Molar mass-functional type distribution

Due to the fact that different end groups can be formed during the polycondensation, the reaction products may exhibit a functionality-type distribution in addition to the molar mass distribution. Although SEC is suitable to analyze the molar mass distribution, it does not yield information on different end groups. For the determination of the functionality-type distribution, other types of liquid chromatography must be used. 

The structural complexity of synthetic polymers can be described using the concept of molecular heterogeneity (see Fig. 1) meaning the different aspects of molar mass distribution (MMD), distribution in chemical composition (CCD), functionality type distribution (FTD) and molecular architecture distribution (MAD). They can be superimposed one on another, i.e. bifunctional molecules can be linear or branched, linear molecules can be mono- or bifunctional, copolymers can be block or graft copolymers, etc. In order to characterize complex polymers it is necessary to know the molar mass distribution within each type of heterogeneity. 

When functional homopolymers are synthesized, in addition to macromolecules of required functionality, functionally defective molecules are formed (see Fig. 4). For example, if a target functionality of f = 2 is required, then in the normal case species with f = 1, f = 0 or higher functionalities are formed as well [7], Deviation of the average functionality from the pre-assigned one may result in a decreased or increased reactivity, cross-linking density, surface activity etc. Each functionality fraction has its own molar mass distribution. Therefore, to fully describe the chemical structure of a functional homopolymer, the determination of the molar mass distribution (MMD) and the functionality type distribution (FTD) is required. 

Heterogeneous or complex polymers are distributed in more than one molecular parameter. For functional homopolymers one has to deal Avith the overlapping effects of molar mass distribution and functionality type distribution, whereas copolymers are distributed at least in molar mass and chemical composition. For many years, detector development and the use of several detectors attached to SEC have been the major thrusts in chromatographic analysis of complex macromolecules. In particular, the combination of a refractive index and an ultraviolet detector has been used extensively, although only a limited number of polymers is UV active. Therefore the application of this technique is certainly not universal. On the other hand, SEC has its merits in the daily routine because it is simple, fast, and very reproducible. 

Despite these obstacles, LC-NMR systems are increasingly available and increasingly applicable to real problems. SEC-NMR canbe used to establish accurate MMDs for relatively low-Mr polymers by online measurement of the number-average molar mass (Hatade etal, 1988 Ute et al, 1998). However, SEC//MALDI seems to be a more attractive option for this application. Determination of the chain regularity is a strong aspect of NMR (see also Section 7.4.2.1) and in combination with LC or SEC, tacticity distributions can be determined (Kitayama et al, 2000 Ute et al, 2001). The chemical heterogeneity of high-conversion poly[styrene-co-ethyl acrylate] (Kramer etal, 1999) and the functionality-type distribution of low-molar-mass polyethylene oxide (Pasch 8c Hiller, 1999) were studied by online SEC-NMR. 

Note 1 An infinite number of molar-mass averages can in principle be defined, but only a few types of averages are directly accessible experimentally. The most important averages are defined by simple moments of the distribution functions and are obtained by methods applied to systems in thermodynamic equilibrium, such as osmometry, light scattering and sedimentation equilibrium. Hydrodynamic methods, as a rule, yield more complex molar-mass averages. 

Using the traditional methods of polymer analysis, such as infrared or nuclear magnetic resonance spectroscopy, one can determine the type of monomers or functional groups present in the sample. However, the determination of functional end groups is complicated for long-chain molecules because of low concentration. On the other hand, these methods do not yield information on how different monomer units or functional groups are distributed in the polymer molecule. Finally, these methods do not in general provide molar mass information. 

Using appropriate analytical methods, the type and concentration of the different functionality fractions must be determined and, within each functionality, the molar mass distribution has to be obtained. To do this, two different methods must be combined, each of which is preferably selective towards one type of heterogeneity. For example, a chromatographic method separating solely with respect to functionality could be combined with a molar-mass-selective method. Another approach would be the separation of the sample into different molar mass fractions which are then analyzed with respect to functionality. 

As has been demonstrated, the combination of selective separation techniques with powerful spectroscopic detectors enables complex polymers to be analyzed with respect to all possible types of molecular heterogeneity. Chemical composition distribution can be monitored across the molar mass distribution. Steric and functional peculiarities can be detected over the entire molar mass range. 

As heterogeneous polymers are distributed in more than one molecular parameter, more than one chromatographic separation technique must be used. For functional homopolymers evidence is first obtained that the optimum separation protocol includes liquid chromatography at the critical point of adsorption as the first dimension of separation, yielding fractions which are homogeneous in functionality. When these fractions are subjected to any molar mass sensitive separation technique, MMD for each functionality fraction, and therefore the complete FTD-MMD relationship, is obtained. Two-dimensional separations of this type are very much susceptible to automation, as has been shown by Much et al. [88] and Kilz and coworkers [89-91]. 

In synthesizing polymers in vivo and in vitro, molecular homogenous ( monodisperse ) polymers (i.e., those in which every macromolecule has the same molar mass or molecular weight ) occur only under quite specific conditions. The overwhelming majority of polymer syntheses proceed more or less randomly, and the resulting macromolecular substances have more or less broad molar mass distributions. The kind of molar mass distribution obtained depends on the nature of the polymerization, which may be either thermodynamically or kinetically controlled. Each kind of distribution is characterized by a definite relationship between the mole fraction x and the degree of polymerization X. Consequently, it is possible in many cases to deduce the kind of polymerization involved from the type of distribution function obtained. 

The analyses were performed on a Polymer Lab apparatus, equipped with five ultraStyragel Waters columns (in the order 1000, 500, 10000,100, and 100000 A pore size) attached in series, using a Polymer Lab differential reffactometer. The solvent was THF or CHCI3, the flow rate was 1 mL/min, and 60 microliters of polymeric solution (15 mg/ml) were injected. Normally 50 fractions of 0.2 mL were collected. In the case of sanq)le M30, four different fractionation experiments were performed, and 50 fractions of 0.2 mL, 25 fractions of 0.4 mL, 15 fractions of 0.8 mL, 15 fractions of 1 mL were collected The chromatogram was calibrated using the result of the analysis of MALDI-TOF spectra of selected fractions (see Tables 1 and 2). The average molar masses (Mn and Mw) of the copolymer were measured using the Cahber software distributed by Polymer Lab. The type of calibration selected by us was a narrow standards the calibration function was polynomial of order 1 and the calculation method was area based. ... 

For the (rare) cases that the distribution function of an unknown polymer sample is known (for example from the type of synthesis), the molar mass or... 

The properties of polycarbonate beside its molar mass distribution (D=Mw/Mn) depend often of type and amount of end groups, cycles, additives and branch. In particular the end chains constitute the fingerprints of its polymerization procedure, of its thermal and mechanical history and of their environmental use. Several tools such as NMR, FT-IR and Mass Spectrometry were used to determine these peculiar characteristics of PC. In particular the matrix assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF MS) has successfully been applied to obtain these information (49,50). MALDI-TOF technique is able to look each molecule even in a complex mixture (51-53), to obtain information on the end groups and structure (linear, cyclic or branched) of the macromlecular chains as a function of the synthesis and processing conditions. 

The chromatogram was calibrated using the result of the analysis of MALDI-ToF spectra of selected fractions (see Table 5.1). The average molar masses (number average molecular weight (M ) and MJ of the copolymer were measured using the Caliber software distributed by Polymer Lab. The type of calibration selected by Montaudo and co-workers [10] was a narrow standards the calibration function was polynomial of order 1 and the calculation method was area based . 

The A2 + B3 polymerization was carried out at different molar ratios of A2 and B3 monomers (A2 B3 = 1 1, 3 2, 2 1, and 3 1). The molar masses of polymers obtained by the A2 + B3 approach were lower = 2,500-68,000 Da, as recorded by refractive index detector) than those of AB2 polymers (37 = 47,000-660,000 Da, as recorded by light scattering detector) due to the off-stoichiometric functional ratios. For AB2-type polymerization, a higher molar mass was attained at longer reaction times. All the AB2 polymers showed a bimodal weight distribution whereas all the polyphenylenes derived from the A2 and B3 monomers showed a... 

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