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6.4 Adsorption Isotherms and Site Distribution  163

             to be heterogeneous and composed of two or three different site classes, and finally
             the Freundlich isotherm model (Equation (3)) with no saturation capacity but instead
             a complete distribution of sites of different binding energies. Depending on the tem-
             plate-functional monomer system, the type of polymer, the conditions for its prepa-
             ration and the concentration interval covered in the experiment the adsorption
             isotherms of MIPs have been well fitted with all the isotherm models [39, 43-45].
               Thus, most MIPs suffer from a heterogeneous distribution of binding sites. In
             noncovalent imprinting, two effects contribute primarily to the binding site hetero-
             geneity. Due to the amorphous nature of the polymer, the binding sites are not iden-
             tical, but are somewhat similar to a polyclonal preparation of antibodies. The sites
             may for instance reside in domains with different crosslinking density and accessi-
             bility [46]. Secondly, this effect is reinforced by the incompleteness of the
             monomer–template association [15]. In most cases the major part of the functional
             monomer exists in a free or dimerized form, not associated with the template. As a
             consequence, only a part of the template added to the monomer mixture gives rise to
             selective binding sites. This contrasts with the situation in covalent imprinting [33,
             45, 47] or stoichiometric noncovalent imprinting [48, 60, 90] where theoretically all
             of the template split from the polymer should be associated with a templated bind-
             ing site. The poor yield of binding sites results in a strong dependence of selectivity
             and binding on sample load at least within the low sample load regime.
               For determining the adsorption isotherm, the equilibrium concentrations of bound
             and free template must be reliably measured within a large concentration interval.
             Since the binding sites are part of a solid, this experiment is relatively simple and
             can be carried out in a batch equilibrium rebinding experiment or by frontal analy-
             sis.
               One powerful technique for the study of the interactions between solutes and sta-
             tionary phases and for the investigation of the parameters of these interactions is
             frontal analysis [49]. This method allows accurate determination of adsorption and
             kinetic data from simple breakthrough experiments, and the technique has proven its
             validity in a number of previous studies. This has also been used for estimating the
             adsorption energies and saturation capacities in the binding of templates to MIPs, but
             often the data have been modeled only at one temperature and graphically evaluated
             using a simple Langmuir mono site model which in most cases gives a poor fit of the
             data [50]. Furthermore, the breakthrough curves are interpreted assuming thermody-
             namic equilibrium, which is often an invalid assumption in view of the slow mass
             transfer in these systems. Rather, based on the mass balance equation and by assum-
             ing kinetic and isotherm values to best-fit isotherms and elution profiles obtained at
             different temperatures, a more accurate picture of the thermodynamics and mass
             transfer data can be obtained [49].
               The isotherms for the two enantiomers of phenylalanine anilide were measured at
             40, 50, 60 and 70 C, and the data fitted to each of the models given in Equations
             (1–3) [42]. The isotherms obtained by fitting the data to the Langmuir equation were
             of a quality inferior to the other two. Fittings of the data to the Freundlich and to the
             bi-Langmuir equations were both good. A comparison of the residuals revealed that
             the different isotherms of D-PA were best fitted to a bi-Langmuir model, while the
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