Polymers polydispersion

Effect of base polymer polydispersity on ease of forming a uniform spiral spray pattern from the corresponding adhesives... 

In order to begin this presentation in a logical manner, we review in the next few paragraphs some of the general features of polymer solution phase equilibrium thermodynamics. Figure 1 shows perhaps the simplest liquid/liquid phase equilibrium situation which can occur in a solvent(l)/polymer(2) phase equilibrium. In Figure 1, we have assumed for simplicity that the polymer involved is monodisperse. We will discuss later the consequences of polymer polydispersity. 

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. 

Here, /u ° and ju are, respectively, the chemical potentials of pure solvent and solvent at a certain concentration of biopolymer V is the molar volume of the solvent Mn=2 y/M/ is the number-averaged molar mass of the biopolymer (sum of products of mole fractions, x, and molar masses, M, over all the polymer constituent chains (/) as determined by the polymer polydispersity) (Tanford, 1961) A2, A3 and A4 are the second, third and fourth virial coefficients, respectively (in weight-scale units of cm mol g ), characterizing the two-body, three-body and four-body interactions amongst the biopolymer molecules/particles, respectively and C is the weight concentration (g ml-1) of the biopolymer. 

Actual curvature in such a plot may signal the presence of a distribution of diffusivi-ties 6), as in polymer polydispersity. This hypothesis may be modelled and compared with experiment19). 

Q = Mw/Mn = Polymer polydispersity index ROT Quenching with tritium labeled alcohol 1 1/mol sec... 

We divide this section into three main themes structure, adsorbed amount, and polydispersity. In sec. 5.7a we discuss the structure of the adsorbed layer, paying attention to the volume fraction profile, the composition in terms of loops and tails, the bound fraction, and the layer thickness. Section 5.7b deals with the adsorbed amount as a function of the polymer concentration, the chain length, the solvency and the surface affinity. These two sections are mainly concerned with monodisperse polymer. Polydispersity, where competition between different chain lengths shows up, is treated In sec. 5.7c. 

In examining this matter, the comparison of the various data from the literature requires caution because of both the uncertainties inherent in the measurement of polymer polydispersity, and the different polymerization conditions which have been adopted and which often have not been clearly indicated. 

Heterogeneous catalytic systems give broad MWD, as a natural consequence of the plurality of surface active species. However the polymer polydispersity can be controlled, to a certain extent, as will be shown in the next sections. 

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. 

Doi et al. studied the effect of different aluminium alkyls on the polydispersity of syndiotactic polypropylene obtained with the V(acac)3-alkyl aluminium halide soluble catalytic system, at temperatures below —65 °C. These authors found that, by varying the type of aluminum alkyl not only the propagation and transfer rates are changed, but also the polymer polydispersity index decreases in the following order ... 

Subsequently, Doi et al. examined other high yield supported catalytic systems and, while they confirmed the accomplishment of narrower MWDs than those obtained with non-supported catalytic systems based on TiCl, they also noticed that polymer polydispersity varied depending on the amount of the Lewis base, the type of aluminum compound used as well as on the type of support. 

Bier et al. found that in propylene polymerization, at 50 °C with aluminum alkyl reduced TiCl3—A1(C H5)2CI, the polymer polydispersity increased (Q from 6 to 10 in the first 30 minutes) and then decreased with time (Q approximately 4). Such a phenomenon could be justified by a decrease in the number of active centres with time after an initial period of rapid increase, together with the living nature of the polymeric chain which is only terminated by monomolecular disproportionation... 

The graphics associated with SEC capture its ability to reveal qualitative structural information in a visual format. The applications discussed show how peak displacement of the triple-detector chromatograms reflects polymer polydispersity (dex-... 

Linse P. 1994. Micellization of poly(ethelene oxide) poly(propylene oxide) block copol5mers in aqueous solution effect of polymer polydispersity. Macromolecules 27 6404 6417. 

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)...

Daivis, et al. [102] used QELSS to measure Dp of relatively dilute 864 kDa dextran in solutions of 20.4 kDa dextran. Polymer polydispersities were in the range 1.24-1.3. 

Termination. With independent measures of kp available, kt can be estimated from the lumped ratio of k /kt. Specialized techniques involving PLP have also been developed to yield accurate estimates of the ratio kp/k [10]. Termination rates in FRP are always diffusion controlled such that the apparent value of kt depends on the conditions under which it has been measured, including the lengths of the radicals involved in the reaction (see Section 3.2.3). Nonetheless, the assumption of chain-length independence is usually made for modeling of commercial FRP systems, as the errors introduced are not large. The mode of termination affects the molecular architecture of the polymer formed and thus some of its properties. The instantaneous polymer polydispersity (PDI = / n )... 

Three capture its ability to reveal qualitative structural information in a visual format. The applications discussed show how peak displacement of the tripledetector chromatograms reflects polymer polydispersity (dextran), how detector response can relate to aggregation (chitosan), and how peak area differences can indicate a change in polymer chemical composition (PS vs. PS-star). The M-H plots (dextran, brominated PS) give information about polymer conformational changes, structural differences, and branching distributions. ... 

This paper proposes a phenomenological analysis, based on laboratory experimental work, of the effects of adsorption properties on pol3nner slug propagation. The adsorption properties studied include kinetic aspects, i.e. instantaneous adsorption, reorganization of macromolecules inside adsorbed layer, exchanges between free and adsorbed polymer, desorption as well as properties at thermodynamic equilibrium which can be described by a partially reversible adsorption isotherm. The conditions for hydro-dynamic retention are also discussed. In addition, an analysis of the effects of polymer polydispersity on each of these adsorption phenomena shows that these effects cannot be neglected in a predictive simulator. 

Quaternary and higher systems have been investigated. In such cases, many phases may coexist. Indeed, since the phase behaviour is dependent on the molecular weight of the polymer, polydispersity itself results in a multicomponent system. 

The complexation of DNA and polycations is a function of the intrinsic properties of the two components. For instance, from the use of synthetic polycations for complexing DNA also arises the problem of polydispersity of polymers (a polymer sample is usually composed of macromolecular species of differing molar masses) compared with DNA, which is monodisperse. Because the polydispersity of the polycation could be an issue in studies of IPECs, sugar-based polymers (usually polydisperse except if fractionated), conjugated polymers (polydispersity, Mw/Mn > 2), branched PEI derivatives, and hyperbranched polymers are out of the scope of this review, as already mentioned. Only polymers synthesized via controlled or living polymerization methods will be discussed [55-57]. 

A polymer comprising molecules non-uniform with respect to relative molar mass or constitution or both is termed non-imiform polymer (polydisperse) [89IUP2]. A polymer imiform with respect to either molar masses or constitution may be termed as uniform polymer (monodisperse) with respect to molar masses or constitution. A mixture of linear and branched macromolecules, both of uniform molar masses is not uniform. lUPAC recommend the use of the terms imiform for monodisperse and non-uniform for polydisperse. 

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