Optimum Particle Diameter

In many ways, column dimensions are predefined by the required resolution. Thus, the goal is narrowed to increase velocity and the ability to reoptimize the separation back to its original resolution. The two known approaches to increase optimum velocity are to use smaller particle diameters (optimum velocity proportional to 1/particle diameter) (Knox and Saleem, 1969 and Nguyen et ah, 2006) and increase the column temperature (optimum velocity proportional to (Antia and Horvath, 1988 Yan et al., 2000). The use of... 

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

It is seen from equation (26) that the optimum velocity is determined by the magnitude of the diffusion coefficient and is inversely related to the particle diameter. Unfortunately, in LC (where the mobile phase is a liquid as opposed to a gas), the diffusivity is four to five orders of magnitude less than in GC. Thus, to achieve comparable performance, the particle diameter must also be reduced (c./., 3-5 p)... 

It should be pointed out that equations (14) and (15) do not give an expression for the minimum column lengths, as the optimum particle diameter has yet to be identified. 

It is seen that there will be a unique value for (dp), the optimum particle diameter, (dp(opt)), that will meet the equality defined in equation (14) and allow the minimum HETP to be realized when operating at a maximum column inlet pressure... 

P). Note the expression for (C) is also a function of the particle diameter (dp) and includes known thermodynamic and physical properties of the chromatographic system. Consequently, with the aid of a computer, the optimum particle diameter (dp(opt)) can be calculated as that value that will meet the equality defined in... 

It follows that knowing the optimum particle diameter, the optimum column length can also be identified. It must be emphasized that this optimizing procedure... 

Thus as (y) will always be greater than unity, the resistance to mass transfer term in the mobile phase will be, at a minimum, about forty times greater than that in the stationary phase. Consequently, the contribution from the resistance to mass transfer in the stationary phase to the overall variance per unit length of the column, relative to that in the mobile phase, can be ignored. It is now possible to obtain a new expression for the optimum particle diameter (dp(opt)) by eliminating the resistance to mass transfer function for the liquid phase from equation (14). 

Consider first the equation for the optimum particle diameter. Reiterating equation (18),... 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

The expression that gives the optimum particle diameter is given by equation (27), chapter 12 and is reiterated here. The optimization of the particle diameter will be considered first, as each of the other operating parameters will, directly or indirectly, be determined by the magnitude of the optimum particle diameter. 

The function f(k ) is shown plotted against the thermodynamic capacity ratio in Figure 1. It is seen that for peaks having capacity ratios greater than about 2, the magnitude of (k ) has only a small effect on the optimum particle diameter because the efficiency required to effect the separation tends to a constant value for strongly retained peaks. From equation (1) it is seen that the optimum particle diameter varies as the square root of the solute diffusivity and the solvent viscosity. As, in... 

Figure 1. The Effect of Solute Capacity Ratio on the Magnitude of the Optimum Particle Diameter...

The optimum particle diameter will decrease as the reciprocal of the available pressure and, thus, pressure will have a very significant effect on the magnitude of (dp(opt)). As already stated, the higher the pressure, the smaller the particle diameter,... 

Figure 2. Curve Relating Optimum Particle Diameter to the Separation Ratio of the Critical Pair...

It is seen that the optimum velocity is inversely proportional to the optimum particle diameter and it would be possible to insert the expression for the optimum particle diameter into equation (2) to provide an explicit expression for the optimum velocity. The result would, however, be algebraically cumbersome and it is easier to consider the effects separately. The optimum velocity is inversely... 

It is seen that as the optimum particle diameter is inversely proportional to (cx-1),... 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

The column used was 25 cm long, 4.6 mm in diameter, and packed with silica gel particle (diameter 5 pm) giving an maximum efficiency at the optimum velocity of 25,000 theoretical plates. The mobile phase consisted of 76% v/v n-hexane and 24% v/v 2-propyl alcohol at a flow-rate of 1.0 ml/min. The steroid hormones are mostly weakly polar and thus, on silica gel, will be separated primarily on a basis of polarity. The silica, however, was heavily deactivated by a relatively high concentration of the moderator 2-propyl alcohol and thus the interacting surface would be covered with isopropanol molecules. Whether the interaction is by sorption or displacement is difficult to predict. It is likely that the early peaks interacted by sorption and the late peaks by possibly by displacement. 

SFE usually requires pre-extraction manipulation in the form of cryogenic grinding, except in cases where analytes are sorbed only on the surface or outer particle periphery. The optimum particle diameter is about 10-50 p,m. Diatomaceous earth is used extensively in SFE sample preparation procedures. This solid support helps to disperse the sample evenly, allowing the SCF to solvate the analytes of interest efficiently and without interference from moisture. 

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