In partition mode, the stationary phase is assumed to have a
large active surface area and P=Cs/Cm. Cs is the concentration
of a solute in the stationary phase. Cm is the concentration of
a solute in the mobile phase. In competition mode, the
stationary phase has a limited number of active sites and
P=Cs/(Cm S). S is the concentration of unoccupied active sites
on the stationary phase. This is equivalent to a Langmuir
absorption isotherm. To get comparable retention between a
partitioning run and a competitive run, divide the partition
coefficient for the partitioning run by the concentration of
stationary sites. For example, if the partitioning partition
coefficient for A is 0.1 and the concentration of stationary
sites is 10 equiv/L, then divide the partition coefficient by 10
equiv/L to get the competitive partition coefficient, P(A)=0.01.
Colby College Chemistry, Thomas W. Shattuck