Molecular weight averaging

Table 1.5 also includes two additional types of molecular weight average besides those already discussed. The following remarks describe some features of these two, the z-average molecular weight, and the viscosity average ... 

Table 1.5 Summary of the Molecular Weight Averages Most Widely Encountered in Polymer Chemistry...

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... 

Ziegler-Natta type catalysts can generate a very high cis-1,4 stmcture (>90%), which is the choice polymer for tires. It is made to specifications similar to SBR, ie, molecular weight average of 100,000—200,000, Mooney viscosity 50, and od-extended. Lithium catalysts on the other hand yield variable chain stmctures, depending on the solvent used, ie, mixed stmctures of cis-1,4 and trans-1,4 and 1,2. These polymers are generally ia the lower... 

While this example shows an extreme difference in the two molecular weight averages, the other extreme is where all of the molecules have the same size, i.e. they are said to be monodisperse. In tbis case the two averages will have the same value. 

One further point might be made here. Although the example illustrates the difference between the two types of molecular weight average, the weight average molecular weight in this example cannot be said to be truly representative, an essential requirement of any measure of central tendency. In such circumstances where there is a bimodal, i.e. two-peaked, distribution additional data should be provided such as the modal values (100 and 100000 in this case) of the two peaks. 

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. 

ASTM D 5296 - 92 (1994). Standard Test Method for Molecular Weight Averages and Moleeular Weight Distribution of Polystyrene by High Performance Size-Exclusion Chromatography. Annual Book of ASTM Standards, Vol.08.03, pp. 419-431. 

ASTM D-3536-91, Standard Test Method for Molecular Weight Averages and Molecular Weight Distribution by Liquid Exclusion Chromatography (Gel Permeation Chromatography-GPC), ASTM Annual Books of ASTM Standards, Vol. 08.02, P. 349—359. This method was deleted in the 1997 edition of the ASTM book. 

Polyethylene displays good heat resistance in the absence of oxygen in vacuum or in an inert gas atmosphere, up to the temperature of 290°C. Higher temperature brings about the molecular-chain scission followed by a drop in the molecular-weight average. At temperatures in excess of 360°C the formation of volatile decomposition products can be observed. The main components are as follows ethane, propane, -butane, n-pentane, propylene, butenes and pentenes [7]. 

Molecular-Weight Average and Molecular-Weight Distribution... 

For a polymer with a molecular weight distribution the proper molecular weight average to use in equations (T) and (lO) can be determined using the following considerations. In the case of a heterogeneous polymer it has been shown that (7 19.20). 

It was found [1] that the values of and a, obtained in minimizing the error of fitting experimental conversion-time data, satisfactorily described the temporal evolutions of the molecular weight averages. Also, the model performed better in the description of the experimental data when a value of 3 = 1/2 was used. 

Ordinate values of the molecular weight distribution rather than molecular weight averages obtained from size exclusion chromatography were used in the modelling (3.9). [Pn] in Equation (1) can be transformed into (log M), the ordinate of the molecular weight distribution using (2) ... 

In the past three decades, industrial polymerization research and development aimed at controlling average polymer properties such as molecular weight averages, melt flow index and copolymer composition. These properties were modeled using either first principle models or empirical models represented by differential equations or statistical model equations. However, recent advances in polymerization chemistry, polymerization catalysis, polymer characterization techniques, and computational tools are making the molecular level design and control of polymer microstructure a reality. 

A challenging goal in this field, particularly from the synthetic point of view, is the development of general AB polymerization methods that achieve control over DB and narrow MWDs. Experimental results and theoretical studies mentioned above suggest that the SCV(C)P from surfaces, which are functionahzed with monolayers of initiators, permit a controlled polymerization, resulting structural characteristics (molecular weight averages, DB) of hyperbranched polymers. In particular, it is expected that the use of polyfunctional initiators with a different number of initiator functionahty, copolymerization, and slow monomer addition techniques lead to control the molecular parameters. 

Type of dextran Molecular weight (average) Product sterilization method Clinical uses... 

An additional complication arises from the different types of molecular weight averages obtained by different methods. If the polymer comprises a broad range of species differing in chain length, as is usually the case (see Chap. VIII) unless a careful fractionation has been performed, different molecular weight methods will give substantially different values on this account. 

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