Derivation retention volume

Once the elution-curve equation is derived, and the nature of f(v) identified, then by differentiating f(v) and equating to zero, the position of the peak maximum can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention. 

Returning to equation (13), it is now possible to derive an equation for the adjusted retention volume, (V r),... 

If the mobile phase is a liquid, and can be considered incompressible, then the volume of the mobile phase eluted from the column, between the injection and the peak maximum, can be easily obtained from the product of the flow rate and the retention time. For more precise measurements, the volume of eluent can be directly measured volumetrically by means of a burette or other suitable volume measuring vessel that is placed at the end of the column. If the mobile phase is compressible, however, the volume of mobile phase that passes through the column, measured at the exit, will no longer represent the true retention volume, as the volume flow will increase continuously along the column as the pressure falls. This problem was solved by James and Martin [3], who derived a correction factor that allowed the actual retention volume to be calculated from the retention volume measured at the column outlet at atmospheric pressure, and a function of the inlet/outlet pressure ratio. This correction factor can be derived as follows. 

The range of concentrations that could be used was somewhat restricted due to the immiscibility of certain solvent mixtures. The data given in Table 1 was fitted to equation (16) and the various constants determined. Employing the constants derived from the curve fitting process, the theoretical values for the retention volumes, at the... 

The equation for the retention volume of a solute, that was derived by differentiating the elution curve equation, can be used to obtain an equation for the retention time of a solute (tr) by dividing by the flowrate (Q), thus,... 

It can now be seen how an expression for the retention volume of a solute can be derived. By differentiating equation (10) and equating to zero, an expression for the volume of mobile phase passed through the column between the injection point and the peak maximum can be obtained. This volume has already been defined as the retention volume (Vr) of the solute. 

An example of a separation primarily based on polar interactions using silica gel as the stationary phase is shown in figure 10. The macro-cyclic tricothecane derivatives are secondary metabolites of the soil fungi Myrothecium Verrucaia. They exhibit antibiotic, antifungal and cytostatic activity and, consequently, their analysis is of interest to the pharmaceutical industry. The column used was 25 cm long, 4.6 mm in diameter and packed with silica gel particles 5 p in diameter which should give approximately 25,000 theoretical plates if operated at the optimum velocity. The flow rate was 1.5 ml/min, and as the retention time of the last peak was about 40 minutes, the retention volume of the last peak would be about 60 ml. 

The GPCV2 equations were developed for conventional log(MW) vs. retention volume calibrations. When used in conjunction with a universal calibration, the slope term (Do) must be corrected for the different molecular size/weignt relationships of the calibrants and the samples as derived in the following equations. To understand this correction, consider the conventional calibration curve that could be created from the universal calibration data. 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

Logarithms of retention indices of alkyl benzenes specific retention volumes of esters, aldehydes and alcohols and retention times of alkanes and alkanes have been correlated with Equations 13 snd 15 or relationships derived from them (l3.). Logarithms of retention times of allyl alkyl ethers on various column packings have also been successfully correlated with Equation 15 (lA). 

To identify isomeric thienothiophenes, the chromatographic behavior of mono- and dialkyl-substituted thienothiophenes 1 and 2 was studied.Thienothiophene 1 and its alkylated derivatives were shown to be characterized by greater retention volumes than the corresponding thienothiophenes 2. The linearity of the retention volume vs. boiling point relationship allowed the thienothiophene isomers to be identified. Studies on solution thermodynamics of thienothiophenes in the stationary phase showed that isomeric thienothiophenes 1 and 2 do not differ appreciably in their heats of solution. For example, the calculated heats of solution of 5-ethyl-3-methylthieno[2,3-h]thiophene (26) and 5-ethyl-3-methylthieno[3,2-b]thiophene (27) in polyethyleneglycol adipate are both about 16 kcWmole. ... 

Fraction I, which consists mainly of low molar mass compounds, also contains a small amount of high molar mass lignin derivatives eluting with relative retention volumes of 0-0.1. These derivatives are polar and some may be bound to carbohydrates, or otherwise they would have been eluted by RPC along with the hydrophobic fractions II-IV. 

Habgood and Harris (5) derived the following equation showing the relationship between isothermal retention volumes and retention volumes obtained under linear temperature-programming ... 

An equation can be derived relating Z A (dtFE) to Z gF ( i>thf ) As was pointed out in step C, the retention volume calibration curve relating i>thf to i>tfe was constructed by relating t>rFE to i>thf at points of equal weight percent polymer on the integral distribution of retention volume curves in tetrahydrofuran and in TFE. At these points the molecular weight of the polymer species in tetrahydrofuran is the same as the molecular weight of the polymer species in TFE. 

The separation obtained with the picolinyl derivatives (of the fatty acids of cod liver oil) is shown in Fig. 7. As with reverse-phase separations with other fatty acid derivatives, the retention volumes for each component increased with chain length and decreased with the number of double bonds. 

Figure 4. Plot of the average supercritical CC>2 extraction recoveries vs. GLC derived retention indexes for anthracene, pyrene, perylene, benzo[ghi]perylene, and coronene using a extraction cell of two different cell geometries (1 1 and 1 8) completely filled and the 1 8 dimensions cell with ca. 70% dead volume.

Unfortunately, in many instances the materials employed as sensor coatings are nonvolatile solids (polymers) for which 6 values cannot be calculated directly. Solubility parameters for these materials can be estimated, however, by immersion testing [172b], inverse gas chromatography [173,174] or ftom coated-SAW sensor responses [166]. In inverse chromatography, the polymeric coating material is used as a stationary phase on a GC column, and the specific retention volumes (V ) for several solutes are determined. Since the Vg is directly related to, Kc, the solubility parameter for the polymer coating can be derived from relationships similar to Equation 5.32. A similar approach is used to derive S, from SAW sensor response data [166]. 

The retention volume is essentially proportional to the derivative of the analyte distribution function definedi per unit of the column length. 

Peak tailing is the most commonly observed effect of sample overloading. In essence, in most cases this effect is associated with nonlinear adsorption isotherms. In Chapter 2 the relationship of the retention volume and the derivative of the excess adsorption isotherm of the analyte on given stationary phase surface was derived. If the isotherm is linear within the injected concentration region, all components of the chromatographic zone are moving... 

As is apparent from its defmition, the newly defined parameter is larger than the former x parameter. Combining data on the pure components and an experimental retention volume, the interaction parameters x and X 2 can be derived. 

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