Chromatographic resolution equation

In most cases, the separation of enantiomers on CSPs is controlled by the difference of adsorption enthalpies and a increases with decreasing temperature. The effects and thus the separation factors are small (which means unfortunately that nonchiral retention is dominating). An a of 1.05 corresponds to a free energy difference of adsorption of 120 J mol and a minimum of 8000 theoretical plates is necessary to obtain good resolution (gas constant, R = 1 with ki = 10 the calculation is performed by means of the chromatographic resolution equation). 

The fundamental resolution equation incorporates the terms involving the thermodynamics and kinetics of the chromatographic system ... 

Now that we have defined capacity factor, selectivity, and column efficiency we consider their relationship to chromatographic resolution. Since we are only interested in the resolution between solutes eluting with similar retention times, it is safe to assume that the peak widths for the two solutes are approximately the same. Equation 12.1, therefore, is written as... 

One of the most important properties of a chromatographic column is the separation efficiency. A measure of this parameter could be the difference of the retention volume for two different compounds. The result of a GPC analysis is usually, however, only one large peak, and a separation into consecutive molar mass species is not possible. Additionally there is no standard for higher molar masses consisting only of a species that is truly monodisperse. Therefore, the application of the equation to the chromatographic resolution of low... 

The variables that control the extent of a chromatographic separation are conveniently divided into kinetic and thermodynamic factors. The thermodynamic variables control relative retention and are embodied in the selectivity factor in the resolution equation. For any optimization strategy the selectivity factor should be maximized (see section 1.6). Since this depends on an understandino of the appropriate retention mechanism further discussion. .Jll be deferred to the appropriate sections of Chapters 2 and 4. 

Another method is to optimize those chromatographic parameters which affect resolution Although this paper is directed at a pragmatic approach to accomplishing this task, a brief detour into the mathematics is needed before we proceed The fundamental equation describing chromatographic resolution, Rg is... 

Equations (105) and (106) provide an important linkage between the three essential parameters that dictate the overall quality of the chromatographic resolution, namely, the relative retention, expressed in terms of the capacity factor k the relative selectivity a, and the extent of peak dispersion Nt or he i. Higher system performances and thus larger values of Rs, per unit time... 

From this master resolution equation, it can be observed that suitable chromatographic procedures can be developed by adjustment of k, a, and N to obtain a resolution of 2.0. 

The chromatographic control of resolution is a function of several factors. The fundamental resolution equation is... 

Since typical biological mixtures are exceedingly complex, adequate chromatographic resolution is imperative for both identification and quantitation purposes. Improved resolution is feasible through either increasing the column efficiency (number of theoretical plates), or phase selectivity. Alternatively, a combination of both can be practiced. The number of theoretical plates, required for adequate resolution of two adjacent peaks (98% separation of the peak areas) is related to the column selectivity (relative retention, a) and to the capacity ratio, k, according to the well-known equation derived by Purnell [70] ... 

In contrast to analytical chromatography, where it is possible to deconvolute overlapping peaks and to obtain even quantitative information from nonresolved peaks, preparative chromatography typically requires complete peak resolution if the components of interest are to be isolated with 100% purity and yield. Chromatographic resolution is a measure of how well two adjacent peak profiles of similar area are separated. is mostly defined as (Equation 2.43)... 

Equation (4.16) has been called the fundamental equation for chromatography. Each and every analyte of interest that is introduced into a chromatographic column will have its own capacity factor, k. The column itself will have a volume Fq. The retention volume for a given analyte is then viewed in terms of the number of column volumes passed through the column before the analyte is said to elute. A chromatogram then consists of a plot of detector response versus tg, where each analyte has a unique retention time if sufficient chromatographic resolution is provided. Hence, with reference to a chromatogram, the capacity factor becomes... 

Equation (4.30) suggests that the degree of chromatographic resolution depends chiefly on three factors N, k, and a. N, the number of theoretical plates in a column, relates how efficient a chromatographic column is. N is... 

Table 4.5 Chromatographic Capacity Factor and the Contribution of k to the Fundamental Resolution Equation...

Equation [1] can be applied to assist in the selection of the appropriate chromatographic conditions to provide the minimum resolution required for the analysis task. Baseline resolution is achieved at Rs>1.5, and will be sufficient to provide accurate quantitative data in most applications. In many cases solutes tend to be over-separated (Rs 2), and excess resolution equates to excessive analysis time. 

The aim of any chromatographic process is the resolution of the sample mixture. The simplest equation expressing the chromatographic resolution (RJ between... 

Finally, solute A s capacity factor is eliminated using equation 12.11. After rearranging, the equation for the resolution between the chromatographic peaks for solutes A and B is... 

Solvent selectivity refers to the ability of a chromatographic system to separate two substances of a mixture. It depends on the chemistry of the adsorbent surface, such as the layer activity and type of chemical modihcation. The separation power or resolution is given by Equation 4.8 [27] ... 

The resolution of two peaks is related to the adjustable chromatographic variables of selectivity, efficiency, and time by equation (1.46) (104-106)... 

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