Dependence of retention volume

The significant intrinsic limitation of SEC is the dependence of retention volumes of polymer species on their molecular sizes in solution and thus only indirectly on their molar masses. As known (Sections 16.2.2 and 16.3.2), the size of macromolecnles dissolved in certain solvent depends not only on their molar masses but also on their chemical structure and physical architecture. Consequently, the Vr values of polymer species directly reflect their molar masses only for linear homopolymers and this holds only in absence of side effects within SEC column (Sections 16.4.1 and 16.4.2). In other words, macromolecnles of different molar masses, compositions and architectures may co-elute and in that case the molar mass values directly calculated from the SEC chromatograms would be wrong. This is schematically depicted in Figure 16.10. The problem of simultaneous effects of two or more molecular characteristics on the retention volumes of complex polymer systems is further amplifled by the detection problems (Section 16.9.1) the detector response may not reflect the actual sample concentration. This is the reason why the molar masses of complex polymers directly determined by SEC are only semi-quantitative, reflecting the tendencies rather than the absolute values. To obtain the quantitative molar mass data of complex polymer systems, the coupled (Section 16.5) and two (or multi-) dimensional (Section 16.7) polymer HPLC techniques must be engaged. 

Starting from r = 3, there is no dependence of retention volumes on the molecular weight at critical conditions. 

In conclusion, it should be said that close to the critical conditions in a weak adsorption mode there exists a strong dependence of retention volume VR on concentration of the solute. Chromatography close to the critical conditions can, therefore, be used as a convenient method for investigating the adsorption isotherms in a weak adsorption mode, which is of the greatest theoretical interest75> and has not yet been studied experimentally. 

Figure 8.19. Temperature dependence of retention volume. Reprinted with permission from W. E. Harris and H. W. Habgood, Talanta 1964,11, 115. Copyright 1964, Pergamon Journals, Ltd.

The dependence of retention volume on temperature was illustrated in Figure 8.19. Let us determine approximately what temperature increase is necessary to cut a given retention volume in half that is ... 

SEC-LAC. To determine the molecular weight dependence of retention volume, the copolymers were fractionated by SEC into six... 

Fig.l Concentration dependence of retention volume for polystyrene in good solvents on polystyrene gel columns ... 

Zero Coverage. The peaks at Infinite dilution were slightly skewed (skew ratio 0.8), with virtually no dependence of retention volume on Injection size. Instead of the peak maximum method, retention volumes were measured by the method proposed by Conder and Young (32). To ensure that the adsorption of n-alkanes on carbon fibers was taking place under equilibrium conditions, the flow rate was varied In the range 20 to 32 cm3 min-1. The net retention volumes were essentially Independent of flow rate. 

Thus liquid chromatography makes it possible to determine the equilibrium constant at small coverage (the retention volume or Henry constant) and to characterize the compounds adsorption from multicomponent solutions. From the dependence of retention volumes on temperature the changes of enthalpy and entropy of adsorption can be calculated. 

Figure 10. Dependence of retention volume of benzene and some of its derivatives on the number carbon atoms on silica gel from water (1) and from n-hexane (2).

The non-equilibrium conditions in region II, characterized by the strong dependence of retention volumes on carrier gas flow rate, are due to the slow solute diffusion into the bulk of the polymer stationary phase. Because of the sharp decrease of diffusion coefficient as Tg is approached, the equilibrium repartition cannot be attained during the passage of the solute through the column and therefore the measured retention volumes differ from equilibrium values denoted by dotted lines in Figure 5.13. 

The peak shape and retention volumes in the non-equilibrium region depend strongly on carrier gas flow rate [161, 220]. The dependence of retention volumes on flow rate at the given temperatures for n-hexa-decane on polystyrene is shown in Figure 5.26 [161]. The linear dependence of retention volume on flow rate extrapolated to zero flow rate yields... 

If the isotherm curvatures are not too large throughout the concentration range of vapours, an empirical extrapolation to zero peak height can be made in order to obtain the retention volumes at infinite dilution [220]. This effect is more important below Tg than above Tg. The ekact dependence of retention volume on injected sample size is determined by the curvature of dissolution isotherms as well as by adsorption isotherms. 

The applicability of the additive retention theory to capillary chromatography with modified adsorbents was demonstrated for the first time in paper [125]. This work used experimental data [126] on n-hep-tane retention on an alkaline treated glass capillary column, the walls of which were coated with squalane, as reported by Bruner and Carton [126]. The dependence of retention volume on the liquid phase content was shown to be linear, being in complete agreement with additive absorption-adsorption theory. 

This mode is called liquid adsorption chromatography at the critical adsorption point (LACCC). The polymeric nature of the sample (that is, the repeating units) does not contribute to the retention of the species. Only defects (such as end groups, comonomers, branching points, etc.) contribute to the separation of the molecules. Figure 3 illustrates this behavior and shows the dependence of retention volume on the molar mass for the different modes of chromatography. 

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