Mn Number-average molecular mass

End group quantification is thus a useful method for number average molecular mass determination. Also, if the end group concentration is higher than the value calculated from an independent Mn determination, chain branching can be deduced and quantified. 

The obvious definition of the number average, Mn, of the distribution is the position on the M-axis that divides the area under the n (A/)- curve in equal parts (cf. Fig. 1.3). Because of the fact that n M) is normalized to 1, each of the subareas is equal to 0.5. As 50% of all the molecules are shorter than Mn, the other 50% are longer than Mn. Bearing in mind the normalization, the number average molecular mass is... 

Molecular weight measured by GPC (polystyrene standard). Mw is weight-average molecular mass and Mn is number-average molecular mass. 

From eqn. (148) an important relation can be derived between the number average molecular mass of the product and catalyst yield, 0, equal to mP/nK (Mn = PM)... 

Mn = number average molecular weight. This quantity is a measure of the number of molecules in a known mass and can be arrived at by osmometry and gel permeation chromatography. 

In this manner, the number average molecular mass (Mn), the mass average molecular mass (M ), the peak molecular mass (Mp), and the polydispersity (M. /Mn) may be calculated. 

Number-average molecular mass (Mn), polydispersity index (PD) and weight-average molecular mass (Mw) are linked to MMD moments by the following expressions ... 

Two heat-sensitive organic liquids of an average molecular mass of 155 kg/kmol are to be separated by vacuum distillation in a 100 mm diameter column packed with 6 mm stoneware Raschig rings. The number of theoretical plates required is 16 and it has been found that the HETP is 150 mm. If the product rate is 5 g/s at a reflux ratio of 8, calculate the pressure in the condenser so that the temperature in the still does not exceed 395 K (equivalent to a pressure of 8 kN/m2). It may be assumed that a = 800 m2/m3, /x = 0.02 mN s/m2, e = 0.72 and that the temperature changes and the correction for liquid flow may be neglected. 

The portion unaccounted for includes all of the lower mass components. For each of these samples, the number average molecular weight would be Mn = 1009.8, but the weight average molecular weights would be Mw = 1013.5 and 1017.1, respectively. A sample prepared with p =. 0975 for both iterations would have a distribution of 80% 12% 7%, Mn = 1009.8, and Mw = 1015.4. 

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, Mn. This is defined by the expression... 

Banthia et al. [44] first performed the polymerization of ethyl hexyl acrylate in DEP conditions (Table 6) but without using any solvent. The calculated carboxy functionalities were around 2 and the molecular weights were about 104. The number-average molar masses (Mn) were unexpectedly high for DEP conditions and were probably due to the bulk conditions. 

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