Lubricating the drive

Much discussed among computer circles is the so-called end of Moore's Law and its predictions of ever-smaller, faster circuits. Less known is a challenge facing the next generation of hard disk drives: lubricant coatings that can hold up to faster speeds and denser data.

Perfluoropolyethers (PFPEs), the current industry standard, are running up against the polymer's limits in protecting hard drives against daily wear and tear. So University of Illinois PhD candidate Wei Xiao developed an entirely new lubricant, based on inexpensive and abundant polyester.

She presented her work today for the first time at the 228th national meeting of the American Chemical Society, the world's largest scientific society.

In short, the lubricant, called SHP - sterically hindered polyester - "acts like a solid when cast as very thin films," says Xiao. "And it has very good adhesion properties."

Both qualities are important for lubricant design. A computer's hard drive is polished to a mirror finish to create as perfect a surface as possible on which to record, retrieve and erase thousands of hours' worth of data over its lifetime. A lubricant coating shields the disk from damage during contact with the head, which can fly back and forth across the disk dozens of times per second.

As a magnetic recording device, the head itself relies on a magnetic field rather than physical contact to read or write to the disk. But at rest, tiny arms called sliders drop down to the disk surface to protect the head.

"The lubricant needs to be solid enough that the sliders don't sink. But it needs to be liquid enough so that any debris from contact between the head and surface would sink back in," says Xiao's advisor James Economy, PhD, a professor with the school's department of material science and engineering. He came to Illinois after 14 years of heading up polymer research at IBM.

The sliders do sink into PFPEs, however, and the attractive forces of 'stiction,' short for static friction, can keep them from retracting quickly enough when the disk begins to spin again. That 'stickiness' can damage the disk or even snap off the head when the disk starts spinning again.

Two other problems have arisen as disk drives spin ever faster to speed performance, he notes. At the 10,000-plus revolutions per minute now typical of computer hard drives, centrifugal forces can ripple the lubricant like a washboard. The uneven surface can hamper reading and writing, and can leave some tracks less protected from slider strikes.

Secondly, PFPE lubricants "can also spin off entirely," says Economy. To prevent that, researchers "often try to chemically bond it to the disk surface. That's a disadvantage because you've got to figure out the chemistry to do that."

"In our approach, the polymer is very polar," Xiao explains. "So it bonds to the surface on its own." The result is a simpler and less expensive solution, the Illinois researchers believe.

To make their lubricant more stable, Xiao used polyester building blocks containing offshoots of bulky organic molecules. As they polymerize, the bulky groups surround and protect the ester bonds. The effect, called steric hindrance, also helped the team achieve the balance of solid and liquid characteristics they wanted.

Their data also suggest the SHP lubricant is more resistant to corrosion than PFPEs.

"Solving the problems [with PFPE] forced us to make a completely new kind of polyester," Economy says. "I don't think any other [research] group has tried to design new materials in this area."

Indeed, the Illinois team believes their invention may have far broader application, such as the mining industry, for example, or metals manufacturing; perhaps even automobile engines. "Any place where there are wear surfaces," says Economy.

Xiao has sent samples of SHP to the Center for Magnetic Recording Research, an industry-sponsored facility at the University of California, San Diego, which can conduct real-world testing.

Was algebra developed in Afghanistan? That was the last thing they did.

While Arabic mathematicians may have refined and furthered the study of algebra (the name "algebra" is derived from the Arabic "al-jabr"), they can not be credited with inventing it. The following is a concise history of the development of algebra:

Algebra has been studied for many centuries. Babylonian, and ancient Chinese and Egyptian mathematicians proposed and solved problems in words, that is, using "rhetorical algebra".

However, it was not until the 3rd century that algebraic problems began to be considered in a form similar to those studied today.

In the 3rd century, the Greek mathematician Diophantus of Alexandria wrote his book Arithmetica. Of the 13 parts originally written, only six still survive, but they provide the earliest record of an attempt to use symbols to represent unknown quantities. Diophantus did not consider general methods in Arithmetica, but instead solved a large number of practical problems.

Several Indian mathematicians carried out important work in the field of algebra in the 6th and 7th centuries. These include Aryabhatta, whose book entitled Aryabhatta included work on linear and quadratic equations, and Brahmagupta, who presented a general solution for a quadratic equation.

The next major development in the history of algebra was the book al-Kitab al-muhtasar fi hisab al-jabr wa'l-muqabala ("Compendium on calculation by completion and balancing"), written by the Arabic mathematician Al-Khwarizmi in the 9th century. The word algebra is derived from al-jabr, or "completion". This book developed methods for solving six different types of quadratic equations, and contained the first systematic consideration of the subject separately from number theory.

In about 1100, the Persian mathematician Omar Khayyam wrote a treatise on algebra based on Euclid's methods. In it he identified 25 types of equations and made the first formal distinction between arithmetic and algebra.

Some time later during the 12th century, Al-Khwarizmi's works were translated and became available to Western scholars. In the 13th century Leonardo Fibonacci wrote some important and influential books on algebra. Other highly influential works were those of the Italian mathematician Luca Pacioli (1445-1517), and of the English mathematician Robert Recorde (1510-1558).

Rules for solving cubic equations were discovered about 1515 by Scipione del Ferro (c. 1465-1526), and for the quartic equation by Ludovico Ferrari (1522-1565) about 1545. In 1824 Niels Henrik Abel (1802-1829) finally proved that, in general, it is not possible to give general rules of this kind for solving equations of the fifth degree or higher.

Further contributions to the symbols used in algebra were made in the late 16th century and the 17th century by François Viète (1540-1603) and René Descartes, among others.

Complex and negative roots were a later discovery, and took some time to become accepted. In 1799, Karl Friedrich Gauss proved the fundamental theorem of algebra, which had been proposed as early as 1629.

In the 19th and 20th centuries algebra has become much more abstract and has grown to include much more than the theory of equations. Modern developments in algebra include group theory and the study of matrices.

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