By differentiating equation (10) and equating to zero, an expression for the volume of mobile phase that passes through the column between the injection point and the peak maximum (V_r) can be obtained which will disclose the parameters that control retention and selectivity.

Thus,

or

Equating to zero, when = 0, n - v = 0 or v = n

This means that at the peak maximum, (n) plate volumes of mobile phase will have passed through the column.

Remembering that the volume flow is measured in 'plate volumes' and not milliliters, the volume in milliliters passed through the column will be obtained by multiplying by the number of 'plate volume's by (v_m + Kv_s).

Thus, the retention volume (V_r) in ml is given by

V_r = n(v_m + Kv_s) = nv_m + nKvs

Now, (nv_m) will be the total volume of mobile phase in the column (V_m) and, similarly, (nv_s) will be the total volume of stationary phase in the column (V_S).

Thus, V_{r =} V_m + KV_S (11)

and as the corrected retention volume is V'_r = V_r Vm

or V'_{r =} KV_S

It is seen that the corrected retention volume is controlled by two parameters: firstly the distribution coefficient of the solute between the two phases and secondly, the amount of stationary phase that is available to the solute.

Consequently, in order to modify or change (V'_r) it is necessary to change either (K), or (V_S), or both_.

_{It is now also obvious from equation (11) how the separation of two solutes (A) and (B) must be achieved.}

_{To separate solutes (A) and (B),}

V'_r(A)<>V'_{r(B), which can be achieved by making either} K_{(A)< >}K_(B)

_{or by adjusting the volume of stationary phase in the column ensure that,}

V_{S(A) < >} V_S(B) or an appropriate combination of both.

It follows that to separate a mixture, either the values of (K) for all components, or the amount of stationary phase (V_S), available to each component, must be made to differ or, again, appropriate adjustments must be made to both.

There are two basic approaches used to determine how to change the magnitude of (K) and (V_s) viz., by the Interaction Theory or by Thermodynamics. These two theories give quite different incites into the control of the magnitude of the magnitude of (K). The Thermodynamics of distribution will be considered first.