Polydispersity, of polymer

A way to increase the precision of the value Mw/Mn extracted from DLS is to consider several correlation functions and to look for a single answer. Stepanek [50] developed a method to determine the polydispersity of polymer samples with narrow distribution by measuring several correlation functions with different sample times on a linear correlator. With this procedure polydispersities in the range Mw/Mn — 1.05 — 2 can be determined. 

The polydispersity of polymers prepared in this way is usually very low for example, a value MJM of 1.05 was found for a sample of poly(a-methylsty-rene). Living polymers can also be used for the preparation of block copolymers after the consumption of the first monomer, a second anionically polymerizable monomer is added which then grows onto both ends of the initially formed block. By termination of the living polymer with electrophilic compounds the polymer chains can be provided with specific end groups for example, living polystyrene reacts with carbon dioxide to give polystyrene with carboxylic end groups. 

The polydispersity of polymers results in competing adsoiption of the thermodynamically favored larger molecules for surface sites filled initially by smaller molecules. Different segments of a block copolymer may exhibit quite different adsoiption characteristics, complicating the rearrangement process farther. This is an effect of considerable interest in protein adsoiption, and is referred to as the rearrangement of a protein layer to maximize hydrophobic interaction of "oily" patches with low energy surfaces such as medical implant polymers. 

Fortunately, the polydispersity of polymers does not significantly affect the vapor-liquid equilibrium of polymer solutions since the polymer remains entirely in the condensed phase. Polydispersity becomes important in the liquid-liquid equilibria of polymer solutions where the... 

Another problem must be overcome to produce high molecular weight polyoxymethylene. The seed crystal must have the proper surface in order to grow properly. The ideal polymer crystal is born by spontaneous nucleation and can then grow exclusively by addition to the chain ends which are aligned and available at the face. The polydispersities of polymers prepared under these conditions are near unity. 

Polymers are mixtures of macromolecules of different molecular weight, and most commercially available products have rather broad distribution of the molecular weight. Some studies were carried out with fractions of a narrow distribution of the molecular weight, separated from commercially available polymers. Adsorption leads to fractionation as discussed above for some types of surfactants. Larger polymer molecules have higher affinity to the surface than smaller molecules composed of the same type of monomeric units. The selectivity is chiefly driven by the difference in the entropy of mixing in solution. Polydispersity of polymers is also one of the factors responsible for hysteresis loops in the adsorption-desorption cycles. 

In contrast, the typical polydispersity of polymers produced with Phillips catalysts varies from 6 to 20, and specialized catalyst treatments can provide polymers of PDI as low as 4.0 or as high as 100. Thus, 2 to 12 unique site types are required to reproduce the MW distribution from Phillips catalysts, because the catalyst contains a heterogeneous population of sites, differing widely in propagation and termination rate constants. Each site type generates polymer with its own characteristic MW, and consequently the polymer MW breadth reflects the heterogeneity of the site population. Differences in site reactivity no doubt derive from the... 

The molecular masses of poly(l) synthesized in aqueous media were typically high (M fs 106), and polydispersity indices (PDIs) were often lower (< 2.0) than the polydispersities of polymers produced by classical systems in organic solvents [27, 29, 30]. These low polydispersities have been attributed to the low occurrence of termination reactions during the polymerization and the relative inactivity of the propagating species toward the acyclic alkenes in the polymer, which suppress-... 

The subsequent study was oriented at the theoretical explanation of the factors that cause and affect zone spreading in TFFF [31]. Contributions of non-equilibrium and polydispersity of polymer samples under study to the total peak width were studied, as was the possibility of determining the precise polydispersity of the polymer by measuring peak width at various linear velocities of the solvent, and by extrapolating to zero velocity, i.e., by eliminating the contribution of non-equilibrium processes [32]. An improved separation in TFFF can be obtained by using... 

Modelling of the polymer particle growth process [82] has resulted in the conclusion that diffusion limitations are the single reason for the wide polydispersity of synthesised polymers. The model has demonstrated that the main transport limitations localise on the level of macroparticles. Modelling results are confirmed by data obtained in gas and liquid polymerisation experiments on titanium-magnesium catalysts. Authors also consider that the wide polydispersity of polymers can be explained by the existence of more than one type of active centre. Each specific type is responsible for a certain portion of polymer with a different MWD. However, the authors did not succeed in characterising the active centre [82] because it required the optimisation of many kinetic parameters. 

In the synthesis process of polymer chains, polymerization is not able to synchronize the initiation, the propagation and the termination steps in all polymers, and therefore leads to a certain width of molecular weight distributions in the product. Such a character is called the polydispersity of polymers. 

The polydispersities of polymers prepared by free radical polymerization are 2 or 1.5 for the termination by disproportionation or combination, respectively. These values apply to products formed dming a short time period when the concentrations of monomer and initiator are constant. In the course of free radical polymerization the monomer and initiator concentrations usually vary with conversion and consequently the polydispersity of the final product is broader. 

Experimental values of g and pg are considerably influenced by the polydispersity of polymer samples used however, both g and pg are universal to a first approximation, the former being mostly found to be in the range (2.0 - 2.7) X lO mor and the latter in the range 1.25-1.35 (6.15-5.70 for Fg). Recently, Oono and Kohmoto [10,11] applied renormalization-group theory to the polymer hydrodynamics of the Krikwood-Riseman scheme and computed the values of g =2.36 x lO moP and Fg = 6.20, which compares rather favorably with experimental values. 

Microemulsion processes may well find applications in areas which have traditionally used emulsion polymerisation. At the present stage of research, it is mainly water-in-oil microemulsion polymerisation which offers the most possibilities and several patents have been taken out [6.5]. This process minimises certain problems encountered in classic inverted emulsions, namely instability of the latexes they produce, large polydispersity of polymer particles, and the large quantity of coagulum which increases production costs. Water-soluble (co)polymers prepared in microemulsion polymerisation can be used in various ways ... 

Figure 15.6 Comparisons of polymer properties in batchwise (circles) and microfluidic (triangles) systems at various Lys-(Z)-NCA concentrations. The square indicates polydispersity of polymer prepared using a microreactor without the micromixer. From T. Honda etal., Lab on a Chip 2005, 5, 812-818. Reproduced by permission from the Royal Society of Chemistry.

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]. 

The tilt angle 0 is a true order parameter of the ferroelectric C phase. With some exceptions [170], its temperature behavior is analogous to that for low molecular mass compoimds. Three examples are shown in Fig. 7.30. First, we notice a rather smooth 6 T) dependence, smoother than the dependence 9(T) oc (Tc a — predicted by theory. This may be accounted for by the polydispersity of polymer liquid crystals which results in blurred phase transition regions. For compound (7.vii) studied in [170]... 

Miscellaneous Fractionation Methods.—Turbidimetric titration by non-solvent addition has virtually vanished since the advent of GPC, but Hay et have recently shown that the method of turbidimetric titration by temperature decrease can give useful information about the polydispersity of polymers. Nonsolvent induced turbidimetry of fractions eluted from a GPC column has been used by Hoffmann and Urban to examine composition distribution in copolymers. 

The molecular weight and polydispersity of polymers remain among the most important properties that are measured. The methods are divided into absolute methods, which determine the molecular weight from first principles, and relative methods, which depend on prior calibration. The latter are usually selected because they are fast and inexpensive. Values obtained from the several methods are summarized in Table 3.15. 

In eq 9.44 the distribution function is called generalized Schulz-Flory distribution (or Schulz-Zimm distribution) because of its introduction by Schulz in 1935, and by Flory in 1936. " To evaluate the polydispersity of polymers U = Mw/M - 1 is an important quantity. The quantity k of the Schulz-Flory distribution is given by k= IU. The two parameters f and k of the... 

Determination of molar masses and polydispersity of /polymers is often complicated because of the limited solubility particularly of highly fluorinated polymers. To avoid different conditions for the polymers and to ensure a certain comparison, SEC with a mixture of pentafluorophenol (PFP)/chloroform (1/3 vol/vol) as eluent (even if some of the samples were soluble in chloroform or tetrahydrofurane, THF), refractive index (RI) detection, and PMMA standards for calibration and determination of relative molar masses was employed. For some samples, molar masses could not be detected due to isorefractive behavior (no signal due to same RI of sample and eluent). This was observed in the series for P(MMA-co-sfMA-H10F10) at 20-25 mol% sfMA-HlOFlO and for P(MMA-co-sfMA-H2F8) at 20-30 mol% sfMA-H2F8. The chemical characterization of selected copolymers used for the present study is given in Table 11.2. 

The overall polydispersity of polymer will be greater than the equilibrium value (2... 

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