Plate height coefficients

TABLE 12.1 Summary of Plate Height Coefficients for Packed and Ideal Capillary Columns a... 

Cm mobile phase plate height coefficient C, stationary phase plate height coefficient... 

Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

In these expressions, dp is the particle diameter of the stationary phase that constitutes one plate height. D is the diffusion coefficient of the solute in the mobile phase. 

The important parameters to consider are the selectivity (dKJdlogR), the ratio of pore volume, Vp, over void volume, Vq, the plate height, H, and the column length, L. The distribution coefficient, Kq, has a slight effect on resolution (with an optimum at Kp 0.3-0.5). In addition to this, extra column effects, such as sample volume, may also contribute to the resolution. 

The contribution to the plate height from molecular diffusion in the mobile phase arises from the natural tendency of the solute band to diffuse away from the zone center as it moves through the column [59,60,63,64]. Its value is proportional to the diffusion coefficient and the. time the sample spends in the column. Its contribution to the total plate height is given by... 

In liquid chronatography where diffusion coefficients are saall, the contribution of to the plate height is ften negligible. Diffusion coefficients are much larger in gases and hence is More inportant, particularly at low Mobile phase velocities. 

The Poppe plot is a log-log plot of H/uq = t(JN versus the number of plates with different particle sizes and with lines drawn at constant void time, t(). H is the plate height, Vis the number of plates, and u() is the fluid velocity (assumed equal to the void velocity). The quantity H/u() is called the plate time, which is the time for a theoretical plate to develop and is indicative of the speed of the separation, with units of seconds. In the Poppe plot, a number of parameters including the maximum allowable pressure drop, particle diameter, viscosity, flow resistance, and diffusion coefficient are held constant. 

FIGURE 6.1 A Poppe plot for the required plate number in conventional HPLC. The parameters are taken from Poppe s original paper (Poppe, 1997). The parameters are maximum pressure AP = 4x 107 Pa, viscosity / = 0.001 Pa/s, flow resistance factor

diffusion coefficient D= lx 1CT9 m2/s, and reduced plate height parameters using Knox s plate height model are A — 1, B— 1.5, C = 0.05. 

In order to evaluate the efficacy of the expanded bed technique the plate height (HETP), plate number (N), resolution (Rs), Bodenstein number (Bo), particle Peclet number (Pep) and axial dispersion coefficient (DJ have been calculated and compared with the corresponding values of a traditional HPLC column. N can be expressed by... 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

Equation 5 Knox equation, with reduced plate height, h reduced velocity (m dpID ), V, coefficient B, describing axial diffusion (typical value 2) coefficient A, describing bed homogeneity (typical value 1-2) and coefficient C, describing mass transfer (typical value 0.05). 

If A is different from zero it is not possible to calculate exactly the numerical coefficient whose value is somewhat larger than 2, as we will show later in this section. As a rule of thumb, the pressure necessary to perform an analysis when working at minimum plate height can be approximated by Eq. (46) (AP in atm, dp in /itn)... 

Temperature hMges can also affect the efficiency of the chrumatogra< phic system sin< the diffusion coefficient of a solute increases with the temperature. In -eluents used in RPC solute diffiisivity increases by a factor of about t/1 over the temperature range 15-72T. As a result the plate height may decrease as much as 30% over this temperature range. 

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