Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -105

Mechanisms and Importance of Zone-Spreading 95\n\nsimply “save the phenomena” by fitting the observed data in a power function. The assumption here is that column design can effectively be based on an accurate description, rather than a prediction, of the plate height plot. By using the reduced variables h and v, these equations are very practical versions of the principle of corresponding states connected through these variables, as discussed in Sec. II.E.4.b. Indeed, in LC, the Knox equation in particular, is renowned for its ability to describe the effect of particle size on plate height for high-density different packing materials and, literally, serves as an extremely valuable tool for assessing the quality of a packed column. For instance, in well-packed columns for LC the reduced minimum plate height (see Sec. II.E.4.a) should be close to 1.5–2 and the associated reduced optimum velocity in the range of 3–7. For the more practical velocities in excess of the optimum value, the Knox equation adequately describes the general curvature observed in the plate height plot. If represented on a logarithmic basis (i.e., as log h vs. log v), the plot becomes linear, with a slope in the vicinity of 0.3–0.4 [Snyder, in older days for less optimal packings, reports 0.3–0.7; see Eq. [47]].\n\nThe power 1/3 in the mobile phase term obviously approximates the complex “coupling” (as Giddings phrases it) or convective dispersion phenomena, leading to the curvature in h versus v plots. The neat and fixed value of 1/3 = 0.33, may in practice vary between 0.30– 0.40 [31]. The experimental fit, rather than the a priori estimation of constants such as a, obscures physical insight, but on the other hand, we do have an accurate description and no further doubts about complexities, such as the role of partitioning \u{1F96A}(f/k), for example) and the influence of support mobile phase in porous packings.\n\nThe latter power functions after Snyder and Knox are, in principle, also found in GC, provided that velocities are high to very high, such as to reach sufficiently reduced velocities (which is not easy in rapidly diffusing gases). Dedicated experiments at high velocities using large particles, yielded values that could be represented by n = 0.45–0.60 for porous packings, and n = 0.25–0.35 for nonporous packings, very much in agreement with predictions made based on differences between porous and nonporous materials in Sec. II.E.4.g.\n\nAfter first treating the case of open tubular columns in the next section, we will return to the Knox and Snyder equations in Sec. IV, because they can play a useful role in the kinetic and time optimization of separations. Also, after treating the capillary column case, we are able to appreciate some additional alternative expressions for the plate height in packed columns, as obtained from adaptation of the capillary column expressions.\n\ne) Open Tubular or Capillary Columns: The Golay Equation. The only geometry that can be analyzed exactly on flow and diffusional mass-transfer phenomena is that of capillary columns, which ideally possess a straight and open tubular (usually circular–cylindrical) geometry, and in which the stationary phase is coated and distributed evenly as a film (or a chemically bonded polymeric network) onto the column perimeter.\n\nThis type of column has largely replaced the packed columns in modern GC, in view of their favorable separation speed. Open columns are able to produce large plate numbers (low plate heights) in relatively short analysis times (see Sec. IV on optimization). Lately, after solving difficult practical problems, such as detection and preparation of stationary phases in open columns with extremely small dimensions, open columns are even becoming of interest for LC [9.50–53]. However, open tubular LC (OTLC) is still in its infancy and in an experimental research stage.\n\nIn comparison with the situation in packed columns, the description of flow and mass-transfer phenomena in open tubular columns are relatively easy, especially if the geometry of the flow channel is simple and symmetrical, as in the circular–cylindrical straight columns. This is exactly the type of column used in practice, although a slight curvature is always present because of loose (relative to the column diameter) coiling of the capillary columns that are too long (several meters up to say 100 m) to fit in normal GC ovens. This coiling.