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      愛因斯坦和汽車電池Einstein and car batteries

      A spark of genius
      Without the magic of relativity, a car's starter motor would not turn 
      ALBERT EINSTEIN never learned to drive. He thought it too complicated and in any case he preferred walking. What he did not know—indeed, what no one knew until now—is that most cars would not work without the intervention of one of his most famous discoveries, the special theory of relativity.
      Special relativity deals with physical extremes. It governs the behaviour of subatomic particles zipping around powerful accelerators at close to the speed of light and its equations foresaw the conversion of mass into energy in nuclear bombs. A paper in Physical Review Letters, however, reports a more prosaic application. According to the calculations of Pekka Pyykko of the University of Helsinki and his colleagues, the familiar lead-acid battery that sits under a car's bonnet and provides the oomph to get the engine turning owes its ability to do so to special relativity.
      狹義相對論同物理極限相關。該理論掌握了亞原子粒子在強大的加速器的作用下可以達到接近光速的速度這一表現行為。相對論的公式也預見了核彈中質(量)能(量)轉換的現象。然而,一篇發表在物理評論快報上的文章,講述了狹義相對論更為一般的應用。根據赫爾辛基大學的Pekka Pyykko和他同事們的計算,我們所熟悉的在汽車發動機罩下,給汽車引擎發動提供能量的鉛酸電池,它之所以有這樣的能力都歸功于狹義相對論。
      Relative values.

      The lead-acid battery is one of the triumphs of 19th-century technology. It was invented in 1860 and is still going strong. Superficially, its mechanism is well understood. Indeed, it is the stuff of high-school chemistry books. But Dr Pyykko realised that there was a problem. In his view, when you dug deeply enough into the battery's physical chemistry, that chemistry did not explain how it worked.

      A lead-acid battery is a collection of cells, each of which contains two electrodes immersed in a strong solution of sulphuric acid. One of the electrodes is composed of metallic lead, the other of porous lead dioxide. In the parlance of chemists, metallic lead is electropositive. This means that when it reacts with the acid, it tends to lose some of its electrons. Lead dioxide, on the other hand, is highly electronegative, preferring to absorb electrons in chemical reactions. If a conductive wire is run between the two, electrons released by the lead will run through it towards the lead dioxide, generating an electrical current as they do so. The bigger the difference in the electropositivity and electronegativity of the materials that make up a battery's electrodes, the bigger the voltage it can deliver. In the case of lead and lead dioxide, this potential difference is just over two volts per cell.
      That much has been known since the lead-acid battery was invented. However, although the properties of these basic chemical reactions have been measured and understood to the nth degree, no one has been able to show from first principles exactly why lead and lead dioxide tend to be so electropositive and electronegative. This is a particular mystery because tin, which shares many of the features of lead, makes lousy batteries. Metallic tin is not electropositive enough compared with the electronegativity of its oxide to deliver a useful potential difference.
      This is partly explained because the bigger an atom is, the more weakly its outer electrons are bound to it (and hence the further those electrons are from the nucleus). In all groups of chemically similar elements the heaviest are the most electropositive. However, this is not enough to account for the difference between lead and tin. To put it bluntly, classical chemical theory predicts that cars should not start in the morning.
      原子越大,其外層電子受原子束縛力越弱,這是解釋鉛和錫兩者差別的一部分原因。在化學性質相似的同族元素中,質量越重帶的正電越強。然而這依然不能充分說明鉛和錫的差別。直截了當地說, 古典化學理論預言了早上(要離家上班)汽車是發不動的。
      Which is where Einstein comes in. For, according to Dr Pyykko's calculations, relativity explains why tin batteries do not work, but lead ones do.
      His chain of reasoning goes like this. Lead, being heavier than tin, has more protons in its nucleus (82, against tin's 50). That means its nucleus has a stronger positive charge and that, in turn, means the electrons orbiting the nucleus are more attracted to it and travel faster, at roughly 60% of the speed of light, compared with 35% for the electrons orbiting a tin atom. As the one Einsteinian equation everybody can quote, E=mc2, predicts, the kinetic energy of this extra velocity (ie, a higher E) makes lead's electrons more massive than tin's (increasing m)—and heavy electrons tend to fall in and circle the nucleus in more tightly bound orbitals.
      That has the effect of making metallic lead less electropositive (ie, more electronegative) than classical theory indicates it should be—which would tend to make the battery worse. But this tendency is more than counterbalanced by an increase in the electronegativity of lead dioxide. In this compound, the tightly bound orbitals act like wells into which free electrons can fall, allowing the material to capture them more easily. That makes lead dioxide much more electronegative than classical theory would predict.
      產生的結果是,金屬鉛的電正性沒有古典化學理論認為的那么強(或者說,更為電負性)——看起來似乎鉛不適合用來做電池。但是, 二氧化鉛電負性的增加不但全部抵消了這個趨勢還有剩余。在這個混合物里,結合緊密的軌道就像一口井,自由電子落入其中,使得物質更容易捕獲電子。二氧化鉛的電負性其實比古典化學理論認為的要更強。
      And so it turned out. Dr Pyykko and his colleagues made two versions of a computer model of how lead-acid batteries work. One incorporated their newly hypothesised relativistic effects while the other did not. The relativistic simulations predicted the voltages measured in real lead-acid batteries with great precision. When relativity was excluded, roughly 80% of that voltage disappeared.
      That is an extraordinary finding, and it prompts the question of whether previously unsuspected battery materials might be lurking at the heavier end of the periodic table. Ironically, today's most fashionable battery material, lithium, is the third-lightest element in that table—and therefore one for which no such relativistic effects can be expected. And lead is about as heavy as it gets before elements become routinely radioactive and thus inappropriate for all but specialised applications. Still, the search for better batteries is an endless one, and Dr Pyykko's discovery might prompt some new thinking about what is possible in this and other areas of heavy-element chemistry.

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