Plate Theory and Extensions - The Plate Theory > Page 2

The chromatogram that depicts the elution of a solute is a graph relating the concentration of the solute in the mobile phase leaving the column to elapsed time. However, at a constant flow rate, the chromatogram will also relate the solute concentration to the volume of mobile phase passed through the column. In figure 1, is shown the elution of a single peak. The expression, f(v), is the elution curve equation and this will be derived using the plate theory.

Figure 1. The Elution Curve of a Single Peak

 

Once the nature of f(v) identified, then by differentiating f(v) and equating to zero, the position of the peak maximum can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention.

The Plate Theory

The plate theory needs to assume that the solute, during its passage through the column, is always in equilibrium with the mobile and stationary phases. However, equilibrium between the phases never actually occurs. To take this non-equilibrium condition into account, the column is considered to be divided into a number of cells or plates. Each plate is allotted a specific length and, thus, the solute will spend a finite time in each plate. The size of the cell is chosen to provide sufficient residence time for the solute to establish equilibrium with the two phases. Thus, the smaller the plate, the faster will equilibrium and the more plates there will be in the column. Consequently, the number of theoretical plates contained in a column will be directly related to the equilibrium rate and, for this reason, has been termed the column efficiency.