Band broadening effect

In order to achieve the best efficiency the SEC column should be operated at optimized operating parameters. The most important ones are flow rate [cf. van Deemter equation for band-broadening effects (21)], sample viscosity (depends on molar mass and concentration of the sample), and injection volume (7). 

As readily observed in most chromatograms, peaks tend to be Gaussian in shape and broaden with time, where W, becomes larger with longer This is caused by band-broadening effects inside the column, and is fundamental to all chromatographic processes.The term, plate number (N), is a quantitative measure of the efficiency of the column, and is related to the ratio of the retention time and the standard deviation of... 

The concentration effects for the oligomers and also for the excluded (high) polymer species, are usually small or even negligible, k values depend also on the thermodynamic quality of eluent [108] and the correlation was found between product A2M and k, where A2 is the second virial coefficient of the particular polymer-solvent system (Section 16.2.2) and M is the polymer molar mass [109]. Concentration effects may slightly contribute to the reduction of the band broadening effects in SEC the retention volumes for species with the higher molar masses are more reduced than those for the lower molar masses. 

Vervoort, N., Billen, J., GzQ, P., Baron, G.V., Desmet, G., Importance and reduction of the sidewall-induced band-broadening effect in pressure-driven microfabricated columns. Anal. Chem. 2004, 76, 4501-4507. 

Let us consider vacant lattice site.s, which have been treated in detail by a number of workers (see, for example, Louie, Sehliiter, Chelikowsky, and Cohen, 1976 Watkins and Messmer, 1973, p. 133 and an extensive set of references given by the same authors in Messmer and Watkins, 1973). Vacant lattice sites have one electron for each hybrid, and we can expect reconstruction for the same reasons we expected it to occur in surfaces. Jahn-Teller distortion (Section 10-B) is even more certain at vacant sites than in surfaces since there are no band-broadening effects for an isolated vacancy and the Jahn-Teller theorem applies more directly... 

In low-pressure liquid chromatography, the flow rate of the mobile phase must be optimized because this influences two band-broadening effects which are dependent on diffusion of sample molecules (i) the flow rate must be slow enough to allow effective partitioning between the mobile phase and the stationary phase and (ii) it must be fast enough to ensure that there is minimal diffusion along the column once the molecules have been separated. To allow for these opposing influences, a compromise flow rate must be used. 

Numerous efforts have been made to describe the band broadening effect and the formation of the concentration profiles. The most interesting models are those that consider band broadening as a two-dimensional process. 

Fig. 1 Separation of rabbit liver metallothionein using CE-ICP-MS. The protein sample (1 mg/mL dissolved in deionized water) was first subjeeted to CZE with UV detection to optimize CE separation parameters for the major metallothionein isoforms (MT-1 and MT-2) shown in the upper panel. The CE instrument was then coupled to an ICP-MS instrument using a specially modified direct injection nebulizer (CETAC Technologies Inc., Omaha, NB) which enabled the entire capillary effluent from the CE to be directly injected into the ICP plasma torch, thus avoiding postcolumn dilution and band-broadening effects of conventional spray chamber nebulizers. Specific isotopes of cadmium ( Cd) and zinc ( Zn) associated with each isoform peak were monitored as shown by the figures in the lower panel.

Usually the retention volume is obtained using peak maxima to define the retention times. In this treatment, since bulk absorption only is assumed, band broadening effects and the existence of a non-linear sorption isotherm are not considered, as these usually reflect some surface adsorption, resulting in skewed peaks. 

Most chromatographic production systems use particulate adsorbents with defined pore structures due to the higher loadability of mesoporous adsorbents compared with non-porous adsorbents. Adsorption of the target molecules on the inner surface of a particle has a tremendous influence on the efficiency of a preparative separation. Several factors with regard to mass transfer that contribute to the total band broadening effect in addition to axial dispersion can be distinguished (Fig. 2.10) ... 

As already mentioned, the effects of several parameters are often lumped into one (see also Section 6.5.3.1). In this case, all band broadening effects are included in a dispersion coefficient. The so-called apparent dispersion coefficient Dapp is used here to distinguish from the axial dispersion coefficient, Dm, which is assumed to be independent of concentration and only influenced by the quality of the packing. The lumped parameter Dapp includes peak broadening effects caused by the fluid dynamics of the packing (axial dispersion), as well as by all other mass transfer effects that might occur, and was first introduced by van Deemter et al. (1956). 

Band broadening effects such as dispersion and mass transfer resistance are represented by the number of tanks (or stages) N. This can be explained by evaluating the moments of the analytical solution of Eq. 6.96. For linear isotherms and the injection... 

As the ideal model does not take any band broadening effects into account, safety margins have to be considered when applying this method for the layout of SMB separations. 

In HPLC peak dispersion is significantly affected by the particle size of the resin. Thus, the band broadening in a suppressor column decreases as the particle diameter of the employed resin decreases. Similarly, the void volume of the suppressor column should be as small as possible to reduce band broadening effects. An optimal suppressor column would therefore have a very low volume and would contain an exchange resin with a very small particle diameter. Both requirements are inconsistent with the analytical practice, which calls for a suppressor column that can be employed at least for one working day without regeneration. This requirement can only be met by suppressor columns with a higher volume. 

The sharp concentration fronts shown in Fig. [4.1-2 and 14.1-3 never occur in practice. The zones are always diluted and broadened by mass transfer and dispersion for both linear and nonlinenr isotherms. The complete solution of (he equilibrium equations, mass balances, and mass transfer equations for nonlinear systems is a formidable task requiring numerical solutions. For I incur systems the task is much easier and very useful solutions have been developed. Even thongh large-scale chromatography often is operated in the u out inear range, the linear analyses are valnable siace they can provide a qualitative feel (quantitative for linear systems) for band broadening effects. 

Other band-broadening effects derive from the fact that solute species in the same flow path will not all move with the same velocity (those in the center will move faster than those at the edge) and that the particle structure may contain pores or eddies of nonmoving mobile phase out of which solute particles must diffuse in order to return to the main flow of mobile phase. 

The sfff technique is versatile it can be used to study both soUds and solutions, no standards are required for cahbration, and it is a nondestmctive technique. Low shear forces are employed and minimal absorption occurs. Hence, sample degradation does not take place. The technique cannot, however, be routinely used for molecular weight characterization of small molecules. Newer variations of sfff include the development of thermal fff (73), whereby a temperature gradient is placed between two parallel metal blocks to allow the particles to migrate toward the wall. This approach is said to allow for the molecular weight characterization of polymeric materials which are much smaller in molecular size. Advantages of this technique over gpc He in the absence of conventional band broadening effects. 

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