink to the bottom and stay there (because D₂O ice is heavier than water.) The heavy water ice cube won't suddenly pop back to the surface after any amount of time. In other words, its D's won't get exchanged with H's and change the ice density into that of normal ice.*

What confuses me is this: if the mobility of protons in ice is faster than it is in liquid water, then why doesn't deuterium get moved around in ice via diffusion? Aren't diffusion and mobility related that way? It seems to me that high mobility of protons through ice would translate into high diffusion rates through ice, and so H/D ratios of glacial layers would get uselessly smoothed into one another especially over time spans of, say, hundreds or thousands of years.


(*I guess it's possible that the ice always melts before it could equilibrate H's ?)

Could one of you geniuses here explain to me the faultiness of my reasoning on this?

many thanks,
Mark

 

[alxm]

What confuses me is this: if the mobility of protons in ice is faster than it is in liquid water, then why doesn't deuterium get moved around in ice via diffusion?

Do you know how the Grotthuss mechanism works? Consider a chain of water molecules (for two-dimensionality I'm only including one of the hydrogens on each water, dots are hydrogen bonds)

H⁺ + O-H..O-H..O-H..O-H --> H-O..H-O..H-O + H⁺

The proton goes in one and and another proton comes out the other end. But since protons are indistinguishable, it's in practice a transfer from one end to the other. Not the same if you throw in the odd deuterium atom!

Tunnelling is a measurable but small effect in proton transfer in some cases and much smaller for deuterium. By and large they move 'classically'

In water, you're constantly breaking and forming new hydrogen bonds. You also have water breaking into H⁺ and OH^-. The protons get around a lot.

In ice, you don't have solvation of the ions and the bonds are more or less static. So the only place a deuterium atom can go via the Grotthuss mechanism is back-and-forth from the neighboring water molecule, until/unless the deuterized molecule reorients itself.

 

[WarpedWatch]

...

In water, you're constantly breaking and forming new hydrogen bonds. You also have water breaking into H⁺ and OH^-. The protons get around a lot...

Okay,
I think I get it now. In water you've got lots of molecular diffusion (the entire D₂O molecule is able to wriggle around in the fluid) taking place while at the same time the H's and D's can exchange places. But in ice, you don't have the molecular diffusion to start with, so that, by itself, slows everything down.

thanks for the help,
Mark