## Separation Mechanisms

Many attempts have been made to explain the mechanism of separation in SEC but steric exclusion (or size exclusion) is accepted to be the main process governing the separation. This mechanism is based on a thermodynamic equilibrium between stationary and mobile phases. As the nature of the solvent is the same in both phases, the question is to explain the dependence of the distribution coefficient Ksec on the size of the separated species. One of the simplest approaches uses the above-mentioned geometrical models; nevertheless, the retention volume is determined not only by the accessibility of a part of the volume of the individual pores but also by the size distribution of the entire system of pores in the column packing material. The distribution coefficient for an individual pore depends on the ratio of the pore size to the size of the separated particles and can be expressed by:

-^sec where the concentrations cp and co refer to the pores and the interstitial volume. If the pore size distribution of the column packing particles is taken into consideration, the retention volume is given by:

K(R, r)^(r) dr where <(r)dr is the total volume of the pores whose radii lie within r and r + dr, and R is an equivalent radius of the retained particles. Hence, the retention volume of a given particulate species is determined coincidentally by the accessibility of a part of the volume of the individual pores and by the size distribution of the entire system of pores inside the column packing particles. Although different column packings exhibit almost identical dependences of VR on separated particles size, porosimetric measurements indicate various pore size distributions. This means that the relationship between the pore size distribution and the retention volume of the separated species is not so straightforward.

An interesting model of separation by flow was proposed by Di Marzio and Guttman. The porous

o structure of the SEC column packing is approximated by a system of cylindrical capillaries. The separated species move down the pores by the action of the flow but cannot get nearer to the pore wall than a distance determined by their radius. Consequently, they move at a velocity higher than the average velocity of the liquid flow due to a parabolic flow-velocity profile established in an imaginary cylindrical pore. Hence, the retention is determined by the ratio of the pore to the particle diameter. There are several factors that militate against this separation mechanism. The model assumes that the liquid can flow through the pores, which will not be true in most cases with polymeric gel particles used as column packing materials. Moreover, even in those cases when the pores are open to through flow, their diameter in comparison with the size of the interstitial voids cannot allow the flow rate to be high enough to explain the real values of the retention volumes. For the same reason, the frequently used explanation of the SEC mechanism of separation by an oversimplified model of molecular sieving is not accurate. This model, however, explains quite well the separation of large particles in hydrodynamic chromatography where either very large open pores are present in the particles of column packing or the packing particles are not porous and the separation by flow is performed in the interstitial volume only.

More complicated mechanisms based on the interactions between the separated species and the stationary phase may occur in an SEC column in addition to the steric exclusion mechanism: adsorption, liquid-liquid partition, electrostatic repulsions between the separated particles and the packing material, etc. The pure SEC separation mechanism can be operating only if the column packing material and the solvent are chosen to suppress these secondary effects. If the distribution coefficient Ksec is larger than 1, it is certain that other interactions, e.g., adsorption, beside the steric exclusion mechanism come into play and increase the retention. Unfortunately, if Ksec lies between 0 and 1, it does not mean that secondary interactions are definitely not interfering. Although such interactions are secondary, they can either improve or worsen the resulting separation. From the thermodynamic point of view, the separation is carried out near equilibrium conditions and the distribution coefficient can be described by:

Dawkins and Hemming considered the enthalpic term on the right-hand side of this equation as a distribution coefficient, the value of which is unity, provided that size exclusion is the only effective mechanism. In such a case, the entropic term represents the pure size-exclusion mechanism. If other attractive interactions come into play AH° becomes negative and, if some repulsive interactions are involved, AH° is positive.

Other mechanisms explaining the separation in SEC have been proposed but most of them apply exclusively to the separation of macromolecules. The details can be found in the specialized literature. The above-presented approaches give an accurate basic idea of the separation of particles by SEC.

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