Molar mass dispersity index

Dispersity is an appropriate word to describe a numerical attribute of the dispersion of a distributiondispersion of a distribution. The use of the term polydispersity index or other words involving the word polydispersity is strongly discouraged [09IUP1]. The general symbol Dj, pronounced D-stroke , is introduced for molar mass dispersity. 

In an attempt to better control both molar masses and the dispersity in polycondensates, a new concept of polycondensation has been recently proposed that proceeds in a chain polymerization manner (Chapter 8). In a context where monomers would have little option but to react first with an initiating site and then with the polymer end-group and would be prevented from reacting each other, all the requirements would be met to bring about so-called chain-growth polycondensations. Under such conditions, the polycondensate would increase linearly with conversion and be controlled by the [monomer]/[initiator] ratio and its mass dispersity index would be close to unity. 

The experimental dependence M = /(V), i.e. the classical SEC calibration curve usually obtained by using narrow standards, in such a case can be obtained directly without calibration from the on-line LS detector. By combining the experimental function M = /(V) and the concentration profile (from DRI), one can construct the complete MMD of the HA sample. The differential and cumulative MMD of a high molar mass HA sample (Mw = 652 kDa, D = 2.1) are shown in Fig. (10). Starting from the initial MMD, the molecular weight averages and dispersity index (Mn, Mw, Mz, and D) could be easily calculated using the appropriate definitions. 

It has been noted (Odian, 1991) that the steady-state approximation cannot be applied in many cationic polymerizations because of the extreme rate of reaction preventing the attainment of a steady-state concentration of the reactive intermediates. This places limitations on the usefulness of the rate expressions but those for the degree of polymerization rely on ratios of reaction rates and should be generally applicable. The molar-mass distribution would be expected to be very narrow and approach that for a living polymerization (with a poly-dispersity index of unity), but this is rarely achieved, due to the chain-transfer and termination reactions discussed above. Values closer to 2 are more likely. 

Mono-disperse fractions of molar masses 200000 and 400000 g mol are added to the polymer of example 3.1 so that the ratios of the numbers of chains, in order of increasing M, become 1 1 2 1 Calculate the number-average and weight-average molar masses of the resulting polymer and hence show that the polydispersity index has increased. 

Fig. 16 Overall conversion versus (a) time and (b) number-average molar mass, M , and poly-dispersity index, A/w/Afn (the line represents the theoretical M ) for the nitroxide-mediated surfactant-free emulsion copolymerizations of methyl methacrylate and styrene in the presence of poly(PEGMA-ct>-MAA-co-styrene)-SGl macroalkoxyamines of different molar masses triangles 9400, and squares 44(X)gmol ) [145]...

The studied triblock copolymer PS-PVP-PEO was purchased from Polymer Source (Dorval, Canada). The number-average molar masses of PS, PVP, and PEO blocks were 2.1 x 10 , 1.2 x 10 , and 3.5 x 10 g mol , respectively, and the poly-dispersity index of the sample was 1.10. The copolymer is insoluble in aqueous media, but the micelles can be prepared indirectly both in acidic and alkaline aqueous solutions by dialysis from 1,4-dioxane-methanol mixtures [88]. The micelles can be transferred from acidic to alkaline alkaline solutions and vice versa, but the addition of a base together with intense stirring promotes aggregation. Two factors contribute to the destabilization of micelles after the pH increase (a) In alkaline media, the PVP blocks become insoluble, collapse and form an upper layer of the core. Since the cores of micelles are kinetically frozen, the association number does not change. The mass of insoluble cores increases, while the length of soluble shellforming chains decreases, which results in a deteriorated thermodynamic stability of micellar solutions, (b) The PVP middle layer shrinks and PEO chains come close to each other, which worsens the solubility due to insufficient solvation of PEO blocks. 

The dispersity index can vary from unity for perfectly nondispersed samples ( isometric systems) up to several tens for samples characterized by a strong dispersion in the size or molar mass of the constituting macromolecules (highly dispersed systems). 

When p increases, one can observe that the molar mass distribution, which is best expressed by the polymolecularity (dispersity) index Dm = Mw/M , tends to widen. 

Conventional step-growth polymerizations occurs in the initial phase through con-densation/addition of monomers with each other and then proceeds via reactions of all size oligomers with themselves and with monomers. In such a process the precise control of the polycondensate molar mass is elusive—in particular, in the initial and intermediate stages where only oligomers are formed. The polycondensate molar mass indeed builds up only in the final stage and its dispersity index increases up to 2. 

The base serves to abstract a proton from the monomer and generate an aminyl anion, which in turn deactivates its phenyl moiety. This anion reacts preferentially with the phenyl ester group of phenyl-4-nitrobenzoate and the amide group formed has a weaker electron-donating character than the aminyl anion of the activated monomer. The reaction of monomers with each other was thus efficiently prevented so that well-defined aromatic polyamides could be obtained up to 22,000 g/mol molar mass and with a dispersity index of 1.1. 

The living polymerization of strained three- and four-membered monomers typically provides polymers with a narrow molar mass distribution, best described by the Poisson function [91], for which the dispersity indexes (D = DP jDP = M /M ) assume values in the range -1.25 > D > 1, depending on the polymer chain length (Equahon 1.24). As discussed earlier, the polymerization of these monomers is essentially irreversible. 

The formation of Sn(ll) alkoxide from Sn(Oct)2 and an alcohol is a reversible reaction. Although the rates of exchange and the position of equilibria have not yet been established, the activation-deactivation reactions must be relatively rapid since, for up to -80% of the monomer conversion at 80°C in THF solvent the MvtjMn dispersity index is less than 1.2 [169], while the molar masses of polyester can be predicted from the ([Mjo- [M])/[ROH]o ratio [162, 163]. The influence of this interconversion on the polymerization kinetics can be approached in two ways, as shown in Scheme 1.4. 

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