Polydispersity value

The polydispersity of melt-phase samples is generally lower than that of solid-state samples. Gel permeation chromatography (GPC) analysis of samples prepared from the solid-state showed polydispersity values in the range of 2.57 to 2.84 compared to 2.27 to 2.49 for melt samples [107], The higher polydispersity of solid-state samples can largely be explained by the non-uniformity in the average molecular weight across the pellet radius caused by a SSP reaction rate that is diffusion controlled [11],... 

An interesting feature of this enzymatic polymerization in [BMIM]PF6 is that the polymeric material exhibited remarkably narrow polydispersity values, Mw/Mn = 1.04-1.03, a value that was maintained in the seven-day test. The authors related this value to the insolubility of the polymer formed in the ionic liquid after it exceeds a certain molecular weight limit. This observation opens the possibility of tailoring ionic liquids with varying solvating abilities for structural manipulation of desired polymeric material. 

Since no adequate SEC standards were available, linear polystyrene was used as standard. As expected, the determined molar masses were not in agreement with the theoretical molar masses. This could be explained by the differences in hydro-dynamic volume between linear polystyrene standards and the dendritic polyesters. SEC analyses showed polydispersity values (A/ /M ) below 1.02 for dendrimers Dl, D2, and D3, which was the maximum resolution of the column (Table 2, Figure 4). 

Very precise appraisals of polydispersities due to branch defects can be made by HPLC fractionation, electrophoresis and mass-spectral analyses of the components. The molecular-mass and polydispersity values thus obtained, corroborate branch-defect ranges determined by high-field 13C-NMR spectroscopy. 

As in so many things in this field, if you want to work through the arguments yourself, you cannot do better than go to Flory— see Principles of Polymer Chemistry, Chapter EX. Stockmayer s equation illustrates the point we wish to make with dazzling simplicity as f the number of branches, increases, the polydispersity decreases. Thus for values of/equal to 4, 5 and 10, the polydispersity values are 1.25, 1.20 and 1.10, respectively. Note also that for / = 2, where two independent chains are combined to form one linear molecule (Figure 5-28), the polydispersity is predicted to be 1.5. Incidentally, an analogous situation occurs in free radical polymerization when chain termination is exclusively by combination. 

The ratio of weight average to number average molecular weight is called the polydispersity, ra. The wider is the molecular weight distribution the higher the polydispersity value. The ra for unimolecular polymer is equal to 1. All natural polymers, such as peptides, DNA, and saccharides, have polydispersity equal to 1. 

In living polymerization processes it is in fact possible to adjust the final degree of polymerization by simply tuning the initiator amount while keeping narrow the chain length distribution (CLD), i.e. with polydispersity values lower than 1.3 (this quantity reflects the broadness of the final CLD typical minimum values in FRP range from 1.5 to 2). Also, by suitable selection of chemistry and structure... 

Figure 6.2 (a) Average DP and polydispersity value versus conversion for bulk living polymerization of styrene by RAFT (b) corresponding gel permeation chromatogram. Reaction conditions T = 80 °C initiator, AIBN RAFT agent, Z = Ph, R = CH(CH3)Ph (cf. Scheme 6.4) styrene RAFT agent initiator = 600 4 1 (w/w)... 

Only a few papers have appeared dealing with LRP by DT [8], and the applications are almost completely limited to the homopolymerization of styrene. In this case, it was possible to obtain good control of the final CLD, with polydispersity values as low as 1.3-1.4. Better performances are difficult with styrene, mainly because of the limited transfer activity of the iodine atoms. This is the main reason for the very poor results obtained when applying this process to the polymerization of acrylates (e.g. n-butyl acrylate) and for the complete lack of control reported for other monomers [8]. 

On the other hand, by fractionating isotactic polypropylene prepared in the presence of hydrogen with a-TiCl3—A1(C2H5)3, Pegoraro found polydispersity values lower than those observed by other researchers in the absence of hydrogen. 

Concerning the production of narrow MWD polyethylene, suitable for injection molding, the most commonly used method seems to be that based on catalyst chemical composition control (often by introducing electron-releasing ligands, i.e. alkoxides, on the transition metal compound). In this way minimum polydispersity values could be obtained (Q approximately 3 or even lower), a rather noteworthv result if one remembers that the catalytic systems dealt with are heterogeneous. 

Fig. 2 Thermal FFF elution profiles before (original) and after (corrected) removing the effects of band broadening. With the poly disperse sample (NBS 706), which was analyzed at a flow rate of 0.4 mL/min, the effect of band broadening on the elution profile is minimal. The polydispersity values listed were determined using thermal FFF.

A final and important observation must be made concerning molecular weight results. Ideally the polydispersity (Mw/M0) of these samples should be close to 2.0. Indeed this was found in most samples with two remarkable exceptions. A decrease of catalyst content in the M-B-40/15-49 and M-E-23/25-48 series lead to higher polydispersity values. The uncatalyzed sample of the M-E-23/25-48 series for instance had a polydispersity of 8.0. Moreover, the GPC traces in these materials indicated the presence of shoulders. Upon close examination, at least one of the shoulders could be assigned to the polyol originally used in the composition, as seen in Figure 15 for the M-E-23/25-48-70-00 sample. Similar results were observed for the M-B-40/15-49-70-05 sample. 

Fairly close polydispersity values of polymer samples prepared in the presence of complexes 1 and 2 having different structures may be explained by the transformation of exo-nido complex 1 into its closo isomer 2, which is known to proceed in high yield at 80 °C 14). This transformation does not occur for the more sterically hindered C,C-dimethyl-substituted exo-nido complex 7, and, in this case, a polymer with a higher polydispersity index (M /Mn = 1.93) is formed. This finding indicates that the propagation step and the molecular-weight characteristics of PMMA are affected by both steric and stractural features of the rathenacarborane catalysts. 

Because the pKa of p-methoxyphenol allows a full deprotonation by potassium ferf-butoxide, it is suggested that the propagation results from nucleophilic attack of the phenoxide on an intermediate quinodimethane formed by dehydrohalogenation of the monomer. Polymerization under these conditions is found to yield polymers with very low polydispersity values. ... 

The most frequently apphed technique for the separation of polymers, namely size-exclusion chromatography (SEC), is based on the well-balanced interactions between the column material, the solvent, and the polymer sample. In order to achieve a complete separation according to size, and also to determine reliable polydispersity values, enthalpic interactions between the sample and column material must be excluded, as only entropic interactions lead to SEC separation. This is not always possible in the case of dendritic polymers which, being multifunctional architectures, have interactions with the column material that are effectively predestined. It has been repeatedly observed that this problem is more severe for higher molar mass products. An example of aromatic hb polyesters with different... 

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