Molecular Basis of Zone Spreading

One cannot expect a molecule that follows a random migration path, full of frivolous excursion, to arrive after a fixed time at exactly the same point as its equally frivolous companions. There will be a mean distance of migration X, but the individual molecules will exhibit fluctuations about this mean due to the peculiarities of their own migration. These statistical fluctuations will lead to zone broadening. The statistical (stochastic) theory of zone broadening was first developed by Giddings and Eyring [4] and has been expanded subsequently by a number of authors [5-8]. 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

Here we review the basic rules governing random walks and their relationship to plate height. First, the concentration (probability) profile generated by a random walk is a Gaussian with a variance r2 given by (see Eq. 5.24) 

Finally, the plate height //, given by cj2 L (see Eq. 5.47), equals the following for a single random walk 

The erratic motion of a chromatographically migrating molecule resembles a random-walk process. In order to apply random-walk ideas to chromatography, we must identify the effective step lengths and step numbers associated with the molecular migration. This is the main task to follow. 

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