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?

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.

The nature of Brownian motion will counteracts the gravity.

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