Application of general retention time formula for gradient liquid chromatography in the studies of ladder-like gradient elution

By not explicitly specifying the type of solvent strength model, the features of ladder-like gradient elution were studied based on the general retention time formula that was derived in our previous work. For the case where the solute is eluted at the slope of the ladder-like gradient, we derived the expression that connects the mobile phase composition (phi(R)), at which the solute is eluted from the column, with the gradient slope (B). It was shown that phi(R) will increase with the increase of B in this case. For the case where the solute is eluted at the last isocratic segment of the ladder-like gradient, it was proven that the retention time (t(R)) will correlate linearly with the reciprocal of the gradient slope (1/B) when the initial and final mobile phase compositions are set to be constant. In experiments, by taking biphenyl as the sample, the values of retention time in isocratic and gradient elution were measured on a C18 column by using a mixture of methanol and water as the mobile phase. The experimental values were found to be well consistent with the theoretical values that were calculated from the expressions. These expressions will be helpful to understand the features of the ladder-like gradient in practice.