The Number Average Molecular Weight Mn

The example of the random polycocondensation may be discussed in some detail. Let a be the reaction probability for a functional group in the A2 monomer, and fi the corresponding probability of a B-group in the B monomer. We have now to distinguish 

These matrices have to be inserted into Eq. (C.lll) from which by the use of Eq. (B.22a) or Eq. (B.22b) the mean-square radius of gyration can be calculated, and from Eq. (B.56) to Eq. (B.58) the dynamic scattering behavior and the apparent diffusion coefficient. 

For comparison with experiment and for numerical calculations, the values of the various link probabilities a, p, p and q must be known. They can be determined as follows  

In practice, p is adjusted in the numerical calculations until the calculated Mapp agrees with the measured one. All other quantities, for instance the molecular-weight dependence of (S2)z, or the shape of the scattering curve, and the whole dynamic scattering behaviour, are now fully determined if the effective bond length is known. 

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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. 

The number average molecular weight (Mn) is calculated from Eq. 1.1. 

Living" carbocationic polymerizations are most difficult to achieve mainly because of chain transfer to monomer and termination processes both of which frequently occur in carbocationic polymerizations. It has recently been demonstrated (JL) that "quasiliving" polymerization of a-methylstyrene (aMeSt) can be achieved by slow and continuous monomer addition and that the number-average molecular weight (Mn) of PaMeSt increases linearly with the weight of added monomer. A theory for quasiliving polymerizations has been developed (2). 

Assuming perfect living polymerization in which all polymer chains are induced to initiate the simultaneous propagation of chains without any termination and chain transfer reactions, in such idealized scenarios, the number-average molecular weight, Mn, can be estimated using... 

Fig. 5. Polymerization of tcrt-butyl methacrylate ( BMA) initiated with (TPP)AlMe (1, X= Me) via an enolatealuminum porphyrin (2, R= Bu) in the presence of trimethylaluminum (Me3Al) [ BMA]o/[l (X=Me)]o=100, [l]o=17.8mM, CH2CI2 as solvent, rt. Correlations of the number-average molecular weight (Mn) and the ratio of the numbers of polymer molecules to 2 (Np/ATxpp) with the initial mole ratio of Me3Al to 2...

It is possible to calculate the number average molecular weight, Mn, using carbon-13 NMR (Table 13.2) [26,29,30], These data compare well with those obtained from gel permeation chromatography (GPC). 

About 25 years ago, F. T. Wall proposed such a method, which depended on the measurement of the so-called partial conversion molecular weight (I). If N is the number of polymeric molecules and W the weight of polymer, then the number average molecular weight Mn is given by W/N, from which it is easy to show... 

Gel permeation chromatography is an attractive technique for the determination of the number average molecular weight (Mn) distribution of petroleum fractions, especially the heavier constituents, and petroleum products (Altgelt, 1968 Oelert, 1969 Altgelt, 1970 Baltus and Anderson, 1984 Hausler and Carlson, 1985 Reynolds and Biggs, 1988). 

As in the case of terpyridine-based polymers, we first reported the application of Zn(II) Schiff base polymers in PLEDs.33 We prepared a family of soluble self-assembled Zn(II) Schiff base polymers, which are thermally stable, structurally diverse and easily modified (Fig. 17). The number-average molecular weight (Mn) of the polymers range from 13580 to 20440, as determined using gel permeation chromatography (GPC) with polystyrene as a standard in THF (tetrahydrofuran) at 35°C. The decomposition temperature (Td) of the polymers range from 389° (2g) to 461°C (2h). No phase transition was observed in DSC up to 300°C for these polymers (Table 4). 

In Table I we list the specimens that were prepared in conjunction with this study, giving the number-average molecular weight (Mn) and weight percent (W.) of the PMMA present in the initial PMMA/S mixture and an indication of the opacity of the final system. 

Figure 7.55. Reaction scheme for the room-temperature synthesis of a CBABC pentablock copolymer, and GPC traces of a,z-dibromo-terminated polystyrene (A, dotted line), poly(fBA-fe-styrene-fe-fBA) (BAB triblock copolymer macroinitiator, dashed line), and poly(MMA-fe-fBA-fe-styrene-fe-f BA-fe-MMA) (CBABC, solid line). The GPC data shows evidence of a successful polymerization route - low polydis-persity index (PDI), and good control over the number-average molecular weight (Mn). Reproduced with permission from Ramakrishnan, A. Dhamodharan, R. Macromolecules 2003, 36, 1039. Copyright 2003 American Chemical Society.

The oxidative chain scission of PVC is better illustrated in Figure 3 depicting the decrease of the number average molecular weight (Mn) of PVC samples as a function of reaction time. As shown in this Figure, significant decrease of M takes place in a short period of time followed by slower Mn... 

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