Polymer length distribution

M. S. Turner, M. E. Cates. The relaxation spectrum of polymer length distributions. J Physique 57 307-316, 1990. 

This theory clearly predicts that the shape of the polymer length distribution curve determines the shape of the time course of depolymerization. For example Kristofferson et al. (1980) were able to show that apparent first-order depolymerization kinetics arise from length distributions which are nearly exponential. It should also be noted that the above theory helps one to gain a better feeling for the time course of cytoskeleton or mitotic apparatus disassembly upon cooling cells to temperatures which destabilize microtubules and effect unidirectional depolymerization. Likewise, the linear depolymerization kinetic model could be applied to the disassembly of bacterial flagella, muscle and nonmuscle F-actin, tobacco mosaic virus, hemoglobin S fibers, and other linear polymers to elucidate important rate parameters and to test the sufficiency of the end-wise depolymerization assumption in such cases. 

Figure 1. Mixing device for microtubule depolymerization kinetic studies requiring prompt dilution while minimizing shearing forces that may alter the polymer length distribution.

Figure 2. Progress curve for dilution-induced microtubule depolymerization. Inset Polymer length distribution prior to dilution-induced disassembly. The data points are experimentally determined, and the solid line is based on the theoretical treatmenF. ...

In many problems of statistical mechanics, such as in computing polymer length distributions (Example 4.2), energies (Chapter 11), fractional helicit> in polymers (Chapter 26), or numbers of ligands bound to proteins or surfaces (Chapters 27 and 29), you will have a polynomial function such as... 

The final example, which we discuss in some detail, is a molecular dynamics study of the self-assembly and phase behavior of reversibly aggregating linear model polymers. Here we consider the coupling between the polymer length distribution and orientational ordering as a function of monomer concentration including the influence of aggregate flexibility (cf. above). In this model, a detailed description is given elsewhere [87] monomers interact via a Lennard-Jones-like potential with anisotropic attraction i.e.. 

Sequence length distributions are occasionally important. They measure the occurrences of structures like YXY, YXXY, and YXXXY in a random copolymer. These can be calculated from the reactivity ratios and the polymer composition. See, for example. Ham. ... 

The properties of a polymer depend not only on its gross chemical composition but also on its molecular weight distribution, copolymer composition distribution, branch length distribution, and so on. The same monomer(s) can be converted to widely differing polymers depending on the polymerization mechanism and reactor type. This is an example of product by process, and no single product is best for all applications. Thus, there are several commercial varieties each of polyethylene, polystyrene, and polyvinyl chloride that are made by distinctly different processes. 

Sorta E. and MeUs L.A., Block length distribution in finite polycondensation copolymers. Polymer, 19, 1153, 1978. 

FIGURE 12.1 Length distribution of short Hbers after mixing. (From Ashida, M., Short Fibre-Polymer Composites, De, S.K. and White, J.R. (Eds.), Woodhead Publishing Ltd., Cambridge, U.K., 1996. With permission.)... 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

Furthermore, in the more general case we are concerned with a variation of composition and sequence length distribution not only as a function of retention volume but within each chromatogram area segment (or "slice ) at each retention volume. A significant polydispcrsity of one of these properties within a chromatogram slice can easily invalidate the polymer analysis described above. 

The previous sections in this chapter have tried to stress upon the significance of distribution of sequence lengths in polyethylene-based copolymers. The sequence length of interest in a system of ethylene-octene copolymers would be the number of methylene units before a hexyl branch point. As was discussed, this parameter has a greater impact on the crystallization behavior of these polymers than any other structural feature like branch content, or the comonomer fraction. The importance of sequence length distributions is not just limited to crystallization behavior, but also determines the conformational,... 

J.E. Mark, Improved elastomers through control of network chain-length distributions. In P.N. Prasad, J.E. Mark, S.H. Kandil and Z.H. Kafafi (Eds.), Science and Technology of Polymers and Advanced Materials, Plenum, New York, 1998, p. 85. 

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