Fig. 1. Two-component simulated example of the type of elution profiles that can be used with (a) the inverse method on plateaus (IMP) and (b) the inverse method (IM). The thin lines are the individual components; the thick line the sum of both components. The sample concentration is the same in all simulations, whereas the sample volume is 11.8 larger in (b). Note how the retention times, shapes, relative compositions, and degree of peak vanishing of the large perturbation peaks are affected at the different plateaus in (a).

Fig. 2. Experimental and simulated binary elution profiles. The thick solid line represents the experimental profiles; the other lines are simulated profiles using the adsorption isotherm parameters presented in Table 2, the thin solid line using the IM parameters and the dotted line using the IMP parameters. In (a) the initial concentration of the components in the eluent was 0 and a binary mixture of 15 mM propranolol and alprenolol was injected. In (b) the initial concentration of both components in the eluent was 0.75 mM and a binary mixture of 15 mM propranolol and alprenolol was injected. Finally in (c) the initial concentration of both components in the eluent was 5 mM and a binary mixture containing no components was injected. For other experimental conditions, see Section 3.

Fig. 3. Bi-Langmuir adsorption isotherm curves, in (a) for propranolol and in (b) for alprenolol. The thick solid line is the single component FA adsorption isotherm and the other are calculated using the parameters in Table 2: thin solid line is the IM adsorption isotherm, the dotted line the IMP adsorption isotherm. The differences between the FA adsorption isotherm and the other adsorption isotherms are presented in the insets.

Fig. 4. Experimental and simulated binary fronts. The thick solid line is the experimental result and the other lines are simulated fronts determined using the adsorption isotherm parameters presented in Table 2: the thin solid line using the IM parameters, the dotted line the IMP parameters. The initial concentration of propranolol and alprenolol is 1.5 mM which is increased to 3 mM in the front step. The average difference in retention time between the experimental and simulated primary fronts is presented in Table 4. For other experimental conditions, see Section 3.

Fig. 5. Experimental and simulated binary elution profiles showing (a) the sum profile, (b) the individual profile for propranolol and (c) the individual profile for alprenolol. A sample of 5 mM propranolol and 15 mM alprenolol was injected on a zero-plateau. The symbols represent experimental data; the thin lines represent simulated profiles using the IMP adsorption isotherm parameters presented in Table 2. For other experimental conditions, see Section 3.

Plateau and injection concentrations for the elution profiles used for adsorption parameter estimation with IM and IMP

Adsorption isotherm parameters obtained using IM, IMP and FA

The b parameters are given in M⁻¹.

Calculated L2-error for the adsorption isotherms over different concentration ranges

Difference between experimental and simulated primary front retention times in binary FA

Average frontal retention times in the low (3.75–37.5 μM), mid (75–750 μM) and high (1.5–15 mM) concentration ranges were studied. Simulations were based on the adsorption isotherm parameter sets presented in Table 2.