Dear Hipster,
That's a fantastic question! Thanks for bringing up the subject of putterhead metals.
The short answer to "should you be concerned about oxidation" is "yes." Oxidation is always at issue with any metal. "Oxidation" is the transfer of electrons between molecules or atoms, and this transfer has the effect of creating pits and changing the surface of the putter. Actually, "oxidation" is the LOSS of electrons, and "reduction" is the gaining of those same electrons -- hence the more general term "REDOX." The most familiar form of oxidation is "rust," most usually associated with iron (Fe). But other forms are also common, including "fire," film developing, silicon chip deposition, biological oxidation, batteries, and other forms.
Every element has a potential for these electron transfers, and cobalt is an element that is resistant to oxidation. Inclusion of cobalt in the alloy of a putterhead is for the purpose of resisting corrosion, but it never truly prevents oxidation.
How soon oxidation / corrosion shows up really depends upon the use and care of the putter. The main substance that joins with the metal to create the REDOX transfer is water. Water is known in chemistry as "the universal solvent" because of it's tendency to dissolve almost anything given enough time. So the main thing about care for the putter is to avoid leaving the putter exposed to mositure. "Pitting" is when electrons transfer from one location on the metal surface through a "water bridge" to a water molecule elsewhere, so pits can actually occur off to the side of so-called "rusting" of the surface. And of course pitting makes the oxidation process faster since it removes the protective coating. So, after every use of the putter, the moisture from the grass or the humidity or the dew or rain should be wiped off and the putter dried. Also, avoid storing the putter in a damp location (e.g., basement of the clubhouse), at least without a putterhead cover.
The function of oil is to create a barrier between the metal surface and moisture (or other agents causing the REDOX). There are different oils, and a good one would probably be the same oil used for care and cleaning of handgun and rifle metals -- available in hardware and firearm stores. This oil can be applied after every use and after prolonged storage, and can also be present inside the putterhead cover. It stands to reason that a putterhead cover that allows water or moisture to get through is not a good idea, so leather and swede are good but permeable plastic is probable not best.
I don't see the harm of putting oil inside the cover, but remember that some oils are thicker and slicker than others, and rubbing the oil in with the proper sort of cloth is part of the protective process. In addition, you can get too much slick oil on the putter so that it adversely affects performance of the face in the ball-face contact. Oil on a polystyrene face insert doesn't make any sense and should be avoided, so to this extent putting oil inside the cover may not be the best approach.
By the way, salt makes the rusting process speed up -- that's why cars at the beach rust faster and need washing more often. So using a putter near the ocean and salt breezes is a special concern.
Finally, you can simply ask the manufacturer what they say you should do. The Scotty Cameron people include this info on their website now. But be aware that if you contact the manufacturer, you may have to get past the sales people to the technical engineer sorts to get good info.
I've created a webpage explaining all this in greater technical detail here:
http://puttingzone.com/Science/sciencematerials.html.
I hope this helps!
Cheers!
Geoff Mangum
The PuttingZone.com
http://puttingzone.com
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