Exclusion effects

Schaaf P and Talbot J 1989 Surface exclusion effects In adsorption processes J. Chem. Phys. 91 4401-9... 

We can imagine the coil tightening up as this point is approached from better conditions. This is not a shrinking to the vanishing point as suggested by the u = 0 criterion, but a contraction to the point where intramolecular exclusion effects are offset by shrinkage. 

Except for the high molecular weight range, nearly all substances can be separated by reversed-phase (RP) HPLC. The many different separation mechanisms in RP HPLC, based on hydi ophobic, hydi ophilic and ion-pairing interactions, and size exclusion effects together with the availability of a lai ge number of high quality stationary phases, explain its great populai ity. At present approximately 90% of all HPLC separations are carried out by reversed-phase mode of HPLC, and an estimated 800 different stationai y phases for RP HPLC are manufactured worldwide. 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

Nonionic polysaccharides are one of the most simple substances to analyze by size exclusion chromatography because they seldom exhibit nonsize exclusion effects. Due to their wide molecular weight distribution, TSK-GEL PW columns are recommended for their analysis. 

Nonionic samples can generally be analyzed vithout an adjustment of the pH or the salt concentration of the mobile phase. However, many typical samples are ionic or ionogenic. Under these circumstances, the addition of salt to the mobile phase is often required to prevent exclusion effects that are not related to the size of the analyte molecule. Ultrahydrogel columns are compatible with a broad range of salt and buffer solutions. Recommended compositions can be found in Table 11.6, but a broader range of buffers can be used. 

TTiis ion exclusion effect can sometimes be exploited beneficially. For example, by purposefully choosing a column with some carboxyl groups and a pH that ionizes them (greater than approximately 6.5), it may allow separation of a charged and an uncharged polymer that have the same hydrodynamic size. Alternatively, one may be able to fine-tune elution of a polymer by adjusting pH. 

The major advantage of the capillary hydrodynamic chromatography is that the mobile phase does not need to have similar solubility parameter as the sample and packing material. (In SEC, nonsize exclusion effects may be observed if the solubility parameter of the sample, packing material, or mobile phase is considerably different.) Therefore, the hydrodynamic size of polymers can be studied in a 0 solvent and even in a solvent that is not compatible with any currently available SEC packing material (9). Figure 22.4 is an example of polystyrene separation in both THF and diethyl malonate. Diethyl malonate is the 0 solvent of polystyrene at 31-36 C. 

As in SEC, the surface chemistry of the HdC gels should be similar to that of the mobile phase and the solute. Otherwise, the retention time may increase as with the nonsize exclusion effects. However, the tolerance of PCHdC for a poorer mobile phase is better than SEC. The polymer size under 0 conditions has been studied using PCHdC (19). 

Another advantage of HdC is its generosity in terms of mobile-phase selection. The polymer size and solution properties of a polymer can be studied using HdC, especially OTHdC, in almost any solvent. In SEC, by comparison, the packing material and mobile phase have to be selected to prevent the nonsize exclusion effect. Because the instrumentation of HdC is similar to SEC, and the packing material and columns have become available commercially, this technique will gain in popularity. 

If exclusion effects are ignored or the solutes (A) and (B) have approximately the same molecular size then... 

The activity of a-chymotrypsin was found to be insensitive to the R value, i.e., from the size of the reversed micelles. This was taken as an indication that this enzyme is able to create its own micelles in the hydrocarbon rather than occupy empty ones and that the so-called exclusion effect, i.e., protein larger than the empty micelle cannot be solubilized, is incorrect [181,182],... 

To ensure a better separation, molecular sieving will act much better This size exclusion effect will require an ultramicroporous (i.e pore size D < 0.7 nm) membrane Such materials should be of course not only defect-free, but also present a very narrow pore size distribution. Indeed if it is not the case, the large (less separative and even non separative, if Poiseuille flow occurs) pores will play a major role in the transmembrane flux (Poiseuille and Knudsen fluxes vary as and D respectively). The presence of large pores will therefore cancel any sieving effect... 

Existing SEC retention theories have been independently developed for each of the molecular-shape models shown in Figure 1. The deep hollow cyclin-drical pore in the figure (A, B, and C) illustrates the SEC exclusion effect on three types of solute molecules, hard-sphere, rigid-rod, and random-coil, respectively. The individual theories and their bases of commonality are now reviewed briefly. 

Figure 1. Exclusion effect in cylindrical cavities (1) ((A) hard sphere of radius r (B) thin rod of length Li in two orientations in the plane of the cross section (C)...

The exclusion effect of hard-spheres is illustrated in Figure lA., which shows a spherical solute of radius r inside an infinitely deep cylindrical cavity of radius a. Here the exclusion process can be described by straightforward geometrical considerations, namely, solute exclusion from the walls of the cavity. Furthermore, it can be shown thatiQJ... 

The exclusion effect of a rigid-rod in the same cylindrical pore is shown in Figure IB., where the length of the rod is L,. Quantifying the exclusion process here is much more complicated than in the hard sphere case. Exclusion of the rod depends on the rod orientation in three dimensions and statistical methods must be used for the evaluation. For rigid-rods it has been shown that Kg is described... 

Figure 2. Theoretically predicted size exclusion effects of different solute types (cylindrical pores of single pore size). (O) random coil (Rg) (%) hard sphere (R, = r VIJJ) CA rod (R, = L, VIT)...

Silica gels with mean pore diameters of 5-15 nm and surface areas of 150-600 m /g have been preferred for the separation of low molecular weight samples, while silica gels with pore diameters greater than 30 nm are preferred for the separation, of biopolymers to avoid restricting the accessibility of the solutes to the stationary phase [15,16,29,34]. Ideally, the pore size distribution should be narrow and symmetrical about the mean value. Micropores are particularly undesirable as they may give rise to size-exclusion effects or irreversible adsorption due to... 

Many synthetic water-soluble polymers are easily analyzed by GPC. These include polyacrylamide,130 sodium poly(styrenesulfonate),131 and poly (2-vinyl pyridine).132 An important issue in aqueous GPC of synthetic polymers is the effect of solvent conditions on hydrodynamic volume and therefore retention. Ion inclusion and ion exclusion effects may also be important. In one interesting case, samples of polyacrylamide in which the amide side chain was partially hydrolyzed to generate a random copolymer of acrylic acid and acrylamide exhibited pH-dependent GPC fractionation.130 At a pH so low that the side chain would be expected to be protonated, hydrolyzed samples eluted later than untreated samples, perhaps suggesting intramolecular hydrogen bonding. At neutral pH, the hydrolyzed samples eluted earlier than untreated samples, an effect that was ascribed to enlargement... 

In the absence of any nonsize exclusion effects or branching effects, the concentration distribution within the chromatographic peak describes the polymer molecular weight distribution. The concentration distribution is deduced from the response of a suitable detector. Detectors which respond to physicochemical properties other than concentration may also be of use in GPC. Over the past 25 years, a variety of detectors have been developed. This section reviews detectors available to the chromatographer. The detectors used in GPC can be grouped as... 

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