Polymer, branched Concentration

Hancock, D. O. and Synovec, R. E., Rapid characterization of linear and star-branched polymers by concentration gradient detection, Anal. Chem., 60,2812, 1988. 

The structure of concentrated solutions of branched molecules has also received little attention. It is probable that the network formed by entangled branched molecules displays a topological structure which is different from that formed by linear chains. It is known that the sedimentation properties of branched synthetic polymers differ, especially in good solvents, from those of linear polymers. The concentration dependence of the sedimentation coefficient is relatively more pronounced for branched polymers than that for linear ones 20). 

Bueche,F. Viscosity of polymers in concentrated solution, J. Chem. Phys. 25, 599-600 (1956). See also Bueche,F. Viscosity of molten branched polymers and their concentrated solutions. J. Chem. Phys. 40,484-487 (1964). 

The computer models described provide a functional simulation of SEC-viscometry-LS analysis of linear polymers. The results for the Flory-Schulz MWD are in qualitative agreement with previous results for the Wesslau MWD. Both models emphasize the importance of determining the correct volume offset between the concentration detector and molecular weight-sensitive detectors. For the Flory-Schulz model, the peak shape, as well as the peak elution volume, can provide information about molecular weight polydispersity. Future work will extend the model to incorporate peak skew and polymer branching. 

Eluent from the SEC separation passes through a capillary or capillaries (one, two and four capillary designs are available) and the pressure drop is monitored by a differential pressure transducer. From the pressure drop and the concentration of the sample (obtained from the DRI) the intrinsic viscosity (ri) can be calculated. Molecular weight averages, Mark-Houwink (for polymer branching studies) and molecular weight distribution plots can then be obtained after suitable data treatment. 

In reality, blocking itself may be wasteful, but is not in itself a reflection of polymer performance, when the polymer density is held constant. The widely accepted association of blocking with poor polymer physical properties is more likely connected with branch concentration into the short chains, which also decreases BDI. 

The information in Table 35 is plotted in a three-dimensional form in Figure 105. The X-axis is the logarithm of MW. The y-axis is the branch concentration, in branches per 1000 carbon atoms. On the z-axis, one would normally plot the amount of polymer found at each (x,y) location. However, it is more informative to know where the branches are rather than where the polymer is in this 3D plot. Therefore, in Figure 105, the z-axis is the number of branches found at each (x,y) location. To clarify this point again The y-axis represents the branch frequency, and the z-axis is the number of branches, or the percentage of all branches. This... 

FIGURE 105 Three-dimensional plots representing the minimum number of Schulz-Flory site distributions needed to reproduce the MW distributions of polymers made with the two low-temperature activated catalysts in Table 35. On the left (Cr/silica), about half of the branches are in an island at low MW and high branch concentration, which has been eliminated on the right (Cr/silica-titania). Adapted with permission from Ref. [435]. 

Figure 5.5 Relationship between the molecular weight reduction and the branching concentration during the PE degradation over amorphous silica-alumina.I3 (Reprinted from J. Appl. Polym. Sci., 38, Y. Ishihara, H. Nambu, T. Ikemura and T. Takesue, page 1491. 1989, with permission from Elsevier Science)...

At high molecular weight where T is small, very small concentrations of branches or cross-links have a large effect on the weight-average molecular weight. A branch concentration equal to T/3 or a cross-link concentration equal to T/8 will produce an infinite polymer network. 

One of the most important technical hurdles to overcome was the development of a practical solution to the capillary separation matrix problem. Early capillary gel work involved the adaptation of cross-linked polyacrylamide gels, used for years in slab-based DNA sequencing separations, to the capillary format. In cross-linked gels, a DNA mixture is sieved through pores formed by a network of polymer branches that are covalently fixed. The size selectivity of this network is tuned through variation of both the monomer (%T) and cross-linker (%C) concentrations. Cross-linked... 

These branch points via the ester bridges can be removed by saponification, causing the degree of polymerization to fall. At the same time, however, nonsaponifiable branching can also occur at the a-C atom. Since the polymer concentration increases with conversion, transfer to polymer branching also increases with the conversion u. 

Similarly, a study of ethyl-branched ADMET PE has also been reported [139]. This work showed that these polymers favored branch inclusion, resulting in a crystal structure similar to that obtained for the precisely methyl-branched ADMET polymers. This crystallization behavior, however, was dependent on branch concentration. When the branch content was 111 ethyl branches per 1000 carbons, the resulting polymer was amorphous, indicating that the steric demands of the ethyl branches precluded their participation in crystallization. Conversely, ethyl branch contents of 50-60 branches per 1000 carbons resulted in polymers able to include the ethyl branch defects in the crystal lattice, presumably due to the presence of kink defects able to accommodate the ethyl branches. 

The effect of branch concentration on the material properties of ADMET PEs has also been studied. An initial study reported the precise placement of a butyl branch on every 39th carbon [144]. This was later expanded to a series of polymers synthesized with one of 13 different alkyl branches on every 39th carbon [145]. While all branched polymers displayed a decreased melting temperature relative to linear PE, the larger branches (ethyl through pentadecyl) all showed similar melting points between 70 and 78 °C, while the methyl-branched polymer melted at92°C. 

Nystrom, et al. examine the effect of polymer branching on sedimentation by comparing sedimentation rates of linear polymethylmethacrylate and branched poly-2-triphenylmethoxyethylmethacrylate (PTEMA) samples(14). For each sample, 5(c) is described reasonably accurately by Eq. 2.6. In dilute solutions, sq varies by no more than 50% between these polymers. At larger concentrations, 5(c) for PTEMA is nearly independent of M. Over the concentrations seen in Figure 2.4, 5(c) falls tenfold. At elevated concentration, nondilute linear chains sediment one-third as fast as the branched chains of close to the same molecular weight, while a for the branched chains is a quarter or a third of a for the linear chain. 

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