Analyte distribution constant

Figure 4.17 General phenonenaloglcal retention model for a solute that participates in a secondary chemical equilibrium in liquid chromatography. A - solute, X - equilibrant, AX analyte-equilibrant coeplex, Kjq - secondary chemical equilibrium constant, and and are the primary distribution constants for A and AX, respectively, between the mobile and stationary phases.

Thus the selectivity a has a thermodynamic interpretation as the ratio of two distribution constants. Consequently a is itself a constant, independently from the injected concentrations of the analyte and the interferent, respectively. 

The sample volume also has an effect on both the rate and recovery in SPME extractions, as determined by extraction kinetics and by analyte partition coefficients. The sensitivity of a SPME method is proportional to n, the number of moles of analyte recovered from the sample. As the sample volume (Vs) increases, analyte recovery increases until Vs becomes much larger than the product of K, the distribution constant of the analyte, and Vf, the volume of the fiber coating (i.e., analyte recovery stops increasing when KfeVf Vs) [41]. For this reason, in very dilute samples, larger sample volume results in slower kinetics and higher analyte recovery. 

As a very rough first approximation the chromatographic retention process could be described on the basis of simple single equilibria of the analyte distribution between the mobile and stationary phases. The equilibrium constant of this process is proportional to the analyte retention factor... 

Vr(csi) is the analyte retention as a function of the eluent concentration, Vo is the total volume of the liquid phase in the column, y Cei) is the volume of adsorbed layer as a function of eluent composition, Kp(cei) is the distribution coefficient of the analyte between the eluent and adsorbed phase, S is the adsorbent surface area, and is the analyte Henry constant for its adsorption from pure organic eluent component (adsorbed layer) on the surface of the bonded phase. 

Because different forms of analyte usually show different affinity to the stationary phase, secondary equilibria in HPLC column (ionization, solvation, etc.) can have a significant effect on the analyte retention and the peak symmetry. HPLC is a dynamic process, and the kinetics of the secondary equilibria may have an impact on apparent peak efficiency if its kinetics is comparable with the speed of the chromatographic analyte distribution process (kinetics of primary equilibria). The effect of pH of the mobile phase can drive the analyte equilibrium to either extreme (neutral or ionized) for a specific analyte. Concentration and the type of organic modifier affect the overall mobile phase pH and also influence the ionization constants of all ionogenic species dissolved in the mobile phase. 

Ca the analytical concentration in the water phase. The value of the distribution ratio varies with experimental conditions such as pH, whereas the value of the distribution constant at zero ionic strength is invariant for a system at a particular temperature. 

The retention of an analyte in the stationary phase can be characterized with several parameters, one of them being the partition coefficient (or distribution constant) K (or Kio). This is defined for a component i by the relation ... 

The retention time tR can be correlated to the distribution constant for a given analyte. For this purpose, each concentration in rel. (1) will be expressed as a ratio between the fraction of molecules in the corresponding phase and the volume of that phase. If R is the fraction of molecules (for the analyte i ) in the gas phase and 1 - R the fraction of molecules in the stationary phase, then... 

Distribution constants are useful because they permit us to calculate the concentration of an analyte remaining in a solution after a certain number of extractions. They also provide guidance as to the most efficient way to perform an extractive separation. Thus, we can show (see Feature 30-1) that for the simple system described by Equation 30-2, the concentration of A remaining in an aqueous solution after i extractions with an organic solvent ([A],) is given by the equation... 

The retention time for an analyte on a column depends on its distribution constant, which in turn is related to the chemical nature of the liquid stationary phase. To separate various sample components, their distribution constants must be sufficiently different to accomplish a clean separation. At the same time, these constants must not be extremely large or extremely small because the former leads to prohibitively long retention times and the latter results in such short retention times that separations are incomplete. 

The phenomena just described are quite similar to what occurs in a liquid partition chromatographic column except that the stationary phase is moving along the length of the column at a much slower rate than the mobile phase. The mechanism of separations is identical in the two cases and depends on differences in distribution constants for analytes between the mobile aqueous phase the hydrocarbon pseudostationary phase. The process is thus true chromatography hence, the name micellar electrokinetic capillary chromatography. Figure 33-15 illustrates two typical separations by MECC. 

Distribution constant The equilibrium constant for the distribution of an analyte in two immiscible solvents approximately equal to the ratio of the equilibrium molar concentrations in the two solvents. 

This equation is simply a rearrangement of the distribution constant equation that relates the mass sorbed to the stationary phase divided by the mass in the solution phase. The authors note that the amount of analyte sorbed by the coating is proportional to the initial analyte concentration in both Eqs. (12.1) and (12.2). However, the additional term of A"V, is now present in the denominator of Eq. (12.2). This term decreases the amount of solute sorbed (nJ when this term is comparable in size to When it is much smaller than then only the volume of sample is important. As KV becomes much greater than V2, then the terms KV in numerator and denominator cancel, and one is left with the conclusion that the majority of the original analyte, C20, is sorbed. Thus, the extraction is quantitative at this point. In practice, the authors have found that for 90% of the sample to be sorbed into the coating, the distribution coefficient must be about an order of magnitude greater than the phase ratio, V2/V,. For this to occur, the K must be approximately 1000, which is equivalent to compounds with an octanol-water partition coefficient ( ow) of approximately the same value, or log of 3. 

The HS-SPME are usually carried out under nonequilibrium conditions. The distribution constants of analytes between the fiber and the sample, between the HS and the sample, and the volume of the three phases (sample, headspace, and coating) must be constant, like the other SPME extraction parameters (sample agitation, fiber exposure time, etc.). The total analyte area (AT) corresponding to a cumulative extraction yield after multiple extractions can be determined as the sum of the areas obtained for each individual extraction when each is exhaustive, or expressed as ... 

Equations 46 have been directly derived from the full model in [19]. On the other hand, they are almost identical with the relations obtained from the so-called two-compartment model (the only difference is that the numerical coefficient is a little bit lower). The two-compartment model was first developed for sensors with receptors placed on small spheres [23]. In [24-26] it was adapted for the SPR flow cell and in [ 18] it was approved and verified by comparison of munerical results with those obtained from the full model. The two-compartment model approximates the analyte distribution in the vicinity of the receptors by considering two distinct regions. The first is a thin layer around the active receptor zone of effective thickness fiiayer> and the second is the remaining volume with the analyte concentration equal to the injected one, i.e., a. While the analyte concentration in the bulk is constant (within a given compartment), analyte transport to the inner compartment is controlled by diffusion. The actual analyte concentration at the sensor surface is then given by the difference between the diffusion flow and the consump-tion/production of the analyte via interaction with receptors. For the simple pseudo first-order interaction model we obtain ... 

Increase in temperature during the extraction process enhances the diffusion during the extraction process towards the fiber, decreasing the time to reach equilibrium. However, the distribution constants of the analytes decrease with increasing temperature because it also favors evaporation of BTEX towards the headspace, reducing the concentration in the liquid phase. Therefore, as seen in Table 14.3, room temperature is often the most suitable temperature for BTEX analysis. 

Anti-Langmuir type isotherms are more common in partition systems where solute-stationary phase interactions are relatively weak compared with solute-solute interactions or where column overload occurs as a result of large sample sizes. In this case, analyte molecules already sorbed to the stationary phase facilitate sorption of additional analyte. Thus, at increasing analyte concentration the distribution constant for the sorption of the analyte by the stationary phase increases due to increased sorption of analyte molecules by those analyte molecules already sorbed by the stationary phase. The resulting peak has a diffuse front and a sharp tail, and is described as a fronting peak. 

---