2 Theory of Solid-Phase Extraction and Related Techniques
Like most of separation methods, SPE is based on the distribution of a solute between two phases. Both batch and column variants of SPE can be used for preconcentration purposes. The column mode can be considered as a version of reversed phase liquid–solid chromatography (RP LSC).13 In fact, alkyl-bonded stationary phases with the alkyl length nc = 8, 16, or 18 and different grain sizes are most often used. Chromatographic retention is conveniently described by the capacity factor, k, which is defined as ki= qi,s/qi,m, where qi,s and qi,m denote the total quantity of a solute (i) to be present in the stationary phase (s) and the mobile phase (m), respectively.14,15 The higher is the k value, the better is the solute retained, and the later is eluted from the column. Correspondingly, the separation selectivity can be defined as the relative retention of two solutes, βi,j, which is sometimes called the separation factor, expressed in terms of the capacity factors, βi,j = kj/ki. If the preconcentration of a group of dissolved ions or molecules is required, the k values for all of the solutes should be as close as possible.
Two approaches can be applied to the treatment of SPE experimental data. The first one may be based on the Snyder “competition” model, which describes the distribution of a solute between liquid and solid phases.14,15 In this model it is assumed that the solid surface is covered with mobile-phase molecules, and that solute molecules have to compete with the solvent molecules in this adsorption layer to occupy an adsorption site. It is the difference between the affinity of the mobile phase and that of solute for the stationary phase that determines the retention in LSC and, therefore, in SPE according to the competition model. Snyder14 formulated the following equation that interrelates the distribution coefficient KD= ci,s/ci,m (c denotes concentration in one phase) with the adsorption area of the solute molecule Ai and the adsorption energy of the solute on a standard adsorbent Si0:
log KD = log Va+ α(Si0 – AiE0), (1)
where Va is the volume of the adsorbed solvent per gram of the stationary phase and α is the adsorbent activity.
In the frames of the second model, which is more practical for our further speculations, the distribution of a solute in SPE can be considered as a partition between two liquid phases. By definition, the capacity factor is a dimensionless quantity, which is in this case described by
k = KDVs/Vm, (2)
where Vs and Vm are the volumes of the stationary and liquid phases, respectively. It is assumed in this model that the analyte-containing phase is a homogeneous solution. Because relative values are used in the calculations, in both cases the experimental values of the capacity factors allow us to discuss the dependence of the chromatographic efficiency on both the properties of the stationary phase and the solutes to be separated and the experimental conditions.
Methods of correlation analysis are used for this purpose, which may be used if the principle of the linearity of free energies (PLFE) is valid, i.e., if the free energy of a chemical or a physicochemical process can be expressed as additive partial energies related to separate fragments of the molecules or process stages.16,17 The correlation analysis is widely applied in chromatography as well as in liquid–liquid extraction, and up to now a great number of data are available that make it possible to discuss and moreover to predict the chromatographic behavior of compounds, depending on their properties and on the chromatographic system used.18 Reversed-phase high-performance liquid chromatography (RP HPLC) has been mainly used for organic separations, and the great majority of data has been obtained for organic substances. We will mention here only some results, which may have interest concerning this work.
The retention (k) first increases exponentially with the hydrocarbon chain length; that is, log k enhances with increasing nc. However, if the chain lengthens further, the retention rise becomes less pronounced and, to a first approximation, one may suppose that the capacity factor tends to be independent of the chain length at nc between 14 and 22. A bend in the log k – nc dependence or the boundary value of nc is dependent on the test sample. It has been shown experimentally that this value increases with the molecular mass of sample molecules. Such a dependence violates simple considerations of the interaction between the sample molecules and an alkyl-bonded surface. One could expect a linear increase of k with nc if such a surface would behave like a liquid. Also on the contrary, the k value should not depend on nc in case of a solid adsorption surface.18