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Molar mass distribution function

Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Dembcing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref la). [Pg.2207]

Due to the statistical character of the polymer forming reactions, macromolecules are not identical. The macromolecules differ in their molar masses, in the sterically arrangement, and in case of copolymers, in their chemical compositions, and so on. Because of the influence of the molecular structure on the properties, all properties of a polymer must show a distribution. The measuring procedures can only determine a mean value of a distribution curve. The mathematical nature of the mean value depends on the physical basics of the measuring procedure. It is necessary to determine not only a mean value of the property, but also the distribution function of the interesting property. The most important distribution for homopolymers is their molar mass distribution function. [Pg.57]

Marano and Holder have calculated the VLE of the Fischer-Tropseh system. The pseudo-components were defined with the aid of an analytical molar-mass distribution function (Anderson-Schulz-Flory distribution). The properties of a pseudo-component were based on a hypothetical model component in each carbon-number cut. [Pg.283]

For a typical condensation polymerisation, the molar mass distribution function is generally in the range 3—20, but is sometimes even greater. On the other hand, in vinyl polymerisation the values typically wiU be in the range 1.05—3.0. The narrowest molar mass distributions are observed with anionic and certain cationic initiated polymerisations. Molar mass effects are observed with aU polymer systems but they are more important in the physical properties of amorphous polymers than in their crystalline analogues. [Pg.16]

Rather than leading to polymers with a unique degree of polymerization, reactions usually result in a mixture of macromolecules with various molar masses. Therefore, for a full characterization, the molar mass distribution function has to be determined, and this is usually accomplished by gel permeation chromatography. We choose the symbol M for the molar mass and introduce the distribution function p M) as a number density, adopting the definition that the product... [Pg.2]

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. [Pg.23]

State-of-the-art polymeric materials possess property distributions in more than one parameter of molecular heterogeneity. Copolymers, for example, are distributed in molar mass and chemical composition, while telechelics and macromonomers are distributed frequently in molar mass and functionality. It is obvious that n independent properties require n-dimensional analytical methods for accurate (independent) characterization of the different structural parameters. [Pg.387]

Due to the fact that different end groups can be formed during the polycondensation, the reaction products may exhibit a functionality-type distribution in addition to the molar mass distribution. Although SEC is suitable to analyze the molar mass distribution, it does not yield information on different end groups. For the determination of the functionality-type distribution, other types of liquid chromatography must be used. [Pg.408]

Reaction mechanisms and molar mass distributions The molar mass distribution of a synthetic polymer strongly depends on the polymerization mechanism, and sole knowledge of some average molar mass may be of little help if the distribution function, or at least its second moment, is not known. To illustrate this, we will discuss two prominent distribution functions, as examples the Poisson distribution and the Schulz-Flory distribution, and refer the reader to the literature [7] for a more detailed discussion. [Pg.211]

In Ref. [107] it has been demonstrated how, based on the scaling law for the diffusion coefficient, molar mass distributions can be calculated from time correlation functions obtained from scattering experiments. [Pg.243]

The more time-consuming task is the establishment of the scaling law, which requires a series of polymer samples of narrow molar mass distribution and known molar mass. Their sedimentation coefficients have to be measured as a function of concentration and extrapolated back to c — 0 in order to obtain So(M) (Figure 18). [Pg.246]

The melt flow index is a useful indication of the molar mass, since it is a reciprocal measure of the melt viscosity p. p depends very strongly on 77 ( ) (doubling of results in a 10.6 times higher 77 ). This relation is valid for the zero-shear viscosity the melt index is measured at a shear stress where the non-Newtonian behaviour, and thus the width of the molar mass distribution, is already playing a part (see MT 5.3.2). The melt index is a functional measure for the molar mass, because for a producer of end products the processability is often of primary importance. [Pg.11]

In this contribution, the experimental concept and a phenomenological description of signal generation in TDFRS will first be developed. Then, some experiments on simple liquids will be discussed. After the extension of the model to polydisperse solutes, TDFRS will be applied to polymer analysis, where the quantities of interest are diffusion coefficients, molar mass distributions and molar mass averages. In the last chapter of this article, it will be shown how pseudostochastic noise-like excitation patterns can be employed in TDFRS for the direct measurement of the linear response function and for the selective excitation of certain frequency ranges of interest by means of tailored pseudostochastic binary sequences. [Pg.6]

Once the scaling relation of Eq. (39) is known, the molar mass distribution can, at least in principle, be obtained from a Laplace inversion of the multi-exponential decay function as defined in Eq. (40). At this point, the differences between PCS and TDFRS stem mainly from the different statistical weights and from the uniform noise level in heterodyne TDFRS, which does not suffer from the diverging baseline noise of homodyne PCS caused by the square root in Eq. (38). [Pg.28]

A step-growth polymerization (with or without elimination of low-molar-mass products) involves a series of monomer + monomer, monomer + oligomer, monomer or oligomer + macromolecule, and macromolecule + macromolecule reactions. The molar mass of the product grows gradually and the molar mass distribution becomes continuously wider. Functionalities of monomers and the molar ratio between coreactive sites are the main parameters for controlling the polymer structure. [Pg.18]

Sample molecules that are too large to enter the pores of the support material, which is commercially available in various pore dimensions, are not retained and leave the column first. The required elution volume Ve is correspondingly small. Small molecules are retained most strongly because they can enter all the pores of the support material. Sample molecules of medium size can partly penetrate into the stationary phase and elute according to their depth of penetration into the pores (Fig. 7.3). No specific interactions should take place between the molecules of the dendrimer sample and the stationary phase in GPC since this can impair the efficiency of separation by the exclusion principal. After separation the eluate flows through a concentration-dependent detector (e.g. a UV/VIS detector) interfaced with a computer. One obtains a chromatogram which, to a first approximation, reflects the relative contents of molecules of molar mass M. If macromolecules of suitable molar mass and narrow molar mass distribution are available for calibration of the column, the relative GPC molar mass of the investigated dendrimer can be determined via the calibration function log(M) =f( Vc). [Pg.257]


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See also in sourсe #XX -- [ Pg.12 ]




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