Theory, size exclusion chromatography

Poly(ethylene oxide). The synthesis and subsequent hydrolysis and condensation of alkoxysilane-terniinated macromonomers have been studied (39,40). Using Si-nmr and size-exclusion chromatography (sec) the evolution of the siUcate stmctures on the alkoxysilane-terniinated poly(ethylene oxide) (PEO) macromonomers of controlled functionahty was observed. Also, the effect of vitrification upon the network cross-link density of the developing inorganic—organic hybrid using percolation and mean-field theory was considered. 

It took a long time before the percolation theory could be proved to be the better one in most cases. The reason for this delay resulted in part from the fact that until ten years ago the size exclusion chromatography (SEC) with on-hne light scattering was not sufficiently well developed. A direct molar mass determination is, however, imperative, since the separation in SEC is due to the hydrodynamic volume of the particles. A branched macromolecule has, however, a significantly higher molar mass than a linear one of the same hydrodynamic volume. Since 1989 a number of results have been reported which all strongly supported the percolation theory [109,111-116]. 

Since the technique was introduced (JJ in 1964, gel permeation chromatography (GPC), or size exclusion chromatography (SEC), has played an increasingly important role for the characterisation of polymers. The theory and practice of this chromatographic method have been extensively reported and a comprehensive text has recently been published on modern size exclusion chromatography (2). 

Fractionation of proteins according to size utilizing cross-linked dextran or polyacrylamide gel columns was first demonstrated by Porath and Flodin 63 in 1959. This technique has become the most widely accepted method for separation and molecular weight determination of hydrophilic and some hydrophobic macromolecules using aqueous buffers with or without organic modifier. While this technique might not be unique in its ability to resolve and separate proteins, it is one additional simple and effective tool in the chemist s armamentarium. The theories behind size-exclusion HPLC and size-exclusion chromatography at low pressure are identical and are described in several publications. 31 34 36 39 44 64 65 ... 

As the pore diameter increases in size (s decreases) relative to molecular or colloidal dimensions, less restrictions are imposed on the motions of contained species. Thus the exclusion effect gradually subsides as the pore size increases and consequently K-+1. For the separation of two molecules of different size, it is important to pick a pore diameter that will substantially exclude one species but not another. Pore size selection is thus of utmost importance in membrane science and in choosing a support for size exclusion chromatography (SEC). Aspects of pore size optimization in SEC based on the above partitioning theory have been developed [28]. 

Size-exclusion chromatography fractionation is steric, that is, dimensional. In theory, a SEC system could be calibrated by means of some appropriate standards of known dimensions and, in this way, to measure sY - SEC fractionation depends on the hydrodynamic radius Rh of the macromolecules ... 

The Soxhlet extraction method discussed in Section 6.6 can be used to separate the sol and gel fractions of a gel in the gelation regime, allowing direct determination of the gel fraction gel- Percolation theory expects the molar mass of a network strand M to be the same as the characteristic molar mass in the sol fraction. Hence, M can be determined by the size exclusion chromatography methods of Section 6.6, applied to the sol fraction. Equation (7.93) is tested in Fig. 7.19, where the shear modulus is shown to be proportional to Pgei/M. ... 

At the present time (1988), it seems that there is no satisfactory theory of the size-exclusion chromatography, perhaps only because we lack a good model. We shall begin with a summary of the classical theory and later we shall run into a difficulty when trying to interpret this theory. 

This traditional interpretation of the m-values, however, is based upon an unrealistic assumption. Experiments suggest that denatured states make compact structures, even in the presence of highly concentrated denaturants (Klein-Seetharaman et al. 2002). Therefore, the fully extended unfolded structures, which have been assumed in the previous models do not reflect reality. In addition, size-exclusion chromatography has cast doubts upon the correlation between the m-value and the expansion in size of proteins upon denaturation (Wrabl and Shortle 1999). This suggests that the SASA proportionality of the m-values may not be an accurate assumption. We therefore need a better theory. FST can hll this gap (Shimizu and Boon 2004). 

Dondi, F. Cavazzini, A. Remelli, M. Felinger, A. Martin, M. Stochastic theory of size exclusion chromatography by the characteristic function approach. J. Chromatogr. A, 2002, 943,185-207. 

Pasti, L. Dondi, F. van Hulst, M. Schoenmakers, R Martin, M. Felinger, A. Experimental validation of the stochastic theory of size exclusion chromatography Retention on single and coupled columns. Chromatographia 2003,57 (Suppl ), S171-S186. 

Gugliotta, L. Alba, D. Meira, G. Correction for instrumental broadening in SEC through a stochastic matrix approach based on Wiener filtering theory. In Detection and Data Analysis in Size Exclusion Chromatography ACS Symposium Series No. 352 Provder, T., Ed. American Chemical Society Washington, 1987 287-298. 

Song, M.S. Hu, GX. Li, X.Y. Zhao, B. Study on the concentration effects in size exclusion chromatography. Vn. A quantitative verification for the model theory of concentration and molecular mass dependences of hydrodynamic volumes for polydisperse polymers. J. Chromatogr. A, 2002, 961 (2), 155-170. 

Fleer, G.J. Skvortsov, A.M. Theory for concentration and solvency effects in size-exclusion chromatography of polymers. Macromolecules 2005, 38 (6), 2492-2505. 

To determine number and mass distributions, the heterodisperse systems are usually fractionated (e.g., by size exclusion chromatography or by sedimentation). In some cases, the distribution functions can be derived from the theory of particle preparation. 

An extensive discussion of the theoretical basis of large zone size exclusion chromatography has been published in a series of papers and review articles by Ackers and his co-workers (ref. 1-3). The goal here is not to present an exhaustive review of the theory behind this approach and the reader is referred to the references cited above. However, a brief overview of the basic principles will be given. The following discussion is a greatly simplified version of the theoretical discussion of Valdes and Ackers (ref. 2). 

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