Polymer characterization number-average

Polymer Characterization. Number average molecular weights (M ) of polymers were determined using an automatic membrane osmometer (Shell Development Design) in toluene solution at 35.5 C. Membranes (Sartorious MembranfiIter, SM 11539) were cautiously conditioned from ethanol into methyl ethyl ketone and finally toluene. Weight... 

This result shows that the square root of the amount by which the ratio M /M exceeds unity equals the standard deviation of the distribution relative to the number average molecular weight. Thus if a distribution is characterized by M = 10,000 and a = 3000, then M /M = 1.09. Alternatively, if M / n then the standard deviation is 71% of the value of M. This shows that reporting the mean and standard deviation of a distribution or the values of and Mw/Mn gives equivalent information about the distribution. We shall see in a moment that the second alternative is more easily accomplished for samples of polymers. First, however, consider the following example in which we apply some of the equations of this section to some numerical data. 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

In addition, the intercept obtained by extrapolating this asymptote back to sin (0/2) = 0 equals (2M )". Note that both Mand are number averages when this asymptotic limit is used. This is illustrated schematically in Fig. 10.15 and indicates that even more information pertaining to polymer characterization can be extracted from an analysis of the curvature in Zimm plots. 

The number average molecular weights, Mq, of the polymers obtained in Table II ranged from 1300 to 3900 as determined by vapor nressure osmometry (VPO), and they were further characterized by - -H- and C-NMR spectrometry at ambient temperature and at 90°C, as well as by IR spectroscopy. The homopolymers of isopropenylferro-cene were found to have the expected structure, P, shown below, obtained by polymerization through the isopropenyl units, as indicated by spectroscopic characterization ... 

It should be noted that the product of a step polymerization is a mixture of polymer molecules of different molecular weights. The molecular weight distribution is characterized by the number-average and weight-average degrees of polymerization, X and Xw> respectively, defined by... 

A given polymer is characterized by its number-average molecular weight (Mn), together with its weight-average molecular weight (Mw), which can both be obtained by analytical techniques. 

Here, /u ° and ju are, respectively, the chemical potentials of pure solvent and solvent at a certain concentration of biopolymer V is the molar volume of the solvent Mn=2 y/M/ is the number-averaged molar mass of the biopolymer (sum of products of mole fractions, x, and molar masses, M, over all the polymer constituent chains (/) as determined by the polymer polydispersity) (Tanford, 1961) A2, A3 and A4 are the second, third and fourth virial coefficients, respectively (in weight-scale units of cm mol g ), characterizing the two-body, three-body and four-body interactions amongst the biopolymer molecules/particles, respectively and C is the weight concentration (g ml-1) of the biopolymer. 

The concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

Anionic polymerizations, when carried out in aprotic solvents, are characterized by the long lifetime of the carbanionic (or oxanionic) sites l2). When neither spontaneous transfer nor termination reactions are involved, the polymers obtained exhibit sharp molecular weight distributions, and their number average degree of polymerization is determined by the [Monomer]/[Initiator] molar ratio, provided initiation is fast as compared to propagation. However, the major advantage of these methods, as far as synthesis is concerned, is the socalled living character of the polymers 12) After completion of the polymerization the active sites retain their reactivity and can be used for functionalizations at the chain end. 

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