Chromatographic theory retention volume

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

So far the Plate Theory has been used to determine the equation for the retention volume of a solute, calculate the capacity factor of a solute and identify the dead volume of the column and how it should be calculated. However, the equation for the elution curve of a solute that arises directly from the Plate Theory can do far more than that to explain the characteristics of a chromatogram. The equation will now be used in a variety of ways to expand our knowledge of the chromatographic process. 

There is a fundamental relationship described in chromatographic theory between the retention volume of a elution peak and the mid-point of a breakthrough curve achieved by operating the column under frontal analysis conditions (41 ). In the Henry s Law region of the adsorption isotherm, the net retention volume and its measurement can be used to describe the variation of sorbate breakthrough volume as illustrated in Figure 8. Utilizing the experimental apparatus described in the last section, retention volumes were measured as a function of pressure at 40°C (T =... 

Void volume is a critical parameter in HPLC, since most theoretical relationships in chromatographic theory deal with the retention factor, and the accuracy of the void volume determination plays an important role in all calculations. 

The chromatographic separations of isotopic hydrogens have indeed verified all of the above mentioned predictions of the theory. The measured retention times, tu or net retention volumes Vm give directly the separation factors... 

A general account of chromatographic theory was presented in volume 2 of Encyclopedia of Pharmaceutical Technology.Therefore, the following discussion will focus specifically on GC theory. The separation of the component of a mixture depends upon the column performance (efficacy) and the relative retention capability of the stationary phase (selectivity). The former determines the width of the peaks relative to the length of time a component spends in the column, while the latter determines the relative position of each emerging component (resolution). 

The Plate Theory shows that retention volume of a solute is directly proportional to its distribution coefficient between the two phases. Classical thermodynamics provides an expression that relates the equilibrium constant which, in the case of chromatographic retention, will be the distribution coefficient to the change in standard free energy of the solute, when transferring from one phase to the other. 

More recently the tendency has been to examine the retention in thermodynamic terms. Under normal chromatograph conditions, solute molecules distribute themselves between the mobile and stationary phases and are in thermodynamic equilibrium. This has been demonstrated experimentally in a number of ways. It has been shown that retention volume is independent of flow rate [19]. A further confirmation was provided by static mixing experiments. These involved measuring the equilibrium polymer concentration in a mixture of a polymer solution and a porous packing material. The results supported the equilibrium theory [20]. 

According to chromatographic theory, the solute net (adjusted) retention volume Vr is related to the solute distribution constant (partition coefficient) K by the equation... 

Another assumption not usually stated is that the solutes do not interact with one another. That is, molecules of solute A pass through the column as though no other solutes were present. This assumption is reasonable because of the low concentrations present in the column and because the solutes are increasingly separated from each other as they pass through the column. If interactions do occur, the chromatographic results will deviate from those predicted by the theory peak shapes and retention volumes may be affected. 

For given values of the retention volumes above, the shape of chromatographic peaks depends on the value of the kinetic parameter k jF. If the only slow process is equilibration of injected substance vapour in the polymer bulk, the simplest theories of chromatographic rate processes [113] give for 7c, ... 

The basic assumption in any chromatographic theory is that retention is determined by the thermodynamic factors. In such a way, mobile and stationary phases are interpreted as true thermodynamic phases with volumes Vm and Vs, respectively, so that retention volume depends on the partition (distribution) equilibrium coefficient A" of the solute in these two phases Vr = Vm +KVs-By definition, all enthalpic and entropic interactions between the macromolecules and the chromatographic surface occur in the stationary phase. If the size of macromolecules in solution is comparable with the internal diameter of pores, the entire pore volume represents the stationary phase. Vs = Vp, yet the mobile phase is formed by the interstitial volume only, Vm = Vq. This is not always the case for... 

Frequently, the stationary phases used in gas chromatographic separations are much more uniform than the general theory given in Section 12.1 implies. Additionally, the amount of material injected is extremely small, corresponding to very low surface coverage. The resultant chromatogram shows little band broadening from adsorption-desorption effects and the retention of the injected material corresponds to the case of an infinitely dilute adsorbate in the stationary phase. The distribution constant may be related to the retention volume, the mobile-phase volume, and the stationary-phase volume. The total number of moles injected onto the column n is divided between the stationary and mobile phases... 

Assumption of the presence of single partitioning mechanism of analyte chromatographic retention has been the basis for the development of various methods for the evaluation of specific analyte interaction energies from retention data [44-46]. All these methods are only applicable in ideal chromatographic systems with proven absence of secondary equilibria effects, and all require specific assumptions regarding the volume of the stationary phase. Equation (2-43) is the main basis for these theories. 

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