Molecular Weights and Their Distribution

In contrast to biological macromolecules such as proteins, synthetic polymers are, in general, polydisperse. Their molar masses, which show a broad distribution of 

Comprehensive Analytical Chemistry, Volume 53 ISSN 0166-526X, DOI 10.1016/S0166-526X(08)00406-6 

Strictly speaking, the terms molar mass and molecular weight refer to different quantities. Molar mass is the mass of one mole of polymer molecules and measured in g/mol, whereas molecular weight is dimensionless and refers to the weight (mass) of a single polymer molecule measured as multiples of the atomic mass unit u. The numerical values of both quantities are identical. Usually, no such strict distinction is made in the literature, and also in this contribution both terms will be used as synonyms for the strict term molar mass. 

As a guide for the reader, Table 1 lists some features of the experimental techniques discussed in this chapter. For each method it is specified whether it allows the determination of an average molar mass and also of the distribution. Estimates of the molar mass range, typical sample amounts and the operating 

Method Average Distribution M range (g/mol) Amount/mg Operating expense 

---

The determination of molecular weights and their distributions is almost always the first technique used to characterize polymers, and this is especially true for inorganic polymers. Additional techniques used to characterize other features of polymeric materials are described in the following sections. 

The amount of thermal initiation which takes place at 138°C. and its effect on molecular weights and their distributions were also studied. Two batches were polymerized thermally using monomer mixture A. 

In polymerization kinetics, not only rates are of interest, but also molecular weights and their distributions. To the extent that this can be done without getting embroiled in major complications, such aspects are included. 

Finally, SEC is merely a separation technique based on differences in hydrodiynamic volumes of molecules. No direct measurement of molecular weight is made. SEC itself does not render absolute information on molecular weights and their distribution or on the structure of the polymers studied without the use of more specialized detectors (e.g., viscometry and light scattering). With these detectors, a self-calibration may be achieved for each polymer sample while it is... 

In conclusion, it should be noted that the molecular weights and their distribution foUow the rules originally discussed under Uving polymers (Quirk and Lee, 1992). This means that, regardless of the solvents and counterions used, if no termination, chain transfer, or side reactions occur, and if the initiation reaction is fast relative to the propagation reaction, then the stoichiometric molecular weight will be obtained and the molecular weight distribution will approach the Poisson distribution, i.e.. 

In conclusion, the transfer reaction leads either to the shortening of the chain or to the formation of side branches. In both cases many physical properties will be affected, as shown later. However, it is possible to harness this reaction under controlled conditions as a chain-transfer regulator, a retarder or inhibitor. The theory of polymerization kinetics has reached a high level of development, which enables an improved engineering design of the process and good control on the rate, molecular weights and their distribution, and the existence of secondary reactions. 

Having presented a general discussion of physical and chemical properties of polymers and plastics, it is appropriate to analyze the effect of structure on mechanical properties. The chemical and steric structures determine the strength of primary and secondary bonds, the location of transition temperatures, as well as the morphology. These act in addition to the effects of chain dimensions—molecular weights and their distribution. 

One can describe polymer samples in a similar way. First of aU, a polymer chain possesses semi-flexibility, that characterizes the intra-chain interactions for the most stable conformation persisting along the chain axis. Secondly, a polymer chain also holds complex inter-chain interactions. These two intrinsic characteristic factors dictate the basic physical behaviors of the same species of polymers. Besides these two intrinsic factors, each individual polymer sample possesses certain extrinsic characteristic factors, i.e., molecular weights and their distributions, topological architectures, and sequence irregularities. These extrinsic characteristic factors are also important in determining the physical behaviors of the polymer samples. 

Table 20.2 Molecular weights and their distributions of grafting PS and homopolymerized PS in the system of nano-Si02 grafted with PS (irradiation dose = 1 0 Mrad). (Reprinted from Polymer, vol. 42, M. Z. Rong eta ., Structure-property relationships of irradiation grafted nano-inorganic particle filled polypropylene composites, p. 167, 2001, with permission from Elsevier)...

The objective of this work is to evaluate the fracture behavior of a series of commercial Medium Density Polyethylenes by the EWF technique and find correlations between the fracture parameters and the polymer properties (comonomer content, crystallinity, molecular weight and their distribution) for neat and annealed samples. 

Table 3 lists the EWF most important parameters for quenched A, B, C and D samples and also for slowly cooled C and D samples. The calculated parameters are in the range of EWF parameters reported in the literature for compression molded polyethylenes [2,14]. When only the quenched samples are considered, the results shown in Table 3 are independent of the differences in between the MDPE s employed i.e SCB contents, molecular weights and their distribution at least in the range these properties were varied in these four samples. 

For the four types of MDPE employed in this study, the energy required to form fracture surfaces (cOe) and that required to deform a volume surrounding the fracture (PWp) are independent of the differences that the samples have on parameters such as SCB content, molecular weights and their distribution and crystallinity. However, the EWF parameters obtained in slowly cooled samples of two MDPE types indicated that the samples tum less ductile upon annealing. 

---