Macromolecules long chain-branched

Strongly short-chain-branched polymers can often be spectroscopically or chemically determined. However, with long-chain branching, the number of branch points is very small compared to the number of chain-links. Consequently, the existence and extent of long chain branching is mostly estimated from the dimensions of the macromolecule in solution. A long-chain-branched macromolecule, namely, exhibits smaller molecular dimensions than the unbranched macromolecule with the same molar mass, as can be clearly seen in Figure 2-4. 

A useful approach to detection in polymer HPLC presents the on-line hyphenation of different measurement principles. For example, an RI detector combined with a UV photometer produces valuable additional information on the composition of some copolymers. Further progress was brought with the triple detection RI plus LALS plus VISCO [313], which is especially suitable for branched macromolecules and the tetra detection UV plus RI plus LALS plus VISCO, which enables characterization of some complex polymer systems, exhibiting a distribution not only in their molar mass and architecture, but also in their chemical composition such as long chain branched copolymers. 

The MALS measurements which eliminate the need for column calibration and all of its subsequent aberrations also permit the direct evaluation of branching phenomena in macromolecules because the basic quantitation of branching may only be achieved from such measurements as shown in the article by Zimm and Stockmayer [7]. Empirical approaches to quantitate branching, using such techniques as viscometry, have been shown to yield consistently erroneous results especially when long-chain branching becomes dominant. 

The determination of the viscosity law in GPC-viscometry is even more important for branched polymers. Branches reduce the sizes of a macromolecule, including its hydrodynamic volume H. This size reduction is reflected by the changes in the shape and position of the viscosity law plot for a branched polymer. Short-chain branches usually do not change the linearity and slope of the Mark-Houwink plot and just decrease the value of parameter K, whereas the long-chain branches cause bending of the corresponding plot. 

Lohse, D.J. Milner, S.T. Fetters, L.J. Xenidou, M. Hadjichristidis, N. Mendelson, R.A. Garcia-Franco, C.A. Lyon, M.K. Well-defined, model long chain branched polyethylene. 2. Melt rheological behavior. Macromolecules 2002, 35 (8), 3066-3075. 

Wang, W.-J. Yan, D. Zhu, S. Hamielec, A.E. Kinetics of long chain branching in continuous solution polymerization of ethylene using constrained geometry metallocene. Macromolecules 1998, 31 (25), 8677-8683. 

Shroff, R.N. Mavridis, H. Long-chain branching index for essentially linear polyethylenes. Macromolecules 1999, 32, 8454-8464. 

Wood-Adams, P. Dealy, J.M. deGroot, A.W. Redwine, O.D. Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 2000, 33 (20), 7489-7499. Trinkle, S. Friedrich, C. Van Gurp-Palmen plot a way to characterize polydispersity of linear polymers. Rheol. Acta 2001, 40 (4), 322-328. Trinkle, S. Walter, P. Friedrich, C. Van Gurp-Palmen plot. II. Classification of long chain branched polymers by their topology. Rheol. Acta 2002, 41 (1-2), 103-113. 

Branching reduces the hydrodynamic volume relative to the mass of the coil. The intrinsic viscosity of branched macromolecules is thus lower than that of their unbranched (linear) counterparts. The effect is particularly marked in the case of long-chain branching. If the number of branch points in a polymer homologous series increases with the molar mass, then the [rj] values also decrease relative to those of linear molecules. Thus, the slope of the log f (log 2) curve continuously decreases with increasing molar mass,... 

Baig, C., Alexiadis, O., and Mavrantzas, V. G. 2010. Advanced Monte Carlo algorithm for the atomistic simulation of short- and long-chain branched polymers Implementation for model h-shaped, aSaaS multiarm (pom-pom), and short-chain branched polyethylene melts. Macromolecules, 43(2) 986-1002. 

Short- and long-chain branching can be introduced into polymers. Extreme forms are cross-linked structures, networks, and gels or even perfect dendrimers (Fig. 2.3). These macromolecules have then a branched... 

FIGURE 2.3 Schematic representation of linear polymers, short- and long-chain branching (brush) polymers, star-type polymers, and cross-linked polymer chains. The dendrimer structure on the right is an extreme form of highly short-chain branched macromolecules. 

Several procedures were proposed to assess the long-chain branching of macromolecules with help of SEC. They are based either on the universal calibration concept or on the employment of absolute detectors that continuously monitor light scattering and viscosity of the column effluent (see sections 11.6.1.4 and 11.7.3.2). 

The structure parameter g was determined over the complete molecular mass distribution, and the number of long-chain branches per macromolecule, n, calculated. The degree of long-chain branching did not appear to vary by much over all ten specimens or with molecular weight. A marked difference was observed between LDPE in that EVA showed an absence of branching at low molecular mass. All the evidence thus pointed to EVA being a random copolymer. 

In this chapter, the analysis of LCB in macromolecules using SEC with multiple detection is described. While the qualitative information obtained from this type of analysis is mentioned, particular attention is paid to the requirements necessary for accurate, quantitative determination of LCB, of the long-chain branching distribution (LCBD), and of the fractal dimension (dt) of macromolecules. 

Recently, SEC/MALS measurements were used to obtain approximate measures of the average molar mass of a long-chain branch and of the average molar mass between branch points, both as a continuous fimction of the molar mass of the macromolecule. Though the particular experiments applied to the study of cross-link-induced branching well below the percolation threshold, the theory and measurements extend naturally to the study of native branching. 

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