Differential equation for the elution curve

Recalling the basic differential equation for the elution curve given in chapter 2 is,... 

The integration of the differential equation that describes the rate of change of solute concentration within a plate to the volume flow of mobile phase through it. The integral of this equation will be the equation for the elution curve of a solute through a chromatographic column. 

Equation (9) is the basic differential equation that describes the rate of change of concentration of solute in the mobile phase in plate (p) with the volume flow of mobile phase through it. Thus, the Integration of equation (9) will provide the equation for the elution curve of a solute from any plate in the column. A simple algebraic solution to equation (9) is given below and the resulting equation for the elution curve from plate (p) is as follows -... 

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. 

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,... 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

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