The Strongest, Most Expensive Material on Earth

Graphene's most problematic superlative is its cost.

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It was so simple. Take a small flake of graphite and put it on piece of regular old Scotch tape. Pinch it in between the tape, peeling off layer after layer until it leaves only the vaguest, most transparent of marks. Transfer those dustings onto a chip; stick the chip under the microscope.
Congratulations, you've just made graphene—the strongest material humans are aware of. It's only one layer of atoms thick, which means to slice it any thinner would require dividing atoms into their elementary particles.
For years, scientists didn't even believe that creating graphene was possible—even Andre Geim, one of the scientists responsible for the scotch tape discovery. As he told CNN:

We live in a 3-dimensional world. My physics intuition, developed over the last thirty years, told me that this material shouldn't exist. And if you had asked 99.9% of scientists around the world they would have said the idea of a 2D material was rubbish and that graphene shouldn't exist.

But it is possible to make it. The problem now is that it's not exactly practical.
There's so much graphene can do. It can make computer chips much, much faster. It can make solar cells more efficient. It can remove salt from water.
Any of these (and there are so many other) applications, though, require more than a tiny flake of graphene, and scaling up production requires something other than a really big piece of scotch tape. As Nature reported last year, when manufacturers rely on the tape method, "just one micrometre-sized flake made in this way can cost more than $1,000 — making [graphene], gram for gram, one of the most expensive materials on Earth."
The challenge now is to develop a less simple but equally effective way to create the stuff. The most commonly used strategy is "chemical vapor deposition," in which a mix of gases react with a surface to create a layer of graphene. The graphene that's produced is of high quality—until it needs to be separated from its substrate, a process that often damages the material.
But there are other ideas in the works. One technique involves mixing graphene with carefully chosen liquids and then sticking the slurry into what's essentially a high tech blender. Another group of researchers took a similar mix and sprayed it at supersonic speeds onto a substrate.
These aren't quite as simple as the scotch tape strategy. But sometimes simple only gets you so far.