Hydrodynamic molecular weight distribution

Let us analyze isothermal polymerization in a tubular reactor of finite length. The formulation of the hydrodynamic problem is based on some obvious assumptions  

Then we can use the following system of equations (reduced to dimensionless variables) to describe the flow in a tubular reactor l l 

Solving the system of Eqs (4.15) - (4.16) allows us to find the velocity and degree of conversion distributions for the stationary state. 

Now we shall discuss the method used to calculate the cup -averaged MWD-H, in which all portions of a polymerized liquid are mixed and averaged in a cup (vessel) positioned after the reactor. In this analysis, recourse was made to the so-called suspension model of a tubular reactor. According to this model, the reaction mass is regarded as an assemblage of immiscible microvolume batch reactors. Each of these microreactors moves along its own flow line. The most important point is that the duration of the reaction is different in each microreactor, as the residence time of each microvolume depends on its position at any given time, i.e., on its distance from the reactor axis. 

The radial distributions of velocity and degree of conversion in each section of the reactor, including the outlet section, are time-independent, as we are considering a steady state working apparatus. Therefore we can find the volume dW, which flows out of the reactor through a layer of the width dr (the subscript showing that r is a dimensionless value is omitted) at a distance r from the axis  

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Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

Size exclusion chromatography (SEC) separates molecules of a polymer sample on the basis of hydrodynamic volume. When the chromatograph is equipped only with a concentration-sensitive detector, i.e. conventional SEC, a molecular weight distribution (MWD) can be obtained from the chromatogram only through use of a calibration function relating molecular weight and elution volume V (2). 

The molecular weight distributions were determined only in terms of the polystyrene equivalent from the polystyrene calibration of the GPC columns. This can only be regarded as semiquantitative, as the method determines only the relative hydrodynamic volumes. If the polysilane chain was significantly stiffer than polystyrene, the molecular weights would be estimated too high. If the chains are... 

Size exclusion chromatography (which is also known as gel permeation chromatography) is based on the premise that a polymer molecule in solution adopts a random coil configuration, which encompasses a volume (known as its hydrodynamic volume) that is proportional to its molecular weight. We fractionate polymers according to their hydrodynamic volumes to generate a molecular weight distribution plot. 

The second new program allows the user to compare the shapes of molecular weight distributions. For example, if we have the cumulative distribution of hydrodynamic volume for two polymers we can plot the hydrodynamic volume corresponding to the 10th percentile of the distribution for polymer A against the similarly defined hydrodynamic volume for polymer B. Such a plot, made for the entire distribution of both polymers, is called a "quantile... 

Equations suitable for simulation of molecular weight distributions for any initial distribution and chosen values of G(scission) and G(crosslinking) have been developed and demonstrated. The molecular weight distributions may be obtained by GPC (with the limitation of changes in relative hydrodynamic volumes) and by sedimentation velocity in the ultracentrifuge. 

Little is known about the chain dimensions of PPC in solution. Recently, a comparison of the hydrodynamic volume of polystyrene (PS) and PPC has been reported for tetrahydrofuran (THF) as solvent in connection with a size exclusion chromatography (SEC) analysis [78, 79]. The basis for the calculation was the assumption of an immortal PO/CO2 alternating copolymerization, and thus that absolute values of Mn relate to starter and PO/CO2 ratios. Narrow molecular weight distributed PPCs with various molecular weights were prepared from adipic acid as starter. The absolute molecular weight has a relationship of K = K(ps)... 

Since the dilute solution theory is considered as the basis for the indicated treatment, it will receive considerable attention. Influences of several parameters as molecular weight, molecular weight distribution, thermodynamic and kinetic chain stiffness, intramolecular hydrodynamic inter-action, optical properties of the chain and solvent power will be considered. 

Harding, S. E., Berth, G., Ball, A., Mitchell, J. R., and Garcia de la Torre, J. (1991b). The molecular weight distribution and conformation of citrus pectins in solution studied by hydrodynamics. Carbohydr. Polym. 16 1-15. 

In order to calculate the molecular weight M) or molecular-weight distribution (MWD) of the polymer, the dependence of the Soret coefficient on M must be known. Because is virtually independent of M, at least for random coil polymers, the dependence of retention on M reduces to the dependence of D on M. The separation of molecular-weight components by D (or hydrodynamic volume, which scales directly with D) is a feature that thermal FFF shares with size-exclusion chromatography (SEC). In the latter technique, the dependence of retention on D forms the basis for universal calibration, as D scales directly with the product [rjjM, where [17] is the intrinsic viscosity. Thus, a single calibration plot prepared in terms of log([i7]M) versus retention volume (F,) can be used to measure M for different polymer compositions, provided an independent measure of [17] is available. In thermal FFF, a single calibration plot can only be used for multiple polymers when the values of for each polymer-solvent system of interest are known. However, a single calibration plot can be used with multiple channels. In... 

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