Elution equation,Gaussian form

Equation (1) is the well-known Gaussian form of the elution curve equation and can be used as an alternative to the Poisson form in all applications of the Plate Theory. 

There is an interesting consequence to the above discussion on composite peak envelopes. If the actual retention times of a pair of solutes are accurately known, then the measured retention time of the composite peak will be related to the relative quantities of each solute present. Consequently, an assay of the two components could be obtained from accurate retention measurements only. This method of analysis was shown to be feasible and practical by Scott and Reese [1]. Consider two solutes that are eluted so close together that a single composite peak is produced. From the Plate Theory, using the Gaussian form of the elution curve, the concentration profile of such a peak can be described by the following equation ... 

Employing the alternative Gaussian form of the elution equation. 

Employing the Gaussian form of the elution equation, this can be put in the... 

Gaussian Form of the Plate Theory Elution Equation... 

However, the elution equation in Poisson form has its zero point at the injection point (v = 0 in Equation [3.11]), whereas a Gaussian form as usually expressed is centred at the peak maximum. Thus conversion of Equation [3.11] to its Gaussian equivalent involves changing the origin in addition to considering the limit for large values of N. Recall that v is defined as the number of plate volumes of mobile phase that have passed through the column, and in the conversion it is convenient to work with dimensionless numbers, so a new quantity w is defined as the number of plate volumes eluted measured relative to the number required to reach the peak maximum of solute A ... 

Equation [3.31 a] is the elution equation written in Gaussian form in terms of the continuous variable V and centered at the peak maximum where V =. This is... 

This is the elution equation expressed relative to an origin located at the maximum of the elution peak, i.e., at CO = 0. It has the general form of a Gaussian Function, but in order to relate it more closely to experimental observables, the elution parameter is changed from numbers... 

In this chapter, the elution curve equation and the plate theory will be used to explain some specific features of a chromatogram, certain chromatographic operating procedures, and some specific column properties. Some of the subjects treated will be second-order effects and, therefore, the mathematics will be more complex and some of the physical systems more involved. Firstly, it will be necessary to express certain mathematical concepts, such as the elution curve equation, in an alternative form. For example, the Poisson equation for the elution curve will be put into the simpler Gaussian or Error function form. 

Like Eq. 6.5, Eq. 6.26 gives the concentration profile of the solute along the column. In this equation the time, is a constant parameter, and the position, zGaussian profile. On the other hand, the elution profile, which is given by writing = 1 m Eq. 6.26 and taking the parameter as the variable, is not a Gaussian distribution. It is written ... 

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