Dispersity of molar mass

Table 4.1.5 Polymer properties and processing in dependence on dispersity of molar mass distribution (based on [llMen])...

Dispersions of molar mass distributions depend on polymerization reactions (see Table 4.1.6). Values of Dm close to 1 can be achieved by cmitrolled or living techniques whereas free radical polymerization leads to broad distributions. 

DISPERSITY OF MOLAR MASSES-AVERAGE MOLAR MASSES 3.4.1. Dispersity ... 

The most practical representation of the dispersity of molar masses is shown in Figure 3.7, which consists in plotting either the number (Ni) of moles of species corresponding to a degree of polymerization (Xi) or their mass (A jAf, ), versus either the degree of polymerization (Xi) or the corresponding molar mass (Af,). This representation of Ni =f(Xi or Mi) affords a curve that gives information about the numeral distribution of chains. 

DISPERSITY OF MOLAR MASSES - AVERAGE MOLAR MASSES... 

In the case of controlled free radical polymerizations (see Section 7.5.8), the initiation period is short compared to that of propagation and all the chains created grow simultaneously at the same rate. The polymer formed under such conditions exhibits a narrow dispersity of molar masses corresponding to a Poisson distribution (see Section 8.4). 

Owing to their propensity to self-organize in mesophases, block copolymers exhibit specific features and properties that are exploited at industrial level. The morphology of these mesophases depends primarily, among other parameters, on the nature of the comonomers and the relative length of the blocks, on the dispersion of molar masses, on the possible presence of residual homopolymers, and on the overall architecture of the copolymer (including more than two blocks, star block copolymers, etc.). It is thus essential to precisely control these structural parameters, and living and/or controlled polymerizations are particularly suitable for their synthesis. 

For a polymer consisting of molecules all of the same molar mass = M, but in all other cases, is greater than M . We can thus use the ratio of to Mjj as an indication of the spread of molar masses in a particular polymer sample. This ratio is called the polydispersity of the polymer where M Mjj = 1 the sample is said to be homo- or mono-disperse. 

Method by which the distribution of the concentration of the solute or dispersed component in a dilute solution or dispersion along the centrifuge cell is measured at sedimentation equilibrium, and the results are interpreted in terms of molar masses or their distribution, or both. 

M. Netopilik, Correction for axial dispersion in gel permeation chromatography with a detector of molar masses, Polym. Bull. 7 575 (1982). 

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. 

A thorough understanding of the reaction kinetics of VAc and its comonomers is important to fully comprehend and enhance the polymer chemist s chances to make a VAc latex tailored for a specific end-use. To this end recent advancements in initiator types, new concepts in undostanding of molar mass development and copolymerization kinetics are reviewed. Particle size, size distribution and the morphology of latexes are also presented. Hnally, film foimaticHi, dispersion stabilization and advances in high-performance VAc copolymer latexes employing branched esters are discussed. 

However, if we consider an extended mass range, these conditions are certainly not met by any MS technique of current use. The most notable case where it is necessary to consider the intensities of peaks spanning over a wide range of mass numbers is the determination of molar masses in poly-disperse polymers (see Chapter 2). 

Since the development of soft ionization mass spectrometry [9], which allows to analyze large organic molecules without fragmentation, various polymer architectures were characterized by mass spectrometry. In principle, different parameters tailoring polymeric material properties such as molar mass (MJ, architecture (linear, branched, cyclic, star, etc.), monomer composition, degree of functionalization, end groups, and the presence of impurities or additives can be evaluated by mass spectrometry, however, with some limitations. The determination of molar masses of polymers by mass spectrometry is only possible for reasonable low dispersity polymeric architectures, which can be achieved by using controllable polymerization techniques such as anionic or... 

With the development of controlled radical polymerization techniques like nitroxide-mediated radical polymerization (NMRP), atom transfer radical polymerization (ATRP), and reversible addition fragmentation chain transfer (RAFT) polymerization (see Section 3.2), the field of linear glycopolymers has significantly flourished, especially as control of molar mass and monomer sequence has become available, even for functionalized monomers. This enables incorporation of new and more complex glycomonomers as well as allows controlled dispersity, end group functionality, and monomer sequences in block, star-shaped, and graft copolymers, and eventually... 

The molar mass dispersity is the best known of all dispersities in moleeular char-acteristies of synthetie polymers and it is most frequently determined. Assessment of dispersities in ehemieal straeture and in physieal arehiteeture is much more demanding. Let us stress again that molar mass dispersity fairly affects numerous utihty properties of industrial polymers. The width of molar mass dispersity is usually expressed with the ratio of particular molar mass averages. This is habitually sufficient for a sound estimate of suitabihty of particular polymer for most particular applications. Molar mass dispersity function quantitatively reflects amount of macromolecules with certain molar mass present in the sample. It can be represented in the integral or in the differential form. The latter possesses a more informative nature and it is more frequently used. 

Considering molar mass of a polymer, amount of macromolecules with given molar mass M. can be expressed by their number N. or by their mass MN.. Hence the molar mass dispersity function is a relation between the number fractionp. or the mass (weight) fraction q. and logarithm of molar mass M. of particular macromolecules. It holds for the number fraction p. 

The ratio A//A/ is called polydispersity (the previously used term was poly-molecularity) of a polymer and it gives important information on the width of its molar mass dispersity. Less frequently, the viscosity average molar mass, A/, and the artificial z and z+1 averages of molar mass. A/ and Af are considered. M is defined... 

Schematic representation of a dispersity function of molar mass is depicted in Figure 1.

FIGURE 1 Typical courses of molar mass dispersity functions, a, b, c—differential, and d- integral representation a- broad molar mass dispersity polymer b-narrow molar mass dispersity polymer c- polymer with bimodal dispersity. 

Distinct shapes of molar mass dispersity functions exist for synthetic polymers of different origin log normal, Schultz-Zimm, and so on. Graphical representations of quantitative dispersity functions are less commonly employed than simple ratios Af/Af otM/M. ... 

Often, size exclusion chromatograms (SEC) (compare section 11.7, Size Exclusion Chromatography) of polymers under study are expressed as differential representations of molar mass dispersity. The chromatographic retention volumes are directly transformed into the molar masses. This approach renders useful immediate information about tendencies of molar mass evolution in the course of building or decomposition polyreactions but the absolute values of molar mass can be only rarely extracted from it. As a rale, polystyrene calibrations are applied for molar mass calculation so that one deals with the polystyrene equivalent molar masses, not with the absolute values. The resulting dispersity (distribution) functions may be heavily skewed because the linear part of the calibration dependence for the polymer under study may exhibit well different slope compared with the polystyrene calibration, which was employed for the transformation of retention volumes into molar masses. 

SIMULTANEOUS DETERMINATION OF DISPERSITY IN MOLAR MASS AND IN CHEMICAL STRUCTURE OR IN MOLECULAR ARCHITECTURE... 

SEC is presently the most important method for separation and moleeular characterization of synthetic polymers. The method enjoys enormous popularity and most institutions involved in research, production, testing and apphea-tion of synthetie polymers are equipped at least with a simple SEC instrument. Size exclusion chromatograms are often directly transformed into the molar mass dispersity functions (compare section 11.3.3, Molar Mass Dispersity). Often, the molar mass data presented are not absolute, beeause polystyrene or other polymer standards distinct from polymer under study have been employed for the column calibration (see sections 11.6.3 and 11.7.3.1). Still, the data equivalent to the polymer applied to the column cahbration, more or less precisely represent the tendencies of molar mass evolution in the course of building-up or decomposition polyreactions. 

The ratio of [tj]/[tj]0 is called the viscosity expansion factor a. The viscosity-averaged molar mass (A/ ) obtained from the MHSS equation may also be used to get information about the degree of molar mass dispersion from the comparison of the M values of a polymer sample in two different solvents [5,6],... 

The ability to prepare a series of sharp fractions (i.e. fractions with a dispersity as close to unity as possible) of a variety of molar masses is vital in order to investigate how a number of properties of a polymer scale as a frinction of chain length [35]. 

Although molecular shape and other factors must always be considered in determining the magnitude of dispersion forces, molar mass can act as a guide when comparing dispersion forces within a family of similar elements or compounds as shown in Figure 11.6 t. 

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