Molecular weight distributions for

The molecular weight distribution for a polymer like that described above is remarkably narrow compared to free-radical polymerization or even to ionic polymerization in which transfer or termination occurs. The sharpness arises from the nearly simultaneous initiation of all chains and the fact that all active centers grow as long as monomer is present. The following steps outline a quantitative treatment of this effect ... 

In addition, subsequent chain transfer reactions may occur on side chains and the larger the resulting polymer, the more likely will it be to be attacked. These features tend to cause a wide molecular weight distribution for these materials and it is sometimes difficult to check whether an effect is due inherently to a wide molecular weight distribution or simply due to long chain branching. 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

The poly(styrene-b-isoprene) (P(S-b-IP)) and poly(-styrene-b-2-vinyl pyridine) (P(S-b-2VP)) block copolymers with narrow molecular weight distributions for blending with the microspheres were also synthesized using the additional anionic polymerization technique. The number-average molecular weights (Mns) and PS contents are also shown in Table 1. 

Figure 7.4 Molecular weight distributions for HEA BA S copolymer prepared...

Saito et w/.217 -19 have examined the polymerization of multimethacrylates prepared from p-cyelodextrin. Polymerization using ATRP conditions gave a bimodal molecular weight distribution for the derived PMMA composed predominantly of oligomers of 7 or 14 units indicating that there was little intcrmolccular reaction... 

Figure 9.8 Comparison of molecular weight distributions for a conventional and RAFT polymerization. Data shown arc GPC distributions (upper trace) for PS prepared by thermal polymerization of S at 110°C for 16 h (Mn 324000, / Mn...

The mixing speed had little or no signficant effect on the monomer conversions or the shape of the molecular weight distributions for mixing speeds of 500 rpm or greater. 

Example 13.4 Calculate the molecular weight distribution for a self-condensing polymerization with — + Stop the calculations... 

Molecular weight distribution for a polymer that has a polydispersity of 1.05. 

Molecular Weight Distributions. The CSTRs produce the narrowest possible molecular weight distributions for fast chain growth, short chain lifetime... 

Good agreement between the experimental and model generated molecular weight distribution for an initiator concentration of 0.9 wt. % and a temperature of 200°C. However, under these conditions the degradation reactions were likely complete by the reaction time of 18.6 s. 

Fig. 56.—Molecular weight distributions for multichain polymers for the several values of / indicated, as calculated from Eq. (22 ). Number averages for the different distributions are identical. (Schulz. )...

Fig. 60.—Molecular weight distribution for thermally polymerized polystyrene as established by fractionation. (Results of Merz and Raetz. o)...

The critical conditions for the formation of infinite networks will be discussed at the outset of the present chapter. Molecular weight distributions for various nonlinear polymers will then be derived. Experimental data bearing on the validity of the theory will be cited also. 

MALDI does not replace chromatography (e.g. SEC) for molecular weight distributions. For PD >1.4 it is necessary to separate in order to reduce the polydispersity. Chromatography is needed to enhance MALDI. 

The second new program allows the user to compare the shapes of molecular weight distributions. For example, if we have the cumulative distribution of hydrodynamic volume for two polymers we can plot the hydrodynamic volume corresponding to the 10th percentile of the distribution for polymer A against the similarly defined hydrodynamic volume for polymer B. Such a plot, made for the entire distribution of both polymers, is called a "quantile... 

These initiators may be used in the presence of protic sources such as MeOH.780 The rapid and reversible exchange of propagating alkoxides with alcohol leads to a narrow molecular weight distribution (for example, Mw/Mn<1.15 for oligomeric PCL), with the number of polymer molecules closely approaching the sum of the number of molecules of initiator and alcohol. In the absence of alcohol, the polymerization of CL is less well behaved with Mw/Mn= 1.5, presumably a consequence of unfavorable initiation and propagation rates. 

Table 1 Key parameters of the molecular weight distribution for three samples of PpPTA polymer from which yarns have been spun. Mz is the z-average molecular weight [52]...

The theoretical lower limit of the molecular weight distribution for the diblock OBC is 1.58. The observed MJMn of 1.67 indicates that the sample contains a very large fraction of polymer chains with the anticipated diblock architecture. The estimated number of chains per zinc and hafnium are also indicative of a high level of CCTP. The Mn of the diblock product corresponds to just over two chains per zinc but 380 chains per hafnium. This copolymer also provides a highly unusual example of a polyolefin produced in a continuous process with a molecular weight distribution less than that expected for a polymer prepared with a single-site catalyst (in absence of chain shuttling). 

The equations relating Mn and Mw to radiation dose which are most frequently used apply to all initial molecular weight distributions for Mn, but only to the most probable distribution (Mw/Mn = 2) for Mw. However, equations have been derived for other initial distributions, especially for representation by the Schulz-Zimm distribution equation. 

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