Multipath effect

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 Multipath effect can also be used to demonstrate the use of the Random Walk Model. 

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. 

In addition it is seen, from equation (12), that the expression for uopt is very similar to that for a packed column but the expression for Hmin. is much simpler as it is devoid of the (A) term from the multipath effect. 

The column diameter dc is also a factor for both packed and open tubular columns. In both cases, the zone spreading is a function of the square of the diameter. Other parameters that enter into this term include the diameter of the coil of the column, which is usually avoided by using uncoiled (straight) columns in LC end effects that cause broadening as the sample enters and leaves the column and the multipath effect, which arises from the fact that each analyte molecule can take a different path... 

The A term is related to multipath effects (eddy diffusion) that are independent of mobile phase flow rate. Analyte molecules can follow multiple pathways of differing lengths that spread the analyte molecules apart and cause peak broadening. Since the smaller the particles, the lower the difference among molecule walks along the column, the A term is linearly dependent on particle diameter, d, according to X, a structure factor ... 

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 ... 

The multipath effect is a flow-independent term, which defines the ability of different molecules to travel through the porous media with paths of different length. 

The effects of gas compressibihty (change of volume as a result of pressure changes) are observed in not only the linear velocity but also the diffusion coefficient of the analyte. For a packed GC column the A-term in the van Deemter equation (multipath effect) is independent of both u and D, so is unaffected. However this is not the case for the B and C terms (see Equations [3.33-3.38]). In fact the van Deemter equation apphes only to each point x along the length of the column if local values of the linear velocity (u ) and diffusion coefficient (D, )) are used. The ideal gas law apphed to the gaseous mobile phase (PVmp = nRT), at constant temperature and constant mass flow rate of mobile phase (dn /dt) leads to the simple relationship for any point x along the length of the column ... 

Sources of signal corruption, such as signal attenuation, amplitude distortion, phase distortion, multipath effects and time-varying channel characteristics, constitute the linear time-variant channel... 

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). 

Figure 2.107 Eddy diffusion in packed columns (multipath effect) (Meyer, 2010).

Figure 2.118 Path differences for laminar flow in capillary columns (multipath effect, caused by turbulence at high flow rates).

Multipath effect in chromatography, the cause of peak broadening through diffusion... 

While the GNSS Compass enables a hi y accurate and long term stable heading determination, its availabdity suffers from an obvious dependence on satelhte signals especially in harsh harbor environments due to shadowing and multipath effects. Here the IMU could serve as an attitude backup system for a hmited time span. 

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