Multipath dispersion

Maximum Column Inlet Pressure Extra Column Dispersion Multipath Packing Factor Longitudinal Diffusion Packing Factor Column Mobile Phase Fraction... 

It is also seen that, at very low velocities, where u E, the first term tends to zero, thus meeting the logical requirement that there is no multipath dispersion at zero mobile phase velocity. Giddings also introduced a coupling term that accounted for an increase in the effective diffusion of the solute between the particles. The increased diffusion has already been discussed and it was suggested that a form of microscopic turbulence induced rapid solute transfer in the interparticulate spaces. 

In order to relate the value of (H) to the solute diffusivity and, consequently, to the molecular weight according to equation (11), certain preliminary calculations are necessary. It has already been demonstrated in the previous chapter (page 303) that the dynamic dead volume and capacity ratio must be used in dispersion studies but, for equation (11) to be utilized, the value of the multipath term (2Xdp) must also be... 

Dispersion equations, typically the van Deemter equation (2), have been often applied to the TLC plate. Qualitatively, this use of dispersion equations derived for GC and LC can be useful, but any quantitative relationship between such equations and the actual thin layer plate are likely to be fraught with en or. In general, there will be the three similar dispersion terms representing the main sources of spot dispersion, namely, multipath dispersion, longitudinal diffusion and dispersion due to resistance to mass transfer between the two phases. 

The multipath dispersion on a thin layer plate is the process most likely to be described by a function similar to that in the van Deemter equation. However, the actual mobile phase velocity is likely to enter that range where the Giddings function (3) applies. In addition, as the solvent composition is continually changing (at least in the vast majority of practical applications) the solute diffusivity is also altered and thus, the mobile phase velocity at which the Giddings function applies will vary. 

HETP of a TLC plate is taken as the ratio of the distance traveled by the spot to the plate efficiency. The same three processes cause spot dispersion in TLC as do cause band dispersion in GC and LC. Namely, they are multipath dispersion, longitudinal diffusion and resistance to mass transfer between the two phases. Due to the aforementioned solvent frontal analysis, however, neither the capacity ratio, the solute diffusivity or the solvent velocity are constant throughout the elution of the solute along the plate and thus the conventional dispersion equations used in GC and LC have no pertinence to the thin layer plate. 

There are four basic dispersion processes that can occur in a packed column that will account for the final band variance. They are namely, The Multipath Effect, Longitudinal Diffusion, the Resistance to Mass Transfer in the Mobile Phase and the Resistance to Mass Transfer in the Stationary Phase. All these processes are random and essentially noninteracting and, therefore, provide individual contributions of variance that can be summed to produce the final band variance. Each process will now be discussed individually. 

In a packed column the solute molecules will describe a tortuous path through the interstices between the particles and obviously some will travel shorter paths than the average and some longer paths. Consequently, some molecules will move ahead of the average and some will lag behind thus causing band dispersion. The multipath effect is illustrated in figure (4)... 

The upper curve, which is the result of a curve fitting procedure to the points shown, is the HETP curve. The column was 25 cm long, 9 mm in diameter and packed with 8.5 micron (nominal 10 micron) Partisil silica gel. The mobile phase was a solution of 4.8 Sw/v ethyl acetate in n-decane. The minimum of the curve is clearly indicated and it is seen that the fit of the points to the curve is fairly good. As a result of the curve fitting procedure the values of the Van Deemter constants could be determined and the separate contributions to the curve from the multipath dispersion, longitudinal dispersion and the resistance to mass transfer calculated. 

The three contributions to dispersion are also shown as separate curves in figure 1. It is seen that the major contribution to dispersion at the optimum velocity, where the value of (H) is a minimum, is the multipath effect. Only at much lower velocities does the longitudinal diffusion effect become significant. Conversely, the mobile phase velocity must be increased to about 0.2 cm/sec before the resistance to mass transfer begins to become relatively significant compared to that of the multipath effect. 

Hm contribution to H from multipath dispersion Hl contribution to H from longitudinal diffusion ion mobile phase Hl(S) contribution to H from longitudinal diffusion ion stationary phase K distribution coefficient K(a) distribution coefficient of solute (A)... 

LPRlNT Maxlmum Column Inlet Pressure LPRINT"Extra Column Dispersion LPRINT Multipath Packing Factor LPRINT longitudinal Diffusion Packing Factor LPRINT"Column Mobile Phase Fraction LPRINT... 

The open-tubular column or capillary column is the one most commonly used in gas chromatography (GC) today. The equation that describes dispersion in open tubes was developed by Golay [1], who employed a modified form of the rate theory, and is similar in form to that for packed columns. However, as there is no packing, there can be no multipath term and, thus, the equation only describes two types of dispersion. One function describes the longitudinal diffusion effect and two others describe the combined resistance to mass-transfer terms for the mobile and stationary phases. 

Figure 9.10 shows energy-dissipation contours for four impellers. The numbers represent fractions of the average energy input. It is important to understand energy distribution because it affects all processes requiring intensive mixing. This includes fast multipath chemical reactions, bubble and drop dispersion, and solids dissolution. Subsequent sections review these topics. 

A second difference, between gas and liquid chromatography, lies in the mode of solute dispersion. In the first instance, virtually all LC columns are packed (not open tubes) which introduces a dispersion process into the column that is not present in the GC capillary column. In a packed column the solute molecules will describe a tortuous path through the interstices between the particles and obviously some will travel shorter paths than the average, and some longer paths. Consequently, some molecules will move ahead of the average and some will lag behind, thus causing band dispersion. This type of dispersion is called multipath dispersion and is an additional contribution to longitudinal diffusion, and the two resistance to mass transfer contributions, to the overall peak variance. 

Multipath dispersion in a packed column the molecules in the mobile phase follow meandering paths of different lengths through the gaps between the stationary phase particles, and thus elute with a range of t values the corresponding contribution to H is = 2 -dp. 

Van Deemter Equation the first theoretical expression of the dependence of H on u H = A-pB/u-pC.u, where the coefficients A, B and C were explicitly derived in terms of physico-chemical parameters. An alternative and quite commonly used formulation is that of Knox h = A.vJ -l-B/v-l-C.v, where h = H/dp and v = u.(dp/D ) are the reducedpbdn height and linear velocity. The Knox equation is a convenient functional form for fitting experimental data (it accounts for a minor coupling observed between multipath dispersion and resistance to mass transfer) but does not provide expressions for the coefficients in terms of more fundamental parameters. 

Golay Equation a modification of the van Deemter equation for a nonpacked (usually capillary) column, i.e., no multipath dispersion effect. When applied to modern capillary gas chromatography the original Golay equation should be corrected for the gas compressibility (use u jit to replace u) and for the film thickness of the stationary phase (Equations [3.53-3.54]). 

There are four independent dispersion processes operating in a packed column that contribute to the total band broadening multipath dispersion dispersion from longitudinal diffusion and dispersion from resistance to mass transfer in each of the mobile and stationary phases. These are now be discussed separately in a somewhat qualitative fashion a rigorous discussion can be found elsewhere (Scott, http //www.chromatography-online.orgZ). It is important to note that, in the following derivations... 

The most striking change is in the A-term that accounts for multipath dispersion (Equation [3.33] in the van Deemter theory) and decreases rapidly with decreasing i.d. This effect was interpreted (Karlsson 1988) as reflecting a decrease in the extent of the flow rate variation over the column cross-section as the i.d. decreases, together with shorter time for solute molecules to diffuse radially through the flow velocity profile (parabolic in the case of a nonpacked column) together these phenomena will decrease the effect of flow anisotropy that is reflected in... 

The positive effects include a reduction in plate height (mainly via reduction in the A-term, multipath dispersion), reduction in chromatographic dilution and thus increased detection sensitivity, and reduction in volume flow rate and thus in solvent consumption. However, offsetting disadvantages include limitations on the volume of sample solution and the amount of analyte that can be injected without overloading the column, and the meticulous attention that is required to reduce the extra-column dead volume (injectors, detectors etc.) to avoid excessive band broadening. As noted above, these columns do not appear to have been used in vahdated quantitative methods. 

---