Small-molecule band broadening

Knox parameters, 218, 304- 303 small-molecule band broadening and, 212-214... 

B is rate of diffusion of the molecule in the liquid phase which contributes to peak broadening through diffusion either with or against the flow of mobile phase the contribution of this term is very small in liquid chromatography. Its contribution to band broadening decreases as flow rate increases and it only becomes significant at very low flow rates. 

In the absence of interferences, arises from the absorption spectrum of the test species. For atoms and certain molecules, the absorption spectrum consists of individual lines or small groupings of lines in which each line is described by a Voigt-type profile. For most molecules, pressure broadening causes a merging together of the lines into absorption bands. The absorption coefficient for an individual line may be written as... 

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

In cases where mass transfer is rapid, as is the case with most small molecule separations, then isocratic elution can offer advantages such as automatic fraction reprocessing and solvent recycle. However, with larger synthetic objectives the rate of mass transfer is comparatively low so isocratic elution leads to band broadening and subsequently to recovery of the peptide at high dilution. Most preparative HPLC based peptide separations are carried out under gradient and overload conditions that allow for maximum throughput in terms of time and quantity. 

Polymer-based adsorbents are not widely used in the HPLC analysis of small molecules, mainly because of the presence of micropores in the structure of polymer resins [29]. These micropores may trap small molecules, and their relatively slow diffusion leads to signihcant band broadening and overall loss of separation efficiency. 

The porosity of particles suitable for packing HPLC columns depends on the size of molecules to be separated. Totally porous particles with a pore size of 7-12 nm and specific surface area of 150-400 m"/g are suitable for the separation of small molecules, but wide-pore particles with a pore size of 15-100 nm and relatively low specific surface area (10-150 nr/g) are required for the separation of macromolecules to allow easy access to the interactive surface within the pores. Packings with perfusion particles contain very broad pores (400-800 nm) throughout the whole particle interconnected by smaller pores. The mobile phase flows through the pores in the particle, which minimises both band broadening and column backpressure (111. Perfusion materials have been designed especially for the separation and isolation of biopolymers. 

In 1957 Marcel Golay published a paper entitled Vapor Phase Chromatography and the Telegrapher s Equation [Anal. Chem., 29 (1957) 928]. His equation predicted increased number of plates in a narrow open-tubular column with the stationary phase supported on the inner wall. Band broadening due to multiple paths (eddy diffusion) would be eliminated. And in narrow columns, the rate of mass transfer is increased since molecules have small distances to diffuse. Higher flow... 

The peak recorded in a chromatogram represents the distribution of molecules in a band as it elutes from the column, the overall broadness being conveniently m sured in terms of the width of the peak. A number of independent factors such as sample-injector and detector characteristics, temperature and column retention processes, contribute to the dispersion of molecules in a band and band broadening. The cumulative effect of small variations in these factors is described in statistical terms as the variance, cr, in the elution process. Classical chromatography theory considers that the separation process takes place by a succession of equilibrium steps, the more steps in a column the greater the column efficiency with less band broadening (variance) occurring, therefore... 

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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