Weight, molecular average

Polymer Molecular weight Derivatization Molecular weight after derivatization Reference 

The molecular weights of the hemicelluloses and their carboxymethylated derivatives were determined by GPC on a PL aquagel-OH50 column (3007.7 mm. Polymer Laboratories Ltd.). Detection was achieved with a Knauer differential refractometer. The weight of carboxymethylated hemicelluloses became lower than that of native hemicelluloses (26800 g.moP), as the Mw range from 12213 to 15312 g/mol. In addition, carboxymethyl hemicelluloses had a relatively low index of polydispersity (2.75-2.87), which indicated that the molecular weights of hemicellulosic derivatives were more uniform [72]. 

If a polymer sample did comprise of macromolecular chains of equal length, it can be shown that M = = M. In real polymer samples, 

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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. 

This method follows the ASTM D 1159 and D 2710 procedures and the AFNOR M 07-017 standard. It exploits the capacity of the double olefinic bond to attach two bromine atoms by the addition reaction. Expressed as grams of fixed bromine per hundred grams of sample, the bromine number, BrN, enables the calculation of olefinic hydrocarbons to be made if the average molecular weight of a sufficiently narrow cut is known. 

Thus the quantitative elemental analysis of the fuel establishes an overall formula, (CH O ) , where the coefficient x, related to the average molecular weight, has no effect on the fuel-air ratio. 

Paraffins consist mainly of straight chain alkanes, with a very small proportion of isoalkanes and cycloalkanes. Their freezing point is generally between 30°C and 70°C, the average molecular weight being around 350. When present, aromatics appear only in trace quantities. 

Waxes are less well defined aliphatic mixtures of n-alkanes, isoalkanes and cycloalkanes in various proportions. Their average molecular weights are higher than those of the paraffins from 600 to 800. 

The ratio of the total weight to the total extended length of the empirical formula unit gives the average molecular weight per length of chain ... 

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 ... 

This quantity is also called the number (subscript n) average molecular weight. 

This result shows that the square root of the amount by which the ratio M /M exceeds unity equals the standard deviation of the distribution relative to the number average molecular weight. Thus if a distribution is characterized by M = 10,000 and a = 3000, then M /M = 1.09. Alternatively, if M / n then the standard deviation is 71% of the value of M. This shows that reporting the mean and standard deviation of a distribution or the values of and Mw/Mn gives equivalent information about the distribution. We shall see in a moment that the second alternative is more easily accomplished for samples of polymers. First, however, consider the following example in which we apply some of the equations of this section to some numerical data. 

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 ... 

The viscosity average molecular weight is not an absolute value, but a relative molecular weight based on prior calibration with known molecular weights for the same polymer-solvent-temperature conditions. The parameter a depends on all three of these it is called the Mark-Houwink exponent, and tables of experimental values are available for different systems. 

Equation (2.39) is the weight average molecular weight as defined in Sec. 1.8. It is important to note that this result. My = M y, applies only in the case of nonentangled chains where 17 is directly proportional to M. A more general definition of My for the case where 17 a is... 

A slightly different but useful way of defining the viscosity average molecular weight is the following ... 

An important application of Eq. (3.39) is the evaluation of M, . Flory et al.t measured the tensile force required for 100% elongation of synthetic rubber with variable crosslinking at 25°C. The molecular weight of the un-cross-linked polymer was 225,000, its density was 0.92 g cm , and the average molecular weight of a repeat unit was 68. Use Eq. (3.39) to estimate M. for each of the following samples and compare the calculated value with that obtained from the known fraction of repeat units cross-linked ... 

Next we turn our attention to the distribution of the molecules by weight among the various species. A corollary of this is the determination of the weight average molecular weight and the ratio... 

An equivalent way of looking at the conclusion of item (2) is to recall that Eq. (5.40) gives the (number average) number of monomers of both kinds in the polymer and multiply this quantity by the average molecular weight of the two kinds of units in the structure (88 + 112)/2 = 100. 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

In the next section we shall describe the use of Eq. (8.83) to determine the number average molecular weight of a polymer, and in subsequent sections we shall examine models which offer interpretations of the second virial coefficient. 

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