Page 138 - MODERN ELECTROCHEMISTRY

78 CHAPTER 2

is short-rangeorder; themolten salts aresomewhatlikeadisordered solution contain-
ing much open space, which some call holes. However, X-ray analysis does not work
well for ionic solutions because the ordered elements (solvated ions) turn up only
occasionally and are interrupted by relatively large distances of disordered solvent
molecules.
Although, as will be seen in this section, the developments of neutron diffraction
during the 1980s (Enderby and Neilson) have led to substantial advances in determin-
ing the coordination numbers of water molecules around ions, there are still some
hurdles to clear before one can use this powerful method:
1. It is necessary to have a neutron source and that, in turn, means that only
laboratories that have access to a nuclear reactor can do such work. 18
2. It is desirable to work with rather than because of the sharper
diffraction patterns obtained are the former. This can become a cost burden.
3. (1) and (2) can be overcome but the last hurdle is too high and must be accepted:
the method is limited (as with most of the spectroscopic methods) to solutions
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of 1 mol or more, whereas most of the data in the literature concern
dilute solutions (e.g., mol ) where the univalent salts are about 12
nanometers apart (one can, then, picture an isolated ion in its solvation shell).
Having given the obstacles to attainment, let it be said that there are two ways in which
neutron diffraction can be used to obtain information on the structure around an ion. In the
first (Soper et al., 1977), the objective is the distribution function in the equation:

where
This equation refers to a reference ion and gives the average number of
particles thatexistin aspherical shell ofradius r and thickness dr(of course, on atime
average). The symbol is the so-called distribution function. For multicompo-
nent systems, one can generalize to include all the possible combinations of
atoms [e.g., NaCl would have a total of 10 values].

I8
In U.S. universities, this means that the professor concerned must write a proposal to ask for time on a
reactor at, for example, Brookhaven or Oak Ridge or Argonne. Such proposals wait in line until they are
evaluated and then, if accepted, the professor’s team must move to the reactor for some days of intense
activity—probably shift work to make 24-hr per day use of the time allotted.
19
It is easy to show that the average distance between ions in a solution of 1:1 salt is where
c is the concentration in mol For a 1 M solution, this comes to 1.2 nm. However, for an ion of 0.1-
nm radius and layer of two waters, the radius is about 0.1 + 4 × 0.16 nm and therefore the internuclear
distance between two ions in contact is about 1.4 nm. For the mol case, the distance apart is
12.2 nm; i.e., the ions are isolated. Thus, it is very desirable to try to get spectroscopic measurements at
these dilute solutions. Only then can the results of spectroscopic work be compared directly with
deductions made about solvation (a concentration-dependent property) from measurements of solution
properties.