INDEX Statistical copolymers

In the past three decades, industrial polymerization research and development aimed at controlling average polymer properties such as molecular weight averages, melt flow index and copolymer composition. These properties were modeled using either first principle models or empirical models represented by differential equations or statistical model equations. However, recent advances in polymerization chemistry, polymerization catalysis, polymer characterization techniques, and computational tools are making the molecular level design and control of polymer microstructure a reality. 

While the percentage composition of copolymers (i.e., the ratio of comonomers) is not given, copolymers with architecture other than random or statistical are identified as alternating, block, graft, etc. Random or statistical copolymers are not so identified in the CA index. Oligomers with definite structure are noted as dimer, trimer, tetramer, etc. 

Besides the absolute value of the refractive index modulation, the stability is an important parameter, particularly for the development of a storage material. In Fig. 27 the temporal variation of the diffraction efficiency of volume gratings is plotted for films of a statistical copolymer 6 (azobenzene content 29.5 wt%) and... 

It was demonstrated above that both the value and the stability of the refractive index modulation are far better for block copolymers than for statistical copolymers with comparable azobenzene content. But the influence of the morphology and the domain size on the refractive index modulation remains unclear. To investigate this we chose a block copolymer series with three different morphologies lamellar, cylindrical, and spherical. In Fig. 28 the growth and decay for different morphologies of the block copolymers 10 (Afn 45,900gmoP1 azobenzene content 31 wt%) and 11 (Mn 42,400gmon1 azobenzene content 25 wt%), which are based on a PMMA-PHEMA backbone, are shown [66, 113]. Both block copolymers exhibit a similar... 

The data tables in each chapter are provided there in order of the names of the polymers. In this data book, mostly source-based polymer names are applied. These names are more common in use, and they are usually given in the original sources too. For copolymers, their names were usually built by the two names of the co-monomers which are connected by -co-, or more specifically by -alt- for alternating copolymers, by -b- for block copolymers, by -g- for graft copolymers, or -stat- for statistical copolymers. Stmcture-based names, for which details about their nomenclature can be fonnd in the Polymer Handbook (1999BRA), are chosen in some single cases only. CAS index names for polymers are not appUed here. Finally, a list of the polymers in Appendix 1 ntilizes the names as given in the chapters of this book. 

Fig. 8. R/Platelet in individual platelets adhering to polymer surfaces. HSB data were statistically confirmed to be different from PSt (P < 0.5), HSR (P < 0.5) and PHEMA (P < 0.5) after 40 s R/Platelet (an index of cytoplasmic free calcium concentration) is the ratio of fluorescence emission intensitie of a Ca2 + indicator dye (Fura 2) loaded in platelets when they are excited at 340 nm and 380 nm. (Reproduced from J Biomed Mater Res [Ref 84 Prevention of changes in platelet cytoplasmic free calcium levels by interaction with 2-hydroxyethyl methacrylate/styrene block copolymer surfaces] through the courtesy of John Wiley Sons, Inc.)...

Here n is the average refractive index, k is Boltzman s constant, and T is absolute temperature (13). If a polyblend were to form a homogeneous network, the stress would be distributed equally between network chains of different composition. Assuming that the size of the statistical segments of the component polymers remains unaffected by the mixing process, the stress-optical coefficient would simply be additive by composition. Since the stress-optical coefficient of butadiene-styrene copolymers, at constant vinyl content, is a linear function of composition (Figure 9), a homogeneous blend of such polymers would be expected to exhibit the same stress-optical coefficient as a copolymer of the same styrene content. Actually, all blends examined show an elevation of Ka which increases with the breadth of the composition distribution (Table III). Such an elevation can be justified if the blends have a two- or multiphase domain structure in which the phases differ in modulus. If we consider the domains to be coupled either in series or in parallel (the true situation will be intermediate), then it is easily shown that... 

Figure 3.51. Use of NIR to predict the melt index (MI) of a series of EVA copolymers with differing VA contents. A three-factor model was used to predict In(MI) using the PRESS and the F-statistic criterion (Hansen and Vedula, 1998). Copyright 1998 John Wiley and Sons, Inc. reproduced with permission.

The phenomenon may be simulated (78) by a blend of two or more copolymers obeying the copolymerization equation, e.g. two or more of the above-mentioned fractions, and the statistical quantities of the blend may be expressed as a function of the same quantities in the starting copolymers. For C2-C3 copolymers, we evaluated (69) this relationship for the fraction of bonds and checked it by means of the IR measurement of the distribution index theoretical predictions, they also supported the assumptions we had previously made to justify the dependence of the ratio of IR absorptions at 10.30 and 10.67 p upon the ratio between the fractions of C2-C3 and C3-C3 bonds. 

Let us consider a system of n comb-shaped copolymers in volume V. Under the mean field approximation, each copolymer can be divided into a set of linear subchains which are jointed at the corresponding junction points and which are statistically independent. To specify the subchains having segments, an index k is introduced. Each subchain contains faNk monomer species of type a. In this case, the contribution from the -th subchain to the monomer density field at point r is given by... 

Soum and Fontanille report that di-s-butyl magnesium generates living polymer from 2-vinylpyridine without the involvement of the side-reactions that afflict the polymerization initiated by alkali metal alkyls the resulting polymer has an isotacticity index of 0.9. Arai et al. have synthesized styrene-butadiene-4-vinylpyridine triblock copolymers. Hogen-Esch et a/. have continued their study of the stereochemistry of the anionic polymerization of 2-vinylpyridine in THF solution. Oligomers were synthesized by addition of alkali salts of 2-ethylpyridine to 2-vinylpyridine termination was effected by reaction with methyl iodide. Highly isotactic products were obtained with U and Na as counterions but with K or Rb there was no stereoselection. Epimerization resulted in the expected statistical mixtures of stereoisomers and it was concluded that stereoselection is kinetically controlled. 

The products obtained under these conditions displayed high molecular weights and polydispersities indexes lower than 1.3. In addition, statistical poly[polystyrene-oxycarbonyl-norbornene)-b-poly(-ethylene oxide)-oxymethylene-polynorbornene)] copolymers were obtained from co-norbomyl-poly-styrene and ot-norbornyl-poly(ethylene oxide) macromonomers by copolymerization under similar conditions. The distribution of PS and PEO grafts along the polymer backbone and the tendency of the copolymerization to blockiness in this case were determined by the reactivity ratios of the two macromonomers. 

With macromolecular systems consisting of more than one type of monomer units (statistical, block, or graft copolymers), the experimenter may be confronted with the problem of the compositional fluctuation of the macromolecules. In such a case the molar mass values measured are only apparent, if the increment of refractive index of the copolymer (dhldCcopo ) is deduced from the weight average of the two components A and B. Benoit suggested instead to carry out the measurements in three different solvents and to use the following relation ... 

Precision—The precision of this test method was determined by statistical analysis of inteilaboratory results. In this study, dilution solvents were limited to xylene or kerosine. Some laboraUnies chose to use Babington-type nebulizers, peristaltic pumps, and background correction. Fourteen laboratories analyz twelve specimens in duplicate. The samples were one gas turbine used oil, four gasoline engine used oils, two truck diesel engine used oils, two marine ei e used oils, SRM 1085 diluted in SRM 1083 (base oil) to contain approximately 40 mg/kg of eleven different metals (this oil also contained 8 mass % of an ethylene-propylene copolymer viscosity index improver), SRM 1085 diluted in SRM 1083 to contain approximately 40 mg/kg of twelve different metals, SRM 1085 diluted in SRM 1083 to contain approximately 2 mg/kg of 12 different metals. 

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