Monday, April 23, 2012

Can You Lift a Polymer from One End?

Neil Withers posed an interesting question at The Sceptical Chymist blog

"A question struck me yesterday afternoon (editorial discretion prevents me revealing exactly why): what weight could you hang from a chemical bond before it broke? How many atoms? I asked the rest of the team if they had any ideas, but got no answers I would be comfortable publishing! Still intrigued, I thought about it more while it was my turn on the tea rota. It’s relatively easy to work out, with a little digging, but might surprise you. I’ll let you all stew on the question over the weekend – and suggest your own answers below – and return with my Fermi-style calculation on Monday!"(Emphasis added)
How many atoms? Doesn't that suggest a polymer hung from one end? Since this is a polymer blog, I decided to look at it from that polymer perspective: what is the longest polyethylene molecule that you could pick up from one end without having the chain break? A quick Google search produced 1600 pN as the force needed to break a typical C-C bond. The force exerted by a suspended mass is mg. For a methylene (-CH2-) unit, that is 14 g/(6.02 x 1023) x 9.8 m/s2 = 22.8 x 10-26 N. To reach a force of 1600 pN, 1.43 x 1012 methylene units would be needed [*], a tremendously large degree of polymerization that is not currently obtainable in linear polymers. Ultrahigh molecular weight HDPE has a molecular weight of about 4 - 5 million g/mole, so the degree of polymerization in that polymer is about 300,000, 7 orders of magnitude less than the number I found. The average length of C-C bond is 1.54 Angstroms, so a polymer of such high degree of polymerization would have a contour length of about 220 m!

Or looking at it another way, 1.43 x 1012 methylene units would have a mass of about 2 x 10-12 g, - 2 picograms. So while the strength of the C-C bond is relatively high, it's not as if you could drag a freight train with it.

The (relatively) large value for the strength of C-C bond seems intuitively correct, as we know polymer molecules don't break during reptation, although the resistance to that longitudinal motion is different than that provided by a suspended mass. But this also suggests that the long hoped-for sky elevator is not impossible if (perfect!) polymers are involved.

[*] I hope the Monday-morning math is correct, but given what I'm finding, being off by a factor of a billion or so isn't going to matter at all, is it?

6 comments:

Neil said...

Thanks for giving us your take! It's an amazing thought that a single C-C bond could support the weight of a 220 metre polymer!

It's got me thinking about the size of the gold particle that I came to in my post too...something for this Friday perhaps.

Materialist said...

To be a bit pedantic, I might ask over what timescale you want the bond to hold.
With so many bonds in a row, and without other molecules to provide stabilizing viscosity, statistical thermodynamics suggests that at a finite temperature one of those C-C will come apart short of the Spectra x 10^7 MW

John said...

@Materialist,

I think you raise a very relevant point, (one that would be very challenging to answer) although I view the initial question as fairly hypothetical, more of a brain tickler than anything in need of an absolute. I think the question you raise would be much more relevant to the whole reptation question - what is the longest molecule that can reptate without breaking.

Even with the existence of molecular tweezers, I wouldn't want to be asked to pick up a polymer from the end. I'll leave that to Maxwell's Demon.

Anonymous said...

what about "Adsorption-induced scission of carbon–carbon bonds" Nature and similar work by those groups?

John said...

@Anonymous,

That seems to be somewhat beside the point. The original question is how much weight (or how many atoms) can you hang from a bond. This implies to me that the atoms are hanging in free space - a vacuum. Even in a normal lab setting, the impact of the air molecules on the polymer could be enough to upset the results.

Andrew Sun said...

The nature of Brownian motion will counteracts the gravity.