Molar mass fractionation

The linear column (PSS SDV 5 /mm linear) has a wider molar mass fractionation range while keeping the analysis time roughly the same. Therefore the slope of the calibration curve is much steeper and the resolution will be poorer in this case. The second column with a single pore size (PSS SDV 5 /mm 1000 A) separates only below 50,000 Da, but does this very efficiently in the same time. 

Monodisperse polymers for this purpose may be obtained from commercial suppliers, but they are expensive and for many polymers not available in sufficiently narrow molar mass fractions. For this reason, the not very satisfactory procedure is sometimes adopted of calibration with polystyrene, since this polymer can be relatively easily prepared in discrete, monodisperse fractions using anionic polymerisation. The unknown polymer is then... 

Elemental molar mass = (Fractional abundance) (Isotopic molar mass)... 

Membrane osmometry measurements were carried out with the capillary osmometer shown in Figure 3. Owing to the short equilibration time of the instrument and the low cut-off molar mass of the membrane, solute permeation through the membrane, which would show up as a drift of the baseline, did not cause problems even for the lowest molar mass fraction. M was obtained from... 

The mechanism and kinetics of RAFT-SIP were studied by Fukuda et al. [326]. Besides the expected linear increase of the molecular weight of the surface grafted polymer with the monomer conversion, they observed the appearance of a prominent low molar mass fraction which was attributed to a combination reaction of the propagating active chains. 

Its related value was originally denoted as X- Numerous % values in terms of volume fractions are collected in Ref. [37]. Unfortunately the scatter in % values found in the literature is large as they reflect also both the polymer source (e.g., narrow molar mass fractions or anionically prepared samples) and the method of measurement, for example, light scattering, osmometry, or inverse gas chromatography. The interaction parameters g (%) for the polymer-good solvent systems assume values between 0 and 0.5 [37]. 

It was shown that high molar mass lignosulfonate compounds can be fractionated by RPC into hydrophilic and hydrophobic compounds. It can be seen from Figures 4 and 5 that the birch lignosulfonates with low molar mass (fractions B and C in Figure 1) were also fractionated into hydrophilic and hydrophobic portions with no clearly resolved peaks. 

According to Scheme 13 a benzyl derivative of Nd is formed. At a polymerization temperature of 60 °C the benzyl Nd intermediate once formed decomposes rapidly as Nd(benzyl)3 is reported to be stable only below - 15 °C [425,426]. As a consequence of the low thermal stability of the Nd benzyl species proton transfer from toluene is irreversible and the overall rate of polymerization is reduced by the decrease of the amount of the active catalyst species. As TBB lacks benzyl protons it can only act as a 7r-donor. Therefore, TBB reduces the polymerization rate to a lower extent than toluene. Beside the interpretations given, the study also presents detailed investigations on the evolution of the MMDs with monomer conversion in the three solvents n-hexane, TBB, toluene [422]. In the two aromatic solvents a high molar mass fraction is more pronounced than in n-hexane. 

The dependence of Mn on monomer conversion for the system NdV/ DIBAH/EASC is more complex than one would expect from the Mv/tempera-ture plot given in Fig. 8. As shown in Fig. 9 straight Mn-conversion dependencies are only obtained at polymerization temperatures > 40 °C. At low polymerization temperatures (20 °C) and at low monomer conversions (< 50%) a high molar mass fraction causes significant deviations from the straight line which is expected for a living polymerization. 

Figure 10 shows that the share of the high molar mass fraction decreases with increasing polymerization temperature. 

A serious contradiction with the requirements of a strictly Uving polymerization are broad or even bimodal MMDs which are in the focus of many studies, e.g. [87,178,620]. This observation of broad and at least bimodal MMDs is the result of the presence of at least two active catalyst species which show different activities. This feature is in contradiction with a strictly living polymerization. Wilson attributed the polymer fraction with a high molar mass to insoluble catalyst species which are invisible to the naked eye whereas the low molar mass fraction of the polymer is supposedly produced by soluble sites which operate in a quasi-living manner [89]. In his study Wilson used catalyst systems of the type Nd(carboxylate)3/DIBAH/tBuCl. 

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. 

The inadequacy of using SEC without further precaution for the determination of MMD of polymer blends or copolymers can be explained with reference to Fig. 5 [24]. For a linear homopolymer distributed only in molar mass, fractionation by SEC results in one molar mass being present in each retention volume. The polymer at each retention volume is monodisperse. If a blend of two linear homopolymers is fractionated, then two different molar masses can be present in one retention volume. If a copolymer is now analyzed, then a multitude of different combinations of molar mass, composition, and sequence length can be combined to give the same hydrodynamic volume. In this case, fractionation with respect to molecular size is completely ineffective in assisting the analysis of composition or MMD. 

Low molar mass fractions polymer molecules may not adopt random coil conformation, the Mark-Houwink coefficients become functions of molar mass. 

Other examples of successful combinations of liquid chromatography and MALDI-TOF have been reported by Kruger et al. who separated linear and cyclic fractions of polylactides by LC-CC [184]. Just et al. were able to separate cyclic siloxanes from linear silanols and to characterize their chemical composition [185]. The calibration of an SEC system by MALDI-TOF was discussed by Mon-taudo et al. [186]. Poly( dimethyl siloxane) (PDMS) was fractionated by SEC into different molar mass fractions. These fractions were subjected to MALDI-TOF for molar mass determination. The resulting peak maximum molar masses were... 

The composition of the figurative point M in the A-B-C system can be read, for example on the A-B axis, where the first section represents the molar (mass) fraction of the component B, the second one represents the molar (mass) fraction of the component C, and the third one is the molar (mass) fraction of the component A. 

Of the three popular methods of v-determlnatlon the sessile drop Is the slowest, the pendant drop faster and the spinning drop the most rapid ( S). For commercial resin pairs the first two may require days before the drop reaches Its equilibrium shape. During this time there Is diffusion of the low molar mass fractions toward the interface gradually decreasing the value of the Interfacial tension coefficient (36). These two factors, the normal stress and the time scale, are generally responsible for the poor correlation between the predicted and measured droplet diameters in commercial blends. 

Compared with phagocytosis, fluid-phase pinocytic capture of molecules is relatively slower, being directly proportional to the concentration of macromolecules in the extracellular fluid. It is also dependent on the size of macromolecules in general, lower molar mass fractions are captured faster than the higher molar mass fractions. The magnitude of the rate of capture by adsorptive pinocytosis is higher than that by fluid-phase pinocytosis and relates to the nature of substrate-membrane interactions. 

Complex Percentage of the total metal in the low molar mass fraction... 

As a first step to solve part of these problems, better quantitative data, using well defined polymers in narrow molar mass fractions are needed, combining steady state and time-resolved experiments. 

It is also possible to determine by H NMR the relative importance of some existing triads [166]. The H NMR results obtained for the three studied fractions are given in Table 8.3. Fraction 2, with an intermediate molar mass fraction exhibits a head-to-head coupling... 

Besides the Wurtz-coupling reaction, other synthetic routes towards non-branched polysilanes have been reported, which overcome the drawbacks of polymodal molar weight distribution and low yield of the high molar mass fraction. However, so far the application of these routes has been very limited. The anionic ring opening polymerization of the strained 1,2,3,4-tetramethyl-1,2,3,4-tetraphenylcyclotetrasilane leads to poly(methylphenylsilane) in high yield but the starting cyclotetrasilane has to be prepared in three steps from diphenyldichlorosilane via octaphenylcyclotetrasilane [84] ... 

Most other liquid polymers are expected to show similar behavior, with the higher molar mass fractions having very low solubility in SCCO2. Lower fractions of PDMS are quite soluble, but again the higher fractions are not. Garg et al. [31] reported that PDMS-308 000 is essentially insoluble. Unfortunately, there are few or no solubility data for other liquid polymers in CO2. 

This polymer was also characterised by SEC. Its bimodal molar mass distribution pointed to a significant contribution from the cyclic polysiloxane fraction. The dialysis of this polymer in water permitted the separation of cyclics into the lower molar mass fraction, while the linear polymer constituted the higher molar mass fraction. The gel chromatograms of both these fractions were also compared. The two-step dialysis performed for the precursor and biocidal polymer led to a narrow polydispersity of the former, MW / Mn = 1.21 [95]. 

According to recent investigations, cluster formation and bound solvent have to be considered, which will influence the phase behavior considerably. Also, the interpretation of careful measurements has to take into account the fact that a high molar mass fraction mixed into the sample will not turn into a liquid crystal, and a too low molar mass fraction may have an influence on the clearing temperature, as shown in Fig. 16. 

El-Aasser et al. [20] studied the difference between batch and semi-continuous polymerization of VAc and determined that batch polymerization produced a narrower molar mass distribution than the semi-continuous process. The semi-batch polymerization produced a high molar mass fraction which was attributed to CTP due to monomer-starved conditions. 

However, a major limitation of this model is the impossibility of fitting cloud-point curves for polydisperse systems. Moreover, it cannot deal with the fractionation effect accompanying phase separation, i.e. the dispersed phase will be enriched in the highest molar-mass fractions of modifier but in the lowest molar-mass fractions of the growing thermosetting polymer. This may produce variations in stoichiometry and conversion between both phases. These phenomena can be conveniently treated taking polydispersity of constituents into account. 

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