Reduced parameters plate height

High-Performance liquid Chromatography. Typical performances for various experimental conditions are given in Table 11.15. The data assume these reduced parameters h = 3, V = 4.5. The reduced plate height is... 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

Column Type Minimum Reduced Plate Height Minimum Reduced Velocity flow Resistance Parameter Separation Impedance... 

Golay equation 21, 611 gradient (LC) 490 height equivalent to a theoretical plate 11 longitudinal diffusion 16 mass transfer resistance 17 nonlinear chromatography SOS plate model 14 rate theory IS reduced parameters 78, 361, 611... 

Upon substitution of the reduced parameters given above the separation time for a packed column and an open tubular column would be Identical if d 1.73 dp given the current limitations of open tubular column technology the column diameter cannot be reduced to the point %diere these columns can compete with packed columns for fast separations. This is illustrated by the practical txanple in Figure 6.3 (57). Ihe separation speed cannot be Increased for an open tubular column by increasing the reduced velocity since the reduced plate height is increased... 

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. 

A more vigorous treatment similar to the van Deemter equation but developed specifically for HPLC is the Knox equation, which uses a number of reduced parameters where h is the reduced plate height (h/dp) and vis reduced velocity (V dJD. ... 

Fio. 4. Double logarithmic plots of the reduced plate height against the reduced velocity. The values of the parameter A are 2,1, and 0 for the data shown by solid, dotted, and dash-dot lines, respectively. Parameter C is shown for each curve on th graph. The coordinates of the minima are given in Table II. ... 

In pHPLC, there are numerous types of columns used. The comparison and characterization of these columns are often discussed in terms of thermodynamic properties and kinetic characteristics. The retention factor, k, selectivity, a, and the peak asymmetry are believed to be representative parameters for the thermodynamic properties, while the kinetic characteristics are often expressed in dimensionless magnitudes of reduced plate height, h, separation impedance, E, and flow resistance factor, ( ). 3... 

The most commonly used criterion for judging column performance is efficiency as measured by the number of theoretical plates or column plate count (N) exhibited by the column during the separation of a test mixture. The larger the number of theoretical plates, the more likely it is that the column will produce the desired separations. However, while popular, N is not a complete performance parameter for making comparisons. For example, N does not take into account particle size as does the reduced plate height, h. Another measurement, hmin, accounts for all of these factors as well as the mobile phase linear velocity and sample diffusion. However, N is the term most commonly recognized as being related to resolution (2), as shown in Equation 1 ... 

The reduced parameters are also helpful in evaluating column performance. The best columns have a reduced plate height of 2 to 5—a number that can be thought of as representing the number of particles between sorptions—and 2 is a practical minimum. The reduced velocity represents the ratio between the flow velocity and the diffusion rate over one particle diameter typical values should be in the range of 3 to 20. 

To illustrate more clearly the effect of these variables on analysis time, reduced parameters can be used for the plate height and velocity. Reduced parameters effectively normalize the plate height and velocity for the particle diameter and the diffusion coefficient to produce dimensionless parameters that allow comparison of different columns and separation conditions. The reduced plate height and reduced velocity are expressed, respectively, as... 

Comparisons of columns of different lengths that are also packed with different sized particles may be made by use of the reduced plate height Qi) which is a dimensionless parameter defined by equation (2.29). 

The basic parameters employed in the analysis of the CPC chromatograms are the retention volume V which is related to the stationary phase and mobile phase volumes V, and V , respectively, and the distribution ratio of the analyte D [Eq. (1)], the chromatographic efficiency, as measured by the number of theoretical plates N, which is calculated from the retention volume V, and the width of the chromatogram w, [Eq. (2)], the chromatographic inefficiency represented by the channel equivalent of a theoretical plate (CETP), which is analogous to reduced plate height and is the ratio of the number of channels (CH) (2400 in our experiments) to N [Eq. (3)], and the selectivity I achieved in the separation of two analytes (1 and 2), which is the ratio of their distribution ratios A and D2 [Eq. (4) [2] ... 

First dimensionless parameter, reduced plate height, h, replaces plate height, H. His compared with the mean particle diameter, dp. ... 

To overcome this problem, it is sometimes preferable to use reduced parameters, the reduced plate height, h, and the reduced fluid velocity, v, respectively, in place of H and y. The dimensionless parameters h and V are respectively defined by the expressions ... 

The reduced plate height, h, is independent of the particle diameter. The reduced fluid velocity (u), a concept conceived by Giddings, is a measure of the rate of flow over a particle relative to the rate of diffusion of solute within the particle. Since both reduced parameters, h and V, are normalized for the particle diameter, when h is plotted against v, the different size fractions of the same packing materials should give similar curves. This has been confirmed in practice, so that use of h vs v curves is preferred over that of plate height curves (H versus mobile phase velocity) when comparison of the efficiency of different columns is to be carried out. 

Column type Minimum reduced plate height Minimum reduced velocity Flow resistance parameter Separation impedance... 

Assumptions viscosity = 3.5 x 10 N.s/m and solute diffusion coefficient = 2.5 x 10" m /s. (h = reduced plate height, v = reduced mobile phase velocity, flow resistance parameter, and dp = average particle size)... 

Thus columns should also be kept short to minimise band dispersion. Since the plate height is a function of particle size it is sometimes useful to refer to the parameter known as the reduced plate height (/i), which is a measure of the number of particles per plate. It can be determined from the equation ... 

These four factors cause band broadening and work additively such that their summation contributes to H, the height equivalent to a theoretical plate. This parameter is dependent on flow rate due to the contribution from longitudinal diffusion and mass transfer. Band broadening can therefore be minimised by use of an optimum flow rate. This relationship is usually visualised in a Knox plot (Fig. 2.4) using the reduced plate height (/j) as the vertical axis and the reduced velocity (u) as the horizontal axis. The reduced velocity is given by the formula ... 

Here, h is the reduced plate height, v is the reduced mobile-phase velocity, and A, B, and C are constants for a given HPLC system. The reduced parameters are given by... 

A dimensional analysis of the perfonnance index shows that it has the dimension of an inverse viscosity. With a little algebra, using the equations for permeability [Eq. (2.51)3, die definitions of the flow-resistance parameter [Eq. (154)3, linear velocity [l s. (110 and (111)3. retention factor [Eq. (161)3 and the reduced plate height [Eq. (113)3, we can lit the performance index into its components ... 

From equations (2.54) and (253) and the definition of the reduced plate height, we can see that it depends primarily on the reduced plate height and the flow resistance parameter ... 

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