Molecular weight averages concept

It is apparent that numerous other special systems or effects could be considered to either broaden the range or improve the applicability of the derivation presented. Our interest, however, is in illustrating concepts rather than exhaustively exploring all possible cases, so we shall not pursue the matter of gelation further. Instead, we conclude this section with a brief examination of the molecular weight averages in the system generated from AA, BB, and Af. For simplicity, we restrict our attention to the case of r . = u... 

This new edition not only includes information on the newer materials but attempts to explain in modifications to Chapter 2 the basis of metallocene polymerisation. Since it is also becoming apparent that successful development with these polymers involves consideration of molecular weight distributions an appendix to Chapter 2 has been added trying to explain in simple terms such concepts as number and molecular weight averages, molecular weight distribution and in particular concepts such as bi- cmd trimodal distributions which are becoming of interest. 

Various molecular weight averages are current in polymer science. We show here that these are simply arithmetic means of molecular weight distributions. It Tiiay be mentioned in passing that the concepts of small particle statistics that are discussed here apply also to other systems, such as soils, emulsions, and carbon black, in which any sample contains a distribution of elements with different sizes. 

To derive the molecular weight averages of the polymer, we shall use here the method described by Lopez-Serrano et. al. (1980), which is identical in concept to the recursive method of Macosko and Miller (1976) cited above. Selecting an A group (marked by ) at random, the in direction will be defined as the direction from the chosen A toward the B group of the same mer unit. Out is then the opposite direction from the chosen A, i.e., toward the A side of the mer. The in and out directions associated with B groups will also be defined in the same way. 

Thus far, how to model radial profiles of monomers and chain transfer agents, as well as temperature, has been described but nothing has been said on how these profiles will be reflected on molecular weight averages or chemical compositions. The equations that were derived in Section 2.3, both for the method of moments and instantaneous distributions, can be applied for each radial position in the polymer particle to retrieve this information. Unfortunately these expressions will not be derived here due to space limitations but they can be found in many references in the literature [54-66]. The concept of instantaneous distributions should, however, be easy to visualize, as illustrated in Figure 2.34. 

Using this concept, Burdett developed a method in 1955 to obtain the concentrations in mono-, di- and polynuclear aromatics in gas oils from the absorbances measured at 197, 220 and 260 nm, with the condition that sulfur content be less than 1%. Knowledge of the average molecular weight enables the calculation of weight per cent from mole per cent. As with all methods based on statistical sampling from a population, this method is applicable only in the region used in the study extrapolation is not advised and usually leads to erroneous results. 

The terminal groups of a polymer chain are different in some way from the repeat units that characterize the rest of the molecule. If some technique of analytical chemistry can be applied to determine the number of these end groups in a polymer sample, then the average molecular weight of the polymer is readily evaluated. In essence, the concept is no different than the equivalent procedure applied to low molecular weight compounds. The latter is often included as an experiment in general chemistry laboratory classes. The following steps outline the experimental and computational essence of this procedure ... 

The various expressions we have developed in this section relating p to the size of the polymer are all based on h. Accordingly, we note that the average reactant molecule in this mixture has a molecular weight of 100 as calculated above. Therefore the desired polymer has a value of = 50 based on this concept. 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

Rieckmann et al. introduced a mass-transfer concept with a mass-transfer coefficient depending on the average molecular weight of the polymer, the melt... 

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