When Aragorn touches the Morgul blade in the Fellowship movie, it dissolves.What is the reason for this?
We don't know
That's a disappointing answer, but it's the only one we have; if Tolkien ever wrote more about the Morgul-knife, those writings have never been discovered.
Some speculation, based on nothing more than a reading of the text:
- It only disappears after Aragorn touches it, so it might be that the blade dissolves when a non-Nazgûl touches it
- It appears to disappear once the light hits it, so that may also be a component of the spell
- A part of the blade has been broken off, so it may be that it disappears once it's been used
Based on the text, I personally favour the second of those possibilities (emphasis mine):
[Aragorn] stooped again and lifted up a long thin knife. There was a cold gleam in it. As Strider raised it they saw that near the end its edge was notched and the point was broken off. But even as he held it up in the growing light, they gazed in astonishment, for the blade seemed to melt, and vanished like a smoke in the air, leaving only the hilt in Strider's hand.
Fellowship of the Ring Book I Chapter 12: "Flight to the Ford"
There does appear to be a connection between the light and the vanishing of the blade, but of course this is nothing more than speculation.
The attack seemed to happen rather late at night, soon after the moon rose, while the morgul blade was not found until shortly before dawn with the grey light of morning.
I always thought it was a big coincidence that the blade evaporated just when Aragorn found it, hours after it stabbed Frodo. Either it took hours for the point to wriggle in deep enough and send a signal to the rest of the blade which said "mission accomplished, you can evaporate" or else it was a change of external conditions which made the blade vanish.
Perhaps it was Aragorn handling it, or maybe the sunlight he held it up into.
I note that the blade may have been covered by a sheath except when in use, and that the hilt did not vanish but remained in aragorn's hand. Thus I tenitively think that the blade, but not the hilt, was sensitive to light, and it was normally kept sheathed. And it may be possible that being used and the point breaking off, and/or being handled by Aragorn, triggered the sensitivity to light.
A good theory should explain the timing of Aragorn finding the blade and its evaporating so it is not a coincidence. We wouldn't want to claim that Tolkien wrote a coincidence into his story if there is any way to say the two events happened at the same time for a reason.
To me the answer is simple, in warfare the worst thing about your weapon is that someone else can use it and possibly use it against you. The Romans knew this which is why they designed their Pilum to bend on impact making it both a hinderance and useless to their enemies, the same can be said for the weapons of the nine who were powerful witches so their weapons were designed to 'dissolve' when an enemy held it in their hands making it useless to them. I don't believe that it was due to the blade being broken because it would have dissolved at the point of its breaking, neither do I think that it was due to its exposure to light because (scientific reasons aside) it had been in the light at weathertop prior to strider holding it, The Nazgul rode from Mordor to the Shire and it would have been exposed to the light at some point during that journey also Tolkien would have made a point about it dissolving in light within his text, something like "For as all wretched things did his blade wilt in the splendour of the sun." which he didn't, he did however note that it dissolved when it was held by Strider. Tolkien was a professor of philology and early Germanic literature this also meant that he would have been a student of history and would have known of this little Roman trick. But as in everything, his works are up for interpretation.