Polymer polydispersity influence

Essentially all Industrial polymers are polydisperse. The effect of polymer polydispersity on phase equilibrium has been discussed previously by many authors, but the treatment of Tompa ( ) Is one of the most complete. For our purposes, the situation can be summarized as follows. Polydispersity has virtually no effect on vapor-liquid equilibria (as long as the polymer Is non-volatile). However, polymer polydispersity does have an Important Influence on liquid-liquid equilibria. 

As well known, the type of transition metal can deeply affect many fundamental aspects of the Ziegler-Natta catalysis (e.g. activity, stereochemical and molecular weight control). Thus a certain influence on polymer polydispersity could be expected. 

Fig. 24. Coexistence curves when the P-phase is semipermeable to mass transfer. A secondary phase separation is produced inside the -phase leading to y and 5 phases at equilibrium (Reprint from Polymer, 35, C.C. Riccardi, J. Borrajo, R. J. J. Williams, Thermodynamic analysis of phase separation in rubber-modiiied thermosetting polymers influence of the reactive polymer polydispersity, SS41-SSS0, Copyright (1994), with kind permission from Butterworth-Heinemann journak, Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK)...

We noted earlier that each relaxation time will contribute to T and hence influence the shape of the correlation function. Consequently, all the information on polymer polydispersity is contained within the intensity correlation function because D is proportional to (molecular weight) The extraction of the molecu-... 

It can be demonstrated that not only the average molecular weight characteristic of a given polymer system influences dispersant efficiency, but also the polydispersity within any molecular weight range ... 

The decompressive release of supercritical carbon dioxide during spray application produces a new type of spray that can have superior atomization characteristics compared to conventional air-less and air-assisted application methods (41). Supercritical carbon dioxide has good solvent properties in a variety of polymers. Solubility of the polymer is influenced by polymer molecular weight, polydispersity, solubility parameter, functionality, and structure (42). Significantly increased solubility has been demonstrated by including fluorine, silicon, and bulky substituent groups in the polymer structure. 

M. Cross, Polymer rheology Influence of molecular weight and polydispersity , J.Appl. Polymer ScL, 13, 765 (1969). 

For acrylic polymers produced via emulsion polymerization, a set of two or more 30-cm-long columns with 10-ju,m or less packing material will usually ensure that the observed polydispersities are minimally influenced by column band broadening. 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

V is the molar volume of the solvent and pp the density of the polymer. For polydisperse polymers A2 is a more complex average, which shall not be discussed here in detail [7]. For good solvents and high concentrations, the influence of the 3rd virial coefficient A3 cannot be ignored, and n/c versus c sometimes does not lead to a linear plot. In these cases, a linearization can frequently be obtained with the approximation A3 = A (M)n/A by plotting [12,13]... 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

All investigators emphasize the importance to check the packing materials for every special cationic polymer since the cationic charge and the chemical structure of the monomer units influence the chromatographic separation. Calibration has been difficult in such cases where the polydispersity of standards and... 

If the signal can be expressed as a sum over exponentials, as in the case of solutions of polydisperse polymers, high-, low-, and band-pass filters which are exponentials in the time domain influence the amplitudes, but not the diffusion time constants of the respective modes [80,81]. 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

Extreme loading of the polymer with dendrons results in a cylindrical shape of the denpol polymer (Fig. 2.19) with polydisperse properties. It is thus possible to influence or even control the size of the coupled dendron and the density of its coverage on the polymer backbone through choice of the type of polymer (e.g. polyacrylate or polystyrene see Table 2.1). 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

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