Dispersion stationary phase expression

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

Unfortunately, any equation that does provide a good fit to a series of experimentally determined data sets, and meets the requirement that all constants were positive and real, would still not uniquely identify the correct expression for peak dispersion. After a satisfactory fit of the experimental data to a particular equation is obtained, the constants, (A), (B), (C) etc. must then be replaced by the explicit expressions derived from the respective theory. These expressions will contain constants that define certain physical properties of the solute, solvent and stationary phase. Consequently, if the pertinent physical properties of solute, solvent and stationary phase are varied in a systematic manner to change the magnitude of the constants (A), (B), (C) etc., the changes as predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered to be the true equation that describes band dispersion in a packed column. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

It can be clearly seen from equation (9) that the expression for the retention volume of a solute, although generally correct, is grossly over simplified if accurate measurements of retention volumes are required Some of the stationary phase may not be chromatographically available and not all the pore contents have the same composition as the mobile phase and, therefore, being static, can act as a second stationary phase. This situation is akin to the original reverse phase system of Martin and Synge where a dispersive solvent was absorbed Into the pores of support to provide a liquid/liquid system. As a consequence a more accurate form of the retention equation would be,... 

The dispersion resulting from the resistance to mass transfer in the stationary phase is exactly analogous to that in the mobile phase. Those solute molecules close to the surface of the stationary phase, will leave the surface and enter the mobile phase a significant time before those that have diffused farther into the stationary phase and have a longer distance to diffuse back to the surface. Thus, as those molecules that were close to the surface will be swept along by the moving phase, they will be dispersed from those molecules still diffusing to the surface. Van Deemter deduced an expression for the contribution to variance due to this effect as,... 

In his analysis of the effect of diffusion on an open-tube distillation column Westhaver (1942) came up with the apparent diffusion coefficient 11 a2 /2/ 48D, and since he assumes a parabolic profile it is at first surprising that this should differ by a factor of 11 from Taylor s result. It appears, however, if the more general problem in which the solute can be retained on the wall be considered, that the value of k varies continuously from to is as the fraction of solute held on the wall varies from 1 to 0. This result is implicit in Golay s analysis of the tubular chromatographic column (Golay 1958). He considers the stationary phase of the column as a very thin retentive layer held on the wall and derives an expression for the dispersion by arguments entirely analogous to Taylor s. He has also discussed the effect of diffusion in the retentive layer. 

Doubling the volume fraction of one phase doubles the probability of solute interaction and, consequently, doubles its contribution to retention. There is another interesting outcome Irom the results of Purnell and his co-workers. Where a linear relationship existed between the retention volume and the volume fraction of the stationary phase, the linear functions of the distribution coefficients could be summed directly, but their logarithms could not. In many classical thermodynamic descriptions of the effect of the stationary-phase composition on solute retention, the stationary-phase composition is often taken into account by including an extra term in the expression for the standard free energy of distribution. The results of PumeU indicate that this is not acceptable, as the solute retention or distribution coefficient is linearly not exponentially related to the stationary-phase composition. The stationary phases of intermediate polarities can easily be constructed from binary mixtures of a strongly dispersive stationary... 

The basic concepts for general chromatographic separations (25) can be applied to SEC (9). For separations of polymers, it was proposed that only two column dispersion terms influence H (26,27), namely eddy diffusion in the mobile phase and mass transfer in the stationary phase. The expression for H for a permeating monodisperse high polymer is... 

Studied the time evolution of the interfacial tension when polyisobutylene (PIB)-b-PDMS was introduced to PIB/PDMS blend, with the copolymer added to the PIB phase in that study both homopolymers were poly disperse. The time dependence of the interfacial tension was fitted with an expression that allowed the evaluation of the characteristic times of the three components. The characteristic time of the copolymer was the longest, whereas the presence of the additive was found to delay the characteristic times of the blend components from their values in the binary system. The possible complications of slow diffusivities on the attainment of a stationary state of local equilibrium at the interface were thoroughly discussed by Chang et al. [58] within a theoretical model proposed by Morse [279]. Actually, Morse [279] suggested that the optimal system for measuring the equilibrium interfacial tension in the presence of a nearly symmetric diblock copolymer would be one in which the copolymer tracer diffusivity is much higher in the phase to which the copolymer is initially added than in the other phase because of the possibility of a quasi-steady nonequilibrium state in which the interfacial coverage is depleted below its equilibrium value by a continued diffusion into the other phase. 

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