Particle diameter-separation factor

It is clear that the major factor controlling the particle diameter will be the separation ratio (a), which reflects the difficulty of the separation. The more... 

Thus, the length of a settling chamber is inversely proportional to the square of the particle diameter. For example, if it is desirable to separate out particles that are two times smaller than the selected size, then the length of the chamber must be increased by a factor of four. The equation may also be used to determine the smallest particle diameter that can be removed by a chamber of specified dimensions. The following example problem illustrates some of these design principles. 

Particle separation can be characterized by the separation factor, Rp, which is the ratio of eluant to particle elution volumes, or, by the difference in elution voliame, AV, between particle and eluant marker turbidity peaks. For polystyrene monodisperse standards, a linear relationship occ irs between the log of the particle diameter and AV, with a series of parallel lines resulting for different concentration of either salt or surfactant below its critical micelle concentration (IT>18,19) The separation factor has also been shown to be independent of eluant... 

Calculations for Rp as a function of the relevant experimental parameters (eluant ionic species concentration-including surfactant, packing diameter, eluant flow rate) and particle physical and electrochemical properties (Hamaker constant and surface potential) show good agreement with published data (l8,19) Of particiilar interest is the calculation which shows that at very low ionic concentration the separation factor becomes independent of the particle Hamaker constant. This result indicates the feasibility of xmiversal calibration based on well characterized latices such as the monodisperse polystyrenes. In the following section we present some recent results obtained with our HDC system using several, monodisperse standards and various surfactant conditions. 

First, we will explore the three fundamental factors in HPLC retention, selectivity, and efficiency. These three factors ultimately control the separation (resolution) of the analyte(s). We will then discuss the van Deemter equation and demonstrate how the particle diameter of the packing material and flow rate affect column efficiencies. 

The presence of the pores adds two parameters - the pore volume fraction and the pore radius. The predicted Rp Increases as the pore radius decreases suggesting a preference tor small pore packings. However, for a small pore radius of 1.0 pm a single value of the separation factor corresponds to two values of the particle diameter (13). Such double-valued behavior Is of course undesirable In an analytic technique. 

Figure 3. Separation factor-particle diameter behavior computed from the pore-partitioning model showing the effect of the Hamaker constant at a low eluant ionic strength (O.OOl M). Other parameters are = 0.60, interstitial capillary radius = l6 fim, pore radius = fim,...

Figure 5. Separation factor-particle diameter behavior as a function of the pore radius for the pore-partioning model. Hamaker constant = 0.05 pico-erg all other parameters are the same as in Figure 3.

Figure 6. Separation factor-particle diameter tehavior as a function of packing diameter for the pore-partitioning model. Parameters are the same as in Figure 3 with the exception of the interstitial capillary radius which was computed from the hed hydraulic radius (Equation 11 (7.) with void fraction = 0.358).

The choice of the FFF technique dictates which physicochemical parameters of the analyte govern its retention in the channel FIFFF separates solely by size, SdFFF by both size and density, ThFFF by size and chanical composition, and EIFFF by mass and charge. The dependence of retention on factors other than size can be advantageous in some applications, and different information can be obtained by employing different techniques in combination or in sequence. On the other hand, the properties that can be characterized by FFF include analyte mass, density, volume, diffusion coefficient, charge, electrophoretic mobility, p/ (isoelectric point), molecular weight, and particle diameter. 

Figure 4.11 Calculated characteristics for optimum chromatograms (r = 1) containing 10 equally resolved peaks as a function of the separation factor S. Plotted on a logarithmic scale are the capacity factor of last peak (1 +k eqn.4.46), the required number of plates (Afne eqn.4.47), the required analysis time under conditions of constant flow rate and particle diameter (rne f>(ji eqn.4.48), and required analysis time under conditions of constant pressure drop fne p eqn.4.49). For explanation see text.

As to the distance traveled by the particles themselves, it is obvious that this varies directly as the diameter. Since the separation factor varies inversely as the diameter, we see that large cyclones are less effective in handling fine particles than would be expected from consideration of the separating factors alone. 

A second assumption is that the particles act as independent scattered, i.e., the scattering of light by one particle does not influence the scattering by another. If particles are separated by more than about 2 diameters, this assumption is met (Van de Hulst, 1957). For 1-p.m-diameter particles, this means concentration on the order of 1.25 x 1011 particles per cubic centimeter before this assumption breaks down. At a concentration of this magnitude, other factors such as coagulation (see Chap. 18) come into play to reduce the concentration, so the assumption is always valid. 

Figure 3 Fractional attainment U(t) of the equilibrium for a heterogeneous mixture five fractions with identical particle diameters but with different separation factors a, ranging from 0.1 to 100. Amount Q, and rate coefficient of each fraction 0.842 mequiv and 1.4 cm s" mequiv, respectively. Total solution concentration 0.00662 M. Rate curves calculated with Eqs. (27), (28), and (29).

Figure 2.31 Peak capacity as a function of analytical run time. The graph is valid for isocratic reversed-phase systems which are run at their van Deemter optimum. The maximum retention factor /ris 20, i.e. the maximum retention time is to 21, then the separation ends. The figure is only valid for small analytes with a diffusion coefficient ofapprox. 1-10 m s and not for macromolecules. Dotted lines represent the particle diameter, dashed lines the column length, and solid lines the pressure, respectively.

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