Linear polymers INDEX

Equation (49) formulated for blends of linear macromolecules also provides the facility to model blends of linear polymers (index L) and branched polymers (index B) synthesized from the same monomer [28]. If the end-group effects and dissimilarities of the bi- and trifunctional monomers can be neglected, the parameter a becomes zero. This means that the integral interaction parameter is determined by the parameter i lb. i c > the conformational relaxation, in combination with the intramolecular interaction parameters of the blend components. Because of the low values of and the first terms in (47) and (48) can be neglected with respect to the second terms (for molar masses of the polymers that are not too low) so that one obtains the following expression ... 

In 1967, the Polymer Nomenclature Committee of the American Chemical Society pubHshed proposals for naming linear polymers on the basis of their chemical stmcture (97), which were then introduced into Chemical Abstracts (CA) Indexes and pubHshed in their final form in 1968 (98). 

Lai et al. [100] proposed the use of the Dow Rheology Index (DRI) as an indicator for comparing branching level in industrial polymers. For a linear polymer molecule, like unbranched polyethylene, the viscosity of the polymer as a function of the applied shear rate is given by the Cross equation [84,100],... 

The Mark-Houwlnk parameters K and a, where appropriate for the sample of interest, are calculated from a plot of log [h] vs. log M(ld) for linear polymers. For branched polymers, the branching index, g, is calculated from... 

In recent years, cyclic polymers (also referred to as polymer rings or macrocycles) became easier to prepare. By a number of different approaches and advances in cyclization techniques, a wide range of novel cyclic polymers have been prepared in good yields [10]. In contrast to linear polymers, cyclic polymers are topologically distinct species, and all monomer units of cyclic polymers are chemically and physically equivalent. This equivalence is due to the fact that their properties are not affected by the nature of the end groups, since cyclic polymers have no chain ends. They include the radius of gyration, intrinsic viscosity, translational friction coefficient, critical solution temperature, refractive index, density, dipole moment, glass transition temperature, and surface property [11]. 

H and Si NMR spectra were recorded on a Brnker Avance 300 spectrometer respectively at 300.13 and 75.6MHz at room temperatnre. CDClj and toluene were used as solvents. For Si NMR, Cr(acac)3 (0.03 M) was added in the tube and a delay between pulses of 20 s was set. IR spectra were recorded on a Perkin-Ehner IR ET 1760-X. The average molecnlar weight of the linear polymers was determined by size exclusion chromatography in TFIF (flow rate l.OmL.min" ) on an apparatus equipped with a Waters refractive index detector, a Waters column pack (Ultrastyra-gel 10, 10 100 A) and a Minidawn Wyatt light scattering detector. 

For branched polymers and for linear polymers that do not have an established Mark-Houwink equation, SEC is typically used in conjunction with light scattering and viscosity detectors. These detectors measure the weight-average molar mass and viscosity of each elution volume. In principle, this experiment directly determines both M and [rj] for any polymer that is soluble in the SEC solvent, but in practice the determination also requires that the polymer have an appreciable difference in refractive index from the solvent so that in Eq. (1.88), dn/dc >0.05 mL g . Often a new polymerization is not understood sufficiently to know for certain whether the polymer produced will have branched chains present or... 

After subjecting the two materials to ultrasonic irradiation, the formation of anthracene was confirmed by photoluminescence spectroscopy. The photoluminescence intensity increases with increasing sonication time (Fig. 30b), which confirms the arm-loss mechanism. Quantifying anthracene (using the photoluminescence intensity at 411 nm) yields two similar reaction constants (3.20 0.14) X 10 and (3.26 0.09) x 10 min for the star and linear polymers, respectively. Boydston also calculated the reaction constant based on refractive index signals (change of M. Again, he obtained two similar reaction constants (3.13 0.11) x 10 and (3.27 0.38) x 10 min for star and linear polymers, respectively. His result reveals the equivalence between star-shaped polymers and linear polymers in terms of chain scission rate if of star-... 

Here the index i refers to a retention volume slice, C, is the polymer concentration measured by SEC for the slice i, Mi is MW determined by light-scattering analysis at retention volume slice i, and [77, ] is the intrinsic viscosity determined by viscometry of slice i. The constants k and a are the Mark-Houwink coefficients for a linear polymer of the same chemical composition My is the viscosity-average MW (Lue and Kwalk 2005). 

As a result of the controlled long-chain branching in otherwise linear polymers, the processability of these resins is claimed to be significantly enhanced compared to the standard LLDPE and EP rubber materials. Envircmmental stress crack resistance of metallocene polyolefin is also claimed to be significantly better. A wide range of densities (0.86-0.93), flexural modulus (10-100 MPa), melting points (60-120 °C), and melt flow index (0.5-125) is available in the commercial metallocene-based ethylene copolymers. 

The linear polymer prepared by Allcock was truly a high polymer with over 15,000 repeat units representing a of about 1.2x10. The polydis-persity index for the polymer [NPCyn prepared by the ring-opening of N3P3CI6 is greater than 2. 

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