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C00002 00002	molecu[f82,jmc]		Detection of single molecules by methods of
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molecu[f82,jmc]		Detection of single molecules by methods of
			 freshman chemistry

	Single molecules can in principle be detected by repeated use
of a sequence of chemical reactions that doubles the amount of a
substance present.  In principle, it seems possible to do this
without excessive losses.

	Such a sequence might take the following form supposing that
we have some small number (perhaps none) of molecules of a substance AX in water
solution.  We wish to determine if there is any  AX,  and if so how much.

	1. We start with a binary reaction

	AX + BY → AY + BX.

In order to drive the reaction, there must be a substantial amount of  BY
added to the solution.

	2. Next we separate  AY  and  BX.  This can be done by any standard
chemical method that doesn't depend on the presence of substantial
amounts of  AY  or  BX  and tolerates the presence of large amounts of  BY.
Imagine that the method is solvent extraction.

	3. We now have two containers - one with some (perhaps none) molecules
of  AY  and the other with some molecules of  BX.
Now we use reactions that destroy all the leftover  BY  with high
probability while leaving  AY  or  BX  unchanged.  We suppose this
All we need are reactions in which the lifetime of a molecule of BY
is at least 100 times shorter than that of  AY  or  BX.  If
the destruction is a Poisson process, this can be done
even though the initial amount of  BY  is 10↑23 times as large
as the amounts of  AY  and  BX.

	4. Next we add to the container with the  AY  a large amount
of  CX  and to the container with  BX  a large amount of  AZ.  We then
create conditions that drive the reactions

	AY + CX → AX + CY

and

	BX + AZ → AX + BZ

respectively.  Now each container has as much  AX  as the original
container did.

	5. Now we must destroy the excess  CX  and  AZ  while
preserving the  AX  in the two containers.

	6. Finally we combine the two containers into the original
container and condense the volume of solvent if necessary to the original 
amount.  The container now contains twice as much  AX  as it had
originally.

	To go from a molecule of  AX  to a mole requires that steps
1 thru 5 be carried out 79 times, since 2↑79 = 6 x 10↑23.



Remarks:

	1. The key problem is to be sure that no  AX  is created
except by the desired system of reactions.  This may require that
the radicals  A  and  X  be relatively complex.

	2. A  and  X  should be chosen to make the doubling process
as effective as possible.  In order to detect small amounts of a
given substance, we require a preliminary sequence of reactions
that will create one molecule of  AX  for every molecule of the substance
to be detected.  There is no special reason why the substance being
detected should have a composition directly related to  AX.
The only requirement is that the conversion reaction not produce
any  AX  if the substance isn't present.