Retention 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.

Equation 7.1 shows that the retention volume of a solufe can be used to estimate its distribution constant, or the partition coefficient in the liquid system used in the CCC colunm ... 

TABLE 1—RETENTION TIME DISTRIBUTION. CONSTANT-LEVEL SKIM TANK... 

DISTRIBUTION CONSTANT. For elution GSC the distribution constant Kn can be obtained from the adjusted retention volume v. and the surface area of the adsorbent, A (rrr ). ... 

The quantity k is the retention factor of the solute, or its mass distribution constant. It allows the straightforward comparison of results obtained with different apparatus and is frequently used in chromatographic literature. The optimum value is k = 2 in isocratic elution. Here, on an average, the solute remains in the stationary phase twice as long as in the mobile phase. The probability of finding the solute in the mobile phase is 1 (1 + 2) = 0.33. 

The capacity factor takes into account the fact that the observed retention will be determined by the equilibrium distribution constant corrected for the relative volumes of the two phases. 

The most important peak parameters are the peak area, the elution time of the centre of the peak and the peak variance. The peak area is proportional to the mass of the eluted compound and is usually used as the basis of quantitation. The elution time of the centre of gravity of the chromatographic peak is the elution (retention) time, fR, or the elution (retention) volume, Vr. of the compound. It is controlled by the distribution constant of the compound between the stationary and the mobile pha.ses and can be used for identification of the individual sample components. Finally, the peak variance, o (in time units) or a (in volume units) is a measure of peak broadening and can be used for the evaluation of the efficiency of the chromatographic column. For a truly Gaussian peak, the distance between the two inflection points (at 0.607 peak height) corresponds to 2(7. The peak width, u>, equals 4a and can be determined as the distance between the intersection points of the baseline with tangents drawn to the inflection points of the peak. 

The velocity of a solute moving along the column is controlled by the ratio of the time spent by the solute in the stationary phase, r , to the time spent in the mobile phase, tni- This ratio, the retention factor k. is equal to the ratio of the masses of the solute in the stationary, M, and in the mobile. N. phases, and is one of the most important retention characteristics. The retention factor, k, is directly proportional to the distribution constant of the solute, Ko. ... 

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... 

The peak separation will depend on the nature of the two components to be separated. The more different are the distribution constants K and K, for the components, the more different are their retention times tR, as seen in rel. (6). The separation factor a is commonly used to characterize the separation, where... 

Figure 2 shows, for various retention factors, the available capacity variation versus the solution concentration in the mobile phase in reversed-phase chromatography. These curves, called distribution isotherms, can be divided into two parts. In the first part, a linear variation of versus Q is observed (bilogarithm scale) in the second part, a plateau is reached. In the first part and for the same retention (A constant), the available capacity is independent of the solute nature. 

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. 

To standardize reported retention times for a given column, manufacturers often report adjusted or relative retention factors rather than distribution constants. The adjusted retention time of a given compound is reported relative to the retention time of an unretained component. The relative distribution coefficient is reported relative to the distribution coefficient of a reference compound ... 

It follows from equation 17 that the distribution constant can be expressed by retention parameters using the relation... 

It follows from the discussion in this paragraph that only standard differential thermodynamic functions can be calculated from any chromatographic distribution constant defined in whatever way. Also, it is necessary to always specify the choice of the standard states for the solute in both phases of the system. Without specifying the standard states the data on the thermodynamic functions calculated from chromatographic retention data lack any sense. When choosing certain standard states it may happen that the standard differential Gibbs function is identical with another form of the differential Gibbs function, or includes such a form situations described by equations 46 and 49 may serve as examples. The same also holds true for standard differential volumes, entropies and enthalpies (compare Section 1.8.3). However, every particular situation requires a special treatment. 

If the distribution constant is independent of the sample amount then the retention factor is also equal to the ratio of the amounts of substance in the stationary and mobile phases. At equilibrium the instantaneous fraction of a substance contained in the mobile phase is 1 / (1 + k) and in the stationary phase k / (1 + k). The retention time and the retention factor are also related through Eq. (1.3)... 

SP is some free energy related solute property such as a distribution constant, retention factor, specific retention volume, relative adjusted retention time, or retention index value. Although when retention index values are used the system constants (lowercase letters in italics) will be different from models obtained with the other dependent variables. Retention index values, therefore, should not be used to determine system properties but can be used to estimate descriptor values. The remainder of the equations is made up of product terms called system constants (r, s, a, b, I, m) and solute descriptors (R2,7t2, Stt2, Sp2 log Vx). Each product term represents a contribution from a defined intermolecular interaction to the solute property. The contribution from cavity formation and dispersion interactions are strongly correlated with solute size and cannot be separated if a volume term, such as the characteristic volume [Vx in Eq. (1.6) or V in Eq. (1.6a)] is used as a descriptor. The transfer of a solute between two condensed phases will occur with little change in the contribution from dispersion interactions and the absence of a specific term in Eq. (1.6) to represent dispersion interactions is not a serious problem. For transfer of a solute from the gas phase to a condensed phase this... 

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