vis-co-e-las-tic-i-ty ex-pi-al-ido-cious or… what can’t you do with carbon nanotubes?

Some words are just so much fun to say.  My father claimed that, as a child, I was inordinately amused by long Latin words from his legal texts.  I would giggle at jurisprudential terms the same way most kids got excited by toys. Or so he always said.

No wonder I turned out the way I did.

But you must admit that viscoelasticity is just a cool word.  Like most words, you can break it down into its component parts: viscous and elastic.  And like the most interesting thing in physics, it's almost always "beyond the scope of the course".  You can talk in a limited way about elasticity (spring constants) and sometimes you'll learn a little about viscosity, but viscoelasticity consistently fails to make it into most introductory physics books.  That's too bad because it's not only a fun concept, it is a useful concept.

My first introduction to applied viscoelasticity was my foray into understanding the physics of tires.  Rubber is one of the most fascinating materials in the world.  Not coincidentally, rubber is viscoelastic.  Remember the coefficient of friction?  The force it takes to start something sliding is proportional to how much force is pushing down on it.  The proportionality coefficient is the coefficient of (static) friction.  A coefficient of friction of 0.3 means that a 100-pound block must be pulled with 30 lbs of force before it can start to move.  Most classes normally deal with simple cases of one solid material (like wood) on another (like sandpaper).  Something like rubber on asphalt might get up to a coefficient of friction of 0.7-0.8. 

Before NASCAR, I didn't realize you could have a coefficient of friction greater than one.  A coefficient of friction greater than one means that if you want to start something sliding, you have to pull or push the object with a force greater than its weight.  In normal-person talk, that means the object is sticky, or changing shape, or any one of a number of interesting things that real objects do when pushed or pulled.

A good race tire can have a coefficient of friction anywhere from 1.2-1.5.  That's what it literally means to 'grab' the road. A race tire doesn't feel sticky to the touch, but get it heated up a bit and it feels a really strong affinity for the track, which means you can go fast around the corner without sliding.  Viscoelasticity at work.

The linear relationship between the amount of force pushing down and the force needed to slide only holds out so long.  Yep, ol' F_f=μN only works within certain limits.  That's OK – Physics is so much more interesting when you push its buttons.

Viscous means able to flow under shear (or tensile) stress.  Shear means that you push on an object somewhere and one part of the object moves relative to other parts of the object, as I've tried to draw at left.  Molten glass, for example, will flow when you pull it.  Honey is the canonical viscous material.  The more viscous a material is, the more difficult it is for it to flow.  And, of course, viscosity is highly dependent on temperature.  Warm syrup is much less viscous than cold syrup, which is why it is easier to pour.

Viscosity relies in large part on the molecules in the solid or liquid being able to move relative to each other.  If the molecules or atoms were locked in place, you'd have a solid and it wouldn't change shape readily.

The problem with a material like honey is that the ease with which molecules slide past each other is just a little overdone, which makes honey somewhat messy, even if it is highly yummy.  If your honey bear tips over at the table, you are highly unlikely to see the honey pull itself back into the bottle.  Although wonderfully viscous, there aren't enough molecular interactions to make honey elastic. 

Although viscosity relies on the molecules being able to move relative to each other, elasticity requires that those molecules exert some type of restoring force on each other – a type of molecular peer pressure that tells the moving molecules, "hey – get back here!"

Elastic implies the ability of an object to return to it's original shape, or at least a shape something like the original shape.  A stretched rubberband deforms, and then returns to its original shape when you remove the deforming force.  The combination of viscosity and elasticity however, an object that is viscoelastic has time dependence.  If you get one of those big heavy rubberbands and hang something heavy from it, it will stretch.  Over time — and time is the important parameter in viscoelasticity — the molecules in the rubber band will shift their positions to adapt to the stress of the weight pulling down.  It's a little like you or me shifting our position when we're standing for a long time.  When the weight is removed, the rubber band molecules can return to their original configuration (or something close to it). 

There are a lot of different types of viscoelastic materials.  Semi-crystalline and amorphous polymers, both made of poorly ordered (or totally disordered) long chains of molecules tend to be viscoelastic.  If you heat a metal to high enough temprature, it will be viscoelastic as well.  Biological structures like muscles and blood vessels are viscoelastic.

Polymeric and biological viscoelastic materials are mostly composed of long chains of intertwined molecules.  The importance of intertwining was demonstrated by the discovery of vulcanization, which does not mean the conversion of someone into a Star Trek fan.

The sap of many trees (like the rubber tree) is naturally much more visco than elastic, which means it is more like chewing gum than tire rubber.  Tree rubber originally was used for erasers – like those gummy art erasers that fall apart and make a mess everywhere.  Natural rubber was pretty much useless for most anything else. It got stinky and soft in hot weather, while cold weather made it brittle and cracked.  Early Mayan people knew how to vulcanize rubber, but that information was somehow lost between then and 1830s New England.

The frequently bankrupt businessman Charles Goodyear was obsessed with finding a way to make rubber stronger and less sticky without losing its elasticity. The story has it that, as Goodyear was showing off his latest result to a snickering group at the Woburn, Massachusetts general store in 1839, the piece of rubber he had been gesturing with flew into the air and landed on a stove.

Goodyear expected to be cleaning up a gooey mess; however, the material on the stove wasn’t melted. It was elastic, durable and–unlike his previous attempts–it didn’t stick to everything.  A true Eureka moment.  Goodyear experimented some more and eventually settled on using steam to cure the sulfur-doped rubber. The curing process was called vulcanization after Vulcan, the Roman god of fire and volcanoes. Goodyear, the poor guy, never profited from his discovery.  (Bonus trivia:  Goodyear never worked for the Goodyear Rubber and Tire Company.)

Vulcanization is the key – you have to get those chains interconnected to each other, otherwise there's nothing inside the material that pushes back when you push on it.

If you take a handful of uncooked spaghetti and push anywhere, those pieces of spaghetti move.  Now cook the spaghetti.  It becomes a tangled mess and it is much harder to move one strand without the others pulling on it, trying to keep it from moving (or moving along with it).

Using this principle of crosslinking, you can tune a fairly large set of parameters to make a polymer material as hard, soft or elastic as you want it to be.  The challenge is that most materials have these desirable properties over fairly limited temperature ranges.  A liquid-nitrogen cooled racquet ball shatters instead of bouncing.  Tires lose grip when they start to get warm because the heat allows the viscous nature of the rubber to win out over the elastic nature of the rubber.

The molecular motion that controls the balance between viscous and elastic in polymers is thermally activated.  That means the rate of motion depends the exponential of the ratio of an energy to kT.  (k being the Boltzmann factor, T being the temperature).  This exponential dependence means that the motion is extremely sensitive to temperature (much more so than a power law, for example) and thus the ideal viscoelastic properties only last over a limited temperature range.

In the December 3rd issue of Science magazine, a group from AIST in Tsukuba, Japan, reports on a material made almost entirely from carbon nanotubes that retains its viscoelasticity from -196 °C (-321 °F, which happens to be liquid nitrogen temperature) to 1000 °C (1832 °F).  That's an astounding temperature range to maintain viscoelasticity compared to most materials we know. 

Carbon nanotubes are rolls of graphene, and the Japanese group used a mixture of single-walled, double-walled and triple walled nanotubes.   The nanotubes play a role analogous to the long-chain polymers, sliding past each other to rearrange; however, the authors suggest that the carbon nanotube motion is very different than the motion of the molecules in a polymer.  The carbon nanotubes are sort of "zipping and unzipping" against each other as they come into contact – that's NOT a thermally activated process and may explain the very wide temperature range over which viscoelasticity is observed.  To make things even better, the nanotubes may have some additional elasticity because the tubes can flatten and then re-round themselves.

You know there's a catch, right?  Here it is:  this only works in a "non-oxidizing atmosphere", meaning the experiments weren't done out in the open where air could get involved.  When you heat small-diameter nanotubes to about 400°C in air, they burn.  The material would also (at least right now) be pretty expensive, but since the most imperative applications are probably the most extreme, the price might not be as much of an issue for the space program or the defense industry.  I don't see this material replacing gel insoles anytime in the near future, but I have a high-temperature furnace that makes me insane because the high-temperature polymer seals I use to protect my samples from oxidation during annealing leak a whole lot more frequently than I'd like them to.  This new carbon nanotube rubber is essentially the equivalent of the cookware that goes from freezer to oven without breaking.

Now, if only there is a story that goes with the discovery of this material that can rival the (OK, possibly apocryphal) story surrounding the Goodyear's discovery of vulcanization…