Molar-mass exclusion limit

In this case, enthalpic interactions within the HPLC system exceed the exclusion effects (Eigure 16.3b). The retention volumes of polymer species as a rule exponentially increase with their molar masses. The limitations of the resulting procedures were elucidated in Section 16.3 the retention of (high)polymers is usually so large that these do not elute from the column (Section 16.6). Therefore, the majority of enthalpy controlled HPLC procedures is applicable only to oligomers—up to... 

Note For particles with molar mass or molecular weight larger than the exclusion limit the separation effect of the size-exclusion chromatography vanishes. 

The concentration effects. This term describes variations in Vr of the polymer samples due to changes of injected concentration, Cj. The retention volumes as a rule increase with raising Cj in the area of practical concentrations [104-107]. This is mainly due to the crowding effects when the concentration of macromolecules is high enough so that they touch each other in solution and shrink due to their mutual repulsive interactions. The concentration effects in SEC are expressed by the slopes k of the mostly linear dependences of Vr on c,. K values rise with the molar mass of samples up to the exclusion limit of the SEC column. 

While polydisperse model systems can nicely be resolved, the reconstruction of a broad and skewed molar mass distribution is only possible within certain limits. At this point, experimental techniques in which only a nonexponential time signal or some other integral quantity is measured and the underlying distribution is obtained from e.g. an inverse Laplace transform are inferior to fractionating techniques, like size exclusion chromatography or the field-flow fractionation techniques. The latter suffer, however, from other problems, like calibration or column-solute interaction. 

Size-exclusion chromatography (SEC) is a well-established method for the determination of the molar mass distribution (MMD) of polymers. However, the determination of the MMD by SEC substantially excludes ultrahigh-molar-mass (UHMM) polymers. Actually, it is well accepted that UHMM polymeric samples degrade, by shearing or elongational forces, in the SEC columns. The upper limit of the molar mass for a successful SEC fractionation without degradation of the sample depends on the broadness of the MMD of the sample, from the SEC columns used and, obviously, from the experimental conditions. Successful SEC fractionations of narrow MMD standards up to 1 X 10 g/mol of molar mass have been reported. Instead, when the MMD of the sample is broad, rarely does the molar mass of the polymeric samples exceed the upper limit of 1 X 10 g/mol. 

The molar mass varies between 122 and 1153. The 500 A column, which has an exclusion limit of around 10 and a permeation molecular mass of about 50, can separate the sugars. The first peak, starch, should be clearly resolved from the other compounds. 

In this case, the enthalpic interactions within the HPLC system exceed the exclusion effects (see Figure 3(e)). The retention volumes of polymer species as a rale exponentially increase with their molar masses. The important limitation of the resulting procedures was presented in section 11.5.2.3. The retention of (high) polymers is usually so intense that the latter do not elute from the column any more. Therefore, the majority of enthalpy controlled HPLC procedures is applicable only to ohgomers - up to molar mass of few thousands g.mol. Still, the reduced sample recovery may affect results of separation even in case of oligomers. The selectivity of enthalpy driven HPLC separation is much higher than in the case of SEC but, naturally, the sequence of molar masses eluted from the column is reversed. If the effect of enthalpy is reduced, problems with sample recovery are mitigated - but at the same time the separation selectivity is reduced. 

At equilibrium conditions, at very low concentration, the elution volume of a macromolecule should be independent of the flow rate. However, with increasing molar mass in the UHMM range, in the absence of degradation, the elution volume strongly depends on the molar mass of the sample. This result does not depend on the concentration of the sample. This retardation effect occurs also at very low concentrations below the overlapping concentration c. The retardation of UHMM macromolecules has been studied by several workers it is a very complex effect and substantially stiU not well understood. The retardation effect is particularly meaningful in proximity to the exclusion limit of the columns and when the pore size approximately equals or is lower than the sizes of the macromolecules. A trivial conclusion is that for a successful fractionation of UHMM macromolecules without retardation effects, one must use SEC columns with ultralarge pore sizes. 

Molar mass independent elution found for PS 900kD, PS 4000 kD above exclusion limit of the col-... 

Illustrative Problem. Consider a spherical solid pellet of pure A, with mass density pa, which dissolves into stagnant liquid B exclusively by concentration diffusion in the radial direction and reacts with B. Since liquid B is present in excess, the homogeneous kinetic rate law which describes the chemical reaction is pseudo-first-order with respect to the molar density of species A in the liquid phase. Use some of the results described in this chapter to predict the time dependence of the radius of this spherical solid pellet, R(t), (a) in the presence of rapid first-order irreversible liquid-phase chemical reaction in the diffusion-limited regime, and (b) when no reaction occurs between species A and B. The molecular weight of species A is MWa. 

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