Multipath process

The multipath term (A) This term applies to columns packed with support particles. It becomes zero for open tubular columns when the mobile phase velocity is slow enough for the flow to be laminar (i.e., without mrbulent eddies). In a packed column, the paths of individual analyte molecules will differ as they take different routes through the spaces between the particles. Thus they will travel varying distances before they exit the column, and the difference between these distances contributes to band broadening. The relative magnitude of the multipath term depends on the particle and column dimensions. If Fig. 11.3 depicted a packed column, A would be a constant value for all values of u, and would appear as a horizontal line raising the curve by a constant amount. The multipath process is illustrated in Fig. 11.4. 

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 similar manner to the design process for packed columns, the physical characteristics and the performance specifications can pe calculated theoretically for the open tubular columns Again, the procedure involves the use of a number of equations that have been previously derived and/or discussed (1). However, it will be seen that as a result of the geometric simplicity of the open tubular column, there are no packing factors and no multipath term and so the equations that result are far less complex and easier to manipulate and to understand. 

Several different processes lead to the band-spreading phenomena in the column which include multipath effect molecular diffusion displacement in the porous beds secondary equilibria and others. Each of these processes introduces its own degree of variance toward the overall band-spreading process. Usually these processes are assumed to be independent and based on the fundamental statistical law, overall band-spreading (variance) is equal to the sum of the variances for each independent process ... 

A better way to look at chromatographic efficiency is to consider the dynamic processes that contribute to peak broadening. Recall that chromatographic peaks are Gaussian and that the width of a peak at its base is approximately four standard deviations w = 4(7. The factors that contribute to peak broadening are additive provided the variance (a ) is used instead of the standard deviation. The total variance (ff tot) is the sum of variances due to multipaths (cT mp). axial diffusion (u dif). resistance to mass transfer (ff mt) and extra-column ([Pg.82]

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. 

Figure 3.20 The CCAP in the continuum scheme A multipath two-photon process links a bound state to M degenerate channels via N intermediate bound states. Taken from Ref. [249].

We consider the PD of CH3I by a multipath two-photon process from the 0,0,0) = 0) of the X Ai surface via excited states l,Vci,v) of the same surface. The J,Vci,v) states on the iPAi surface are obtained using the potential surface of Ref. [254] within the rigid-rotor approximation the corresponding... 

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. 

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... 

Here H is the theoretical plate height, a parameter that characterizes the effectiveness of the chromatographic separation. The smaller the H the more powerful is the separation. A is the Eddy diffusion term (or multipath term), B relates to longitudinal diffusion, C represents the resistance of sorption processes (or kinetic term), and u is the linear flow rate. For a given chromatographic system. A, B, and C are constants, so the relationship between H and u can be plotted as shown in Fig. 6. 

In the ideal case, the peaks eluting are in the shape of a Gaussian distribution (bell-shaped curve, Figure 2.106). A very simple explanation of this shape is the different paths taken by the molecules through the separating system (multipath effect), which is caused by diffusion processes (Eddy diffusion) (Figure 2.107). 

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