Mass transfer stationary phase

Figure 15.2E shows the effect of stationary phase mass transfer. After molecules of sample diffuse into a pore, they migrate to the stationary phase (shaded region) or become attached to it in some fashion. If a molecule penetrates deep into the stationary phase, it spends a longer time in the particle and travels a shorter distance down the column, just as in Fig. 15.2D. Molecules that spend only a little time moving into and out of the stationary phase return to the mobile phase sooner, and move further down the column.

As a general rule, in the case of CSPs featuring hydrophobic pockets, a decrease of mobile phase flow-rate results in an increase of chromatographic resolution (Rs), as a consequence of better stationary phase mass transfer [78]. This change has significant impact mostly in RP mode [17]. In the NP enantioselective separations of two test solutes (4-hexyl-5-cyano-6-methoxy-3,4-dihydro-2-pyridone and... 

If the stationary phase is a liquid, the original stationary phase mass transfer term of van Deemter is basically correct. For example, Eq. (7) shows that H is proportional to the square of the thickness of the stationary liquid film, d, and inversely proportional to the diffusion coefficient in the liquid phase, DL. Thus a good column will have a small film thickness, and the stationary liquid will be chosen for its high diffusion coefficient. 

The other part of the stationary phase mass transfer term is the ratio k + k)2, which is also equal to Rr( 1 — Rr), an alternative ratio some-... 

A high electroosmotic flow through the stationary-phase particles may be created when the appropriate conditions are provided. This pore flow has important consequences for the chromatographic efficiency that may be obtained in CEC. From plate height theories on (pressure-driven) techniques such as perfusion and membrane chromatography, it is known that perfusive transport may strongly enhance the stationary-phase mass transfer kinetics [30-34], It is emphasised... 

One effect of pore flow is that it enhances the mass transfer rate between the pore and interstitial volumes. Instead of by molecular diffusion only, which is by nature slow in solution, mass exchange occurs also by perfusive EOF. This effect can be treated as a form of stimulated diffusion. Following the original treatment for pressure-driven LC according to Rodrigues et al. [31], the plate height contribution from stationary-phase mass transfer resistance HCs in the presence of pore flow can be written as... 

Figure 7 The stationary-phase mass transfer enhancement for nonsorbed tracers. Diffusion coefficients (a) 5x 1CT9 m2/s (b) 1CT9 m2/s and (c) 10 ° m2/s. Other values used in calculations dp= 7.0 pm ua = 2.0 mm/s.

In addition to the enhanced diffusivity effect, another issue needs to be taken into account when considering stationary-phase mass transfer in CEC with porous particles. The velocity difference between the pore and interstitial space may be small in CEC. Under such conditions the rate of mass transfer between the interstitial and pore space cannot be very important for the total separation efficiency, as the driving mechanism for peak broadening, i.e., the difference in mobile-phase velocity within and outside the particles, is absent. This effect on the plate height contribution II, s has been termed the equilibrium effect [35], How to account for this effect in the plate height equation is still open to debate. Using a modified mass balance equation and Laplace transformation, we first arrived at the following expression for Hc,s, which accounts for both the effective diffusivity and the equilibrium effect [18] ... 

The Stationary Phase Mass-Transfer Term C u When the stationary phase is an immobilized liquid, the mass-transfer coefficient is directly proportional to the square of the thickness of the film on the support particles, d, and inversely proportional to the diffusion coefficient, D, of the solute in the film. These effects can be understood by realizing that both reduce the average frequency at which analyte molecules reach the interface where transfer to the mobile phase can occur. That is, with thick films, molecules must on the average travel farther to reach the surface, and with smaller diffusion coefficients, they travel slower. The consequence is a slower rate of mass transfer and an increase in plate height. 

Stationary phase mass-transfer term, Cs A measure of the rate at which an analyte molecule enters and is released from the stationary phase. 

The plate height contribution of stationary phase mass transfer, Hs, is given by ... 

Cj = stationary-phase mass transfer term L = column length... 

Analogous arguments can be developed to take account of stationary phase mass transfer effects which can similarly be expressed as... 

According to Scott the average linear velocity can be replaced by (4uq / [P -i- 1]) in Eq. (1.23) to permit evaluation entirely in terms of the outlet velocity [130]. If X = 0, y = 1, and dp = rc is substituted into Eq. (1.23) then this equation can be used as an alternative to Eq. (1.22) to account for band broadening in evaluating open tubular columns [121,130]. For gas-solid chromatography the stationary phase mass transfer... 

Since only flow and diffusion effects couple, while longitudinal diffusion and stationary phase mass transfer don t, the complete equation for the dependence of the HETP on the linear velodty diould be written as... 

When we sum up the mobile-phase mass-transfer term and the stationary-phase mass-transfer term, we obtain the total mass-transfer term ... 

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