Solute band, longitudinal diffusion

The B-term in the equation is the contribution to the plate height resulting from longitudinal diffusion (molecular diffusion in the axial direction) and arises from the tendency of the solute band to diffuse away from the band center as it moves down a column. It is proportional to the time that the sample spends in the column and also to its diffusion... 

To determine how the height of a theoretical plate can be decreased, it is necessary to understand the experimental factors contributing to the broadening of a solute s chromatographic band. Several theoretical treatments of band broadening have been proposed. We will consider one approach in which the height of a theoretical plate is determined by four contributions multiple paths, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase. 

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. 

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. 

The dispersion described in figure 2 shows that the longer the solute band remains in the column, the greater will be the extent of longitudinal diffusion. Since the length of time the solute remains in the column is inversely proportional to the mobile phase velocity, so will the dispersion be inversely proportional to the mobile phase velocity. Van Deemter et al derived the following expression for the... 

The plate theory assumes that an instantaneous equilibrium is set up for the solute between the stationary and mobile phases, and it does not consider the effects of diffusional effects on column performance. The rate theory avoids the assumption of an instantaneous equilibrium and addresses the diffusional factors that contribute to band broadening in the column, namely, eddy diffusion, longitudinal diffusion, and resistance to mass transfer in the stationary phase and the mobile phase. The experimental conditions required to obtain the most efficient system can be determined by constructing a van Deemter plot. 

The major source of band-broadening in CZE is longitudinal diffusion. Longitudinal diffusion refers to the axial diffusive spreading of the solute from the solute zone into the bulk solution as it travels down the capillary. The variance in peak width contributed by longitudinal diffusion is given by... 

In capillary gel electrophoresis, one of the major contributors to band broadening, besides the injection and detection extra-column effects, is the longitudinal diffusion of the solute molecules in the capillary tube [14], The theoretical plate number (N) is characteristic of column efficiency ... 

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

Three mechanisms produce dispersion of a band of solute in a chromatographic system as it passes through the separation column 1) eddy diffusion 2) longitudinal diffusion and 3) mass transfer effects. These effects are discussed, in some detail, in this article. 

Longitudinal diffusion refers to the natural spreading of a solute band from regions of high concentration to those of lower concentration as it passes through a chromatographic system [1], It is a simple process which is dependent on the time that the solute spends on the chromatographic system, which, in turn, is related to the flow rate of the mobile phase. 

The contribution of longitudinal diffusion and other factors to band broadening in liquid chromatography can be quantitatively described by the following equation, which relates the column plate height H to the linear velocity of the solute, jU- ... 

The second term in Eq. (3), Blfi, describes the contribution of longitudinal diffusion to band broadening of the solute as it passes through the chromatographic system. This is the only term in the equation inversely proportional to the linear velocity of the mobile phase the other terms increase in value as the linear velocity increases. Giddings and others have also shown that this term is also directly proportional to the diffusion coefficient D , of the solute in the mobile phase according to the following equation, where Q is a constant [3] ... 

On the other hand, the capability of sample preconcentration for instruments such as AAS, ICP-AES, ICP-MS, and so forth was studied [3]. After metal ions were enriched, they were eluted almost simultaneously by inorganic acid at low pH, because of their diffusion in the column is at a disadvantage for improvement of the detection limits. It has been demonstrated that metal ions such as Ca, Cd, Mg, Mn, Pb, and Zn were enriched with a good recovery at a concentration of 10 ppb each in 500 mL of the sample solution. However, the final enriched sample volume eluted from the CCC column was as large as several milliliters, due to longitudinal diffusion of the sample band in the retained stationary phase [1,3]. Additional band spreading occurred in the flow tube when the concentrated solution was eluted with an acid solution for subsequent analysis. 

The mathematical description of CZE separations assumes that heat dissipation is efficient (for air-cooled systems, this means thick-walled capillaries, while water-cooled capillaries are thin walled), and that the only significant cause of band broadening is the longitudinal diffusion of solute within the capillary. 

The B term represents longitudinal diffusion of the solute band in the mobile phase and is proportional to Dm of the solute. Note that contribution from the B term is only important at very low flow rate. 

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. 

Considering a chromatographic process controlled by a partition equilibrium and neglecting extracolumn effects (i.e., band broadening caused by factors outside the column, e.g., tubings, detector etc.), several factors can contribute to the overall solute band broadening eddy diffusion, longitudinal diffusion, and resistance to mass transfer in mobile and stationary phase. 

Since it is a batch process, and the band broadens due to longitudinal diffusion as it travels down the column, it is not suitable for preparative separations. An example of its use is the work of Aaltonen in 1972 on the separation of, say, Sr from Sr on a PSS resin of small grain size (400 mesh) with elution by a-hydroxyisobutyrate solutions. The heavier isotope formed the more stable complex (the less well sorbed cation) and was enriched at the front of the band. A mathematical model for the elution separation of from by NaOH (converting NH/ in the cation exchanger to NH3 in the solution), based on the experimental results of Spedding and co-workers (1955), was recently presented by Fuji and co-workers (1997). 

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